MODE I INTERLAMINAR FRACTURE PROPERTIES OF OXIDE AND NON-
OXIDE CERAMIC MATRIX COMPOSITES
A Dissertation
Presented to
The Graduate Faculty of The University of Akron
In Partial Fulfillment
of the Requirements for the Degree
Doctor of Philosophy
Rabih Mansour
May, 2017 MODE I INTERLAMINAR FRACTURE PROPERTIES OF OXIDE AND NON-
OXIDE CERAMIC MATRIX COMPOSITES
Rabih Mansour
Dissertation
Approved: Accepted:
Advisor Department Chair Dr. Gregory Morscher Dr. Sergio Felicelli
Committee Member Interim Dean of the College Dr. Minel Braun Dr. Donald Visco
Committee Member Dean of the Graduate School Dr. Kwek Tze Tan Dr. Chand Midha
Committee Member Date Dr. Gary Doll
Committee Member Dr. Alper Buldum
ii ABSTRACT
This work provides a novel method for determining interlaminar fracture properties at both room and elevated temperature, offering the first glimpse of the interlaminar fracture behavior of CMCs at elevated temperatures.
Interlaminar fracture properties play an important role in predicting failure of structural components for CMC materials. Elevated temperatures induce more severe conditions for interlaminar properties resulting in a weaker interlaminar toughness. The main challenges associated with determining interlaminar fracture toughness are the ability to measure crack growth without visual observation and to develop an experimental setup that can be used at both room and high temperature. Hence, a non- visual crack monitoring technique has been successfully introduced to estimate crack length in CMCs using electrical resistance. In a parallel effort, a wedge-loaded double cantilever beam method has been developed to determine the interlaminar fracture properties of CMCs at room and elevated temperatures. It has been found that the wedge method does not depend on the wedge material, as long as the correct coefficient of friction is taken into consideration. Additionally, the wedge method was found to be comparable to the traditional double cantilever beam method.
The interlaminar fracture properties depend immensely on the composite microstructure and the weave architecture; the interlaminar crack propagates along the longitudinal fiber tows, passing through the porosities, which serve as stress
iii concentration points. Moreover, depending on the fiber tows orientation along the crack propagation path, a rising or flat R-curve behavior can be seen for the same composite system.
High temperature testing revealed that the energy required to initiate a crack at room temperature is greater than that at 815 °C. However, more energy is required to propagate the interlaminar crack at high temperature for some CMC systems (such as PIP
SiC/SiNC). This behavior was attributed to softening of the matrix, which was evident when comparing crack growth rate at elevated temperature to room temperature. The data presented provides the first glimpse of the interlaminar fracture properties of CMCs at elevated temperatures.
The wedge method was also verified using finite element analysis and micromechanics approaches. However, in order for a model to accurately predict the interlaminar behavior of the material and assist in optimizing specimen’s geometry, the mechanical response of the studied composite should be well-known, especially shear properties.
Finally, a method for determining the out-of-plane electrical resistivity for composite materials has been proposed, while introducing the concept of length constant as a composite property. This method was utilized and successfully verified for two ceramic matrix composite systems with significantly different electrical properties. The out-of-plane electrical resistivity was found to be 8-9 times greater than the in-plane electrical resistivity.
iv ACKNOWLEDGEMENTS
First and foremost, I would like to express my sincere gratitude to my advisor Dr.
Gregory Morscher for his guidance, support and above all friendship. He is an inspiration to both my professional and personal life, and I am forever grateful to have had him as an advisor and a mentor.
I would like to thank the Naval Air Systems Command (NAVAIR), specifically
Dr. Sung Choi, for financially supporting this project under STTR N13A-T008. My appreciation is also extended to Dr. Frank Abdi for supporting this project and for the time I spent at AlphaSTAR Corporation.
I also would like to thank my committee members for their valuable comments and suggestions. Dr. Minel Braun has been a mentor and a friend throughout graduate school, and for that I am extremely grateful.
A most special acknowledgement is made to my family and friends for the support that they have always provided me with. I also would like to express my appreciation for the enjoyable collaboration with my colleagues in my research group and the help I received from them.
v TABLE OF CONTENTS
Page
LIST OF TABLES ...... x
LIST OF FIGURES ...... xi
CHAPTER
I. INTRODUCTION ...... 1
II. MOTIVATION, HYPOTHESIS AND SCOPE OF WORK ...... 4
III. LITERATURE REVIEW ...... 7
3.1 Processing of CMCs ...... 7
3.1.1 Processing of Non-Oxide CMCs ...... 7
3.1.2 Processing of Oxide CMCs ...... 10
3.2 Damage Classification in CMCs ...... 11
3.2.1 Interlaminar Fracture Toughness in Composites ...... 12
3.3 Damage Monitoring and Non-Destructive Evaluation of CMCs ...... 21
3.3.1 Acoustic Emission ...... 21
3.3.2 Electrical Resistance ...... 29
3.3.3 Digital Image Correlation ...... 32
3.3.4 Micro-Computed Tomography ...... 33
3.4 Micromechanical Modeling of Composites ...... 35
IV. DESIGN OF THE EXPERIMENT ...... 41
4.1 Introduction ...... 41
4.2 Materials ...... 44
vi
4.3 Mechanical Testing ...... 47
4.4 Electrical Resistance ...... 48
4.5 Acoustic Emission ...... 49
4.6 Optical Microscopy, Digital Image Correlation (DIC), and Micro-CT ...... 50
4.7 Results and Discussion ...... 51
4.7.1 Selection of the wedge material ...... 51
4.7.2 Implementation of electrical resistance to monitor crack growth ...... 52
4.7.3 Implementation of acoustic emission to monitor damage accumulation .. 71
4.7.4 Mechanical Behavior ...... 79
4.8 Conclusions ...... 93
V. THE EFFECT OF FRICTION AND WEDGE ANGLE ON THE WEDGE-LOADED DOUBLE CANTILEVER BEAM METHOD ...... 95
5.1 Introduction ...... 95
5.2 Experimental Procedure ...... 95
5.2.1 Material and Mechanical Testing ...... 95
5.2.2 Friction Measurement ...... 97
5.3 Analytical Analysis ...... 97
5.4 Results and Discussion ...... 101
5.4.1 Friction Study ...... 101
5.4.2 Mechanical Data ...... 104
5.5 Conclusions ...... 106
VI. COMPARISON BETWEEN THE WEDGE-LOADED DOUBLE CANTILEVER BEAM AND THE TRADITIONAL DOUBLE CANTILEVER BEAM ...... 107
6.1 Introduction ...... 107
6.2 Experimental Procedure ...... 108
6.2.1 Material and Mechanical Testing ...... 108
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6.2.2 Optical Microscopy ...... 110
6.2.3 Energy Release Rate ...... 111
6.3 Results and Discussion ...... 112
6.4 Conclusion 122
VII. DETERMINATION OF INTERLAMINAR FRACTURE PROPERTIES OF CMCS AT ELEVATE TEMPERATURES ...... 123
7.1 Introduction ...... 123
7.2 Experimental Procedure ...... 124
7.2.1 Materials ...... 124
7.2.2 High Temperature Testing ...... 125
7.2.3 Electrical Resistance Measurements ...... 126
7.3 Results and Discussion ...... 127
7.3.1 Electrical Behavior and Crack Length Measurements in SiC-Based CMCs at Elevated Temperatures ...... 127
7.3.2 Electrical Behavior and Crack Length Measurements in Oxide-Based CMCs ...... 133
7.3.3 Mechanical and Electrical Behavior ...... 134
7.3.4 Energy Release Rate ...... 140
7.4 Conclusions ...... 145
VIII. MODELING OF THE WEDGE METHOD ...... 147
8.1 Introduction ...... 147
8.2 Material Characterization ...... 149
8.3 Finite Element Analysis Modeling ...... 155
8.3.1 Building the Finite Element Analysis Model ...... 155
8.3.2 Results and Discussion ...... 158
8.3.3 Verification of the FEA Model ...... 162
8.4 Conclusion ...... 166
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IX. DETERMINATION OF OUT-OF-PLANE RESISTIVITY FOR NON-OXIDE CERAMIC MATRIX COMPOSITES ...... 168
9.1 Introduction ...... 168
9.2 Materials ...... 169
9.3 Experimental Procedures, Results and Discussion ...... 170
9.4 Conclusions ...... 179
X. CONCLUSIONS ...... 180
XI. FUTURE WORK ...... 184
11.1 Modeling the Electrical Behavior in Non-Oxide CMCs ...... 184
11.2 Mode II Interlaminar Fracture Testing of CMCs ...... 185
REFERENCES ...... 188
ix
LIST OF TABLES
Table Page
1. Comparison between extensional and flexural waves for SiC/SiC composites ...... 27
2. List of physical and mechanical properties of the tested material systems ...... 46
3. Summary of the coefficients of friction for the tested materials ...... 104
4. Constituents and composite input properties for ZMI SiC/SiC ...... 152
5. Composite output properties for ZMI SiC/SiC ...... 153
6. Specimen geometry ...... 155
7. Constituents and composite input properties for HN SiC/SiC ...... 163
8. Composite output properties for HN SiC/SiC ...... 164
9. List of the electrical properties of the materials tested ...... 178
x
LIST OF FIGURES
Figure Page
1. A brief summary of the temperature limits of aero-engine materials [4] ...... 2
2. CMC impacted sample showing multiple transverse and interlaminar cracks behind the impact site [52] ...... 13
3. Different testing techniques that can be used to determine fracture properties of CMC [53] ...... 14
4. Load-displacement curves for (a) [0°]24 and (b) [0°/90°]12 specimens [57] ...... 15
5. Schematic representation of crack propagation between plies, including typical dimensions of the crack pattern [57] ...... 16
6. Unit cell for a five-harness stain weave [67] ...... 17
7. Schematic crack propagation around a fill yarn showing (a) stick (b) slip phenomenon [67] ...... 18
8. Schematic and micrographs of interlaminar crack propagation in 5 harness stain woven composites for stacking pattern of (a) double 0s (b) 0-90 and (c) double 90s [69] ...... 19
9. A typical RSP signal [79] ...... 22
10. A typical waveform produced by boron fiber breakage ...... 23
11. Velocity curves of two different lamb waves in an aluminum plate as a function of frequency × thickness [80] ...... 24
12. Dispersion curves in SiC/SiC sample with 4 mm thickness ...... 26
13. Propagation of a) non-dispersive S0 mode and b) dispersive A0 mode at low frequencies [80] ...... 26
14. Electric field distributions for (a) intact sample, and (b) after introducing a crack .....31
15. Relationship between electrical resistivity and temperature for SiC, where ρo is the resistivity at room temperature [107] ...... 32
xi
16. Crack initiation and development in a single-tow SiC/SiC composite at room (top) and high (bottom) temperature [117] ...... 34
17. Repeating volume element (RVE) for the rule of mixture ...... 36
18. Predicted E11 and E22 based on the rule of mixtures ...... 37
19. RVE for Chamis model ...... 37
20. Predicted E11 and E22 according to Chamis model ...... 38
21. Plain weave architecture, representative unite cell, and one quarter cell [126] ...... 40
22. Typical microstructure of (a) ZMI SiC/SiC (b) HN SiC/SiC (c) PIP SiC/SiNC and (d) N720/alumina (Oxide/Oxide) [132] ...... 45
23. Test setup ...... 48
24. Schematic of test setup with the two ER configurations: (a) arm-to-arm (b) straight...... 49
25. Change of load and resistance vs. mouth opening displacement for a ZMI SiC/SiC 50×5×4 sample during a wedge test when using a metallic wedge ...... 52
26. ER change during interlaminar wedge testing for a ZMI SiC/SiC 50×5×4 sample in the case of (a) arm-to-arm configuration (b) straight configuration ...... 53
27. Schematic of test setup for the arm-to-arm configuration showing the different geometries ...... 56
28. Schematic of test setup for the straight configuration showing the different geometries ...... 57
29. Crack morphology and crack tip location at certain times throughout the test for a ZMI SiC/SiC 50×5×4 sample ...... 58
30. Measured crack length and estimated crack length from raw and post-precrack ER data (ZMI SiC/SiC 50×5×4 sample with crack pattern shown in Figure 29) ...... 59
31. Crack morphology and crack tip location at certain times throughout the test for a ZMI SiC/SiC 75×5×4 sample ...... 60
32. Measured crack length and estimated crack length from raw and post precrack ER data assuming a central crack and off-center crack for ZMI SiC/SiC 75×5×4 sample with crack pattern shown in Figure 31 [136] ...... 60
33. Measured and estimated crack length for a HN SiC/SiC 80×5×4 sample ...... 61
34. Measured and estimated crack length for a PIP SiC/SiNC 65×5×5 sample ...... 62
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35. ER change during interlaminar wedge testing for a PIP SiC/SiNC 65×5×5 sample ...... 63
36. An example of multiple crack initiation at the notch tip (for HN SiC/SiC 80×5×4 sample) ...... 64
37. Example of crack branching and secondary cracks along the path of the main interlaminar crack (PIP SiC/SiNC 65×5×5) ...... 65
38. (a) Picture of Oxide/Oxide sample with silicon coat on the edge (b) micrograph of the edge surface ...... 66
39. Electrical current and resistance of silver film on a glass substrate as a function of film thickness for different applied voltages [139] ...... 67
40. Micrograph of a conductive layer of silver (a) without (b) with heating to 815 °C temperature ...... 68
41. Change of load and resistance vs. mouth opening displacement for an Oxide/Oxide 70×10×3 (a) without pre-heating to 815 °C (b) with pre-heating to 815 °C ...... 69
42. Crack length vs. resistance for an Oxide/Oxide 70×10×3 without pre-heating ...... 70
43. Strain fields in an Oxide/Oxide 70×10×3 sample indicating crack tip location, using DIC ...... 71
44. Actual waveforms produced during the wedge testing: (a) with clear separation between the extensional and flexural modes (associated with chipping, friction and/or grooving at the wedge surface) and (b) with a short extensional region prior to the superimposed modes (associated with material damage) [140] ...... 73
45. Load, ER change, and cumulative AE energy vs. time during wedge test for ZMI SiC/SiC 50×5×4 sample ...... 74
46. Load, ER change, and cumulative AE energy vs. MOD during wedge test for PIP SiC/SiNC 65×5×5 sample ...... 75
47. Load and AE events energy vs. time for a HN SiC/SiC 80×5×4 sample ...... 76
48. Cumulative AE energy vs crack length for a HN SiC/SiC 80×5×4 sample ...... 77
49. Number of events vs. time for HN SiC/SiC 80×5×4, PIP SiC/SiNC 65×5×5, and Oxide/Oxide 70×10×3 ...... 77
50. Load and AE events energy vs. time for an Oxide/Oxide 70×10×3 sample ...... 78
51. Different forces acting on the wedge surface ...... 79
52. Determination of MOD using optical measurements ...... 80
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53. Load, ER change, and cumulative AE energy during wedge testing of ZMI SiC/SiC 50×5×4 sample ...... 81
54. Crack morphology and crack tip location at certain times throughout the test for a ZMI SiC/SiC 50×5×4 sample, with the data shown in Figure 51 (Reprinted from Figure 29) ...... 82
55. Load, ER change, and cumulative AE energy during wedge testing of PIP SiC/SiNC 65×5×5 sample ...... 82
56. Load and double the load vs. crosshead displacement for ZMI SiC/SiC 50×5×5 in comparison to the load data for ZMI SiC/SiC 50×10×5 ...... 83
57. Load vs. crosshead displacement for five PIP SiC/SiNC sample: two 65×5×5, two 65×10×5, and one 65×15×5 in comparison to the load data for ZMI SiC/SiC 50×10×5 ...... 84
58. Notch shape for sample PIP SiC/SiNC 65×5×5-2 before and after sharpening, and post test ...... 86
59. Notch shape before testing (notch not sharpened) and after testing, showing two interlaminar crack. Sample PIP SiC/SiNC 65×5×5-1 ...... 87
60. Modified beam theory for a HN SiC/SiC 80×5×4 sample ...... 89
61. GI based on the compliance method and modified beam theory for an HN SiC/SiC 80×5×4 sample ...... 90
62. Energy release rate vs. crack length using compliance method for three HN SiC/SiC 80×5×4 samples ...... 91
63. Energy release rate vs. crack length using compliance method for five PIP SiC/SiNC with varying widths ...... 92
64. Crack path for PIP SiC/SiNC 65×5×5-2 showing sections of fiber bridging and others with fiber bridging ...... 92
65. Friction specimen ...... 97
66. The forces acting on the wedge ...... 99
67. Mouth opening load to applied load vs. coefficient of friction for different wedge angles ...... 100
68. Coefficient of friction (μ) vs. laps number for ZMI SiC/SiC samples on (a) alumina silicate (b) alumina and (c) silicon nitride ...... 103
69. Load vs. crosshead displacement for different wedge materials ...... 105
xiv
70. Mouth opening load produced by the different wedges vs. crosshead displacement 106
71. Schematic showing the cutting directions for the Horizontal (H) and Vertical (V) samples ...... 109
72. Schematic of test setup for the (a) wedge test and (b) DCB test ...... 110
73. Different forces acting on the wedge surface ...... 112
74. Mouth opening load vs. mouth opening displacement for wedge tested and DCB tested Vertical samples ...... 113
75. Mouth opening load vs. mouth opening displacement for wedge tested and DCB tested Horizontal samples ...... 114
76. Boundary condition for (a) wedge test showing fixed-end boundary condition and (b) DCB test showing free-end boundary condition ...... 115
77. Mode I energy release rate for wedge tested and DCB tested Vertical samples ...... 116
78. Mode I energy release rate for wedge tested and DCB tested Horizontal samples ...116
79. Fiber bridging in sample a) 4 V DCB (flat R-curve) and b) 18 H DCB (rising R- curve) ...... 117
80. Fracture surface of a sample with Vertical orientation ...... 118
81. Fracture surface of a sample with Horizontal orientation ...... 119
82. Crack morphology in the center of sample a) 4 V DCB (flat-R curve) and b) 18 H DCB (rising-R curve) ...... 120
83. Load vs. mouth opening displacement for a sample with Vertical orientation, showing load curve correlation with crack morphology ...... 121
84. Load vs. mouth opening displacement for a sample with Horizontal orientation, showing load curve correlation with crack morphology ...... 122
85. Furnace temperature profile at 815 °C ...... 126
86. High temperature test setup showing the ER probe attachment ...... 127
87. Change of ER during heating (up to 815 °C) and cooling for a PIP SiC/SiNC sample ...... 129
88. Change of ER during heating (up to 815 °C) and cooling for a HN SiC/SiC sample ...... 130
xv
89. Measured ER as a function of displacement for actual high temperature testing and high temperature test simulation with further propagating the interlaminar crack for a SiC/SiNC sample ...... 131
90. ER change due to crack propagation during high temperature testing ...... 132
91. Change of ER during heating (up to 815 °C) for an Oxide/Oxide silver painted sample ...... 134
92. ER change during high temperature interlaminar testing for a ZMI SiC/SiC sample, including pop-in crack at room temperature ...... 135
93. Load and change of ER during crack re-opening and crack propagation at 815 °C for ZMI SiC/SiC sample ...... 136
94. Mechanical, electrical behavior and crack length during high temperature (815 °C) interlaminar testing for PIP SiC/SiNC ...... 137
95. Mechanical, electrical behavior and crack length during room temperature interlaminar testing for PIP SiC/SiNC ...... 138
96. Mechanical, electrical behavior and crack length during high temperature (815 °C) interlaminar testing for an HN SiC/SiC sample ...... 139
97. Mechanical, electrical behavior and crack length during room temperature interlaminar testing for an HN SiC/SiC sample ...... 140
98. Energy release rate at room temperature and at 815 °C for PIP SiC/SiNC ...... 142
99. Crack growth rate at room temperature and at 815 °C for PIP SiC/SiNC ...... 143
100. Energy release rate at room temperature and at 815 °C for HN SiC/SiC ...... 144
101. Crack growth rate at room temperature and at 815 °C for HN SiC/SiNC ...... 145
102. Main steps of progressive failure analysis for a tensile stress-strain curve of a typical SiC/SiC CMC system ...... 150
103. Tensile stress-strain curve of ZMI SiC/SiC material from micromechanics simulation using progressive failure analysis in comparison to the stress-strain curve from tensile mechanical test ...... 154
104. Wedge model ...... 156
105. Mesh (a) of the model and (b) in the vicinity of the notch...... 157
106. FEA model showing the wedge, specimen, boundary conditions and interaction properties...... 158
xvi
107. Simulation vs test results for a 50×10×4 ZMI SiC/SiC specimen ...... 159
108. Damage distribution after crack initiation ...... 159
109. Polished cross sectional area of a tested ZMI SiC/SiC specimen showing an interlaminar crack and no damage in the arms ...... 160
110. FEA model showing the no-damage regions along with the interlaminar region ...161
111. Simulation results showing crack morphology in the interlaminar region ...... 161
112. Simulation vs test results for a 50×5×4 ZMI SiC/SiC specimen ...... 162
113. Tensile stress-strain for HN SiC/SiC from micromechanics simulation using PFA vs. the actual stress-strain curve from mechanical testing ...... 165
114. Simulation vs test results for a 75×5×4 HN SiC/SiC specimen ...... 166
115. (a) Schematic of specimen layout with the leads locations and (b) the cut part for out-of-plane resistivity measurements ...... 171
116. Potential drop as a function of the distance from (a) current leads and from the notch tip using (b) 0.5 mA and (c) 1 mA current for PIP SiC/SiNC ...... 175
117. Potential drop as a function of the distance from (a) current leads and (b) from the notch tip using a current of 500 mA for MI SiC/SiC ...... 176
118. End-notched flexure test for determining Mode II interlaminar fracture properties...... 186
119. End-loaded-split test for determining Mode II interlaminar fracture properties at room and elevated temperatures, illustrating the use of ER to determine crack length ...187
xvii
CHAPTER I
INTRODUCTOIN
Over the past five decades, the desired operating temperature for aerospace engines continued in increasing. Nickel-based superalloys with thermal and environmental ceramic coatings are the current state-of-the-art materials that are used for aerospace engines at temperatures ~1100 °C [1, 2]. These superalloys depend on thermal barrier coatings and thin film air cooling to reduce the metal substrate temperature below the engine combustion temperature. With these techniques, the superalloys are operating at their maximum limit, which is ~90% of their melting point [3]. Therefore, due to demands for an increase in aero-engine efficiency, reduced fuel consumption and higher operating temperatures, materials that outperform superalloys are required. Ceramic matrix composites (CMCs) are approximately one-third the density compared to Ni-based superalloys. Moreover, CMCs can be made as strong as metals, yet they can operate at temperatures exceeding the capability of current nickel alloys, because their chemical properties allow them to reach higher temperatures without failing. Figure 1 shows a brief summary of the temperature limits for different aero-engine materials.
1 Figure 1. A brief summary of the temperature limits of aero-engine materials [4].
Nevertheless, in order to implement CMC materials into components for aero- engines, their mechanical performance under various loading and environmental conditions, such as strength, fracture resistance, and fatigue tolerance, must be well- understood. One of the areas of concern is the delamination failure of CMCs materials under Mode I, Mode II and Mixed Mode loading conditions. This type of failure is unusual in metallic alloys, but common in composite materials since they are made of assemblies of layers / plies. Therefore, separation between the layers under mechanical and thermal loading is prone to occur.
Up to today, little published studies on the interlaminar properties of CMCs are available. Furthermore, there is no data, in open literature, on the interlaminar fracture toughness of CMC materials at elevated temperatures. Therefore, this work will aim at designing a standardized testing method for measuring interlaminar fracture properties of 2 CMCs at both room and high temperature. Non-destructive evaluation (NDE) techniques, such as acoustic emission (AE) and electrical resistance (ER), will be utilized extensively to evaluated and understand the nature of interlaminar damage initiation and propagation.
The design of the proposed method for evaluating interlaminar properties at room temperature is presented in Chapter IV. Verifications of the proposed method can be found in Chapter V (the role of friction) and in Chapter VI (comparing the proposed method to the traditional double cantilever beam technique). Chapter VII focuses on extending the proposed method for elevated temperatures. Chapter VIII verifies the proposed wedge method using finite element analysis. Chapter IX introduces a technique for measuring the out-of-plane resistivity in CMCs. This technique will assist in monitoring damage more accurately during testing. Conclusions of this work can be found in Chapter X. Finally, Chapter XI presents future work which will focus on modeling the electrical behavior of CMCs and Mode II interlaminar testing of CMC materials.
3 CHAPTER II
MOTIVATION, HYPOTHESIS AND SCOPE OF WORK
Due to their high-temperature capability, environmental stability, and low density, ceramic matrix composites (CMCs) are currently under development to replace the superalloys that line the hot-section of aero-engines. CMC materials offer much higher stress-temperature capabilities up to 1315 °C [5-7] allowing an increase in the operating temperature for aerospace jet engines.
In order to successfully develop these composite systems for such critical conditions, their mechanical behaviors must be well-understood. The mechanical response of CMCs under unidirectional on- and off-axis tensile loading has been intensively studied [8, 9], however, limited work has been done on other types of damage, such as interlaminar crack growth, and its impact on the material’s life expectancy [10, 11].
Interlaminar fracture properties play a vital rule in ceramic matrix composites, especially when they are used in engine applications. This is because, in engine applications, CMCs are exposed to large thermal gradients, which induce interlaminar normal or shear stresses [12]. Also, the weakest plane for CMCs is the interlaminar plane where most of the fibers are aligned in one of the orthogonal axial directions.
4 The complex architecture of woven CMCs and the internal porosity in the material, due to processing, introduce many stress concentration points. These stress points are prone to develop interlaminar cracks under different types of loading. For instance, CMC samples that have been subjected to foreign object damage suffer from interlaminar delamination, in addition to transverse cracking in the block of the material, below the impacted site [13]. Interlaminar cracks occur mostly at the interphase between the fiber tows and the matrix. Therefore, the understanding of interlaminar fracture toughness of CMCs is essential.
There are two main challenges associated with interlaminar fracture testing for
CMCs at elevated temperatures. First of all, during high temperature testing it is not possible to have direct measurements of crack length, simply because the sample is concealed inside a furnace. The second challenge is the lack of a standardized testing method that can be employed for determining interlaminar fracture properties at both room and high temperatures. The only standardized method available is the double cantilever beam technique, which is used for determining interlaminar fracture properties of unidirectional fiber-reinforced polymer matrix composites [14]. This method could be suitable for room temperature testing, however, it is not applicable for testing at elevated temperatures since it requires the use of adhesive bonding.
Therefore, this work will focus on introducing a non-visual technique for monitoring interlaminar crack growth at room temperature. The method will be later utilized for crack monitoring at high temperature testing. To overcome the second challenge, a method that permits direct application of load (without the need for loading
5 pins or hinges) will be introduced and compared to the traditional double cantilever beam method.
Finally, it worth mentioning that there is no data available on the interlaminar fracture toughness of CMCs at elevated temperatures. However, it has been shown that the mechanical behavior of CMCs, in general, shows some degree of degradation due to the exposure of high temperature [15, 16]. Therefore, the hypothesis of this work is that the interlaminar facture properties of CMCs at elevated temperature would be lower compared to the ones at room temperature.
6 CHAPTER III
LITERATURE REVIEW
3.1 Processing of CMCs
CMCs can be broadly classified into two main categories: oxide and non-oxide
CMCs. Non-oxide CMCs consist of SiC-based matrix reinforced with either carbon or silicon carbide fibers. Currently, the most advanced ceramic composites are based on silicon carbide fibers, which consist of SiC fibers and a predominantly SiC matrix. These composites offer high temperature capability, environmental stability, low density and good creep and rupture resistance [5, 17]. However, their lifespans are limited by their susceptibility to oxidation and degradation in combustion environments [18, 19]. Oxide- oxide CMCs (which consist of oxide fibers, matrices and interface) are immune to oxidation embrittlement and thus offer superior environmental stability, in exchange for some reduction in mechanical performance. Moreover, oxide-based composites generally have significant cost advantage over SiC-based composites [20].
3.1.1 Processing of Non-Oxide CMCs
There are several processing methods commonly used for the manufacturing of non-oxide SiC/SiC composites with the most common being polymer infiltration and pyrolysis (PIP), chemical vapor infiltration (CVI), and liquid silicon melt-infiltration
(MI) techniques. It is actually common to combine two or more processing techniques to 7 optimize the microstructure and/or the densification of the CMC system [21]. Regardless of the technique used, chemical vapor deposition is usually used to deposit the interphase.
In CMCs, the interphase can be defined as a thin layer of a compliant material with a low shear strength deposited on the fibers surface to create a weak interface between the fibers and the matrix. It has been argued that the best interphase materials are the ones with layered crystal structure, such as pyrolytic carbon (pyC) or hexagonal boron nitride
(BN) [22, 23].
After coating the fibers with an interphase, the fiber preforms are arranged into an architecture, consisting of either laminate or woven (2D, 2.5D, or 3D) fiber plies, based on the intended application for the composite.
3.1.1.1 Polymer Infiltration and Pyrolysis (PIP) Technique
The PIP method is widely used to manufacture CMCs since it produces relatively dense composite at lower temperatures than other approaches. In this method, the fiber layups are impregnated with a polymeric precursor then cured under pressure at ~150-
250 °C in an autoclave. The polymer precursor is then decomposed into a ceramic by pyrolysis in a high temperature vacuum (800-1200 °C). Weight loss during pyrolysis, in addition to shrinkage results in 20-30% porosity. Therefore, the newly formed ceramic matrix is re-infiltrated and the process is repeated until the desired density is achieved
(typically 6-10 cycles are performed) [24, 25].
3.1.1.2 Chemical Vapor Infiltration (CVI) Technique
In the CVI method, also referred to as the gas phase route, the composite matrix is deposited using vapor means. After fabricating the porous fiber preform, a thin interphase
8 is deposited on the fiber surface. The preform is then exposed to a gaseous mixture, at moderate temperatures (900-1100 °C), that infiltrates the fibers and begin to decompose and form a ceramic deposit on the fiber surface. The process continues until the open porosity on the preform surface is closed, which usually require multiple cycles of infiltration [26, 27]. The main advantage of this technique is that it yields high purity and well-controlled composition and microstructure of the SiC deposited matrix.
Unfortunately, in this method, the deposition on the fiber preforms eventually closes the interior of the composite resulting in relatively high residual porosity (typically 10-15%, mainly open porosity) and a relatively low thermal conductivity, which ultimately affect the mechanical behavior of the material.
3.1.1.3 Liquid Silicon Melt-Infiltration (MI) Technique
In order to produce SiC/SiC composites with minimum porosity and improved thermo-mechanical performance the liquid silicon infiltration process was developed [28-
30]. This technique begins with coating deposit on the fibers using CVI. The fibers are then cut and stacked to produce a preform. Then a thin SiC layer is deposited using CVI to protect the fibers and the interphase from the final densification steps, with liquid silicon. Following this, SiC particles are slurry-cast in to the preform at room temperature. Finally, molten silicon is infiltrated (melting point of silicon is 1410 °C), filling the remaining porosity. Therefore, the produced composite contains SiC fibers, interphase, CVI SiC coating, and a matrix containing SiC particulate in a silicon metalloid. This processing method is simpler and requires shorter processing time.
However, the matrix formed by this method usually contains free silicon which limits it
9 creep resistance. Also, the relatively low melting temperature of silicon limits the maximum usage temperature of MI SiC/SiC composites [5, 31].
3.1.2 Processing of Oxide CMCs
Tough behavior in ceramic matrix composites is often achieved through an engineered weak fiber-matrix interface. Carbon and boron nitride have unique combinations of properties that establish them as ideal fiber coating choices, making them the main coating materials for non-oxide CMCs. However, their poor oxidation resistance hinders their use in all-oxide CMCs. Therefore, oxidation resistant coatings must be developed [20]. LaPO4 (monazite) and CaWO4 (scheelite) have demonstrated to provide crack-deflection function and substantial improvement in alumina-based composite properties [32-35].
The most advanced all-oxide composites utilize a sufficiently weak, porous matrix [36-39]. Obtaining a controlled rate of porosity helps to dissipate the energy associated with the propagation of cracks in the matrix, where a matrix crack is deflected within the matrix in the region of the fiber/matrix interface.
In all-oxide CMCs, the reinforcing fibers are typically alumina-based continuous, polycrystalline fibers produced by the sol-gel process. The presence of the reinforcing fibers constrains the densification of the matrix material and can limit the pressures, temperatures, and chemicals that can be used to avoid fiber damage.
There are few processing methods that can be employed to infiltrate the woven fiber structure with an oxide matrix. The most common techniques are prepreg processing and pressure infiltration. 10 3.1.2.1 Prepreg Processing
This approach is similar to the techniques used in polymer matrix composite fabrication. In this process, the fibers are immersed within a slurry to form a matrix- infiltrated fabric (prepreg). Following lay-up, the fiber cloth is dried with a vacuum bag process under low pressure and low temperature (<150 °C), followed by a pressureless sintering at high temperature (1000-1200 °C) [40].
3.1.2.2 Pressure Infiltration
In this technique, layers of desized fabric are stacked into a mold in the desired orientation. Then, a dispersed slurry is poured into the mold. Once the slurry has filtered through the sample, the panels are dried producing green body with a packing density of
~60%. The green body is then sintered at 900 °C. Following that, the panel is infiltrated with an alumina precursor solution and then pyrolyzed after drying. This step is repeated twice, resulting in a rapid increase in the density [41], however, the densifying effect greatly diminishes after that as the interior channels begin to fill and/or the outer pores fill up.
3.2 Damage Classification in CMCs
The use of composite material in engineering applications improves the structural efficiency of the structure. High strength per weight and stiffness per weight ratios are some of the desirable features in many engineering components. For example, aerospace components are usually weight sensitive structures in which composite materials are highly desirable. However, due to their anisotropic nature, composite materials impose many engineering difficulties, mainly in modeling. Moreover, the effort to make
11 composite materials stronger in one direction, while maintaining low density, often causes reduction in the out-of-plane material properties. As a result, out-of-plane damage becomes easier to occur compared to in-plane (tensile) damage. The mechanical response of CMCs under unidirectional on- and off-axis tensile loading [8, 42, 43] and under shear loading [16, 44, 45] have been intensively studied, however, limited work has been done on other types of damage, such as interlaminar crack growth resistance, and its impact on the material’s life expectancy [10, 11, 46].
It has been reported that the on-axis mechanical performance is mainly dominated by fiber properties, whereas, off-axis properties are strongly dependent on the matrix properties, in particular the stiffness and load-carrying ability of the matrix, which is governed by its porosity content [9]. Interlaminar properties, on the other hand, seem to depend on the strength of fiber/matrix interphase. A weaker fiber/matrix bonding, which is desired for CMC materials, would result in lower fracture properties [47]. Interlaminar properties are also highly affected by porosity; interlaminar cracks propagate faster through defects and open porosities as they serve as localized stress concentration points.
3.2.1 Interlaminar Fracture Toughness in Composites
The interlaminar fracture properties of composite materials have aroused considerable attention from a durability and damage tolerance point of view. Interlaminar failure is of special concern because interlaminar cracks are not visible and are hard to be detected. Fiber reinforced CMCs are susceptible to delamination under interlaminar normal or shear stresses due to the inherit defects in the matrix rich interlaminar region and/or interface region. Such failure may result in loss of stiffness and might cause, in
12 some cases, structural failure, especially at high temperature and/or in the presence of thermal gradients [16, 46, 48-51]. Another area of concern is foreign object damage
(FOD). FOD usually induces multiple delamination cracks in the structure. Figure 2 demonstates a cross-sectional area of an impacted SiC/SiC CMC sample with multiple delamination cracks behind the impact site.
Figure 2. CMC impacted sample showing multiple transverse and interlaminar cracks behind the impact site [52].
Evans [53] discussed the different methods that can be used to determine fracture properties of ceramic materials (Figure 3). These techniques were compared based on the type of material (porous or non-porous), loading rate (slow or fast), or testing temperature
(ambient or high). Among the most suitable methods for determining Mode I interlaminar fracture properties in CMC are the double cantilever beam test, and the wedge loaded double cantilever beam test. For Mode II interlaminar fracture testing the most common technique is the end-notched flexure test.
13 Figure 3. Different testing techniques that can be used to determine fracture properties of
CMC [53].
An extensive amount of work has been done on the interlaminar fracture toughness of laminate and woven polymer matrix composites (PMCs). Most of this work has been carried out using double cantilever beam (DCB) method [54, 55]. In fact, an
ASTM standard was developed for determining Mode I interlaminar fracture toughness of unidirectional fiber-reinforced PMC [14].
The delamination behavior of unidirectional fiber-reinforced PMC is quite different from the ones for cross-ply or woven composites. The mechanical behavior of unidirectional composites, [0/0] for example, during interlaminar testing shows a sharp increase in load until a crack is initiated. As soon as a critical crack size, necessary for the delamination to propagate, is reached, a continuous decrease of load is observed, indicating limited crack growth resistance. Symmetrical cross-ply composite, on the other 14 hand, displays slight decrease in the load after crack initiation, this decrease occurs as oscillation in the load around a midpoint [56, 57]. Figure 4 demonstrates a typical load- displacement curve for laminate ([0°]) and symmetrical cross-ply PMCs.
(a)
(b)
Figure 4. Load-displacement curves for (a) [0°]24 and (b) [0°/90°]12 specimens [57]. 15 It is generally reported that strain energy release rate values (GIC) at initiation, and especially at propagation, are higher for cross-ply than laminate composites. Unlike laminate composites, a rising R-curve behavior is evident for symmetrical cross-ply materials [58, 59]. “Stick-slip” phenomenon is common in materials with multi- directional fiber layout. Stick-slip propagation is defined as sudden limited unstable crack growth. For a [0°/90°] composite, “stick-slip” behavior can be related to crack jumping between two neighboring 0°/90° interfaces (Figure 5), and the periodical intralaminar cracking of the transverse fiber mid-layer. Berglund [60] proposed that the sudden failure of bridging fibers is the mechanism responsible for the “stick-slip” behavior witnessed during crack propagation.
Figure 5. Schematic representation of crack propagation between plies, including typical dimensions of the crack pattern [57].
In angle-ply composites, the governing characteristics seems to be that after a small interlaminar crack propagation, the crack would jump to a neighboring interface. In
16 fact, it was found that fiber bridging behind the crack tip and intralaminar damage were responsible for the increase of GIC [61-64]. However, when interlaminar fracture energy
GC is plotted as a function of delamination length, very complex relationships are observed. This complexity is a clear indication of the complex failure paths that occur during interlaminar testing.
Interlaminar fracture behavior for woven fiber-reinforced composites is highly dependent on the fibers architecture [65]. Variations in the load-displacement curve during crack propagation are related to the difference of the microstructure between neighboring plies [66]. Due to the interactive weave structure, matrix cracks are less likely to propagate in woven composites. Rather, delamination occurs in the interphase between the plies. Figure 6 shows the fiber weave pattern for a unit cell of a five-harness stain woven composite.
Figure 6. Unit cell for a five-harness stain weave [67].
In woven composites, crack propagation is governed by the weave geometry. Alif et al [67] showed that during interlaminar crack propagation in woven carbon/epoxy composites, peaks occur in GIC curve at crack length separated by a distance corresponds
17 closely to the unite cell size. The authors pointed out that the stick-slip behavior was witnessed when the crack was temporarily arrested as it propagated to a transverse fiber bundle (stick), then after further loading, the crack would propagate around the transverse bundle (backward crack propagation, or crack branching) corresponding to “slip” propagation. Figure 7 illustrates interlaminar crack propagation around a transverse fiber bundle.
(a)
(b)
Figure 7. Schematic crack propagation around a fill yarn showing (a) stick (b) slip phenomenon [67].
The peaks in the GIC curve is therefore explained by excess energy required for fill debonding. The occurrence of secondary cracks around fill bundles is limited by the closest weft yarn at the secondary crack plane, and usually this debonding occurs at both specimens’ edges. Gill et al reported that higher toughness was observed for crack propagation between plies with more transverse bundles [68]. This was attributed to transverse fibers pinning the crack and forcing it to arrest. Crack branching was also
18 observed around the debonded yarn and it could also contribute to the increase in fracture energy.
The stacking patterns of the woven fibers play an important role in the crack propagation path. Because the secondary cracks occur around fill bundles closest to main crack path, the fracture energy of the woven composite depends on the architecture of the mid-plane. Figure 8 illustrates the three different stacking patterns for woven five-harness stain composite [69]. The highest interlaminar fracture toughness values were found for the stacking sequence of double 90s (transverse) fiber bundles in the crack path (Figure
8c), while the lowest interlaminar GIC values for one are for the stacking sequence of double 0s (longitudinal) fiber bundles in the crack path (Figure 8a)
Figure 8. Schematic and micrographs of interlaminar crack propagation in 5 harness stain woven composites for stacking pattern of (a) double 0s (b) 0-90 and (c) double 90s
[69].
It is difficult to determine the contribution of fiber bridging versus transverse bundle debonding to the toughening effect in woven composite. Friedrich et al. [70]
19 proposed a micromechanics model for energy absorption during interlaminar loading for laminate PMCs. In his model, he considered three factors for energy absorption: (i) formation of the fracture surface of the main crack; (ii) microcracking of the matrix in the damage zone around the crack; (iii) crack fiber bridging which result in fiber fractures.
Depending on the geometry of the unit cell, one can estimate the mechanical energy consumed during fiber breakage. A similar micromechanical model for interlaminar toughness of composite was proposed by Crick et al. as well [71]. In order to investigate the relationship between matrix toughness and composite toughness Johnson and
Mangalgiri [72] eliminated the effect of fiber bridging by laying the delamination halves with small angles (1.5° and 3°) to each other to prevent fiber bridging while avoiding twisting of fibers upon loading. Interestingly, samples with slightly tilted mid-planes showed increase in GIC for a short crack length, but leveled off after some crack propagation. The authors attributed the limited increase in GIC to some fiber bridging at the beginning of crack propagation due to large crack tip yield zone or to weak fiber/matrix interfaces.
Fiber bridging effect on the interlaminar fracture toughness does not necessarily invalidate GIC values, and one can look at this phenomenon in two different ways. The first viewpoint is that one can consider the high toughness values due to bridging as representative of the actual structure if bridging is likely to occur in the structure.
Nonetheless, these values can be misleading if bridging does not occur. The second point of view is that fiber bridging hinders the direct measurement of fracture toughness of a composite matrix materials.
20 3.3 Damage Monitoring and Non-Destructive Evaluation of CMCs
The implementation of CMCs in hostile environments, such as hyper-sonic flight applications and gas turbines, requires non-destructive evaluation (NDE) of the material integrity. Therefore, the in-situ assessment of internal damage and the accurate prediction of the remaining life of a component is crucial. Numerous non-destructive testing methods, such as X-ray, ultrasonic C-scan, thermography and eddy current, have been shown to be sensitive to out-of-plane damage (delamination-type cracks) in CMCs but insensitive to flaws developed perpendicular to the surface (in-plane-type cracks) under tensile and creep conditions [73]. Also, these techniques cannot be used for in-situ damage monitoring. Thus, this review will focus mainly on in-situ monitoring techniques, namely, modal acoustic emission (AE) monitoring, electrical resistance (ER) measurements, digital image correlation (DIC), and micro-computed tomography (µ-CT).
3.3.1 Acoustic Emission
Acoustic emission (AE) is a nondestructive evaluation technique that captures sound waves produced in the material due to localized damage. AE has been used as a method to detect damage onset and accumulation in CMCs for over two decades now
[74]. One of the main advantages of AE method is its ability to detect low stress damage.
AE can detect signals at very low stresses corresponding to matrix microcracking during tensile testing, prior to any observable non-linearity in the stress-strain curve [74-77].
There are multiple sources of damage that can occur in CMCs during testing, including longitudinal cracks, transverse matrix cracks, and fiber breakage. When damage occurs in a part, energy is released in the component and sound is emitted. The sound travels in the
21 material in the form of high-frequency stress waves. The waves are then received by sensors that convert the energy into voltage. The voltage is then electronically amplified and further processed as an AE signal data. Analysis of the collected data comprises the characterization of the received voltage according to their source location, voltage intensity and frequency content.
The use of AE to detect damage in material during testing has started in the early
20th century when researches started to report audible sounds during investigation of material deformation [78]. Initially, Resonant Sensor Parameter (RSP) Technology was used. In this method, resonant transducers, 150 kHz were employed. Analyzing the signals consisted of correlation counts, duration, energy, amplitude, and energy with the mechanical properties of the material being tested. A typical RSP signal is shown in
Figure 9.
Figure 9. A typical RSP signal [79].
22 The foundations of RSP technology can be summarized by two fundamental assumptions: an acoustic emission is a damped sine wave, and the wave propagates at a constant velocity. These assumptions are clearly incorrect, an AE wave is not a damped since wave; a simple boron fiber break on a plate surface can show that clearly, as in
Figure 10.
Figure 10. A typical waveform produced by boron fiber breakage.
Moreover, for a typical plate, AE is not a single propagating sound wave but rather multiple wave modes with many frequencies for each mode, and propagating at different velocities, as shown in Figure 11.
23 Figure 11. Velocity curves of two different lamb waves in an aluminum plate as a function of frequency × thickness [80].
To overcome the limitations and the invalid assumptions of the RSP analysis, new method (AE Modal analysis) was introduced by Gorman [81]. The main difference between the two methods was the use of high-fidelity, wideband sensors in AE Modal instead of the resonant sensors used in AE RSP. This resulted in capturing non-distorted signals before they have been digitized, in comparison to heavily filtered signals for the
RSP analysis; which made all signals look the same.
In general, wave modes depend on the dimensions of the component. When the wave length () is greater than one of the dimensions, it is considered a thin plate condition. Early studies of wave propagation in plates were carried out by Rayleigh
(1945) and Lamb (1917). The Rayleigh-Lamb theory related to the propagation of continuous straight waves in a plate with infinite extent and having traction-free surfaces
24 while plane-strain conditions are applied. Rayleigh-Lamb frequency equations give the relationship between frequency and wave number. When Lamb waves are transmitted, particles move in one of two ways: symmetric with respect to the mid surface (S0, S1,
S2…) and anti-symmetric with respect to the mid surface (A0, A1, A2…), where the subscript represents the mode number for the Lamb wave. The solution for Lamb waves is derived in details elsewhere [82]. One way to describe the propagation characteristics of Lamb waves is by using dispersion curves based on plate mode phase velocity as a function of the product of frequency and thickness.
Figure 12 shows the dispersion curve of propagating wave modes in a SiC/SiC plate with 4 mm thickness (typical thickness for CMC panel). Except for the zero mode, all other modes present a threshold value (or a cut-off frequency). Below the first cut-off frequency, only S0 and A0 propagating modes exist. At low frequencies, the zero mode antisymmetric component (A0) is approximated by the flexural component of plate waves. In this mode the velocity changes with the frequency resulting in a dispersive component of the waveform. On the other hand, the zero mode symmetric component
(S0) can be approximated by the extensional mode where the velocity is constant (almost non-dispersive).
25 Figure 12. Dispersion curves in SiC/SiC sample with 4 mm thickness.
The following figure shows the propagation of a dispersive versus non-dispersive wave.
(a) (b)
Figure 13. Propagation of a) non-dispersive S0 mode and b) dispersive A0 mode at low frequencies [80].
In the frequency range considered in AE for CMC materials, the dispersion relation for an extensional wave in a thin plate is given as [81]: 26 퐸 퐶 = √ (1) 푒 휌(1 − 2) where E is the Young’s modulus, is the density, and is the Poisson’s ratio
The dispersion relation for flexural wave is expressed as:
1⁄ 퐸ℎ2 4 퐶 = [ ] √휔 (2) 푓 12 (1 − 2)휌 where is the circular frequency and h is the plate thickness.
The following table summarize the main differences between extensional and flexural waves.
Table 1. Comparison between extensional and flexural waves for SiC/SiC composites
Wave Extensional Wave Flexural Wave
Mode Symmetric Asymmetric
Higher frequency and Frequency Lower frequency and slower faster
Dispersion Non-dispersive Highly dispersive
1 퐸 퐷 ⁄4 Wave speed 퐶푒 = √ 퐶 = [ ] √휔 휌(1 − 2) 푓 휌h
27 During mechanical testing, usually two or three AE sensors are used to record the waveforms generated. By comparing the arrival times of the extensional modes of the waveforms from different sensors, it is often possible to determine the velocity and the initiation location of the AE waveform. Then it becomes possible to discard the events that were initiated outside the area of interest, allowing to correlate localized damage to
AE events. Morscher et al [83-85] was able to use modal AE to monitor damage accumulation during testing of different SiC/SiC CMC systems. Modal AE also gives indication of the type of damage occurring in the material; large matrix cracks are assumed to be the loudest events since the matrix is stiffer than the fibers and the surface area produced from larger cracks is much greater than individual fiber breaks or matrix microcracks. Moreover, Morscher [85] was able to show that the accumulated AE energy is directly proportional to the stress-dependent transverse matrix cracks obtained by microscopic observations.
Recent studies have attempted to further analyze AE waveforms based on their characteristic to identify different damage modes that occurs during testing, assuming that the same damage mode would generate waveforms with the same characteristics [86-
88]. However, due to the dispersive nature of these composite systems, many AE properties are affected by how they propagate. An energy-based method was developed to evaluate energy attenuation and how it relates to strain during testing [89, 90]. It was found that the energy-based approach also offers the potential for damage monitoring and in-situ determination of wave propagation properties, which will help in better identifying the characteristic in the different damage.
28 3.3.2 Electrical Resistance
Electrical resistance (ER) has been shown to be a sensitive measure of internal damage and strain accumulation in different composite systems containing electrical conductive constituents. Many studies have investigated the ER behavior of carbon fiber- reinforced polymer (CFRP) during mechanical testing. In such composites, the carbon fibers are the conductive phase, while the matrix is insulating. Thus, the ER change of the composite during mechanical testing is indicative of fiber behavior and damage [91-101].
The electrical response of SiC/SiC is quite different, however. Unlike CFRP, for
SiC/SiC composites both the fibers and the matrix are semi-conductor materials that have the ability of carrying electrical current. As a result, the change of ER during mechanical testing could be an indicative of damage in the matrix as well as the fibers. However, the electrical conductivity of the matrix depends mainly on the processing method to create the composite. For example, in melt-infiltrated SiC/SiC composite, the matrix is usually more conductive than the fibers due to the presence of free silicon in the matrix. On the other hand, for CVI SiC/SiC the electrical conductivity of the matrix could be of the same order of magnitude as the fibers.
The change in ER in a composite system, due to mechanical loading, could be reversible or irreversible. Chung listed three main reasons for resistance increase in
CFRP. Two of these reasons cause permanent increase in ER (irreversible): delamination and fiber breakage. This permanent increase allows for post-test inspection to estimate the damage occurring in the material due to mechanical loading. Fiber alignment results in a reversible increase in ER and it can be used as an in-situ measure of strain [97].
29 The correlation between the increase in ER and matrix cracking during tensile testing at room temperature have been successfully addressed for CVI-[102] and MI-
SiC/SiC CMCs[103]. Preliminary efforts by Morscher et al have developed a model to predict the ER behavior based on the tensile stress state of SiC/SiC CMCs [103].
Modeling of ER provides insight into understanding the damage progression in CMCs and it allows to further validate micromechanics models based on physical damage phenomenon.
Potential drop method (increase in electrical resistance) has been used for measuring crack growth in metals during fracture and fatigue testing for over 50 years
[104-106]. This method depends on passing a constant direct- or alternating-current through a specimen and monitor the change in voltage (or resistance) during mechanical testing. The potential drop technique depends on the phenomenon that the presence of a crack in an electric field results in a disturbance that can be interpreted in terms of crack size. To represent the change in the electric field for a specimen after introducing a crack, one can solve Laplace’s equation (Equation 3) after applying it for the appropriate boundary conditions, specimen geometry, crack size, and location of current leads
(Figure 14)
∇2∅ = 0 (3) where 훻 is the Laplace operator and Ø is the scalar electric potential field.
30 (a)
(b)
Figure 14. Electric field distributions for (a) intact sample, and (b) after introducing a crack.
With a given geometry and for a contact current, the voltage drop across the crack will be a direct indication of the crack size. With increasing crack length, the un-cracked cross-sectional area between the leads decreases, resulting in an increase in electrical resistance and thus change in potential across the crack faces. The magnitude of the potential drop also depends on the electrical resistivity of the material; the lower the resistivity of the material, the more sensitive this method is to crack size.
Most monolithic ceramics are, in general, electrically non-conductive material, therefore the potential drop method cannot be used to monitor crack length. Silicon carbide, however, shows some degree of electrical conductivity at room temperature, but
31 its electrical resistivity was considered too high to acquire reliable results for crack growth measurements. At temperatures above 600 °C, silicon carbide shows decrease in electrical resistivity which allows to the use of potential drop method at those temperatures as shown by Chen et al [107, 108]. Figure 15 show the change of resistivity of SiC as a function of temperature.
Figure 15. Relationship between electrical resistivity and temperature for SiC, where o is the resistivity at room temperature [107].
One drawback to this method is the lack of direct physical relation that correlates the drop in voltage with crack growth, instead calibration curves are used to establish such correlation.
3.3.3 Digital Image Correlation
Digital image correlation (DIC) is an optical technique that utilizes image tracking and correlation algorithms for accurate measurements of changes in images. It is
32 often used to measure deformation, vibration and strain fields in materials and structures.
By tracking blocks of pixels (usually produced by a speckle pattern on the surface of the specimen) the system can measure surface displacement and build up full field strain maps. The main advantage of DIC is that it is a non-contact visual technique that uses conventional digital photography and can be employed in the labs or outdoor environments. Additionally, DIC provides full-field measurement of the strain, rather than the single point strain measurements using traditional strain gage. In order for DIC to work effectively, the pixel blocks need to be random and unique with a range of contrast and intensity levels. DIC was developed in the early 1980s [109-111]. Advances in computer technology and digital cameras have been the enabling factors for the rise of
DIC, which use has been extended to almost any imaging technology. DIC has been utilized to determine stress intensity factor in materials during fracture testing [112, 113].
This method has been improved and applied to measure crack growth by tracking the surface strain that corresponds to failure of the material [114].
DIC can also be used to study materials with low failure strain, such as CMCs.
Yet, retaining a high-fidelity results post matrix crack initiation could be challenging
[115]. Ultimately, to utilize the full potential of DIC, it needs to be implemented during high temperature testing of CMCs (while using laser-heating, for instance) [116]. Still, many challenges need to be overcome in this regard.
3.3.4 Micro-Computed Tomography
Micro-computed tomography (µ-CT) is a NDE technique that characterize the material’s microstructure in a three dimensions at a micron level spatial resolution. In this
33 technique, the object is illuminated by a micro-focus X-ray source to create cross- sections of the object that can be used to recreate a virtual 3D model. By interpolating sections along different planes, one can inspect the internal structure of the material. Bale et al [117] investigated damage mechanics of a SiC single-tow composites under tensile load at room and elevated (1750 °C) temperatures. In this study, crack formations, crack densities, and fiber/matrix debond lengths were all monitored during mechanical loading
(Figure 16). This resulted in high fidelity information about the interaction between composite’s constituents, allowing to quantify important parameters such as debond length and fiber breakage, which would improve the accuracy of micromechanics model that uses these parameters.
Figure 16. Crack initiation and development in a single-tow SiC/SiC composite at room
(top) and high (bottom) temperature [117].
34 3.4 Micromechanical Modeling of Composites
CMCs are highly heterogeneous materials as they are made of constituents with various properties and shapes. Flaws are inherently found in these composites and they act as stress concentration points, causing cracks to commonly initiate in the vicinity of these porosities/flaws. There are four main constituent properties that highly influence the mechanical response of CMCs [118].
1. The elastic properties of fibers and matrix: the elastic damageable behavior of
CMCs is influenced by the Young’s modulus of the fibers and the matrix.
2. Fiber/matrix interphase: the debond energy between the fibers and the matrix is an
important factor in the composite behavior.
3. Fiber and matrix resistance to fracture.
4. The fiber volume fraction in the composite.
Generally, in the micromechanics approach, the response of a material (such as stress) is computed based on a physical input (such as strain). Simplifying assumptions make it necessary to specify the stress and strain distributions at the micromechanical level. Using the theory of models requires the solution of actual stresses and strains at the micromechanical level, while taken the fiber-packing geometry into account [119].
Among the simplest micromechanics models to predict the mechanical properties of a composite, based on the properties of its constituents, is the rule of mixture, which is suitable for unidirectional composite. In this model, the composite is assumed to consist of a block of matrix with a volume fraction Vm and a block of fiber with a volume fraction Vf, where the regions of the fiber and matrix are assumed to be under uniform
35 states of stress and strain (as shown in Figure 17). The model is developed based on two assumptions:
1. The fibers and matrix are considered to be perfectly bonded.
2. The geometry of the fiber and the interphase layer thickness are neglected, where
only the volume fractions are important.
Figure 17. Repeating volume element (RVE) for the rule of mixture.
By applying one-dimensional form of Hooke’s Law to the fiber, matrix and composite, one can derive the longitudinal and transverse moduli of the composite.
퐸11푐 = 푉푓퐸11푓 + (1 − 푉푓)퐸푚 (4)
퐸22푓퐸푚 퐸22푐 = (5) 푉푓퐸푚 + (1 − 푉푓)퐸22푓
36 Figure 18. Predicted E11 and E22 based on the rule of mixtures.
To develop a more realistic micromechanics model, Chamis [120] introduced a method which used a more realistic geometry for the repeating volume element (RVE). In this model, strips of matrix were mixed with strips of fiber and matrix combine, where a square fiber array is assumed (Figure 19). Also, the bonding between the fiber and the matrix is assumed to be perfect.
Figure 19. RVE for Chamis model. 37 The governing equations for the longitudinal and transverse moduli of the composite are:
퐸11푐 = 푉푓퐸11푓 + (1 − 푉푓)퐸푚 (6)
√푉푓 퐸22푐 = + (1 − √푉푓)퐸푚 √푉 (1 − √푉 ) (7) 푓 + 푓 퐸22푓 퐸푚
From equations (4) and (6) we can notice that the expression for the longitudinal modulus is identical for rule of mixture and Chamis model. This demonstrates that the effective longitudinal modulus predictions are not sensitive to geometry assumptions.
Figure 20 illustrates the predicted E11 and E22 moduli as a function of fiber volume fraction according to Chamis model and how the transverse modulus compares to the one of rule of mixture.
Figure 20. Predicted E11 and E22 according to Chamis model.
38 Another model that presented solutions based on a mechanics approach involving the use of displacement continuity and force equilibrium conditions is the Sun and Chen
Model [121]. This model is used to predict the elastic constants of a composite system and can be applied in finite element analysis.
In some cases, one may wish to obtain effective elastic properties of a composite, in addition to calculating the stress distributions in the fiber and matrix of a unit cell. The multi-continuum method permits determining the strains and stresses in the individual constituents of a composite, for a given total strain state [122]. This procedure can be generalized to a composite system with three constituents.
The Method of Cells has been shown to accurately predict the overall behavior of various types of composites from the knowledge of the constituent properties [123]. This method relies on the fundamental assumption that the double-phased composite has a periodic structure, in which the reinforcing phase is arranged in a periodic manner. This assumption allows to analyze a doubly periodic repeating unit cell (RUC), representative of a continuously reinforced composite material [124]. The RUC consists of four subcells, usually depicted as rectangular, one of which is occupied by the fiber. Although the fiber may appear square, this is not the case since the subcell stresses and strains are associated with the subcell centroid. In the Generalized Method of Cells, the RUC is subdivided into an arbitrary number of subcells. This generalization allows the modeling capability of the method of cells to include the modeling of various fiber shapes, analysis of different fiber arrays, modeling of damage and flaws effect among many other capabilities [125].
39 Woven composites present more challenges for modeling due to the complicated architecture. A method of cells type of approach was applied to model a plain weave woven composite. In this method, modeling one fourth of the RUC is assumed to be sufficient due to symmetry [126]. Figure 21 shows a RUC for a woven composite with one quarter cell.
Figure 21. Plain weave architecture, representative unite cell, and one quarter cell
[126].
This model was shown to have very good accuracy for predicting elastic properties of woven composites, despite having relatively simple formulations. This model also allows to compute the strains and stresses in the constituent fiber and matrix of a plain weave composite, allowing to homogenized constitutive properties of the entire composite lamina.
40 CHAPTER IV
DESIGN OF THE EXPERIMENT
4.1 Introduction
In the recent years, many efforts have been made to develop highly engineered composite systems with the aim to utilize them as high-temperature components for commercial jet engines. On the top of the list of these composite systems are ceramic matrix composites (CMCs), with their high temperature capability, environmental stability, low density, and good creep and rupture resistance [17, 127]. Compared to the nickel-based superalloys that are currently used in the hot-section of gas turbine engines,
CMC materials can operate at higher temperatures without the need for cooling air. Those factors can result in engines with improved thermal efficiency, reduced NOx emissions and increased thrust-to-weight ratio.
CMCs typically consist of carbon or ceramic fibers (that might be 2D or 3D woven) embedded in a ceramic matrix. Usually, the fibers are coated with an interface layer that creates a weak bond between the fiber and the matrix. The weak interface helps in improving fracture toughness due to debonding of the fiber-matrix interface. In order to successfully develop CMC materials to be applied in critical applications, their mechanical behaviors must be well-understood. Although the mechanical response of
CMCs under unidirectional on- and off-axis tensile loading has been widely studied [8,
41 9], the effort made to understand other types of damage, such as interlaminar crack growth, remains modest [10]. This area of research gains its importance from the fact that fiber reinforced CMCs are more susceptible to failure in the matrix rich interlaminar region and/or interface region under interlaminar normal or shear stresses. Such failure may result in loss of stiffness and might cause, in some cases, structural failure, especially at high temperature.
There are two main challenges associated with interlaminar fracture testing for
CMCs at elevated temperatures. First of all, during high temperature testing it is not possible to have direct measurements of crack length, simply because the sample is concealed inside a furnace. The validity of interlaminar fracture tests relies on accurate monitoring of crack growth. Numerous non-destructive testing methods such as x-ray, ultrasonic C-scan, thermography and eddy current have been shown to be sensitive to out-of-plane damage (delamination-type cracks) in ceramic matrix composites [73].
However, these techniques either cannot be used for in-situ monitoring or do not have the required high-temperature capability at a moderate cost [117]. It has been reported that electrical resistance (ER) provides a sensitive measure of internal damage in CMCs. In melt-infiltrated SiC/SiC composites electrical resistance is particularly sensitive to matrix cracking, due to the presence of Silicon, which results in low electrical resistivity of the matrix [102, 103]. Therefore, in this chapter a method is presented to monitor and measure interlaminar crack growth during fracture testing using electrical resistance.
Moreover, acoustic emission was shown to be a sensitive technique for monitoring damage accumulation during testing of different CMC systems [83-85]. In fact, Morscher
[85] was able to show that the accumulated AE energy is directly proportional to the
42 stress-dependent transverse matrix cracks obtained by microscopic observations. Similar analysis will be followed in this chapter to obtain a relationship between crack length and
AE energy.
The second challenge for interlaminar fracture testing is to develop a testing procedure that is simple and can be employed at room and high temperature. Evans proposed a number of methods for interlaminar fracture testing of CMCs [53]. Among these methods the double cantilever beam (DCB) is the most frequently adopted. Despite its simplicity, if the “free end” in this method deviates from the center, it may become a source of uncertainty, especially at high temperature where the temperature profile becomes non-uniform. Moreover, DCB is not applicable for testing at high temperature, due to the difficultly of maintaining adhesion between the loading pins and the sample during high temperature testing, where the region adjacent to the furnace could reach a couple hundred degrees Fahrenheit. Therefore, the alternative is to develop a technique that does not require the usage of loading pins to apply load on the sample. A wedge- loaded DCB is employed in this work, where a central force could be easily applied with the need for the use of adhesive bonding.
In the present chapter, different CMC systems with various geometries (variation of width and length) were tested. Acoustic emission and electrical resistance were employed to monitor damage accumulation in the material during testing. Supported by microstructural observations of crack morphology, effects of early damage and specimen geometry on the proposed testing and monitoring methods are discussed. Finally, expressions for measuring Mode I energy release rate were introduced.
43 4.2 Materials
Four CMC systems were interrogated in this chapter at different levels: melt- infiltrated SiC composite with ZMI fibers (ZMI SiC/SiC), melt-infiltrated SiC composite with Hi-Nicalon fibers (HN SiC/SiC), polymer impregnation and pyrolysis SiC/SiNC composite (PIP SiC/SiNC) and an alumina/alumina silicate (Oxide/Oxide) composite.
The ZMI SiC/SiC system (Goodrich, Santa Fe Springs, CA) consisted of 16 plies of balanced 0°/90°, five-harness-satin woven fiber preforms of Tyranno ZMI fibers (Ube
Industries, Kyoto, Japan). The total fiber volume fraction was about 25% with half of the fibers in the 0° direction and half in the 90° direction. The fiber preforms were coated with a boron nitride (BN) interphase then by a slurry cast molten silicon melt-infiltrated process creating a matrix consists of a continuous SiC phase as well as continuous Si phase. The HN SiC/SiC (Rolls Royce, Huntington Beach, CA) was manufactured similarly to the ZMI SiC/SiC but with Hi-Nicalon fibers type (Nippon Carbon, Tokyo,
Japan). The PIP SiC/SiNC system (known as S200) fabricated by COI Ceramics, Inc. San
Diego, CA was composed of eight-harness-satin weave non-stoichiometric SiC CG
NicalonTM fibers with boron nitride interphase in a matrix of silicon-nitrogen-carbon matrix that was prepared by multiple iterations of polymer pyrolysis process. The
Oxide/Oxide composite (COI Ceramics, Inc. San Diego, CA) was a 2-D woven, Nextel
720TM alumina fiber-reinforced alumina matrix CMC. The N720TM oxide fibers consisted of fine grained polycrystalline alpha alumina plus mullite (85Al2O3 + 15SiO2 % in weight). These fibers were woven into a balanced eight harness satin weave cloth. The cloth was then slurry-infiltrated with the matrix, and was then ply-stacked followed by consolidation and sintering to produce the test panel. The fiber volume fraction was about
44 48% and the fibers had no interphase coating, as verified by Energy Dispersive
Spectroscopy (EDS) analysis [128]. It has been reported that the N720/alumina CMC contains ~25% porosity, while the matrix porosity is ~48% [20]. The existence of porosity and microcracks in this type of material was found to enhance damage tolerance
[36, 40, 41, 129-131].
Figure 22 presents a typical microstructure of the materials tested in this study.
Note the significate difference in porosity between the two melt-infiltrated systems: ZMI
SiC/SiC and HN SiC/SiC (Figure 22a and Figure 22b). The microstructure of the
Oxide/Oxide system was obtained from [132].
Figure 22. Typical microstructure of (a) ZMI SiC/SiC (b) HN SiC/SiC (c) PIP SiC/SiNC and (d) N720/alumina (Oxide/Oxide) [132].
45 Table 2 summarizes some of the physical and mechanical properties of the material used in this chapter. E33 was determined using wave propagation approach
[133]:
2 휌퐸22 (1 − 12)퐶11 퐸33 = 2 2 (8) 퐸22 (1 − 12) + 2휌13퐶11
where C11 is the longitudinal wave velocity of wave propagation along the thickness of the composite. is the density of the material, is the Poisson’s ratio, and E is the
Young’s modulus.
Table 2. List of physical and mechanical properties of the tested material systems.
E11 Properties Density Resistivity E22 E33 12 Materials (g/cc) (-mm) (GPa) (GPa) (GPa)
ZMI SiC/SiC 2.70 0.2 200 200 74.5a 0.17+
HN SiC/SiC 2.79 0.11 274 274 192a 0.17+
PIP SiC/SiNC 2.34 950 115 115 67.6a 0.108*
Oxide/Oxide 2.85 - 90 90 48.5a 0.09*
+ From reference [134]
* From reference [135] a Ultrasonic estimate.
Different geometries were considered for this study by varying the length and the width of the samples. The thickness of the samples, on the other hand, was controlled by
46 the panel thickness. In this work, the samples will be referred to by their geometry as length×width×thichness (in mm). For ZMI SiC/SiC the samples dimensions were
50×5×4, 50×10×4, and 75×5×4. HN SiC/SiC had a uniformed geometry of 80×5×4. For
PIP SiC/SiNC the studied samples had the following geometry: 65×5×5, 65×10×5, and
65×15×5. The Oxide/Oxide samples had uniformed geometry of 70×10×3. After preparing the samples, a notch was machined in each specimen in the mid-plane with a thickness of ~0.4 mm and a length of ~25 mm for all the samples, except for the ZMI
SiC/SiC 50×5×4. Those had a notch length of ~15 mm.
4.3 Mechanical Testing
A ceramic wedge with 18° head angle (2α) was used in this study. In this method, a splitting force is created by inserting a vertically-moving wedge in a notch causing the arms to separate and forcing an interlaminar crack at the sharpest end of the notch (Figure
23). The wedge was held in the top grips of an MTS machine Model 43 (with a load cell of 30 kN) while the specimen was held in the bottom grips over a length of about 5 mm.
The wedge was inserted in the specimen’s notch at a constant displacement rate of
1 mm/min to initiate and propagate the interlaminar crack. It was found that the load required during interlaminar testing was less than 300 N, therefore, an Instron model
5582 with a load cell of 500 N was used instead to reduce the mechanical noise.
47 Figure 23. Test setup.
4.4 Electrical Resistance
Electrical Resistance was measured by four-probe method using an Agilent
34420A micro-ohm meter for the ZMI SiC/SiC and HN SiC/SiC samples and a Keithely
2450 SourceMeter® for the PIP SiC/SiNC and Oxide/Oxide samples (using ER on
Oxide/Oxide samples will be explained later). During the measurement, a direct current was applied through the outer probes, and the voltage was measured across the two inner probes to monitor the resistance of the material. The advantage of this procedure is that it minimizes the effect of contact resistance on the measurements, since the current going through the inner probes must be near zero. Two configurations were considered for probe attachments in this work: arm-to-arm and straight configurations (Figure 24). In the arm-to-arm configuration, all probes were attached to the arms with the current passing around the notch, compared to two probes attached to the arms and two connected at the bottom of the specimen for the straight configuration. The arm-to-arm configuration was 48 selected as the method of choice because of its ease of use, accuracy (as will be discussed later) and suitability for high temperature testing since all the probes would be away from the hot zone. For probe attachments, thin strips of conductive silver paste were applied around the specimen surface.
(a) (b)
Figure 24. Schematic of test setup with the two ER configurations: (a) arm-to-arm (b) straight.
4.5 Acoustic Emission
Modal acoustic emission was also monitored during tests using two wide band sensors (B1025, high sensitivity from 50 kHz to 2 MHz). The AE sensors were clamped to the specimen surface and vacuum grease was used as a coupling agent. The waveforms were recorded by a four-channel Fracture Wave Detector acquisition system (Digital
49 Wave Corporation, Centennial, CO). Software from the same company and an in-house
Matlab program were used to filter and analyze the recorded waveforms [90]. The sensors were placed back to back just above the bottom grips in the 50-mm long specimens and in series (with about 15 mm spacing between the two sensors) for the other longer specimens. The latter configuration helped discern events that initiated in the machine lower grips using the difference in times of arrival at top and bottom sensors.
However, it was found that very few if any events were generated in the lower grips.
4.6 Optical Microscopy, Digital Image Correlation (DIC), and Micro-CT
Optical microscopy was used to monitor crack growth during tests on the back surface of the specimens. Every ~2 seconds an image was captured by a camera connected to the microscope for the ZMI SiC/SiC samples. For the other three material systems, a Grasshopper3 camera was connected to a 105 mm micro-lens and used with a capturing rate of two frames per seconds (FPS). The surface was painted with white paint prior to testing in order to help elucidate the crack [10]. For the Oxide/Oxide samples, crack lengths were difficult to measure directly using the captured images; the interlaminar cracks were very narrow and barely perceptible. Therefore, digital image correlation (DIC) was incorporated on these samples to monitor crack growth. A contrasting speckle pattern was applied to the back surface of the samples. After testing, the recorded images were processed and analyzed using ARAMIS Professional V8 distributed by GOM.
Post-test inspection was carried out as well. Specimens were polished and examined under optical microscopy at two locations: near the surface and halfway along
50 the width. Test specimens were also scanned by micro-CT to better understand the crack morphology and interactions between the interlaminar crack and the material structure and defects. Micro-CT images were taken at the National Polymer Innovation Center at the University of Akron using a SkyScan 1172. The resolution of the scans was 5 µm.
4.7 Results and Discussion
4.7.1 Selection of the wedge material
The first wedge-loaded DCB test was performed using a stainless steel wedge.
The problem with using a metallic wedge for loading was that as soon as the wedge touched the sample arms, the current passed through the wedge instead of the CMC sample, simply because the wedge had much lower resistivity compared to the CMC material. As shown in Figure 25, in the first part of the test, the electrical resistance decreased, instead of increasing, as the load continued to increase. After the crack propagated to a certain length, the resistance started increasing with load. Therefore, when using a metallic wedge, the increase in ER is not only related to damage, but it also depends on the altered current direction because of the presence of more a conductive part (the metallic wedge). As a result, in order to use ER to monitor damage and crack propagation during wedge-loaded interlaminar testing, a wedge with an electrical resistivity higher than that of the tested material must be used.
51 Figure 25. Change of load and resistance vs. mouth opening displacement for a ZMI
SiC/SiC 50×5×4 sample during a wedge test when using a metallic wedge.
4.7.2 Implementation of electrical resistance to monitor crack growth
Figure 26 shows the change in ER, for arm-to-arm configuration (Figure 26a) and straight configuration (Figure 26b), during interlaminar wedge testing for two ZMI
SiC/SiC 50×5×4 samples. The total change in ER for each case is clearly different; upon crack propagation (~ 80 N) the percentage increase in ER for the straight configuration is
~20% compared to 70% for the arm-to-arm configuration. This indicates that the arm-to- arm configuration is more sensitive for crack propagation than the straight configuration.
52 (a)
(b)
Figure 26. ER change during interlaminar wedge testing for a ZMI SiC/SiC 50×5×4 sample in the case of (a) arm-to-arm configuration (b) straight configuration.
53 To estimate the crack length using electrical resistance, first we need to derive an equation for measured resistance.
Assuming that the axial resistivity of the composite is homogeneous and that the notch is perfectly centered in the middle of the specimen, the resistance will increase as the crack forms and propagates, since the current has to travel a longer distance around the crack tip. The total resistance can be expressed as follows for the arm-to-arm configuration:
휌퐿 휌푎 푅 = 2 + 2 + 푅 푡표푡푎푙 퐴 퐴 푂푃 (9) 푎푟푚 ⁄2
where ρ is the axial electrical resistivity of the undamaged composite, Aarm is the cross- sectional area of the arm, A is the cross-sectional area of the composite, L is the distance from the inner lead to the end of the notch, a is the crack length, and ROP is a constant resistance term that corresponds to the current traveling around the notch.
Solving for the crack length a and substituting the dimensions h (arms thickness), t (specimen thickness) and w (specimen width) for the appropriate areas, the crack length can be estimated using the following equation:
푤푡 퐿푡 푎 = (푅 − 푅 ) − (10) 4휌 푂푃 2ℎ
The term ROP can be calculated based on the initial resistance i.e. before the test starts, by using the following equation:
휌퐿 푅 = 푅 − 2 (11) 푂푃 0 푤ℎ
54 where R0 is the initial measured resistance value.
Although the dominant crack might be located exactly at mid-thickness in some tests, it is not always the case. Therefore, the equations must account for the case of an off-center crack as well.
For an off-center crack, and two arms with different thicknesses, the resistance equation becomes:
휌퐿1 휌퐿2 휌푎 휌푎 푅푡표푡푎푙 = + + + + 푅푂푃 (12) 퐴푎푟푚1 퐴푎푟푚2 퐴푥 퐴푦
where Ax, Ay are fractions of the area A and x, y are fractions of the thickness t: t = x + y
(see Figure 27)
The crack length equation is now:
푥푦푤 푥푦퐿1 푥푦퐿2 푎 = (푅 − 푅푂푃) − − (13) 푡휌 푡ℎ1 푡ℎ2
And the equation for ROP becomes
휌퐿1 휌퐿2 푅푂푃 = 푅0 − − (14) 푤ℎ1 푤ℎ2
55 Figure 27. Schematic of test setup for the arm-to-arm configuration showing the different geometries.
For the straight configuration (Figure 28), as the crack propagates, the current has to travel through a region with a smaller cross section area, resulting in an increase in resistance. The total resistance for a central crack can be expressed as:
휌퐿1 휌푎 휌[퐷푖푛 − (퐿1 + 푎)] 푅푡표푡푎푙 = + + + + 푅′푂푃 (15) 퐴 퐴 퐴 푎푟푚 ⁄2
where L1 is the distance between the top probe and the notch tip, Din is the distance between the inner probes and R’OP is a constant resistance term that corresponds to the current flowing through the thickness of the sample beyond the crack tip. Solving for a gives:
56 푤푡 퐿 푡 푎 = (푅 − 푅′ ) − 1 + 퐿 − 퐷 (16) 휌 푂푃 ℎ 1 푖푛
The generalized crack length equation for an off-center crack become:
푤푡푥 퐿1푡푥 퐿2푥 푎 = (푅푡표푡푎푙 − 푅′푂푃) − − (17) 휌푦 ℎ1푦 푦
Figure 28. Schematic of test setup for the straight configuration showing the different geometries.
Although both methods are valid to estimate crack growth depending on the increasing electrical resistance, the arm-to-arm configuration is more accurate since it has higher sensitivity compared to the straight configuration; from Equation 10 and Equation
16 and for 1 mm increase in crack length, the arm-to-arm configuration shows 75% more sensitivity compared to the straight configuration, using the same values for ρ, w, t, h, and
L. Therefore, the arm-to-arm configuration method will be used to estimate crack length.
57 For a ZMI SiC/SiC 50×5×4 sample, the crack shape and the crack tip location at various times through the test are shown in Figure 29. In this case the crack can be considered centered in correspondence to the sample thickness.
Figure 29. Crack morphology and crack tip location at certain times throughout the test for a ZMI SiC/SiC 50×5×4 sample.
Estimated crack lengths based on ER are shown in Figure 30 (from Eq. (9)). If Rx was assumed to be zero, the predicted crack length would be severely overestimated.
However, the trend for crack growth is in line with the optically measured crack growth.
When sitting Rx to the electrical resistance at the initiation of the main crack, the resulting prediction is in excellent agreement with the measure crack growth. The slight deviation after subtracting the value of Rx, however, could be a result of assuming a central crack. It may also be caused by a degree of uncertainty in the crack length measurement, which could be due to the low acquisition rate of the camera (for this test, the acquisition rate
58 for the images was 1 image every 2 seconds) and the difficulty in discerning the crack tip on the edge of the sample.
Figure 30. Measured crack length and estimated crack length from raw and post- precrack ER data (ZMI SiC/SiC 50×5×4 sample with crack pattern shown in Figure 29).
For the case of an off-centered crack (as shown in Figure 31), the estimated crack length is in excellent agreement with the actual length when using the off-center crack equation (Equation (13)). However, assuming a central crack (Equation (10)) would lead to an overestimation of crack length as shown in Figure 32.
59 Figure 31. Crack morphology and crack tip location at certain times throughout the test for a ZMI SiC/SiC 75×5×4 sample.
Figure 32. Measured crack length and estimated crack length from raw and post precrack ER data assuming a central crack and off-center crack for ZMI SiC/SiC
75×5×4 sample with crack pattern shown in Figure 31 [136]. 60 As a matter of fact, Equation (13) can provide precise estimate of crack length if the parameters in Equation (13) were measured accurately and if the arms resistivity were taken into consideration (the arms longitudinal resistivity could be slightly different from the longitudinal resistivity of the undamaged section of the composite) as shown in
Figure 33. It worth mentioning that switching to a camera system with higher acquisition rate (4 FPS compared to 0.5 FPS) improved the accuracy of the measured values significantly.
Figure 33. Measured and estimated crack length for a HN SiC/SiC 80×5×4 sample.
The same method was used for PIP SiC/SiNC samples to estimate crack lengths.
However, in this case the readings were taken through thin copper wires that was attached to the samples through sliver epoxy, compared to ZMI SiC/SiC and HN SiC/SiC where the clips were placed directly on the sample. Although it has been argued otherwise [107, 108], Figure 34 shows that predicting crack length based on ER can be
61 employed for materials with high resistivity as well (resistivity of PIP SiC/SiNC is ~1000
-mm). The increase in ER, as illustrated in Figure 35, is approximately 230% (initial resistance was 1250 ). One can conclude that, ER-based crack length measurements do not depend on the resistivity of the material, as long as the material is not an insulator. It worth mentioning that the use of sliver epoxy improved the accuracy of the ER data significantly. This technique allows for obtaining reliable ER data with minimum scatterings, which makes a detailed investigation of the ER features possible [137].
Figure 34. Measured and estimated crack length for a PIP SiC/SiNC 65×5×5 sample.
62 Figure 35. ER change during interlaminar wedge testing for a PIP SiC/SiNC 65×5×5 sample.
It was found that for some samples multiple crack might initiate at the notch tip – one of which become the dominant crack. This could be influenced by the presence of porosity at the notch tip, which serve as local stress concentration points. The notch tip radius could also induce multiple cracks, where a blunt notch tip introduces two stress concentration points that might lead to the initiation of multiple cracks (as shown in
Figure 36).
63 Figure 36. An example of multiple crack initiation at the notch tip (for HN SiC/SiC
80×5×4 sample).
Moreover, crack branching and secondary cracks might occur along the path of the main interlaminar crack (Figure 37), and when measuring crack length manually, one can choose to account for secondary cracks or not. However, ER takes into account branching and secondary cracks, because this method is damage driven. Therefore, the estimated crack length based on ER would include any secondary damage. As a result, an effective crack length must be introduced and properly defined to account for any type of secondary damage.
64 Figure 37. Example of crack branching and secondary cracks along the path of the main interlaminar crack (PIP SiC/SiNC 65×5×5)
As it has been shown, ER-based crack length estimation requires the material to have some degree of electrical conductivity. Non-conductive materials (such as oxide/oxide CMCs) does not allow for using ER directly. To overcome this challenge, a process is developed to reliably coat the specimen with a conductive coating along one edge of the tested specimen. The conductive coating will crack at the same rate as the tested specimens resulting in an increase in the coating resistivity. This increase in ER will be related to the crack length in the Oxide/Oxide material.
In order for such a coating process to be applicable, the deposited material must be uniformly conductive across the specimen’s edge, the deposited material must not affect the interlaminar properties of the specimen, and the chosen conductive material should not be expensive [138]. 65 At first, the material was coated with silicon using sputter coating. Such a coating method would produce a thin uniform layer on the sample surface. Unfortunately, the deposited layer was not conductive. This is probably due to the small silicon particle size and the spacing between the particles. Figure 38 shows a picture of the deposited silicon layer on an Oxide/Oxide sample.
(a)
(b)
Figure 38. (a) Picture of Oxide/Oxide sample with silicon coat on the edge (b) micrograph of the edge surface.
66 Silver paint was applied then on a ceramic material with a brush to create a conductive layer. It was noticed however that there is a minimum thickness of the sliver layer to ensure that a current can pass through it. This can be found in literature, as shown in Figure 39, where the increase in layer thickness result in an increase in conductivity.
Figure 39. Electrical current and resistance of silver film on a glass substrate as a function of film thickness for different applied voltages [139].
The disadvantage with using a brush to apply silver paint was the difficulty in maintaining a uniform silver paint thickness across the edge. The most common way to apply a uniform coating to a surface is by spraying; and the best way is to apply the paint is with an airbrush. Few attempts showed that the airbrush provided a good regularity of coating.
67 After achieving a uniform conductive layer of silver paint, the coat was cured at
100 °C for 10 mins. After that, one of the coated samples was heated up in a furnace to
815 °C (the projected testing temperature) to ensure that the silver layer will remain conductive during testing. After cooling the sample down, the conductivity of the silver layer was tested again. Interestingly, the conductivity of the silver layer improved; the contact resistance for the silver coating after curing at 100 °C for 10 mins was ~1.8 ohms.
However, after heating up to 815 °C the contact resistance become 0.2 ohms. One reason behind the improved conductivity could be the removal of the organic material found in the silver paint and creating better connections between the silver particles. Figure 40 shows a micrograph of a conductive silver layer with and without heating to 815 °C.
(a) (b)
Figure 40. Micrograph of a conductive layer of silver (a) without (b) with heating to 815
°C temperature.
The change in ER of the silver coating during wedge testing is shown in Figure
41. The percentile change for both cases is comparable, although for the sample without
68 pre-heating the increase in ER is continuous compared to the sample with pre-heating where the increase occurs in segments.
(a)
(b)
Figure 41. Change of load and resistance vs. mouth opening displacement for an
Oxide/Oxide 70×10×3 (a) without pre-heating to 815 °C (b) with pre-heating to 815 °C.
69 Figure 42 shows that the crack length is directly proportional to the increase in resistance. Therefore, one can predict the crack length at different times during the test using a linear fit.
Figure 42. Crack length vs. resistance for an Oxide/Oxide 70×10×3 without pre-heating.
It worth mentioning that crack tip locations were difficult to detect using the optical images for the Oxide/Oxide samples; the interlaminar cracks were very narrow and barely perceptible, probably due to the porous matrix. Therefore, crack lengths were determined based on the strain field ahead of the crack tip using DIC. Figure 43 shows the strain fields in an Oxide/Oxide sample, indicating the crack tip location.
70 Figure 43. Strain fields in an Oxide/Oxide 70×10×3 sample indicating crack tip location, using DIC.
4.7.3 Implementation of acoustic emission to monitor damage accumulation
A typical AE waveform recorded during mechanical test of a CMC specimen consists mostly of the zero-order flexural and extensional modes, A0 and S0 respectively.
In the frequency range considered in AE (up to 2 MHz), the high-frequency S0 mode has a constant velocity greater than that of the lower-frequency A0 mode. As a result, the recorded waveforms will show an increasing separation between the extensional mode
(reaching the sensor first) and the flexural mode (travelling at lower velocity) with increasing propagation distance. During wedge test, two main types of AE waveforms were recorded; one with clear separation between the high-frequency extensional mode and the low-frequency flexural mode, the other with superimposed low- and high- frequency components (Figure 44). The first type (Figure 44a) was associated to chipping, friction, and/or grooving at the wedge surface. The corresponding AE waves propagated significant distance to reach the AE sensors, leading to the clear separation observed between the two modes. This type of waveforms, being not related to material 71 damage, was filtered out. The second type of waveforms (Figure 44b) originated from sources closer to the sensors as shown by the shorter extensional region prior to the superimposed modes dominated by the flexural component. Therefore, these waveforms were associated to material damage. The cumulative energy of damage-related AE events
(second type) is used here as a measure of damage progression [85].
(a)
72 (b)
Figure 44. Actual waveforms produced during the wedge testing: (a) with clear separation between the extensional and flexural modes (associated with chipping, friction and/or grooving at the wedge surface) and (b) with a short extensional region prior to the superimposed modes (associated with material damage) [140].
During mechanical testing, AE offers an insight into the damage state in the material; cumulative AE energy is one way to estimate damage propagation at a given time during mechanical testing. One key advantage of using AE is the ability to determine crack initiation, which can be defined as the first “jump” in cumulative AE energy. Figure 45 shows an example of using AE to determine crack initiation during the wedge test. For this case, ER shows slight increase prior to any observable cracks, this might be due to the strain in the arms as a result of deflection. However, the first jump in
73 AE is in correspondence with the first drop in load, allowing us to determine the time of crack initiation.
Figure 45. Load, ER change, and cumulative AE energy vs. time during wedge test for
ZMI SiC/SiC 50×5×4 sample.
Another example is shown in Figure 46 for a PIP SiC/SiNC 65×5×5 sample: The first jump in AE is in line with the first drop of load, indicating crack initiation. AE then continuous to increase with damage in the material, when the big change in AE cumulative energy indicate the severity of damage at certain points.
74 Figure 46. Load, ER change, and cumulative AE energy vs. MOD during wedge test for
PIP SiC/SiNC 65×5×5 sample.
Looking at the individual AE events (Figure 47) shows that must of the events are low energy events (soft events) and just few high energy events (loud events). Soft events probably correspond to delamination along the crack path. Loud events, on the other hand, are most likely due to matrix cracks and sudden advancements in crack length.
Figure 47 shows also that must of the loud events are accompanied by drops in load, which is probably due to relief of stresses as the crack propagates.
75 Figure 47. Load and AE events energy vs. time for a HN SiC/SiC 80×5×4 sample.
Figure 48 shows that cumulative AE energy follows a bilinear relationship with crack length. In other words, after the crack propagates a certain distance, the cumulative
AE energy is directly proportional to crack length. This can be related to cumulative AE energy being directly proportional to stress-dependent transverse matrix cracks during tensile testing of CMC [85]. However, during tensile testing, two or three AE sensors are usually used, at the top and the bottom of the specimen. During interlaminar testing, on the other hand, AE sensors can only be placed at the bottom of the sample (due to the presence of the notch). As a result, AE signals are more attenuated during crack initiation and in the early stages of crack propagation, compared to crack propagation towards the end of the test, where the crack tip becomes physically much closer to the AE sensors.
76 Figure 48. Cumulative AE energy vs crack length for a HN SiC/SiC 80×5×4 sample.
This can be seen more clearly in materials with lower Young’s modulus, which result in higher signal attenuation (Oxide/Oxide for example). In the beginning of the test, only few events can be detected, nevertheless, the number of events increases exponentially towards the end of the test. On the other hand, material with less signal attenuation shows linear increase in the number of events detected during the test, as showing in Figure 49.
Figure 49. Number of events vs. time for HN SiC/SiC 80×5×4, PIP SiC/SiNC 65×5×5, and Oxide/Oxide 70×10×3. 77
For materials with high signal attenuation, it is not only that soft events do not get detected in the beginning of the test, but also loud events that occur during crack initiation are recorded as low energy events due to attenuation. Figure 50 illustrates that only soft events are detected in the first half of the test, and loud events occurs merely towards the end of the test. This was not the case for HN SiC/SiC (Figure 47) where loud events were spread out throughout the test.
Figure 50. Load and AE events energy vs. time for an Oxide/Oxide 70×10×3 sample.
Therefore, one must be careful when using the first “jump” in cumulative AE energy for detecting crack initiation in materials with high signal attenuation.
78
4.7.4 Mechanical Behavior
4.7.4.1 Determination of load and mouth opening displacement
In the wedge testing method, the load required to initiate and propagate an interlaminar crack is different from the load measured directly from the load cell. Figure
51 demonstrates the different forces acting on the wedge surface, where P is the applied force on the wedge produce by the testing machine, R, the specimen reaction needed to propagate an interlaminar crack, Ff, the friction force, µ, the coefficient of friction between the wedge and the sample, and 훼, half the wedge head angle. The equilibrium condition of the vertical forces acting on the wedge, assuming symmetry, yields an equation for Fx which is the mouth opening load (the load required to initiate and propagate load) as follow:
(cos 훼 − 휇 sin 훼) 퐹 = 푃 (18) 푥 2(sin 훼 + 휇 cos 훼)
More detailed analyzes of the forces introduced in Equation (18) and the role of friction will be discussed in detail in the next chapter.
Figure 51. Different forces acting on the wedge surface. 79 Crosshead displacement could be measured directly from the testing machine.
Mouth opening displacement, on the other hand, could be calculated using the recorded crosshead displacement values as shown in Equation (19)
푀푂퐷 = 2 × 퐷𝑖푠푝 × tan 훼 (19)
Alternatively, mouth opening displacement could be measured directly using a spring-loaded LVDT (linear variable differential transformer) placed against one of the sample’s arms, or by using optical measurements, as shown in Figure 52.
Figure 52. Determination of MOD using optical measurements.
4.7.4.2 Mechanical Behavior
Figure 53 shows an example of the load, ER and AE data versus time for a ZMI
SiC/SiC 50×5×4 sample. The load curve shows a steady increase in load until a first crack initiates (after ~7 seconds). This corresponds to stress building in front of the crack tip to cause crack initiation. After limited crack propagation the load will drop, only to 80 start building again in front of a new crack tip. Therefore, a series of crack initiations and crack arrests would result in what seems as an oscillation in the load. This series of cracks will form one main crack along the mid-plane. Figure 54 shows the crack after it had propagated a few millimeters in addition to the location of the crack tip at various times throughout the test. It illustrates well the described crack propagation pattern; the crack does not grow continuously, but rather appears as small segments every few seconds.
Figure 53. Load, ER change, and cumulative AE energy during wedge testing of ZMI
SiC/SiC 50×5×4 sample.
81 Figure 54. Crack morphology and crack tip location at certain times throughout the test for a ZMI SiC/SiC 50×5×4 sample, with the data shown in Figure 51 (Reprinted from
Figure 29).
The mechanical behavior described above (steady increase in load up to crack initiation, then oscillation in load) can be seen in the different CMC systems tested.
Figure 55 shows the mechanical, ER, and AE data for a PIP SiC/SiNC 65×5×5 sample.
Figure 55. Load, ER change, and cumulative AE energy during wedge testing of PIP
SiC/SiNC 65×5×5 sample. 82 4.7.4.3 Effect of specimen Width
To understand the effect of width on the interlaminar properties of CMC, samples from the ZMI SiC/SiC and PIP SiC/SiNC panels were cut with different widths (5 and 10 mm for ZMI SiC/SiC and 5, 10 and 15 mm for PIP SiC/SiNC). Figure 56 presents the load data for the ZMI SiC/SiC samples for the different widths considered. The figure shows that for the 10 mm wide sample, the interlaminar crack propagates at double the load in comparison to the 5 mm wide sample. As a matter of fact, the load data for the 10 mm wide sample overlaps with double the load curve of the 5 mm wide sample, which suggests that the width does not play a major role in the mechanical behavior for this materials system.
Figure 56. Load and double the load vs. crosshead displacement for ZMI SiC/SiC
50×5×5 in comparison to the load data for ZMI SiC/SiC 50×10×5.
When comparing the PIP SiC/SiNC samples (Figure 57), however. Only prior to crack initiation, the load-displacement curve for the samples of identical geometry is comparable. However, after crack initiation these curves diverge, showing scattering in 83 the mechanical data. This material system contains considerable amount of porosity (due to processing), in comparison to the materials prepared using melt infiltration technique.
The presence of porosity can explain the scattering of mechanical data for samples with identical geometry. It can also explain the significant drop in load for the 15 mm wide sample, where an increase in the width of the sample, rises the chances of having large porosity in the crack path.
Figure 57. Load vs. crosshead displacement for five PIP SiC/SiNC sample: two 65×5×5, two 65×10×5, and one 65×15×5 in comparison to the load data for ZMI SiC/SiC
50×10×5
84 4.7.4.4 Effect of Notch Tip Radius
To understand the effect of a sharp notch tip on crack initiation, a notch sharpening apparatus was built, similar to [141], where a thin blade (0.2 mm wide with a
0.09 mm edge width) was used to guide a polishing compound with a 3 µm size particles.
If the sharpening process performed precisely, the final notch radius would be 3
µm (based on the polishing compound used). However, this sharpening process still need a lot of improvement. For now, the achieved notch radius was in the range of 70 µm.
Figure 58 shows a notch pre- and post-sharpening. Two samples (PIP SiC/SiNC 65×5×5 and PIP SiC/SiNC 65×5×5) were sharpened prior to testing while two other samples were tested without notch sharpening in order to compared the effect of sharpened notch.
From Figure 57, by comparing the data for PIP SiC/SiNC 65×5×5-1 (notch not sharpened) with S200-65×5×5-2 (sharpened notch) and PIP SiC/SiNC 65×10×5-4 (notch not sharpened) with PIP SiC/SiNC 65×10×5-3 (notch sharpened), we find that it is difficult to discern any clear effect of notch sharpening on mechanical data. This is mainly due to the presence of porosity in this material and the fact that the notch did not have a tip with small enough radius. The main effect of sharpening the notch is to change the location of the crack initiation as shown in Figure 58 and Figure 59. After sharpening, the crack would initiate at the weakest point closet to the new notch radius. Yet, before sharpening, the crack does not start at the notch tip, but instead it initiates at a stress concentration point within the vicinity.
85 Figure 58. Notch shape for sample PIP SiC/SiNC 65×5×5-2 before and after sharpening, and post test.
86 Figure 59. Notch shape before testing (notch not sharpened) and after testing, showing two interlaminar crack. Sample PIP SiC/SiNC 65×5×5-1
It might worth mentioning that for the two tested samples with sharpened notch, only one crack initiated at the notch. However, for two out of three tested samples without sharpened notch, multiple cracks initiated near the notch tip; one of the cracks would propagate to become the dominant interlaminar crack.
4.7.4.5 Mode I Energy Release Rate
The energy release rate can be determined based on the beam on elastic foundation model [142]. In constant force conditions, when the un-cracked length is significantly greater than the sample thickness, the stress intensity factor can be expressed as follows:
퐹 푎′ ℎ 퐾 = 2√3 푥 (1 + 0.64 ) (20) 1 푤ℎ3⁄2 푎′
87 where KI is the stress intensity factor, Fx is the mouth opening load, a` is the total crack length, w is the sample width, and h is half the sample thickness and the energy release rate is
2 퐾퐼 퐺퐼 = (21) 퐸11
GI is the energy release rate in Mode I, and E11 is the Young’s modulus in the 11 direction
Another method to determine the energy release rate is by using the compliance method. The compliance method has been used extensively to evaluate interlaminar facture toughness of PMCs [54, 143, 144].
In the compliance method, the crack growth resistance of a perfectly built-in double cantilever beam can be expressed as follows:
퐹2 휕퐶 퐺 = 푥 (22) 퐼 2푤 휕푎` where C is the compliance and can be defined as
훿 퐶 = (23) 퐹푥
is the mouth opening displacement.
Equation (22) can be further simplified using appropriate compliance relations based on the modified beam theory to become:
88 3퐹 훿 퐺 = 푥 (24) 퐼 2푤푎`
In reality, this expression overestimate GI because rotation may happen at the delamination front, therefore, the modified GI equation becomes:
3퐹 훿 퐺 = 푥 (25) 퐼 2푤(푎` + |∆|) where account for a slightly longer delamination to compensate for the rotation. can be determined empirically by generating a least squares plot of the cube root of
1 compliance, 퐶3, as a function of delamination length, as shown in Figure 60.
Figure 60. Modified beam theory for a HN SiC/SiC 80×5×4 sample.
Figure 61 compares GI for an HN SiC/SiC 80×5×4 sample based on the compliance method and the modified beam theory. The two methods show very comparable data for a short crack, however, after the crack propagates a certain distance, the compliance method report lower values for GI compared to the modified beam theory
89 method. The difference between the two methods will be further investigated in future work.
Figure 61. GI based on the compliance method and modified beam theory for an HN
SiC/SiC 80×5×4 sample.
When looking at the energy release rate versus crack length the CMC composites
(Figure 62), we often see a rising R-curve behavior. This behavior is probably due to fiber bridging, which occurs at certain segments on the crack path. The composite microstructure plays a role also in the interlaminar fracture behavior, especially the fiber weave. The effect of fiber weave on the rising R-curve will be investigated in a later chapter.
90 Figure 62. Energy release rate vs. crack length using compliance method for three HN
SiC/SiC 80×5×4 samples.
Another example of rising R-curve behavior is shown in Figure 63 for PIP
SiC/SiNC material. In this case fiber bridging, seems to occur only at certain segments on the crack path. While other parts in the crack path does not have fiber bridging, and the crack would probably have minimum resistance propagating through these sections, which result in drop in GI (Figure 64).
91 Figure 63. Energy release rate vs. crack length using compliance method for five PIP
SiC/SiNC with varying widths.
Figure 64. Crack path for PIP SiC/SiNC 65×5×5-2 showing sections of fiber bridging and others with fiber bridging. 92 4.8 Conclusions
The presented work in this chapter introduces the wedge DCB technique for determining interlaminar fracture properties of CMC materials. Four material systems were investigated in this study: two of them were manufactured using melt infiltration
(ZMI SiC/SiC and HN SiC/SiC), one was prepared using polymer impregnation and pyrolysis (PIP SiC/SiNC), and one oxide/oxide system. Unlike the traditional DCB technique, the proposed method does not require the use of adhesive bonding to attach loading pins, and therefore holds promise for high temperature testing.
A new technique was also introduced for monitoring interlaminar crack growth without optical observation using electrical resistance. The basic principle for this method is to correlate crack growth with the increase in ER. Crack lengths measured using ER were in excellent agreement with visual observations for various CMC systems with significantly different electrical properties. The presented method, therefore, has great potential for use during high-temperature testing. This method was also utilized for insulating Oxide/Oxide systems by applying a thin layer of sliver on the material edge.
Acoustic emission was used during interlaminar testing to monitor damage accumulation in the material. Depending on the waves properties, it was possible to discern damage events from the one produced at the wedge surface due to friction. It was found that AE is valuable approach for determining the onset of crack initiation for the materials processed using melt-infiltration. However, crack initiation for materials with high signal attenuation properties was less clear.
93 The mechanical behavior of all the tested CMC systems showed similar pattern; a continuous increase in load until a crack was initiated, followed by load oscillation due to a series of crack openings and arrests. Where it was found that the interlaminar crack does not propagate continuously but rather but rather appears as small segments every few seconds.
Estimates of Mode I energy release rate were carried out using beam on elastic foundation model and compliance method. GI showed comparable results for samples with identical geometry. It was also found that GI exhibit continuous increase after crack initiation (rising R-curve behavior). Evidence of crack bridging were found and it is believed that this phenomenon result in the rising R-curve behavior. However, future work will investigate this behavior.
94 CHAPTER V
THE EFFECT OF FRICTION AND WEDGE ANGLE ON THE WEDGE-LOADED
DOUBLE CANTILEVER BEAM METHOD
5.1 Introduction
The wedge-loaded double cantilever beam is a friction-dependent testing method; the measured load consists of the load required to initiate and propagate an interlaminar crack, in addition to the friction force between the wedge surface and the specimen. The friction force depends on the coefficient of friction between the wedge material and the specimen material. It also depends on the wedge angle. Ideally, one wants to minimize the frictional forces and produce pure or near-pure interlaminar force.
This chapter will focus on verifying the wedge method by understanding the role of friction between the wedge and the specimens on the interlaminar properties of CMCs.
5.2 Experimental Procedure
5.2.1 Material and Mechanical Testing
The material tested in this chapter were the ZMI SiC/SiC system (introduced in the previous chapter). Three specimens with identical geometry (50 mm long × 10 mm
95 wide × 4 mm thick) were tested in this study. A notch of 0.4 mm thickness and ~15 mm length (1/3 of total specimen length) was machined in the mid-plane of each specimen.
For mechanical testing, the methodology introduced in Chapter IV was employed here: a ceramic wedge with an 18° head angle (2α) was used to create a splitting force by inserting the wedge in the notch, forcing the arms to separate and inducing an interlaminar crack. The wedge was held in the top grip of an MTS machine with a load cell of 30 kN while the specimens were kept stationary at the bottom grip. Since the wedge tip was narrower than the notch width, the wedge was inserted in the middle of the notch slowly until a slight contact with both arms was achieved. Then, the test was started by inserting the wedge at a constant displacement rate of 1 mm/min. Throughout the test, the contact between the wedge and the inner edge of the sample’s arms was a line contact [145], were the points of contact on the wedge surface changed during the test, while the contact points on the sample arms remained the same.
To understand the effect of the wedge material on the wedge-loaded DCB test and the role of friction between the specimen and the wedge, three wedges were used for this study. The materials used for the wedges were: Gray Wonderstone alumina silicate
(29.2% Al2O3 and 59% SiO2) from McMaster-Carr, 99% density alumina (Al2O3) from
McMaster-Carr, and polycrystalline silicon nitride (Si3N4) GN10 from Allied Signal,
Torrance, California.
Optical microscopy was used to measure crack growth during testing. The accusation rate was two frames per second. Unfortunately, due to technical challenges, crack length measurements are only available for the sample tested with the silicon nitride wedge. 96 5.2.2 Friction Measurement
The coefficient of friction between the samples and the wedge material was measured using a pin on desk apparatus. To simulate the contact between the wedge and the specimens’ arms, the friction test conducted was line contact test. Samples were cut from the bottom intact part of the SiC/SiC specimens, glued to a holder, and machined with a diamond grinder wheel to introduce curvature as shown in Figure 65. The measured radius for the different specimens ranged from 2.7 mm to 3.8 mm. Counter material was identical to the wedge material. The tests were run for 100 meters with 2 N load on the specimen and a speed of 2 cm/s. In order to verify the coefficient of friction, multiple tests were run for a given counter material using different rotation radii.
Changing the rotation radii ensures a clean surface is created for each test.
Figure 65. Friction specimen.
5.3 Analytical Analysis
When choosing a wedge angle, the main criteria to take into consideration is the friction force between the wedge and the specimen. 97 From the analysis of static equilibrium of the wedge, one can find the relationship between the forces acting on the wedge surface (Figure 66). Let P be the applied force on the wedge produced by the MTS, R, the specimen reaction needed to propagate an interlaminar crack, Ff, the friction force, µ, the coefficient of friction between the wedge and the sample, and 훼, half the wedge head angle. The equilibrium condition of the vertical forces acting on the wedge, assuming symmetry, gives:
푃 = 2퐹푓 cos 훼 + 2푅 sin 훼 (26) where
퐹푓 = 휇푅 (27) therefore
푃 푅 = (28) 2(휇 cos 훼 + sin 훼)
By balancing the horizontal forces we find
퐹푥 = −퐹푓 sin 훼 + 푅 cos 훼 (29)
where Fx is the mouth opening load. Finally, the relationship between Fx and the applied load P is:
(cos 훼 − 휇 sin 훼) 퐹 = 푃 (30) 푥 2(sin 훼 + 휇 cos 훼)
98 Figure 66. The forces acting on the wedge.
Equation 30 shows that the relationship between the applied load and resulting mouth opening load depends on the coefficient of friction between the wedge and the sample, and on the wedge angle. Figure 67 compares the ratio of mouth opening load to the applied load as a function of friction for different wedge angles. From the figure, we notice that for a specific coefficient of friction, there is a wedge angle at which the applied load equals the mouth opening load (Fx/P = 1). Choosing a greater wedge angle would result in a friction force hindering the movement of the wedge, and the applied load would be greater than the mouth opening load to overcome friction force. Vice versa, choosing a smaller wedge angle would result in a wedge with ‘mechanical advantage’ in which the friction force is beneficial and it adds up to the force applied by the wedge [146].
99 Figure 67. Mouth opening load to applied load vs. coefficient of friction for different wedge angles.
In reality, the coefficient of friction is mostly controlled by the wedge material.
Therefore, it is recommended to choose a wedge material that is known to have low coefficient of friction. The wedge angle, on the other hand, should be optimized to achieve mechanical advantage of the wedge, where the narrower the wedge, the greater will be the mechanical advantage. However, the wedge angle should be large enough to allow the wedge to propagate an interlaminar crack.
100 5.4 Results and Discussion
5.4.1 Friction Study
Figure 68 shows friction data between SiC/SiC samples and three different counter surfaces: alumina silicate, alumina, and silicon nitride. For each of the rotation radii tested on a given counter material, the friction behavior was consistent. However, the behavior differs between the different counter materials. In the case of alumina silicate (Figure 68a), there is a sharp increase in the coefficient of friction in the beginning of the test, followed by a gradual decrease. Towards the end of the test, the coefficient of friction stabilizes and seems to be constant. The SiC sample is harder than the alumina silicate plate causing a groove to appear on the plate surface.
According to Figure 68b, the behavior of SiC against alumina is quite the opposite compared to the case for alumina silicate; a sudden drop of the coefficient of friction is seen in the beginning of the test, followed by a gradual increase. A small trace of SiC was left on the alumina plate after the test.
Among the three counter materials, silicon nitride had the most comparable hardness to SiC; very minimal wear appeared on the silicon nitride surface at the end of the friction test.
One must point out, however, that as we move the samples to a smaller inner rotation radius, the friction coefficient increases i.e. in Figure 68c the first sample rotated in a 10 mm radius (total laps 1592), the second one rotated in a 7.1 mm radius (2244 laps), and the third in a 5 mm radius (3197 laps). Therefore, the increasing coefficient of
101 friction is attributed to the increasing number of laps over the same path. This is presumable due to the decrease in heat dissipation when the rotation radius decreases.
(a)
(b)
102
(c)
Figure 68. Coefficient of friction (μ) vs. laps number for ZMI SiC/SiC samples on (a) alumina silicate (b) alumina and (c) silicon nitride.
Since the data is following the same trend, the coefficients of friction of only the first test for each counter material (the one with the greatest rotation radius) will be taken into consideration for later wedge related calculations, since these conditions resemble the wedge test the best. Table 3 shows that silicon nitride has the lowest coefficient of friction against SiC/SiC, followed by alumina, while the alumina silicate disk reported the highest coefficient of friction.
103
Table 3. Summary of the coefficients of friction for the tested materials.
Counter Sample Sample Rotation μ SD Material Radius Width Radius
Alumina 0.7 0.038 2.8 mm 2.7 mm 13.4 mm Silicate
Alumina 0.39 0.028 3.5 mm 2.5 mm 18.3 mm
Silicon Nitride 0.26 0.019 3.3 mm 2.4 mm 10.0 mm
5.4.2 Mechanical Data
Figure 69 shows the mechanical data for three identical samples tested with three different wedges. The figure clearly displays that the alumina silicate wedge, having the highest coefficient of friction, produced the highest load. While silicon nitride produced the lowest. It is also worth mentioning that the increase in the coefficient of friction results in more scattering in the load. This could be due to the grooving and chipping at the surface of the wedge when the friction force is high. Also, as shown in Figure 67, a coefficient of friction above 0.32 (for an 18° wedge angle) would produce an opposing friction force, which might ascribe to some mechanical noise.
104 Figure 69. Load vs. crosshead displacement for different wedge materials.
To compare the mouth opening load produced by the different wedges, we use
Equation 30 after inserting the appropriate coefficients of friction found previously. From
Figure 70 one can notice that the mouth opening load versus displacement is matching for the different wedges. In other words, by cancelling the effect of friction forces, the load required to introduce an interlaminar crack is the same regardless of the wedge material.
This finding gives validation to the wedge testing method as a technique that does not depend on the material used for the wedge as long as the correct coefficient of friction is used.
105 Figure 70. Mouth opening load produced by the different wedges vs. crosshead displacement
5.5 Conclusions
The wedge-loaded double cantilever beam testing method has been verified considering the role of friction and the wedge angle. An analytical analysis showed that friction forces between the wedge and the samples play an important role in this testing technique. By choosing a material with low coefficient of friction, or a wedge with small head angle the wedge can achieve mechanical advantage. In that case, the useful load is greater than the applied load, and friction forces do not hinder the wedge movement and assist in crack propagation.
An independent friction study using three different wedge materials showed that the load required to introduce and propagate an interlaminar crack is independent of the wedge material as long as the correct coefficient of friction is being considered.
106 CHAPTER VI
COMPARISON BETWEEN THE WEDGE-LOADED DOUBLE CANTILEVER
BEAM AND THE TRADITIONAL DOUBLE CANTILEVER BEAM
6.1 Introduction
The second validation of the wedge-loaded double cantilever beam method is performed by comparing it to the traditional double cantilever beam technique. The traditional DCB technique is a well-established method for determining interlaminar fracture properties in composite materials. This method has been used extensively for testing unidirectional and woven PMC. In fact, an ASTM standard has been established on the use of the traditional DCB for PMC materials [14]. However, a comparison between the wedge-loaded DCB and the traditional DCB cannot be found in the open literature.
Although both testing techniques (wedge-loaded DCB and traditional DCB) can be easily utilized to determine interlaminar fracture properties at room temperature, the use of the traditional DCB during high temperature testing is not straightforward. An elaborated setup is essential to overcome the limitation imposed by the need of adhesive agent to attach the loading pins or blocks. This is not a problem for the wedge-loaded
DCB since the load is applied thorough direct contact between the wedge and the
107 specimen. However, the friction between the wedge surface and the specimen introduces difficulties that do not exist in the traditional DCB technique.
The comparison between the wedge-loaded DCB and the traditional DCB will be carried out by comparing load-displacement data and strain energy release rate obtained from both methods. Also, this chapter will examine the effect of fiber layout direction on the interlaminar fracture properties in 2D woven SiC/SiC composites.
6.2 Experimental Procedure
6.2.1 Material and Mechanical Testing
The material tested in this chapter was the HN SiC/SiC CMC system (introduced in Chapter IV). The material was provided in the form of a panel (160 mm × 80 mm × 4 mm). Specimens were cut in both the longitudinal and transverse directions, as shown in
Figure 71. In this chapter, the samples cut in the longitudinal direction will be referred to as Horizontal (H), and the ones cut in the transverse direction will be called Vertical (V).
All samples had identical geometry: 80 mm long, 5 mm wide and 4 mm in thickness. A notch was machines on each specimen in the mid-plane with a thickness of ~0.4 mm and
25 mm length.
108 Figure 71. Schematic showing the cutting directions for the Horizontal (H) and Vertical
(V) samples.
A silicon nitride wedge with 18° head angle (2α) was used for the wedge-loaded
DCB test, as discussed in Chapter IV. The wedge was held in the top grip of an MTS machine Model 43 with a load cell of 30 kN. The specimens were held in the bottom grips over a length of ~5 mm. The wedge was inserted in the notch at a constant displacement rate of 1 mm/min. The test was interrupted after 5 mm displacement of the wedge.
For DCB testing, two stainless steel loading pins were glued to the specimen’s arms approximately 5 mm from the arms’ ends. The pins were attached to an Instron
5582 with a 500 N loading cell. A crosshead displacement rate of 0.25 mm/min was applied to the top pin, while the bottom pin remained stationary. To balance the weight of the sensors (electrical resistance clips and acoustic emission sensors), a counter weight was attached to the sample’s free-end through a pulley system prior to testing, as illustrated in Figure 72. The sample end was then allowed to move freely during the test.
109 For this Chapter, the data obtained from ER and AE will not be covered. A thorough discussion of similar analysis can be found in Chapter IV.
Figure 72. Schematic of test setup for the (a) wedge test and (b) DCB test.
6.2.2 Optical Microscopy
Crack growth was monitored during testing using a camera connected to a magnifying lens with a capturing rate of four frames per second. The backside of the sample was covered with white paint prior to testing to help elucidate the crack. Post-test inspection was performed as well. Samples were polished and examined under optical microscopy at two locations: near the surface and half way along the width, to understand crack morphology and the interactions between the interlaminar crack and the material structure.
110 6.2.3 Energy Release Rate
The energy release rate was determined using the compliance method. This method has been utilized extensively to evaluate interlaminar facture toughness of PMCs.
In the compliance method, the crack growth resistance of a perfectly built-in double cantilever beam can be expressed as follows:
퐹2 휕퐶 퐺 = 푥 (31) 퐼 2푤 휕푎` where C is the compliance and can be defined as
훿 퐶 = (32) 퐹푥
is the mouth opening displacement.
Equation (31) can be further simplified using appropriate compliance relations based on the modified beam theory to become:
3퐹 훿 퐺 = 푥 (33) 퐼 2푤푎`
In reality, this expression overestimate GI because rotation may occur at the delamination front, therefore, the modified GI equation becomes:
3퐹 훿 퐺 = 푥 (34) 퐼 2푤(푎` + |∆|) where account for a slightly longer delamination to compensate for the rotation. can be determined empirically by generating a least squares plot of the cube root of
1 compliance, 퐶3, as a function of delamination length. 111 6.3 Results and Discussion
To compare the mechanical behavior of the samples tested with the wedge method to the ones testing using the DCB method, the mouth opening load versus mouth opening displacement will be compared for each sample.
For the DCB test, both mouth opening load and displacement can be recorded directly from the testing machine. However, for the wedge test, the displacement recorded by the machine is the wedge vertical displacement. The mouth opening displacement can be calculated from the equation:
푀푂퐷 = 2 × 퐷𝑖푠푝 × tan 훼 (35)
Similarly, the load recorded by the machine is not the mouth opening load and it includes the friction forces. Therefore, the mouth opening load should be calculated from the following equation (as discussed in the previous chapter)
(cos 훼 − 휇 sin 훼) 퐹 = 푃 (36) 푥 2(sin 훼 + 휇 cos 훼)
Figure 73. Different forces acting on the wedge surface.
112 In order to calculate the mouth opening load from Equation (36), the coefficient of friction between the sample and the wedge should be determined. As was shown in the previous chapter, the measured coefficient of friction between SiC/SiC and Si3N4 is µ =
0.26
Figure 74 compares the mechanical response of six Vertical samples, half were test with DCB and half with the wedge method. It worth noting that the point at which the measurements were taken for the DCB tested samples and the wedge tested samples were not identical, rather they were 5 mm apart. However, such difference should not have major effect on the mechanical behavior. The mechanical performance between the samples tested with wedge and DCB is very comparable until a crack is initiated and propagated for a short distance (crack initiation occurred around 0.5 mm MOD). Beyond certain crack length, unlike the wedge tested samples, the DCB tested samples shows slight decrease in load.
Figure 74. Mouth opening load vs. mouth opening displacement for wedge tested and
DCB tested Vertical samples. 113 This behavior is not observed in the Horizontal samples, (Figure 75). As a matter of fact, the opposite occurs; after crack propagation for a short distance, the DCB tested samples shows slight increase in load, compared to the wedge tested samples.
Figure 75. Mouth opening load vs. mouth opening displacement for wedge tested and
DCB tested Horizontal samples.
Figure 74 and Figure 75 shows that the mechanical response of the wedge tested samples in contrast to the DCB tested ones is not identical, yet comparable. This is mainly due to the difference between the boundary conditions between the two method
(Figure 76). The wedge test has a fixed boundary condition at the sample end. At the beginning of the test, the wedge location is chosen (in the middle of the notch), and the force direction does not change during the test. However, the DCB test has a free boundary condition at the sample end. During the test, and as the crack propagates, the sample rotates allowing higher stress on the weaker half of the sample. This condition
114 aggravates when having one arm thinner than the other, where the sample rotates more towards the thinner arm.
(a) (b)
Figure 76. Boundary condition for (a) wedge test showing fixed-end boundary condition and (b) DCB test showing free-end boundary condition
Regarding the mechanical behavior for the samples with different cutting directions (H vs. V), as shown in Figure 74 and Figure 75, the two types have quite different performance. Looking at the Mode I energy release rate for the two types
(Figure 77 and Figure 78), we notice that the main difference between the two types is the R-curve behavior. For the Vertical samples, crack growth resistance exhibits a flat or slightly rising R-curve behavior. The Horizontal samples, on the other hand, show rising
R-curve behavior with a greater slop than the one for the Vertical samples.
115 Figure 77. Mode I energy release rate for wedge tested and DCB tested Vertical samples.
Figure 78. Mode I energy release rate for wedge tested and DCB tested Horizontal samples.
The main difference between the Horizontal and Vertical samples is the fiber layout in the middle ply. The fiber layout on both sides of the panel (top and bottom) is in the longitudinal direction (0 direction). Since the panel has an even number of plies, the
116 mid-plane for the Horizontal samples is double fiber tows in the transverse direction of the sample (double 90s). While for the Vertical samples, the mid-plane is double fiber tows in the longitudinal direction of the sample (double 0s).
In composite material, the rising R-curve behavior is usually attributed to fiber bridging. Almost all of the tested samples showed signs of fiber bridging, even Sample 4
V DCB, which had a flat R-curve (Figure 79a). Therefore, the rising R-curve behavior is probably due to other mechanisms.
(a)
(b)
Figure 79. Fiber bridging in sample a) 4 V DCB (flat R-curve) and b) 18 H DCB (rising
R-curve). 117 To understand this difference in the behavior between the Horizontal and Vertical samples, one sample from each group (tested with the DCB method) was pulled until separated into two pieces. Figure 80 and Figure 81 show the fracture surfaces of a sample with Vertical orientation and a sample with Horizontal orientation, respectively. It is clear from the figures that the two orientations produced different fracture surfaces. In the
Vertical orientation, the fractured fiber tows were mostly longitudinal fibers, whereas transverse fiber tows were fractured in the Horizontal orientation. This suggests that the transverse bridging fibers cause the rising R-curve behavior rather than the longitudinal bridging fibers.
Another observation we can make from Figure 80 and Figure 81 is that the fractured fiber tows were on the edge, and very few to no central fiber tows fractured.
Figure 80. Fracture surface of a sample with Vertical orientation
118 Figure 81. Fracture surface of a sample with Horizontal orientation
Next, the crack morphology near the center were studied for sample 4 V DCB
(flat R-curve) and sample 18 H DCB (rising R-curve). We notice that for both cases the crack propagates along a longitudinal fiber tow (in corresponds to the sample’s layout).
However, for sample 4 V DCB, when encountering a transverse tow, the crack leaves the longitudinal two to travel around the transverse one (Figure 82a). For sample 18 H DCB, on the other hand, when encountering a transverse tow, the crack travel around the transverse crack, as well as the longitudinal crack (Figure 82b). This behavior is associated with stick-slip phenomena and believed to result in a rising R-curve behavior
[67]. Moreover, for sample 4 V DCB, and for long crack propagation lengths, it seems that the crack leaves the longitudinal tow and propagate within the ply (intralaminar).
Such behavior is not observed for sample 18 H DCB.
119 (a)
(b)
Figure 82. Crack morphology in the center of sample a) 4 V DCB (flat-R curve) and b)
18 H DCB (rising-R curve).
By relating the load curve with the crack morphology, we notice that the changes in the load curve correlate with the architecture. The correlation seems to be more dominant with the fiber architecture near the center of the sample, rather near the edge. 120 Looking at the load curve for a sample with a Vertical orientation (Figure 83) we notice that the load drops correspond to the interlaminar crack propagating along the transverse fiber tows; lack of stick-slip behavior. Also, it seems that the load drops when the crack propagates within the ply. The sample with Horizontal orientation, on the other hand, exhibit an increase in the load whenever the crack propagates around the transverse fiber tows (stick-slip behavior) and the load drops slightly after leaving the transverse fiber tows.
Figure 83. Load vs. mouth opening displacement for a sample with Vertical orientation, showing load curve correlation with crack morphology.
121 Figure 84. Load vs. mouth opening displacement for a sample with Horizontal orientation, showing load curve correlation with crack morphology.
6.4 Conclusion
A comparison between the wedge-loaded DCB and the traditional DCB testing methods was carried out in this chapter. The results suggest that the two methods are comparable but not identical. The variance between the two methods is due to the difference in the boundary conditions.
Additionally, it was found that the cutting direction of the samples play a role in their interlaminar properties. Horizontal samples shown to have rising R-curve with a higher slop compared to the Vertical samples. Fiber bridging was not the only reason for the rising R-curve behavior; it is believed that stick-slip behavior that occurs around the transverse fiber tows has the major contribution to the increase in R-curve.
122 CHAPTER VII
DETERMINATION OF INTERLAMINAR FRACTURE PROPERTIES OF CMCS AT
ELEVATE TEMPERATURES
7.1 Introduction
The main advantage of CMCs materials is their low density, and their good thermo- mechanical properties. Therefore, CMCs materials are targeted for high temperature application. As a result, it is their high temperature properties that we are more interested in. By understanding the room temperature behavior of CMCs, we can obtain a better knowledge and understanding of their high temperature behavior. Further, more damage monitoring techniques can be employed during room temperature testing. Not to mention that high temperature testing of any component is not that simple. This all justifies the focus of the previous chapters on the room temperature interlaminar properties of CMCs; the interlaminar fracture testing methodology needed to be established at room temperature first, then it can be applied at elevated temperatures.
When testing CMCs at elevated temperatures, there are few temperatures to be considered: 815 °C (1500 °F), 1204 °C (2200 °F), and 1315 °C (2400 °F). 1204 °C is the upper use temperature of combustor liners, while 815 °C is the temperature of the attachment region between the combustor and the metal support structure. Both of these temperatures were determined during the Enabling Propulsion Materials (EPM) program
123 [147, 148]. 1315 °C is the target temperature for the inlet turbine vanes under the Ultra
Efficient Engine Technologies (UEET) program [5].
This chapter aims at establishing a methodology for determining interlaminar fracture properties for CMC materials at elevated temperatures. The wedge-loaded DCB method, discussed in the previous chapters, will be employed here to compare interlaminar toughness of the studied materials at room and 815 °C, while using the change in electrical resistance to determine crack growth during interlaminar testing.
After understanding the interlaminar fracture behavior of CMCs at 815 °C, one can move on to investigate the interlaminar performance of CMCs at higher temperatures (1200 and
1315 °C).
It worth mentioning that there is no data available on the interlaminar behavior of any CMC system at elevated temperatures in open literature. Hence, this chapter will provide the first glimpse of the interlaminar fracture properties of CMCs at elevated temperatures.
7.2 Experimental Procedure
7.2.1 Materials
The same four CMC material systems discussed in Chapter IV will be used here.
The materials are: melt-infiltrated SiC composite with ZMI fibers (ZMI SiC/SiC), melt- infiltrated SiC composite with Hi-Nicalon fibers (HN SiC/SiC), polymer impregnation and pyrolysis SiC/SiNC composite (PIP SiC/SiNC) and an alumina/alumina silicate
(Oxide/Oxide) composite.
124 The ZMI SiC/SiC system will only be used as a proof of concept. The samples dimensions were 75×5×4 (length × width × thickness in mm). HN SiC/SiC had a uniformed geometry of 80×5×4. For PIP SiC/SiNC the studied samples were 70×10×5, and the Oxide/Oxide samples had a geometry of 70×10×3. After preparing the samples, a notch was machined in each specimen in the mid-plane with a thickness of ~0.4 mm and a length of ~25 mm for all the samples.
7.2.2 High Temperature Testing
The testing methodology developed in Chapter IV will be employed here. An
Instron 5582 machine with a load cell of 500 N was used for mechanical loading using a constant displacement rate of 1 mm/min. The wedge used for high temperature testing was a ceramic wedge (polycrystalline silicon nitride GN10) with an 18° head angle (2α).
For high temperature testing, a single-zone furnace with silicon carbide heating element and a total height of 38.1 mm was used. The furnace had a temperature profile as shown in Figure 85. Measurements of temperature profile were taken throughout the height of the furnace using an R-type thermocouple. The temperature profile shows that the hot zone for 815 °C is ~6 mm. However, due to the chimney effect, there is a significant drop in temperature above the hot zone. Therefore, in order to maintain the area of interest of the sample (notch and crack tip) in the hot zone throughout the test, the sample was held in the top fixture of the Instron while the wedge was kept stationary at the bottom grip. The high temperature test started with the notch tip in the hot zone. As the sample moved down towards the bottom of the furnace, the crack propagated in the
125 opposite direction. As a result, the crack tip was maintained inside the hot zone throughout the test.
Figure 85. Furnace temperature profile at 815 °C
7.2.3 Electrical Resistance Measurements
Electrical resistance (ER) was measured by four-point method using an Agilent
34420A micro-ohm meter. During the measurement, a direct current (10 mA) was applied through the outer probes, and the voltage was measured across the two inner probes to monitor the resistance of the material during testing. The advantage of this procedure is that it minimizes the effect of contact resistance on the measurements, since the current flowing through the inner probes must be near zero. For probe attachments, thin nickel chromium wires were glued to the material using high temperature silver epoxy (Figure 86). All probes were attached to the arms, forcing the current to flow from
126 one arm to the other around the notch/crack tip. It has shown that this ER configuration is an effective way for monitoring crack growth and thus it will be utilized in this chapter.
Figure 86. High temperature test setup showing the ER probe attachment
7.3 Results and Discussion
7.3.1 Electrical Behavior and Crack Length Measurements in SiC-Based CMCs at
Elevated Temperatures
The measured electrical resistance during crack propagation for an arm-to-arm configuration has been derived in Chapter IV and it can be expressed as:
휌퐿 휌퐿 휌푎 휌푎 푅 = + + + + 푅푂푃 (37) 퐴푎푟푚1 퐴푎푟푚2 퐴푥 퐴푦 where is the axial electrical resistivity of the undamaged composite, L is the distance from the inner lead to the notch tip, a is the crack length, Aarm1, Aarm2 is the cross- 127 sectional area of the arm1, arm2, respectively. Ax, Ay are the areas created by crack propagation, and ROP is a resistance term related to the out-of-plane resistivity of the sample. By substituting the dimensions h (arms thickness), t (specimen thickness) and w
(specimen width) for the appropriate areas, the equation for the estimated crack length a at room temperature becomes:
푥푦푤 푥푦퐿 푥푦퐿 푎 = (푅 − 푅푂푃) − − (38) 푡휌 푡ℎ1 푡ℎ2
During high temperature testing, however, the measured ER depends on two factors: interlaminar crack growth and the temperature variations along the current path.
Due to the furnace profile and heat conduction through the sample, the current path has a varying temperature, and therefore, the sample has varying electrical resistivity. Thus, in order to estimate crack growth during high temperature testing, the contribution of temperature gradient to ER should be eliminated.
Figure 87 and Figure 88 show the change in ER during heating up to 815 °C with a heating rate of 50 °C/min for PIP SiC/SiNC and HN SiC/SiC, respectively. For the PIP
SiC/SiNC system, the conductive phase is the SiC matrix. Since SiC is a semiconductor, its electrical resistivity decreases significantly with temperature (behaving like an intrinsic semiconductor [149]), and the measured ER between the two arms decreased by
~75%. These values are in line with data reported in literature [107, 108].
128 Figure 87. Change of ER during heating (up to 815 °C) and cooling for a PIP SiC/SiNC sample
However, in the melt-infiltrated HN SiC/SiC composite, the conductive phase is the silicon-rich matrix. Due to the presence of impurities in the silicon (mostly boron), the MI SiC/SiC follows an extrinsic semiconductor behavior. The temperature dependence of extrinsic semiconductor varies based on the impurity concentration and the temperature range [150]. It has been shown that for MI SiC/SiC, the electrical resistivity increases with temperature until reaching a maximum around 900 °C [151,
152]. That explains the continuous increase in resistance upon heating up to 815 °C in
Figure 88.
129 Figure 88. Change of ER during heating (up to 815 °C) and cooling for a HN SiC/SiC sample
Regardless of the change in ER during heating, what matters is the change in ER during the high temperature interlaminar test, since the main use of ER is to derive crack length.
After heating up and testing the sample at 815 °C, the effect of temperature gradient on ER was estimated by repeating the test (lowering the tested sample inside the furnace) in the absence of the wedge. In this case, the change in ER was only due to temperature gradient, after a crack was propagated in the sample. Figure 89 illustrates the displacement dependence of ER for actual test and simulated loading without inducing a new crack (after testing). The ER values at the end of the displacement in both cases agree very well. This suggests that the change in ER is a sum of ER increase due to crack growth and due to temperature gradient effect. The difference in ER at zero displacement is associated with the presence of the interlaminar crack after high temperature testing. 130 Figure 89. Measured ER as a function of displacement for actual high temperature testing and high temperature test simulation with further propagating the interlaminar crack for a SiC/SiNC sample.
Therefore, to determine the contribution of crack growth to the increase in ER, we first estimate the ER change due to temperature gradient without a crack by subtracting the crack effect on ER from the ER change due to temperature gradient with a crack. The new curve is then subtracted from the total ER change during high temperature testing to obtain a relationship between ER change and crack growth during high temperature testing as shown in Figure 90.
131 Figure 90. ER change due to crack propagation during high temperature testing
To calculate crack growth during the high temperature test using Equation (38), one must find first the resistivity of the material throughout the crack path. However, this task is challenging due to temperature gradient and its effect on resistivity. Therefore, one can find an effective resistivity instead. To do so Equation (37) will be used at the beginning and the end of the high temperature test, where in both scenarios the crack length a is known (a can be measured at the end of the high temperature test).
휌′퐿 휌′퐿 휌′푎푖 휌′푎푖 푅퐻푇,푖 = + + + + 푅′푂푃 (39) 퐴푎푟푚1 퐴푎푟푚2 퐴푥 퐴푦
휌′퐿 휌′퐿 휌′푎푓 휌′푎푓 푅퐻푇,푓 = + + + + 푅′푂푃 (40) 퐴푎푟푚1 퐴푎푟푚2 퐴푥 퐴푦
By subtracting the previous two equations we can get an expression for effective resistivity as follows:
132 푥푦푤 ∆푅 휌′ = (41) 푡 ∆푎 where R is the change in ER during the high temperature testing due to crack growth, as shown in Figure 90. a is the total crack growth during high temperature testing.
7.3.2 Electrical Behavior and Crack Length Measurements in Oxide-Based CMCs
In order for the ER-based crack length equation to work (Equation (38)), the material should be conductive to a certain degree. Oxide-Oxide CMCs are insulating materials. Therefore, in Chapter IV a method of painting the Oxide/Oxide samples with silver paint has been successfully employed, and the electrical resistance was measured in the conductive silver layer during interlaminar testing of the Oxide/Oxide samples.
The same methodology and equations used for SiC-based CMCs can be used for the Oxide/Oxide samples. Although the electrical behavior might be slightly different, considering the fact that a semiconductor is the conductive phase for SiC-based CMCs compared to a metallic layer in the silver-painted Oxide/Oxide samples.
Figure 91 shows the change in the electrical resistance of the silver-painted
Oxide/Oxide sample during heating, which displays a typical curve of a linear increase in resistance with temperature.
133 Figure 91. Change of ER during heating (up to 815 °C) for an Oxide/Oxide silver painted sample
Similar to SiC-based CMCs, Equation (39) and (40) can be used to find a effective resistivity of the silver layer during the high temperature testing. Then the change in ER during high temperature testing will be correlated to crack length.
7.3.3 Mechanical and Electrical Behavior
In order to estimate crack length during high temperature interlaminar testing, one must know the initial crack length. This could be achieved through a controlled pop-in crack at room temperature (for 1 or 2 mm), prior to performing the high temperature test.
Figure 92 shows the change in ER for a ZMI SiC/SiC sample during the whole procedure of testing at high temperature, including the introduction of a pop-in crack at room temperature. In Figure 92, ER exhibits slight recovery upon unloading. This is due to partial crack closure after removing the wedge.
134 Figure 92. ER change during high temperature interlaminar testing for a ZMI SiC/SiC sample, including pop-in crack at room temperature.
ER change serves as a great technique to understand the mechanical performance during high temperature loading, especially since the crack growth cannot be observed directly. The ER change in Figure 93 shows two distinct regions; the first one represents the reopening of the pop-in crack, and the second one corresponds to crack growth during high temperature testing.
135 Figure 93. Load and change of ER during crack re-opening and crack propagation at
815 °C for ZMI SiC/SiC sample.
One setback of introducing a pop-in crack at room temperature is the fact that some fiber bridging might occur and affect crack initiation during high temperature testing. Therefore, the remaining samples will be tested at high temperature without introducing a pop-in crack at room temperature. The initial crack length in Equation (41) will be considered zero, in this case.
The mechanical behavior during high temperature testing for a PIP SiC/SiNC is presented in Figure 94. The increase in ER is in line with damage onset, identifying clear crack initiation. Interestingly, the load continuous to increase during crack propagation.
This indicates crack growth resistance is greater during high temperature testing.
136 Figure 94. Mechanical, electrical behavior and crack length during high temperature
(815 °C) interlaminar testing for PIP SiC/SiNC.
This behavior is not seen during testing PIP SiC/SiNC at room temperature
(Figure 95); after the interlaminar crack propagates a certain distance, there is a continuous decrease in load, which indicates minimum crack growth resistance, mostly likely lower than that at 815 °C.
137 Figure 95. Mechanical, electrical behavior and crack length during room temperature interlaminar testing for PIP SiC/SiNC.
Moving on to investigate the high temperature interlaminar behavior of an HN
SiC/SiC sample tested at 815 °C (Figure 96), we notice sharp drops in load accompanied with sudden increases in ER, indicating that these load drops corresponds to sudden crack growth. Following that is a typical zig-zag behavior with slight increase in load, along with steady increase in ER, demonstrating stable crack propagation.
138
Figure 96. Mechanical, electrical behavior and crack length during high temperature
(815 °C) interlaminar testing for an HN SiC/SiC sample.
The mechanical behavior for a room temperature test of a sample from the same panel (HN SiC/SiC) does not reflect these drastic changes in load, seen during the test at elevated temperature. In fact, a clear change in the slope pre- and post-crack initiation can be observed (Figure 97). Moreover, during crack propagation, the load is almost constant, and it oscillates slightly due to crack propagation.
139
Figure 97. Mechanical, electrical behavior and crack length during room temperature interlaminar testing for an HN SiC/SiC sample.
By comparing Figure 96 and Figure 97, a clear difference can be seen in regards to crack initiation; the load required to initiate a crack at 815 °C is clearly lower than the one at room temperature. Therefore, this material system (HN SiC/SiC) is more susceptible to crack initiation at elevated temperatures than at room temperature.
7.3.4 Energy Release Rate
The energy release rate can be evaluated using beam on elastic foundation model
[142] introduced in Chapter IV
푃2푎′2 ℎ 2 (42) 퐺퐼 = 12 2 3 (1 + 0.64 ) 푤 ℎ 퐸11 푎′ where P is the load inducing interlaminar crack initiation and propagation and h is half the sample thickness, assuming a sample with identical arms and a notch with negligible
140 thickness. Since this is not the case in this study h will be consider equal to x (distance from the main interlaminar crack to the sample edge, where x < y)
This analysis in Equation (42) was developed for an isotropic material, in the case of anisotropic material, Equation (42) becomes [153]:
푃2 2 (43) 퐺퐼 = 12 2 3 (푎′ + 푎0) 푤 ℎ 퐸11 and
4 퐸11 푎0 = ℎ√ (44) 6퐸33
In order to determine the load P (in Equation (42)), one must first know the coefficient of friction between the wedge and the sample during room and high temperature testing. To avoid that, the load P will be derived in terms of arms displacement as shown in the following equation:
1 푤ℎ3퐸 푃 = 푀푂퐷 11 (45) 2 8푎′3
To compare the energy release rate at room and high temperature for PIP
SiC/SiNC, first E11 and E33 were determined using ultrasonic techniques (E11 = 115 GPa and E33 = 67 GPa). For the material moduli at 815 °C, it was assumed that the modulus decreased by 5% (E11 has been reported to decrease by 6.25% at 1000 °C [154]). Figure
98 shows the energy release rate at room and high temperature. From the figure, it seems that energy required to initiate a crack at room temperature is higher than that at 815 °C. 141 However, GI exhibit a flat R-curve behavior at room temperature and a rising R-curve behavior at high temperature. The phenomenon of a rising R-curve at high temperature has been seen in repeated tests. This behavior can be attributed to the slight softening of the matrix, which resulted in a lower crack propagation rate at high temperature, compared to room temperature. In other words, due to matrix softening the crack requires more energy (and thus more load as shown in Figure 94 and Figure 95) to propagate in the material at high temperature, resulting in an improved crack growth resistance at 815
°C.
Figure 98. Energy release rate at room temperature and at 815 °C for PIP SiC/SiNC.
This behavior can be further verified by comparing crack growth rate at room and elevated temperature, the crack growth rate at room temperature is double the rate at 815
°C (Figure 99). This is speculated as being due to slight softening of the matrix as a result of heating. Matrix softening would cause the interlaminar crack to propagate slower through the matrix. Also, it would allow the arms to be more compliant, therefore,
142 bending more before forcing the crack to propagate. This claim can be supported by the fact that strain to failure increases significantly with temperature for this material (by
40% during testing at 1000 °C [13]).
Figure 99. Crack growth rate at room temperature and at 815 °C for PIP SiC/SiNC.
Looking at the energy release rate for HN SiC/SiC at room and elevated temperature (Figure 100), we notice that unlike PIP SiC/SiNC, the data is more consistent at room temperature, yet shows less repeatability at 815 °C. The figure shows that the energy required to initiate a crack at 815 °C is lower than that at room temperature, which indicate better crack initiation resistance at room temperature. Beyond crack initiation, the energy release rate values for the tests performed at elevated temperature is scattered, and more results need to be obtained before one can reach a solid conclusion.
143 Figure 100. Energy release rate at room temperature and at 815 °C for HN SiC/SiC.
The crack growth rate at 815 °C seems to be comparable to the one at room temperature (Figure 101), however, these results are still preliminary and thus more investigation is required to understand the effect of temperature on interlaminar properties for melt-infiltrated SiC/SiC CMCs.
144 Figure 101. Crack growth rate at room temperature and at 815 °C for HN SiC/SiNC.
7.4 Conclusions
Interlaminar fracture testing was conducted on woven SiC-based CMCs at room temperature and at 815 °C, using wedge-loaded DCB testing method. Electrical resistance was utilized to provide measures of crack lengths during the test. Results suggest that the proposed method is an effective way to measure interlaminar toughness at both room and elevated temperature. For the performed tests, the increase in ER was in-line with the onset of interlaminar damage. The mechanical data for PIP SiC/SiC at room temperature showed a continuous drop in load after limited crack propagation length. Such behavior was not observed during high temperature testing. Crack growth rate at room temperature was double the rate at 815 °C, which contributed to a flat R- curve behavior for the material at room temperature compared to a rising R-curve at 815
°C for PIP SiC/SiC. The interlaminar properties for MI SiC/SiC at 815 °C seems to be
145 comparable to the one at room temperature, although crack initiation occurs at lower loads. Nonetheless, this data is still preliminary and more tests and analysis should be performed.
146 CHAPTER VIII
MODELING OF THE WEDGE METHOD
8.1 Introduction
As it has been mentioned in previous chapters, the purpose of this work is to develop a standardized test for determining interlaminar fracture properties for CMC at room and elevated temperature. Therefore, this work, to the most part, is experimental.
However, modeling can serve as a helpful tool to control and understand the effect of some variables that are too time-consuming or expensive to investigate experimentally.
Moreover, modeling can help us verify the percentage of pure Mode I interlaminar loading produced during testing. Ideally, the proposed testing method should yield a
100% interlaminar tension load, however, this cannot be achieved in many cases.
Modeling can help us modify the test to minimize the secondary damage and achieve a pure interlaminar tension test.
Finite element analysis (FEA) is a powerful numerical method for solving complex
(and simple) engineering problems. The technique is based on the assumption that an approximate solution, to any complex engineering problem, can be reached by dividing the component / structure into smaller more manageable (finite) elements. In the FEA method, the structural system is modeled by a set of elements interconnected at discrete points called nodes. By combining these elements together, a mesh model can be created.
The element type could be a 1-D (line) element, 2D (plane) element or 3D (solid) element 147 based on the problem being investigated. In FEA, each element has a specific geometric shape, with a defined internal strain function. Using the actual geometry and strain functions of the elements, one can write the equilibrium equations between the external forces acting on the element and the displacements occurring on its nodes. The degrees of freedom are defined at each node, and for each node there will be one equation for each degree of freedom. These equations are often written in matrix form for use in a computer algorithm.
An essential step in FEA modeling is assigning proper material properties to a finite element model. The material properties are used to calculate the stress and strain in a structure. The material properties are often obtained through mechanical testing.
However, for anisotropic materials, such as composites, the material properties cannot be obtained directly. Therefore, the material analyses can be performed using a macroscopic or a micromechanics approach. In the macroscopic approach, the properties of the composite are homogenized to produce an anisotropic, yet homogeneous continuum before the analysis is performed [155]. The micromechanical approach, on the other hand, takes into account the constituents’ properties of the composite by considering the properties of the fibers and matrix separately and applying the loading and boundary conditions at the fiber/matrix level. The overall properties of the composite are then developed by relating the average stresses and strains. Therefore, the micromechanical approach provides more details on the interaction between the constituents, leading to a more accurate model of the composite behavior.
The objective of this chapter is to provide an accurate FEA model understand the interlaminar fracture behavior of the studied CMC systems and to verify the model 148 against experimental results. Ultimately, it is through modeling the optimized specimen geometry would be chosen, where the interlaminar Mode I fracture will be maximized while minimizing all the other types of damage. However, future work will focus on this task.
8.2 Material Characterization
Material characterization will be performed using progressive failure analysis
(PFA). An overview of the basic steps for performing a progressive failure analysis can be found in the work of Ochoa and Reddy [156]. In short, at each load step, during a typical PFA, a nonlinear analysis is performed until a converged solution is obtained assuming no changes in the material model. Then from the nonlinear analysis solution, the stresses within each lamina are determined, using the equilibrium state. These stresses are then compared to the material stress limits to determine if failure occurs per predefined failure criteria. If failure is detected in the lamina, the lamina properties are adjusted according to a defined degradation model. After that, the equilibrium of the structure needs to be re-established using the modified lamina properties of the failed lamina while maintaining the same load level. This iterative process of obtaining nonlinear equilibrium solutions for each change in a local material model (due to damage) is continued until no additional lamina failures are detected. The load step is then increased until catastrophic failure of the structure occurs, as defined by the progressive failure methodology. Figure 102 shows the typical features of a stress-strain for a SiC/SiC CMC system (during tensile loading), along with the main steps of PFA
[157]
149 Figure 102. Main steps of progressive failure analysis for a tensile stress-strain curve of a typical SiC/SiC CMC system.
The PFA was conducted using MCQ-CompositesTM, a commercially available software developed by AlphaSTAR Corporation. The stress and strain limits for lamina failure criteria are the following: longitudinal tensile and compressive stresses, transverse tensile and compressive stresses, in-plane shear stress, longitudinal and transverse normal shear stresses, longitudinal tensile and compressive strains, and the modified distortion energy theory.
The FEA model was first built considering the ZMI SiC/SiC material system.
Consequently, materials characterization was performed for the same material system.
The first step in material characterization is to introduce the properties of the different composite constituents. Starting with the fibers, tensile ultimate strength (UTS11) and
150 Young’s modulus (E11) were obtained from the manufacturer datasheet [158]. However, other mechanical properties were not available, therefore, they were estimated taking same ratios as of Graphite AS4 (from MCQ-CompositesTM materials library) since E11 and U11T for both fibers were comparable (Graphite AS4: E11 = 221.8 GPA and UTS11 =
3432 MPa compared with ZMI SiC fiber: E11 = 200 GPa and UTS11 = 3400 MPa).
The only properties for the matrix available in the literature was for the matrix modulus Em = 410 GPa (for CVI SiC/SiC) [159]. The rest of the properties must be backed out from the composite and fiber properties using micromechanical models
(Chamis model), which have been discussed extensively in the literature review.
The ZMI SiC/SiC composite properties were obtained from similar panels, while taking the panel thickness into consideration [8].
Table 4 summarizes the constituents and composite proposed properties, while
Table 5 provides the composite properties output values after performing the material characterization using MCQ-CompositesTM.
151 Table 4. Constituents and composite input properties for ZMI SiC/SiC.
Mechanical Property Input Value Unit
+ E11f 131 GPa
E22f 115 GPa
G12f 150 GPa
G23f 6.3 GPa roperties roperties 12f 0.07 - (ZMI SiC)(ZMI 23f 0.36 - Fibers P Fibers + UTS11f 3400 MPa
UTC11f 1460 MPa
Em 310 GPa
m 0.23 -
UTSm 224 MPa
(MI SiC)(MI UTCm 355 MPa
Matrix Properties Properties Matrix SSm 255 MPa
* E11 180 GPa
* E22 180 GPa
a E33 74.5 GPa
G12 - GPa
^ 12 0.17 -
perties perties * UTS11 215 MPa
UTC11 622 MPa
*
(ZMI SiC/SiC)(ZMI UTS22 215 MPa
Composite Pro UTC22 622 MPa
# SS12 50 MPa
* Vf 25 % Porosity 10b %
152 + From reference [158]
* From reference [8]
# From reference [44]
^ From reference [160] a Ultrasonic estimate b Estimated from polished micrographs using ImageJ software
Table 5. Composite output properties for ZMI SiC/SiC.
Mechanical Property Output Value Unit
E11 197.2 GPa
E22 197.2 GPa
E33 74.5 GPa
G12 138 GPa
G23 120.5 GPa
G13 120.5 GPa
12 0.17 -
23 0.24 -
13 0.24 -
UTS11 215.5 MPa
(ZMI SiC/SiC)(ZMI UTC11 432.5 MPa
Composite Properties Composite Properties UTS22 215.5 MPa
UTC22 432.5 MPa
UTS33 204.7 MPa
UTC33 297 MPa
SS12 113 MPa
SS23 181 MPa
SS13 143.5 MPa
153 Figure 103 shows the calibrated laminate stress-strain curve, for ZMI SiC/SiC, along with the experimental tensile stress-strain curve. The predicted composite tensile stress-strain curve matches the initial modulus and nonlinearity well. However, it slightly overestimates the proportional limit and the mechanical response past matrix crack initiation.
Figure 103. Tensile stress-strain curve of ZMI SiC/SiC material from micromechanics simulation using progressive failure analysis in comparison to the stress-strain curve from tensile mechanical test.
There is no doubt that many of the mechanical properties were estimated based on educated guesses. The impact of these estimations on the model will be discussed later.
154 8.3 Finite Element Analysis Modeling
8.3.1 Building the Finite Element Analysis Model
The FEA model was built in Abaqus for the ZMI SiC/SiC samples considering the three different geometries 50×5×4, 50×10×4, and 75×5×4. Table 6 lists the geometry used for building the model for the 75×5×4. The only differences in geometry between the three cases were the length and the width of the sample.
Table 6. Specimen geometry.
Geometry Dimension Unit Specimen length (L) 75 mm
Arms’ length or Notch length (a0) 25 mm Width (w) 5 mm Total thickness (t) 4.15 mm
Arm1 thickness (h1) 2.1 mm
Arm2 thickness (h2) 1.75 mm Notch opening 0.3 mm
The wedge was built as discrete rigid shell part (three shell faces) with 18° head angle, as shown in Figure 104. The boundary conditions constrained the axial and rotational displacement of the wedge expect in the x direction (U2 = U3 = UR1 = UR2 =
UR3 = 0). The meshing element used for the wedge was rigid three-dimensional element, with four nodal points (R3D4). The total number of elements was 3,800.
155 Figure 104. Wedge model
The model for the specimen was built as a deformable solid part with fixed end boundary condition (U1 = U2 = U3 = 0). The mesh consisted of 40,392 three-dimensional hexahedral elements (C3D8R), with eight nodal points. The mesh was refined around the notch and was kept coarse far from the area of interest. Figure 105 displays the mesh of the specimen and the wedge, showing the refined mesh region around the notch.
156 (a)
(b) Figure 105. Mesh (a) of the model and (b) in the vicinity of the notch.
The contact between the wedge and the specimen was established using surface to surface contact with automatic stabilization and 0.7 coefficient of friction, as discussed in 157 Chapter V. Figure 106 illustrates the final model with the boundary condition and interaction properties.
Figure 106. FEA model showing the wedge, specimen, boundary conditions and interaction properties.
8.3.2 Results and Discussion
The simulations were carried out with GENOA (a commercially available software developed by AlphaSTAR Corporation) calling Abaqus standard solver. The property shown in Table 5 were used to perform the analysis.
Figure 107 shows the simulation results and how it compares to the experimental data for a 50×10×4 ZMI SiC/SiC sample. The two curves exhibit comparable behavior
158 until crack initiation, after that the load generated from simulation displays continuous decline, compared to a slight increase in the load produced during testing.
Figure 107. Simulation vs test results for a 50×10×4 ZMI SiC/SiC specimen.
Looking at the crack propagation and damage in the vicinity of the notch (Figure
108), we notice significant damage in the arms; mostly compression and shear damage.
Figure 108. Damage distribution after crack initiation.
However, when looking at a polished cross-section of a tested specimen with the same geometry, one cannot find any damage in the arms; only an interlaminar crack starting from the notch (Figure 109). 159 Figure 109. Polished cross sectional area of a tested ZMI SiC/SiC specimen showing an interlaminar crack and no damage in the arms.
The contradiction between the experimental results and the FEA model can be explained by the fact that the shear and compression properties of the composite were estimated, due to the lack of reliable experimental and literature data as it has been shown previously.
To overcome this problem, the elements in the FEA model where divided into two groups. The first group consisted of the elements in the interlaminar region. These elements were subject to damage (property degradation) and fracture (element removal).
The second group, on the other hand, contained the remaining elements. For these elements a no-damage, no-fracture criteria was enforced. Figure 110 shows the two elements’ groups in the FEA model.
160 Figure 110. FEA model showing the no-damage regions along with the interlaminar region.
The simulations were performed again with the new criteria (no damage expect in the interlaminar region). In this case, the crack morphology was comparable to the actual test (compare Figure 111 and Figure 109).
Figure 111. Simulation results showing crack morphology in the interlaminar region.
But more importantly, the load-displacement behavior became very comparable between the mechanical test and the simulation results, as shown in Figure 112. The simulation results did not show the drastic drop in load post crack initiation (which can be seen in Figure 107), indicating that the load drop was due to damage in the vicinity of the notch.
161 Figure 112. Simulation vs test results for a 50×5×4 ZMI SiC/SiC specimen.
8.3.3 Verification of the FEA Model
To further validate the FEA model, the model was applied for the HN SiC/SiC material system. For that, material characterization was first performed using MCQ-
CompositesTM software. Similarly to ZMI SiC/SiC, the available constituents’ properties were obtained from literature and previous mechanical test data [161]. The unknown properties were estimated as discussed previously. Table 7 summarizes the constituents and composite proposed properties for HN SiC/SiC. Table 8 provides the composite properties output values after performing the material characterization using MCQ-
CompositesTM.
162 Table 7. Constituents and composite input properties for HN SiC/SiC.
Mechanical Input Value Unit Property
+ E11f 270 GPa
E22f 170 GPa
G12f 94 GPa
G23f 33 GPa
12f 0.076 - (HN SiC) (HN 23f 0.5 - Fibers Properties Properties Fibers + UTS11f 2880 MPa
UTC11f 2438 MPa
Em 290 GPa
m 0.23 -
UTSm 150 MPa
(MI SiC)(MI UTCm 570 MPa
Matrix Properties Properties Matrix SSm 110 MPa
* E11 226 GPa
* E22 226 GPa
a E33 190 GPa
G12 - GPa
^ 12 0.17 -
* UTS11 215 MPa
UTC11 622 MPa
*
(HN SiC/SiC)(HN UTS22 215 MPa
Composite Properties Composite Properties UTC22 622 MPa
SS12 50 MPa
Vf 34 % Porosity - %
163 + From reference [162]
* From reference [134]
^ From reference [160] a Ultrasonic estimate
Table 8. Composite output properties for HN SiC/SiC.
Mechanical Output Value Unit Property
E11 226 GPa
E22 226 GPa
E33 190 GPa
G12 109 GPa
12 0.2 -
UTS11 390 MPa
(HN SiC/SiC)(HN UTC11 600 MPa Composite Properties Composite Properties UTS22 390 MPa
UTC22 600 MPa
SS12 40 MPa
Figure 113 shows the calibrated laminate stress-strain curve for HN SiC/SiC along with the experimental tensile stress-strain curve. The predicted composite tensile stress-strain curve matches the initial modulus, nonlinearity, and it shows good overall agreement with the mechanical data.
164 Figure 113. Tensile stress-strain for HN SiC/SiC from micromechanics simulation using
PFA vs. the actual stress-strain curve from mechanical testing
Finally, the FEA simulation was carried out using GENOA calling Abaqus standard solver. The same model used for ZMI SiC/SiC was employed for HN SiC/SiC, taking into account the geometry of the HN SiC/SiC specimens (75×5×4). Figure 114 shows the results of the interlaminar mechanical data of two tested specimens. The simulation results are also plotted for the original model, in which all elements are subject to damage and fracture. The data of the modified model are shown as well in
Figure 114. In the modified model only the elements in the interlaminar region are subject to damage and fracture, whereas a no-damage no-fracture criteria was enforced on the remaining elements.
Similarly to ZMI SiC/SiC, the original model for HN SiC/SiC exhibits comparable mechanical performance in the elastic region. However, after crack initiation,
165 the model shows significant drop in load, due to secondary damage in the vicinity of the notch, as shown previously. Upon modifying the model to prevent damage except in the interlaminar region, the load generated from simulation shows excellent agreement with the mechanical data.
Figure 114. Simulation vs test results for a 75×5×4 HN SiC/SiC specimen.
8.4 Conclusion
Modeling is a powerful tool that allows for faster investigation of materials performance compared to mechanical testing. Micromechanics approaches accompanied with progressive failure analysis can be used to determine the mechanical behavior of materials, while finite element analysis allow for studying the mechanical response under different loading conditions. In this chapter a FEA model was build and verified for two material systems: ZMI SiC/SiC and HN SiC/SiC. However, due to the lack of shear and
166
compression properties of the investigated materials, some assumptions had to be made.
Although the mechanical response of the modified FEA model matched the mechanical behavior obtain from the wedge interlaminar test, one cannot optimize the specimen geometry while suppressing secondary damage that might occur, especially shear damage. Optimizing the specimen geometry would be achieved through minimizing shear damage, mostly in the specimen’s arms region, and maximizing interlaminar tension damage. To do that, one must obtain accurate information about the all the mechanical properties of the studied materials, then by adjusting the specimen geometry
(width, length, and notch length) an optimum specimen for studying Mode I interlaminar fracture properties can be designed.
167
CHAPTER IX
DETERMINATION OF OUT-OF-PLANE RESISTIVITY FOR NON-OXIDE
CERAMIC MATRIX COMPOSITES
9.1 Introduction
Ceramic matrix composites (CMCs), for example woven silicon carbide (SiC) fiber reinforced SiC matrix (SiC/SiC) composites, present unique thermo-mechanical characteristics making them candidates for high temperature applications in gas turbine engines [17, 127]. In order for these materials to be used in such critical conditions, it is important to utilize health-monitoring techniques to determine and monitor damage development in these materials during service. Acoustic emission has been shown to be an excellent technique for damage monitoring in these composite systems [85, 163, 164].
However, acoustic emission is a passive technique and it could be impractical for high temperature conditions, and if one wants to assess damage in components after service.
Other non-destructive evaluation (NDE) techniques, such as X-ray, ultrasonic C-scan, and thermography, have been shown to be sensitive to out-of-plane damage in CMCs
[73]. Nonetheless, these techniques cannot be used for in-situ monitoring of damage.
Moreover, it is challenging to relate the damage measured with these techniques to the retained strength of CMCs.
168 Electrical resistance (ER) provides a sensitive measure of internal damage in
CMCs. Modeling efforts have been introduced and successfully correlated increase in ER with stress-dependent matrix crack and damage accumulation during tensile testing [102,
103, 165]. However, in order for a model to accurately predict the electrical behavior of
CMC materials during mechanical testing, the electrical properties of the composite in all directions should be well-understood. During tensile loading, out-of-plane type damage is the most dominant mode of damage. In order to detect such damage, the electrical current should be traveling perpendicular to the out-of-plane direction, i.e. the current should flow in-plane. Other types of loading / damage produce cracks in different planes. For example, foreign object damage (FOD) results in a combination of transverse and interlaminar cracks (in-plane and out-of-plane type damage) [52], and interlaminar type loading induces in-plane cracks [10, 140]. Therefore, in order to measure the magnitude of in-plane damage, the electrical current must travel in the out-of-plane direction.
Unfortunately, there is no data on the out-of-plane electrical resistivity for CMCs.
One of the reasons is the difficulties associated with measuring these properties due to the small thickness of most CMC panels. This work aims at determining the out-of-plane resistivity for two different CMC systems, verifying the validity of the measured values, and introducing a method that allows for indirect determination of the out-of-plane resistivity.
9.2 Materials
The materials used for this study were: melt-infiltrated SiC/SiC composite (MI
SiC/SiC) and polymer impregnation and pyrolysis SiC/SiNC composite (PIP SiC/SiNC).
169 The MI SiC/SiC system consisted of 16 plies of balanced 0°/90°, five-harness-satin woven fiber preforms of Hi-NicalonTM fibers. The fiber preforms were coated with a boron nitride interphase then by a slurry cast molten silicon melt-infiltrated process creating a matrix consists of a continuous SiC phase as well as continuous Si phase. The
PIP SiC/SiNC system was composed of eight-harness-satin weave CG NicalonTM fibers with boron nitride interphase in a matrix of silicon-nitrogen-carbon matrix that was prepared by multiple iterations of polymer pyrolysis process.
The MI SiC/SiC sample was 80 mm in length, 5 mm in width, and 4.2 mm in thickness, compared to 65 mm in length, 5 mm in width, and 5.2 ± 0.2 mm in thickness for the PIP SiC/SiNC sample. A notch was machined in the mid-plane for each sample with a thickness of ~0.4 mm and a length of ~25 mm.
In terms of their electrical properties, the two materials had orders of magnitude difference in their electrical resistivities (~104). MI SiC/SiC had an average in-plane resistivity of 0.11 ± 0.011 -mm, compared to 950 ± 68 -mm for PIP SiC/SiNC. All electrical measurements in this study were carried out using a Keithely 2450
SourceMeter®.
9.3 Experimental Procedures, Results and Discussion
Figure 115 shows a schematic of the sample layout, where the current was flown between the top lead on each arm. In this configuration, the current is force to travel from one arm to the other arm around the notch, passing through the thickness of the material.
One can obtain a relationship of the resistivity of the current traveling around the notch as follows [140]:
170 휌1퐿푛 휌2퐿푛 푅 = + + 푅푂푃 (46) 퐴푎푟푚1 퐴푎푟푚2
where R is the measured resistance, ρ1 and ρ2 are the in-plane resistivities of arm1 and
th arm2, respectively. Ln is the distance between the notch tip and n voltage lead on the arm, as shown in Figure 115a, and Aarm1 and Aarm2 are the cross-sectional areas of arm1 and arm2, respectively. Finally, ROP is a resistance term that correlate to the current traveling around the notch.
(a) (b)
Figure 115. (a) Schematic of specimen layout with the leads locations and (b) the cut part for out-of-plane resistivity measurements.
By substituting the dimensions h1,2 (arms thicknesses), and w (specimen width) for the appropriate areas, the equation for ROP becomes: 171 휌1퐿푛 휌2퐿푛 푅푂푃 = 푅 − ( + ) (47) 푤ℎ1 푤ℎ2
For both samples, ROP calculations were based on four different measurements by changing the lead used in Equation (47) i.e. changing Ln. For PIP SiC/SiNC, ROP was found to be 456.87 ± 3.35 , and for MI SiC/SiC, ROP = 0.0327 ± 0.0035 .
Since ROP represents resistance, it can also be expressed in terms of the out-of- plane resistivity (ρOP) of the material, assuming the current will travel a distance beyond the notch tip:
휌 푡 푅 = 푂푃 (48) 푂푃 푤 where t is the thickness of the un-notched section of the sample, and is the travel distance of the current beyond the notch tip.
The two unknowns in Equation (48) are the out-of-plane resistivity (ρOP) and the travel distance of the current beyond the notch tip ()
To determine the out-of-plane resistivity for the materials, the method of four collinear probes was used. Specimens were prepared by cutting a cubical piece from the bottom of each sample (5×5×5 mm), then thin copper wires (0.18 mm diameter) were glued to the surfaces using silver epoxy. The placement of leads on the specimen was chosen in such a way that the current flows across the thickness and the through- thickness voltage is measured. To obtain the bulk resistance of the sample the voltage leads were attached on the two opposite faces, such that the sets on the two faces were directly opposite to one another, and then the leads from top and bottom faces were
172 twisted together to measure the resistance. (See Figure 115 for description). The distance between voltage leads in each set was ~2.5 mm. The current amplitude was chosen so that it was high enough to provide a continuous path for the charge carriers without causing Joule heating.
The measured out-of-plane resistivity for PIP SiC/SiNC was ρOP = 8870 ± 340 - mm (compared to 950 -mm for in-plane resistivity). For MI SiC/SiC ρOP = 0.88 ± 0.068
-mm (compared to 0.11 -mm for in-plane resistivity).
To determine the current travel distance beyond the notch tip, potential drop was measured through the thickness of the sample by attaching lead pairs on the sample surface, with ~3 mm spacing between each pair, as shown in Figure 115a. The leads were attached at the sample arms, and beyond the notch tip reaching the sample bottom. Figure
116a shows the potential drop as a function of the distance from current leads for PIP
SiC/SiNC using two different current amplitudes, 0.5 mA and 1 mA (a current above 1 mA causes Joule heating due to the high resistivity of this material). The measurements were taken for the lead pairs between the two arms and across the sample thickness, beyond the notch tip. It is clear from Figure 116a that the voltage drop across the arms shows linear decrease as we move away from the current leads, indicating homogeneity in the electrical resistivity of the arms. However, beyond the notch tip, the decay of potential drop changes from linear (for the lead pairs on the arms) to exponential (for the lead pairs beyond the notch tip). This potential drop approaches zero as we move further away from the notch tip towards the bottom of the sample (as shown in Figure 116b and
Figure 116c) and can be fitted using an equation of the form:
173 −푥⁄ 푉푥 = 푉푚푎푥푒 (49)
where Vx is the potential drop across the sample thickness at a given distance x from the notch tip, Vmax is the maximum potential drop at the notch tip, x is the distance from the notch tip, and is a “length constant” that will be defined later
(a)
(b)
174 (c)
Figure 116. Potential drop as a function of the distance from (a) current leads and from the notch tip using (b) 0.5 mA and (c) 1 mA current for PIP SiC/SiNC.
By setting x = in Equation 49
푉 푉 = 푚푎푥 = 0.368푉 (50) 푒 푚푎푥
Therefore, V is always 36.8% of Vmax, meaning that the length constant is the distance at which ~37% of Vmax has been reached during the current flow beyond the notch. From this analysis we find that = 4.23 mm for PIP SiC/SiNC
Applying the same methodology for measuring the potential drop for the MI
SiC/SiC sample, with a current amplitude of 500 mA, we notice that the current flow follows the same trend as in PIP SiC/SiNC, with a linear potential drop in the arms and exponential potential drop beyond the notch tip. The value of for MI SiC/SiC was found to be 3.93 mm (Figure 117 a and b). The concept of length constant has been
175 established in the field of neurology [166]. However, to the best of our knowledge, this concept has not been introduced in materials science.
(a)
(b)
Figure 117. Potential drop as a function of the distance from (a) current leads and (b) from the notch tip using a current of 500 mA for MI SiC/SiC.
176 By comparing Figure 116b with Figure 116c one can see that by changing the current amplitude, only Vmax changes and the length constant is not affected. This indicates that the length constant can be considered as a composite property and is found to depend on the ratio of the out-of-plane resistivity to the in-plane resistivity as follows:
If the in-plane resistivity is much smaller than the out-of-plane resistivity, the current will spread for a longer distance when passing from one arm to the other [167], and vice versa. This behavior can be explained by the fact that the current continues to travels through the more conductive phase even beyond the notch tip while “avoiding” to flow through the high resistive part of the material.
When comparing for the two material systems used in this study, in accordance to the ratio of ρOP to ρ we find that PIP SiC/SiNC = 4.23 > MI SiC/SiC = 3.93 and (ρOP/ρ)PIP
SiC/SiNC = 9.34 > (ρOP/ρ)MI SiC/SiC = 8
Figure 116 and Figure 117 illustrate that the current does not decay completely after a distance from the notch tip, but at the same time, due to the constraints on the instrument resolution, one cannot measure potential drop accurately too far away from the notch tip. Therefore, a protocol must be introduced to account for an effective current travel distance ().From the measurements taken for PIP SiC/SiNC (Figure 80b), it seems that an acceptable value for is 5, which is in good agreement when verified using Equation (48) as shown in Table 9. The same protocol works well for the current travel distance for MI SiC/SiC (Figure 117b).
177 To validate the measured out-of-plane resistivity values, ROP will be compared in
Table 9 using Equation (47) and Equation (48) while including the obtained value for the travel distance .
Table 9. List of the electrical properties of the materials tested
ρ ρ R Eq. R Eq. Properties OP = 5 OP OP Error* (- (- (47) (48) Materials (mm) (mm) (%) mm) mm) () () PIP 950 ± 8870 ± 456.87 ± 4.23 21.15 427.58 6.4 SiC/SiNC 68 340 3.35
0.11 ± 0.88 ± 0.0327 ± MI SiC/SiC 3.93 19.65 0.0374 14.37 0.011 0.068 0.0035
|푅퐸푞.3− 푅퐸푞.2| * 푂푃 푂푃 The error was calculated using the formula: 퐸푟푟표푟% = 퐸푞.2 × 100 푅푂푃
Table 9 shows a good agreement between the measured values for ROP using
Equation (47) and Eq. (48), where the calculated error is within the bounds of the standard deviation for ρOP. Table 9 also shows that the largest error is produced from ρOP measurements (expressed as standard deviation), mainly because of the small dimensions used to obtain out-of-plane resistivity. However, in comparison to ρOP, can be measured to a much better accuracy. Therefore, from the current results and analysis, it is recommended to determine the out-of-plane resistivity by measuring and using
Equation (47) and Equation (48) combined. By doing so, the out-of-plane resistivity for
PIP SiC/SiNC is found to be ρOP = 9477 -mm and for MI SiC/SiC ρOP = 0.77 -mm.
178 9.4 Conclusions
To conclude, the presented work introduces a method for determining the out-of- plane resistivity for CMC materials. We have shown that the proposed method works very well for two samples with significantly different electrical properties. Thus, the proposed method can actually be used for any composite system with a conductive phase.
The concept of length constant and current travel distance, introduced in this work offers a better understanding of the electrical behavior in anisotropic composites systems.
179 CHAPTER X
CONCLUSIONS
The purpose of this work was to develop a testing technique for determining interlaminar fracture properties of oxide and non-oxide CMCs. The data available in the literature on the interlaminar properties at room temperature is limited. Further, there is no data available on the interlaminar behavior of CMCs at elevated temperatures, mainly due to the lack of an interlaminar testing technique that can be employed at high temperature. Ultimately, the purpose of this work is to develop an ASTM standard that can be used to determine the interlaminar fracture properties of CMCs at room and elevated temperatures, and help in establishing a national database for this important property of CMCs.
Extensive amount of work has been done to understand the interlaminar fracture behavior of PMCs at room temperature. Although the testing technique used for PMCs cannot be copied directly to study the interlaminar properties of CMCs at elevated temperatures, the effect of fiber architecture on the interlaminar properties can be very comparable between PMCs and CMCs. This serves as a great asset in understanding the interlaminar behavior of laminate and woven CMCs.
The method developed in this work for investigating the interlaminar fracture properties of CMCs was the wedge-loaded double cantilever beam method. This
180 technique has been proposed in literature, but never utilized for determining the interlaminar fracture toughness of composite materials. In this technique, a ceramic wedge is pushed into the notch, causing the sample’s arms to separate and inducing an interlaminar crack in the vicinity of the notch tip. One of the advantages of this method is the ability to apply the load directly through the wedge, without the need for loading pins or hinges, which makes it suitable for high temperature testing. However, the main disadvantage of this method is the frictional force between the wedge and the sample arms. The friction contribution on the load can be calculated, but it requires an extra step.
Crack length measurement was the other limiting factor for high temperature testing, because if the high temperature test is performed using a closed furnace, which is often the case, crack lengths cannot be measured with the conventional methods.
Therefore, an ER-based method was developed to determine crack growth without optical observation. The method was suitable for all Si-based CMCs, regardless of the initial resistivity of the material. For non-conductive CMCs (oxide-based CMCs), the materials were painted with a thin layer of silver so the crack would propagate in the sample and the silver layer at the same rate. Crack length measurements were then calculated based on the increase in resistance in the conductive silver layer.
Acoustic emission has been shown to be a great technique for detecting crack initiation in all CMC materials. Moreover, the cumulative AE energy can be related to crack length, which potentially can be used as well to determine crack length indirectly.
The role of friction in the wedge method has been investigated. It was found that by choosing a wedge material with a low coefficient of friction and a small wedge angle, one can achieve “mechanical advantage”, in which the measured load would be lesser 181 than the interlaminar load. This would result in a smooth load curve with minimum scatter. Moreover, it was found that in the wedge method, the interlaminar load does not depend on the wedge material or angle, as long as the correct coefficient of friction is taken into account.
Since the traditional DCB method is an established technique for evaluating interlaminar fracture properties of PMCs, the wedge-loaded DCB method was compared to the traditional DCB. The two methods yielded comparable results. The slight variation, however, was attributed to the difference in the boundary conditions between the two methods; the wedge-loaded DCB method has a fixed-end boundary condition compared to a free-end boundary condition for the traditional DCB.
The composite architecture was found to have a major effect on the interlaminar properties in woven CMCs. Depending on the fiber tows layout along the crack path, the composite might exhibit a flat or rising R-curve behavior. Stick-slip behavior, in which the crack propagates around the transverse fiber tows forming a loop, seemed to dominate the interlaminar fracture energy in woven CMCs over fiber bridging.
Interlaminar fracture testing of CMCs was successfully conducted at elevated temperatures. The ER-based crack growth measurement technique demonstrated validity regardless of the effect of temperature on the resistivity of the material. It was found that the energy required to initiate a crack at 815 °C was lower than that at room temperature.
However, some materials showed improved interlaminar properties during crack propagation (PIP SiC/SiNC specifically). This was attributed to slower crack propagation rate at elevated temperature due to slight matrix softening. Therefore, this research hypothesis was partially correct. The interlaminar crack initiation energy at elevated 182 temperature is lower than that at room temperature. However, crack propagation energy could be greater at elevated temperature compared to room temperature conditions.
Finite element analysis and micromechanical modeling were employed to validate the wedge method. However, due to the lack of shear and compression properties of the studied CMC materials, some assumptions had to be made. The mechanical response of the modified FEA model showed good agreement with the mechanical data obtain from the wedge interlaminar test. Nonetheless, these assumptions demonstrated the importance of obtaining reliable shear properties for the studied CMC materials. By incorporating the shear properties in the FEA model, one can design a specimen with optimized geometry for Mode I interlaminar fracture testing.
Finally, a method for determining the out-of-plane electrical resistivity of non- oxide CMCs was established. The method was utilized and successfully verified for two
CMC systems with significantly different electrical resistivity (PIP SiC/SiNC and MI
SiC/SiC). It was found that the out-of-plane electrical resistivity was 8-9 times greater than the in-plane electrical resistivity. This was a direct consequence of the current flowing through the less conductive phases of the composite. Moreover, it was found that the magnitude of direct current drops exponentially when moving away from the path of lowest resistance. The concept of length constant was also introduced as a new composite property, which would offer a better understanding of the electrical behavior in anisotropic composite systems.
183 CHAPTER XI
FUTURE WORK
Future work will focus on two areas: modeling the electrical behavior in non-oxide
CMCs and Mode II interlaminar fracture properties of CMCs at room and elevated temperatures.
11.1 Modeling the Electrical Behavior in Non-Oxide CMCs
In order to model the electrical behavior in CMCs, it is better to start with a system with simple architecture. For example, unidirectional CMCs would offer a good starting point in understanding the electrical behavior in composite materials with one phase having more conductivity than the other. Following that, one can investigate the electrical behavior in laminate CMCs with different fiber orientation. After that, the understanding of the electrical behavior for systems with woven fibers would be made easier.
Moreover, it is important to distinguish the conductive phase in the studied composites. In SiC/SiC composites with pyrolytic carbon (pyC) interphase, the electric current would be mostly carried through the interphase. For carbon-fiber-reinforced SiC composites, the current would flow through the fibers, since carbon is a better conductive than silicon carbide. Carbon-fiber-reinforced SiC composites resemble carbon-fiber- reinforced PMC materials, at least from the electrical behavior point of view. The
184 electrical behavior in carbon-fiber-reinforced PMCs has been well-documented by D. D.
L. Chung [168], among others. Thus, one can refer to literature to study this system.
In most SiC-fiber-reinforced CMCs, however, the conductive phase is the SiC matrix. For melt-infiltrated SiC/SiC composites, the silicon would play a major role in the conductivity of the matrix and it would carry most of the current. Unless, a continuous silicon path exists in the matrix, this system will be more challenging to study. SiC/SiC composites prepared using polymer infiltration and pyrolysis (PIP) or chemical vapor infiltration (CVI) techniques would be easier to study, since only the SiC- based matrix would carry the current, in most cases.
11.2 Mode II Interlaminar Fracture Testing of CMCs
The design of a Mode II interlaminar fracture testing technique should take into consideration testing at elevated temperatures. The most common technique for Mode II interlaminar fracture testing is the end-notched flexure (ENF) technique [169], as shown in Figure 118. In fact, an ASTM has been developed for employing this technique in testing unidirectional fiber reinforced polymer matrix composites [170]. The samples prepared for Mode II interlaminar fracture testing can be identical to the one prepared for
Mode I. The applied load differs, nonetheless. In the ENF test, the load is applied similarly to the three-point bending test.
185 Figure 118. End-notched flexure test for determining Mode II interlaminar fracture properties.
In order to utilize this technique for high temperature testing, the whole system
(sample as well as the loading pins) need to be inside a furnace. In this case, the ER technique cannot be used to determine crack length. Therefore, another crack length measurement technique needs to be developed.
Another approach is to employ a testing technique in which the load is applied away from the notch tip. The end-loaded-split (ELS) test is an option [171, 172]. In this testing method, the load is only applied to the arms, while the bottom of the sample is fixed; generating a pure Mode II interlaminar shear (Figure 119). Moreover, this technique allows for the use of ER, similar to the wedge test, during room or elevated temperatures.
186 Figure 119. End-loaded-split test for determining Mode II interlaminar fracture properties at room and elevated temperatures, illustrating the use of ER to determine crack length.
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