CORRELATION OF STRESS INTENSITY RANGE WITH DEVIATION OF THE CRACK
FRONT FROM THE PRIMARY CRACK PLANE IN BOTH HAND AND DIE FORGED
ALUMINUM 7085-T7452
Thesis
Submitted to
The School of Engineering of the
UNIVERSITY OF DAYTON
In Partial Fulfillment of the Requirements for
The Degree of
Master of Science in Mechanical Engineering
By
Jared Adam Neely
Dayton, Ohio
May 2019
CORRELATION OF STRESS INTENSITY RANGE WITH DEVIATION OF THE CRACK
FRONT FROM THE PRIMARY CRACK PLANE IN BOTH HAND AND DIE FORGED
ALUMINUM 7085-T7452
Name: Neely, Jared Adam
APPROVED BY:
______David H. Myszka, Ph.D. James J. Joo, Ph.D. Advisory Committee Chairman Committee Member Professor Graduate Faculty School of Engineering School of Engineering
______Thomas J. Spradlin, Ph.D. Mark A. James, Ph.D. Committee Member Committee Member Aerospace Structures Engineer Technical Specialist Air Force Research Laboratory Arconic Technology Center
______Robert J. Wilkens Ph.D., P.E. Eddy M. Rojas, Ph.D., M.A., P.E. Associate Dean for Research and Innovation Dean, School of Engineering Professor School of Engineering
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© Copyright by
Jared Adam Neely
All Rights Reserved
2019
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ABSTRACT
CORRELATION OF STRESS INTENSITY RANGE WITH DEVIATION OF THE CRACK
FRONT FROM THE PRIMARY CRACK PLANE IN BOTH HAND AND DIE FORGED
ALUMINUM 7085-T7452
Name: Neely, Jared Adam University of Dayton
Advisor: Dr. David H. Myzka
Experimental study accomplished the characterization of fatigue crack growth rates and mechanisms in both hand and die forged Aluminum 7085-T7452. Testing was conducted at various positive and negative loading ratios, primarily focused on L-S and T-S orientations to discover a correlation between crack tip branching or turning mechanisms and stress intensity.
Interior delaminations were found to originate in the interior of the specimen and propagate outward to the surface and manifested as splitting cracks parallel to the loading direction. Stress intensity ranges have been correlated with the onset of crack deviation from the primary crack plane, as well as, the transition to branching dominated fatigue crack growth.
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Dedicated to my mother, Rhonda J. Schilling
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ACKNOWLEDGEMENTS
I would first like to thank my sponsor, Dr. Thomas Spradlin, from the Aerospace Systems
Directorate of the Air Force Research Laboratory. Dr. Spradlin made himself available on
countless occasions to offer his expertise, guidance, patience, and finely-honed repartee. I would
also like to thank Dr. Mark James of the Aerospace and Defense Arconic Technology Center,
who on numerous occasions, offered his knowledge and experience pertaining to the crack
branching behavior in Aluminum alloys. I would like to thank my Advisor, Dr. David Myszka,
for his guidance and assistance in drafting and formalizing this Thesis document.
I would additionally like to thank Dr. Steve Thompson and Nick Jacobs of the Materials
Test and Evaluation Team for the Air Force Research Laboratory, who provided testing
equipment, ACORN crack growth testing software, and technical support. I would also like to thank Brian Smyers and his team from the Air Force Research Laboratory’s Structural Validation
Branch, for providing testing space, load frames, specimen fabrication, and technical support throughout the testing process.
Finally, I would like to thank my wonderful wife and my best friend, Jamie Neely. The unconditional love, encouragement, patience and the continuous support of my goals and aspirations she has provided throughout this and all other endeavors. This accomplishment would not have been possible without the assistance and support of each of these individuals. Thank you.
Jared A. Neely
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TABLE OF CONTENTS
ABSTRACT ...... iv
DEDICATION ...... v
ACKNOWLEDGEMENTS ...... vi
LIST OF FIGURES ...... ix
LIST OF TABLES ...... xiii
LIST OF ABBREVIATIONS AND NOTATIONS ...... xiv
CHAPTER I INTRODUCTION ...... 1
1.1 Motivation ...... 1
1.2 Prior Work ...... 2
CHAPTER II BACKGROUND ...... 5
2.1 Fatigue Crack Growth ...... 5
2.1.1 Linear Elastic Fracture Mechanics (LEFM) ...... 6
2.1.2 Fatigue Crack Growth (FCG) Rate Testing ...... 10
2.1.3 Compliance and Crack Closure ...... 12
2.2 Importance of Microstructure ...... 16
CHAPTER III TESTING PROCEDURES ...... 23
3.1 Fatigue Specimens Details ...... 23
3.1.1 M(T) Specimens ...... 24
3.1.2 C(T) Specimens ...... 25
3.1.3 Polishing Procedure ...... 27
3.2 Testing Standards ...... 29
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3.2.1 Compliance Based Crack Calculation Method ...... 29
3.2.2 Validity Criteria ...... 31
3.3 Test Setup ...... 32
3.3.1 Load Frame and Control Systems ...... 32
3.3.2 Sensors, External Command and Data Acquisition ...... 32
3.3.3 ACORN Fatigue Crack Growth Software ...... 34
3.3.4 Test Fixtures and Measuring Instruments ...... 36
3.4 Testing Methods ...... 41
3.4.1 Precracking ...... 41
3.4.2 M(T) Testing and Data Collection ...... 41
3.4.3 C(T) Testing and Data Collection ...... 43
CHAPTER IV DATA REDUCTION ...... 46
4.1 Calculation Methods ...... 46
4.2 Crack Length Correction Methods ...... 48
CHAPTER V RESULTS ...... 51
5.1 L-S and S-L Orientations ...... 52
5.2 T-S and S-T Orientations ...... 61
5.3 L-T Orientation ...... 69
CHAPTER VI DISCUSSION AND CONCLUSIONS ...... 71
6.1 Discussion ...... 71
6.2 Conclusions ...... 79
6.3 Future Work ...... 80
REFERENCES ...... 82
APPENDIX A Testing Setup and Procedures ...... 84
APPENDIX B Specimen Photographs ...... 86
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LIST OF FIGURES
Figure 1.1: Final crack splitting in Al 7050-T7451 with L-S orientation ...... 4
Figure 2.1: The three modes of crack loading [13] ...... 6
Figure 2.2: Stress field around leading edge of crack [11] ...... 7
Figure 2.3: Plastic and elastic (denoted as K-field) zones surrounding crack tip [11] ...... 8
Figure 2.4: Plastic zones size and fracture planes for states of a) plane stress and b) plane strain [11] ...... 9
Figure 2.5: Plastic zone with planar dimensions [11] ...... 10
Figure 2.6: Three regions of crack growth rate [14] ...... 11
Figure 2.7: Diagram of critical force, displacement and compliance parameters for the ACR method [16] ...... 13
Figure 2.8: Evaluation of the variation of compliance with load for use in determination of opening force [16] ...... 14
Figure 2.9: Determination of opening force using the compliance offset method [16] ...... 14
Figure 2.10: Material extraction orientation from parent material [11] ...... 17
Figure 2.11: Microstructure orientation [10] ...... 18
Figure 2.12: Three micromechanisms of fracture in metals [12] ...... 18
Figure 2.13: Mechanism for ductile crack growth [12] ...... 19
Figure 2.14: River patterns form as a result of a cleavage crack crossing a twist boundary between grains [12] ...... 19
Figure 2.15: Schematic illustration of crack interactions with weak planar grain boundaries: (a) L-S/T-S orientations, ‘crack arrest’, (b) S-L/S-T orientations, ‘crack delamination/splitting’, and (c) L-T/T-L orientations, ‘crack divider’ [9] ...... 20
Figure 2.16: Crack branching configurations with respect to the rolling axes [8] ...... 21
Figure 3.1: Specimen naming convention...... 24
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Figure 3.2: M(T) specimen with through thickness center hole ...... 25
Figure 3.3: Notched hole diagram for M(T) specimens (X.XXX = ± 0.005”) ...... 25
Figure 3.4: Drawing of 3W C(T) specimen with starter notch ...... 26
Figure 3.5: Diagram of C(T) specimen extraction orientations from parent M(T) material ...... 27
Figure 3.6: Polishing region for M(T) specimens ...... 28
Figure 3.7: Polishing region for C(T) specimens ...... 29
Figure 3.8: M(T) specimen dimension nomenclature [16] ...... 30
Figure 3.9: C(T) specimen nomenclature ...... 30
Figure 3.10: Out-of-plane cracking limits [16] ...... 31
Figure 3.11: ACORN main dashboard, load vs. displacement plot ...... 35
Figure 3.12: Orthogonal view of buckling guide mounted on M(T) specimen ...... 37
Figure 3.13: Buckling guide on M(T) specimen with mounted COD gages during test ...... 38
Figure 3.14: Clevis and pin assembly for gripping C(T) specimens [16] ...... 39
Figure 3.15: 22 kip MTS load frame pictured during fatigue test of C(T) specimen ...... 40
Figure 3.16: C(T) specimen loaded in test fixture. COD gage mounted at the mouth of starter notch (left) and taking initial measurements at starter notch with travelling microscopes (right)...... 40
Figure 3.17: Front and side views of M(T) specimen during test ...... 42
Figure 4.1: C(T) specimen possible extensometer measurement locations [16] ...... 47
Figure 4.2: Sensitivity relationship identified between visual crack lengths and calculated effective modulus for M(T) specimen geometry...... 50
Figure 5.1: Growth rate plot of all L-S M(T) specimens f(ΔKACR) ...... 54
Figure 5.2: Growth rate plot of all L-S M(T) specimens f(ΔK) ...... 54
Figure 5.3: Growth rate plot of all L-S M(T) specimens f(Kmax) ...... 55
Figure 5.4: Growth rate plot of L-S and S-L C(T) specimens f(ΔKACR) ...... 55
Figure 5.5: Growth rate plot of L-S and S-L C(T) specimens f(ΔK) ...... 56
Figure 5.6: Growth rate plot of L-S C(T) specimens f(Kmax) ...... 56
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Figure 5.7: Sinusoidal pattern in growth rate as f(ΔK) in L-S orientation for M(T) specimens of varying load ratios ...... 57
Figure 5.8: Sinusoidal pattern in growth rate as f(Kmax) in L-S orientation for M(T) specimens of varying load ratios ...... 57
Figure 5.9: Sinusoidal pattern in growth rate as f(ΔK) in L-S orientation for C(T) specimens of varying load ratios ...... 58
Figure 5.10: Sinusoidal pattern in growth rate as f(Kmax) in L-S orientation for C(T) specimens of varying load ratios ...... 58
Figure 5.11: Fracture surfaces of L-S and L-T M(T) specimens ...... 59
Figure 5.12: Fracture surfaces of L-S and L-T M(T) specimens marked overlaid with locations of values: Kmax-dev (Minor), Kmax-dev (Major), and the start of sinusoidal behavior in the growth rate plot ...... 60
Figure 5.13: Growth rate plot of all T-S M(T) specimens f(ΔKACR) ...... 63
Figure 5.14: Growth rate plot of all T-S M(T) specimens f(ΔK) ...... 64
Figure 5.15: Growth rate plot of T-S M(T) specimens f(Kmax) ...... 64
Figure 5.16: Growth rate plot of T-S C(T) specimens f(ΔKACR) ...... 65
Figure 5.17: Growth rate plot of T-S C(T) specimens f(ΔK) ...... 65
Figure 5.18: Growth rate plot of T-S C(T) specimens f(Kmax) ...... 66
Figure 5.19: Comparison between T-S and S-T for R = 0.1 ...... 66
Figure 5.20: Fracture surfaces of T-S M(T) specimens ...... 67
Figure 5.21: Fracture surfaces of T-S M(T) specimens marked overlaid with locations of values: Kmax-dev (Minor), Kmax-dev (Major), and the start of sinusoidal behavior in the growth rate plot ...... 68
Figure 5.22: Growth rate plot of die forged L-T f(Kmax) ...... 69
Figure 5.23: Growth rate plot of die forged L-T f(ΔK) ...... 70
Figure 5.24: Growth rate plot of die forged L-T f(ΔKACR) ...... 70
Figure 6.1: Sinusoidal pattern in growth rate data from Schubbe’s investigation into branching in Al 7050-T7451 [10] ...... 72
Figure 6.2: Correlation of abrupt change in crack growth rate events with specific occurrences of crack tip splitting and branching, illustrated on CD-LS-01. Primary crack path is from right to left...... 73
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Figure 6.3: Subsurface-to-surface cracking events (a),(b), and (c) impact growth rate for die forged MD-LS-01 ...... 74
Figure 6.4: Subsurface-to-surface cracking events (d),(e), and (f) impact growth rate for die forged MD-LS-01 ...... 75
Figure 6.5: Subsurface-to-surface cracking events (g),(h), (i), and (j) impact growth rate for die forged L-S specimen (MD-LS-01)...... 76
Figure 6.6: Symmetric branching in hand forged L-S C(T) specimen ...... 78
Figure A.1: Drawing of 1.04” gage knife edge placement for MTS 623 extensometers ...... 84
Figure B.1: Die forged L-S raw material as received ...... 86
Figure B.2: Die forged T-S raw material as received ...... 86
Figure B.3: Die forged L-T raw material as received ...... 87
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LIST OF TABLES
Table 4.1: Coefficients for C(T) crack calculation for possible measurement locations [16] ...... 48
Table 5.1: Summary of crack branching and turning results in L-S orientation ...... 53
Table 5.2: Summary of crack branching and turning results in T-S orientation ...... 62
Table 6.1: Summary of stress intensity ranges associated with the onset of crack branching and turning ...... 80
Table A.1: Test matrix ...... 85
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LIST OF ABBREVIATIONS AND NOTATIONS
AA Aluminum Alloy
ACR Adjusted Compliance Ratio
AFRL Air Force Research Laboratory
Al Aluminum
Al-Li Aluminum-Lithium
AMS Aerospace Material Specification
ASTM American Society for Testing and Materials
C(T) Compact Tensile
COD Clip On Displacement
EDM Electrical Discharge Machining
FCG Fatigue Crack Growth
LEFM Linear Elastic Fracture Mechanics
M(T) Middle-crack Tensile
NDE Non-Destructive Evaluation
PFZ Precipitate Free Zone
PTFE Polytetrafluoroethylene
SEM Scanning Electron Microscopy
SIF Stress Intensity Factor
UNC Unified Course
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CHAPTER I
INTRODUCTION
1.1 Motivation
The ever-growing demand for lighter, stronger, and faster aircraft continues to push the limits of existing material systems and creates the need to develop more complex alloys to meet new engineering design challenges. Aluminum has been used in aircraft in since the late 1920’s for structural components such as skin, spars, stringers, ribs, and bulkheads [1]. In large structural components such as bulkheads, the aerospace industry is moving away from multi-component assemblies, and is now using single unitized monolithic components as aircraft structure. This requires the use of thick plate materials or large scale forgings [2][3]. Creating structural bulkheads as a single piece, reduces weight and increases structural performance. In order to manufacture these primary aircraft structural components, thick plates of aluminum are needed to forge and machine to the desired profile. AA7085 (Al 7085), developed by Alcoa, is one of the latest additions to the 7xxx series aluminum alloys. Al 7085 was developed as a response to the aerospace industry’s need for an aluminum with improved thick section properties [2].
Al 7085 is now being used in primary structural components in aircraft. Due to its excellent corrosion resistance and similar nominal mechanical properties to 7075, 7085 appears to be an excellent replacement alloy, however, some prior testing raises concerns for its use as primary structure in a cyclically loaded application, due to atypical crack growth behavior.
Recent investigations have uncovered that particular grain orientations of Al 7085-T7452 demonstrate atypical fatigue cracking behavior. In particular material orientations, the crack tip deviates from the primary crack path and often results in crack tip splitting or branching.
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Aerospace Material Specification (AMS) datasheets, do not provide fracture toughness values for
orientations exhibiting the aforementioned cracking behavior [4][5].
The anisotropic fatigue and fracture behavior of Al 7085-T7452 requires further characterization, in all grain orientations, to truly understand the capabilities of this material
system and understand how to sustain these components throughout the lifecycle of the airframe.
A chain is only as strong as its weakest link, therefore, the aerospace and materials communities
need to agree on a quantifiable substitute for the traditional fracture toughness metric that is
below the threshold at which the crack path becomes unpredictable.
The purpose of this project is to determine stress intensity thresholds at which deviation
from the primary crack front occurs in Al 7085-T7452 that can be determined using current
testing practices, in both hand and die forged product forms.
1.2 Prior Work
The aerospace and materials communities have been continuously working to
characterize many aluminum alloys that exhibit a similar crack branching behavior for decades. A
small change in either the configuration or orientation of a “well known” material system, is all
that is necessary to make it a “less known” material system, with regard to some or all of its
material properties [6]. This is even more significant for highly anisotropic materials, which
require full characterization to use.
Rao and Ritchie [7] conducted early key research on fatigue and fracture properties in
2090, 2091, 8090 and 8091, second generation Aluminum-Lithium (Al-Li) alloys, in the late
1980’s. They found that deflection and shielding of the primary crack were caused by the
formation and propagation of secondary delamination cracks. They concluded that the
microstructure, specifically the interaction of the matrix and grain boundary precipitates, and
associated Precipitate Free Zones (PFZs), played a critical role in the occurrence of delamination
cracking. This behavior was common in peak overaged aluminum alloys.
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Third generation Al-Li alloys, have been found to exhibit similar delamination mechanisms as the earlier generation Al-Li alloys [8]. A significant amount of research has been conducted on various tempers of Al 7050. Sinclair studied the influence of mixed mode loading on Al 7050-T7651 and concluded that grain boundary fatigue crack growth, at levels of high stress intensities, is favored by increasing shear loading parallel to the grain boundary plane [9].
Sinclair noted that in mixed mode loading, the crack path was dependent on maximum stress intensity levels, as opposed to stress intensity range.
Various branching mechanisms were examined in Al 2099 through the mesoscopic modeling of grain boundaries by Messner, who found that grain misorientation or texture can induce localized transverse shear stresses along grain boundaries. Messner concluded that the induced transverse shear stresses lead to microvoid formation and growth, and increased potential for branching behavior [8]. Schubbe observed similar microvoids along grain boundaries in Al
7050-T7451, which coalesced to form large cracks on the interior surface, growing parallel to the loading direction [10]. Schubbe found that crack splitting and branching initiate first at the interior, then propagate outward to the surface and progressed until rupture [6]. An example of progressed crack branching and splitting behavior in Al 7050-T7451, is shown in Fig. 1.1.
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Figure 1.1: Final crack splitting in Al 7050-T7451 with L-S orientation [10]
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CHAPTER II
BACKGROUND
2.1 Fatigue Crack Growth
The following sections include a brief introduction to the history and purpose of fracture mechanics and fatigue crack growth. Society has faced the problem of fracture ever since man- made structures began being erected. One of the common causes for fracture is fatigue, which is failure due to repeated loading [11]. Fracture presents more of a problem today than it did centuries ago, because more can go wrong with the increasing complexity of today’s technological society. A catastrophic failure in today’s aerospace structures could result in a substantiating number of casualties. Some of the potential dangers associated with these technological advancements have fortunately been offset by advancements if the field of fracture mechanics. Since World War II, our understanding of how and why metals fail has been greatly expanded, however much remains to be learned [12].
According to Anderson [12], there are two categories into which most structural failures can fall. The first category being comprised of structural failures due to negligence during design, construction or the operation of the structure. The second, being when the application of a new material or new design produces an unexpected and undesirable result. The first category could be attributed to ignorance, human error or inexperience. The second category, into which structural failures can fall, is more difficult to control and predict.
The utilization of high strength materials for weight reduction, increased after World War
II. During that same timeframe, stress analysis methods for predicting local stresses were improved, which lead to further weight savings and consequently, the practice of using lower
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factors of safety [13]. Materials with high strength properties generally have low fracture toughness, and vice versa. Fracture toughness is a material property that measures a material’s resistance to brittle fracture in the presence of a crack. Brittle fracture can be defined as fracture that occurs under loading, where little of no plastic deformation occurs. The development of fracture mechanics was developed to explain the occurrence of low stress fracture in high strength materials [11][13].
2.1.1 Linear Elastic Fracture Mechanics (LEFM)
The first major contribution to fatigue crack growth came from Griffith’s criterion which focused primarily on brittle materials and the linear elastic cracks or sharp flaws that grow with increasing surface energy. Griffith showed that the growth occurs when the energy rate provided from the applied loading is greater than a threshold rate of energy for crack growth. Griffith’s criterion only applied to brittle materials such as glass [12]. It could not be used to describe the failure of ductile structural metals, e.g., steel. Building on Griffith’s work, Irwin developed a modification which incorporated the concept of plasticity and expanded the concept to explain the failure of ductile materials. Irwin found the presence of a plastic zone around the crack tip in that is surrounded by an elastic zone, and thus an elastic and plastic component driving fatigue [12].
Figure 2.1: The three modes of crack loading [13]
The crack tip in a solid can be stressed in three different modes, as illustrated in Fig. 2.1.
Mode I or “opening mode”, occurs when the load is applied in a direction normal to the crack
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plane. Mode II or “sliding mode”, occurs as a result of in-plane shear. Mode III or “tearing mode”, occurs as a result of out-of-plane shear [13].
Figure 2.2: Stress field around leading edge of crack [11]
Stress intensity factor (SIF), refers to the magnitude of stress that is culminated at the crack tip and is represented by the variable K and has units of ksi√in, as seen in the following form:
𝐾𝐾𝐼𝐼 (1) 𝜎𝜎𝑖𝑖𝑖𝑖 = 𝑓𝑓𝑖𝑖𝑖𝑖(𝜃𝜃) √2𝜋𝜋𝜋𝜋 where σij is the stress field at an angle θ from the crack plane, distance r from the crack tip and a geometric relationship fij(θ) which is known for values of θ, as illustrated in Fig. 2.2. KI is the SIF
in mode I loading and can be used to describe the stress field around the crack tip [13].
The theory of LEFM utilizes two similitude parameters, which remove geometric
constraints and allow the stress fields around crack tips to be compared between bodies. For
LEFM to be applicable, the crack tip stresses need to be below the yield stress, σys, in order to
avoid the plastic zone size and plasticity limitations. The first similitude parameter, stress
intensity, allows for differing bodies of the same material to be in exact similitude if crack tips of
both bodies are subjected to equal stress intensity. This is only true if the plastic zone surrounding
the crack tip is sufficiently small relative to the elastic zone that surrounds it, as illustrated in Fig.
2.3. The plastic zone increases in size with increasing load or crack length. It is possible to
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maintain similitude on the basis of only the KI parameter, given that the plastic zone is small and the stress field can be governed by the first term of Eq. (1) [11][13].
Figure 2.3: Plastic and elastic (denoted as K-field) zones surrounding crack tip [11]
The second similitude parameter, is the classification of a plane stress or plane strain constraint. In order to simplify the mathematics of the linearly elastic stress field, it must be determined if Poisson effects can be neglected, i.e., a plane stress situation where no transverse shear forces are significant. As a general rule of thumb, crack tips in bodies of small transverse thickness are typically in a state of plane stress, whereas a crack tip in a body of large transverse thickness is in a state of plane strain.
For the state of plane stress, Poisson effects are neglected and there are no through- thickness stress states, i.e., in the z-direction. Assuming θ = 0, the stress field for a state of plane stress simplifies to:
𝐾𝐾 (2) 𝜎𝜎𝑥𝑥 = 𝜎𝜎𝑦𝑦 = , 𝜎𝜎𝑧𝑧 = 𝜏𝜏𝑥𝑥𝑥𝑥 = 𝜏𝜏𝑦𝑦𝑦𝑦 = 𝜏𝜏𝑧𝑧𝑧𝑧 = 0 √2𝜋𝜋𝜋𝜋 From this stress field, the maximum plastic zone size for a state of plane stress, without yielding the material, can be approximated by substituting σys for σy.
2 1 𝐾𝐾 (3) 2𝑟𝑟𝑜𝑜𝑜𝑜 = 𝜋𝜋 �𝜎𝜎𝑦𝑦𝑦𝑦�
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For a state of plane strain, a small Poisson effect is assumed in the z-direction, where
εz = 0. The Poisson effect results in a tensile stress, σz, in the interior. Using Hooke’s law, and
assuming a Poisson’s ratio ν = 0.3 and σx = σy, results in σy = 2.5σz or σy = 2.5σys using yield stress,
σys. Irwin’s research suggests that for the state of plane strain, an appropriate yield stress approximation of . Similarly to plane stress, the maximum size of the plastic zone 𝜎𝜎𝑦𝑦 = √3𝜎𝜎𝑦𝑦𝑦𝑦 without yielding, for the state of plane strain can be given by the following expression:
2 1 𝐾𝐾 (4) 2𝑟𝑟𝑜𝑜𝑜𝑜 = 3𝜋𝜋 �𝜎𝜎𝑦𝑦𝑦𝑦� The plastic zone for states of plane stress and plane strain are illustrated in Fig. 2.4.
Figure 2.4: Plastic zones size and fracture planes for states of a) plane stress and b) plane strain [11]
Through the use of the similitude parameters, one can compare specimens with equal
SIFs, provided they are both classified as a state of plane stress and likewise between specimens classified as a state of plane strain. The following, is commonly used to make the distinction between the two:
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2 𝐾𝐾𝐼𝐼 (5) Plane Strain: 𝐵𝐵 ≥ 2.5 �𝜎𝜎𝑦𝑦𝑦𝑦� where B is the specimen thickness, KI is the SIF in mode I loading, and σys is the material yield stress [13]. If Eq. (5) holds true, a state of plane strain is present, otherwise plane stress should be used.
Figure 2.5: Plastic zone with planar dimensions [11]
In order to satisfy the plasticity limitations on LEFM, the following must be satisfied for LEFM to be applicable:
2 4 𝐾𝐾 (6) 𝑎𝑎 , (𝑏𝑏 − 𝑎𝑎) , ℎ ≥ 𝜋𝜋 �𝜎𝜎𝑦𝑦𝑦𝑦� where the dimensions a, b, and h are defined in Fig. 2.11.
2.1.2 Fatigue Crack Growth (FCG) Rate Testing
Fatigue crack growth refers to the material damage that occurs under repeated load cycles. The applied force range for a given loading cycle is given as:
(7) ∆𝑃𝑃 = 𝑃𝑃𝑚𝑚𝑚𝑚𝑚𝑚 − 𝑃𝑃𝑚𝑚𝑚𝑚𝑚𝑚
where Pmax is the maximum applied force and Pmin is the minimum applied force. The force ratio
R, also referred to as load ratio or stress ratio, is a ratio between the minimum and maximum
forces and is calculated as:
𝑃𝑃𝑚𝑚𝑚𝑚𝑚𝑚 (8) 𝑅𝑅 = 𝑃𝑃𝑚𝑚𝑚𝑚𝑚𝑚
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The stress intensity factor range, ΔK is the variation of stress intensity throughout a given cycle, and is calculated as:
(9) ∆𝐾𝐾 = 𝐾𝐾𝑚𝑚𝑚𝑚𝑚𝑚 − 𝐾𝐾𝑚𝑚𝑚𝑚𝑚𝑚
where Kmax and Kmin are the maximum and minimum stress intensity factors for a given cycle respectively.
Figure 2.6: Three regions of crack growth rate [14]
Fatigue crack growth rate is defined as the change in crack length with respect to the number of cycles elapsed from the previous crack length measurement and can be explained using the following relationship:
∆𝑎𝑎 (10) = 𝑓𝑓(∆𝐾𝐾) ∆𝑁𝑁 where ΔK is the SIF range, Δa is the change in crack length, ΔN is the number of cycles since the previous crack length measurement and, therefore, Δa/ΔN is the crack growth rate. This
11
explanation was refined by Paris [11] to characterize crack growth rate in region II, the largest region of interest, as seen in Fig. 2.6. Crack growth rate can also be expressed as:
𝑑𝑑𝑑𝑑 𝑚𝑚 (11) = 𝐶𝐶(∆𝐾𝐾) 𝑑𝑑𝑑𝑑 where C is a material constant and m is the slope on the log-log plot. The fracture toughness of a given material is given by KC, and is the Kmax value at which an asymptote exists and the crack
growth curve diverges to infinity, as seen in Fig. 2.6. A KC value is associated with each loading mode. For example, mode I loading is represented as KIC.
2.1.3 Compliance and Crack Closure
The effects of crack closure was introduced in the early 1970’s by Elber, to account for
the zone of tensile residual deformations that are left in the wake of a moving crack tip [15].
Elber found that these residual deformations, upon unloading, could cause the crack to close
above zero load. It was believed that the determination of stress crack closure was a critical
component to understand fatigue crack propagation. Crack closure refers to when the fracture
surfaces of a fatigue crack come into contact, at some point during the unloading cycle, and force
is transmitted through the fracture surfaces [16].
Techniques for measuring crack closure effects were adopted by the fatigue community,
following a recommendation by Donald in 1988, to standardize the measurement technique [17].
Up until that point, no standardization of the process by which closure measurements were made
was available and there were inconsistencies with values reported in literature. This measurement
technique was adopted into American Society for Testing and Materials (ASTM) testing standard
E647, where it still serves as a foundation for the recommended practice for determining fatigue
crack opening force from compliance [16][18].
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Figure 2.7: Diagram of critical force, displacement and compliance parameters for the ACR method [16]
Compliance values are obtained from the force-displacement curve as, illustrated in Fig.
2.7, where an initial loading and progressed loading cycle are shown. Initial compliance values,
Coi and Csi, were taken from the compliance values, Co and Cs, of the first cycle, prior to crack
initiation. Co is the open-crack compliance obtained from the inverse slope, /P, of the best-fit 𝑣𝑣 line through points of the upper region of load-displacement curve above the crack opening force,
Pop. Secant compliance, Cs, is the inverse slope of the line connecting the points consisting of the
maximum and minimum forces and respective displacement values.
𝑣𝑣𝑚𝑚𝑚𝑚𝑚𝑚 − 𝑣𝑣𝑚𝑚𝑚𝑚𝑚𝑚 (12) 𝐶𝐶𝑠𝑠 = 𝑃𝑃 − 𝑃𝑃𝑚𝑚𝑚𝑚𝑚𝑚 The crack opening force compliance method𝑚𝑚𝑚𝑚𝑚𝑚 is a technique that attempts to estimate the effect of crack closure on SIF range, ΔK. The driving principle being, that applied loads, Papp, below the crack opening load, Pop, do not contribute to crack growth. If the opening force is
known and, if Pop > Pmin, the effective force range can be calculated as: ΔPeff = Pmax – Pop, instead
of using the applied force range (ΔPapp = Pmax – Pmin). There is an effective stress intensity factor
range ΔKeff, which can be calculated from the effective driving force, Peff. The recommended
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procedure for determining Pop is the compliance offset method. This method consists of dividing the upper portion of the force-displacement curve into several individual overlapping segments, for each of which the segment slope is calculated and is the compliance of a line segment, Csegment,
as illustrated in Fig. 2.8.
Figure 2.8: Evaluation of the variation of compliance with load for use in determination of opening force [16]
𝐶𝐶𝑜𝑜 − 𝐶𝐶𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 (13) Compliance offset = × 100 𝐶𝐶𝑜𝑜
Figure 2.9: Determination of opening force using the compliance offset method [16]
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The compliance offset (percent of open-crack compliance value), is calculated for each segment using Eq. (13). The mean force for each line segment is calculated and then plotted as a function of compliance offset. The desired percent (X%) opening force is found at the intersection of line (connecting two adjacent points), with the vertical line at the compliance offset (X% of
open crack compliance value), as illustrated in Fig. 2.9. An opening force compliance offset
criteria of 2% is recommended for determining ΔKeff above the near-threshold regime [17].
There have been objections to the usefulness of ΔKeff as determined by the compliance offset method and may be misleading in certain cases [18]. The method for finding opening force using the compliance method was evaluated during ASTM Round Robin programs and found that the method produced a significant amount of scatter that had be subjected to strict accept or reject criteria [19]. An alternative method, referred to as the Adjusted Compliance Ratio (ACR) technique, was introduced in an attempt to account for the cyclic stress intensity factor below the opening load and calculate a more fundamentally sound expression for ΔKeff.
𝐶𝐶𝑠𝑠 − 𝐶𝐶𝑜𝑜𝑜𝑜 (14) 𝐴𝐴𝐴𝐴𝑅𝑅 = 𝐶𝐶𝑜𝑜 − 𝐶𝐶𝑜𝑜𝑜𝑜 It is believed that Eq. (14) results in a compliance ratio, due solely to the presence of a crack, and that this ratio can be used to directly calculate an alternative to ΔKeff. The ACR method accounts for the bulk shielding mechanism that in the wake of the crack, as well as, its effect in the cyclic strain field that is in front of the crack [19]. This ratio can also be normalized to compensate for any bias that may occur due to signal conditioning noise or nonlinearity of the open-crack compliance (Co) or the secant compliance (Cs). Normalized ACR (ACRn) is represented as:
𝐶𝐶𝑜𝑜𝑜𝑜 𝐶𝐶𝑠𝑠 − 𝐶𝐶𝑜𝑜𝑜𝑜 (15) 𝐴𝐴𝐴𝐴𝐴𝐴𝑛𝑛 = ∙ 𝐶𝐶𝑠𝑠𝑠𝑠 𝐶𝐶𝑜𝑜 − 𝐶𝐶𝑜𝑜𝑜𝑜 where the effective stress intensity range is calculated as:
(16) ∆𝐾𝐾𝐴𝐴𝐴𝐴𝐴𝐴 = 𝐴𝐴𝐴𝐴𝐴𝐴𝑛𝑛 ∙ ∆𝐾𝐾𝑎𝑎𝑎𝑎𝑎𝑎
where ΔKapp is the applied stress intensity range, also referred to as ΔK. It should be noted, that for all reported values of ΔKACR in this report, the normalized ACR method was used in
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conjunction with Eq. (16). The ACR technique is considered an accepted method for calculating effective stress intensity range, and is detailed in Appendix (X4) of ASTM E647 [16].
2.2 Importance of Microstructure
To fully understand the how cracks begin their life, grow and lead to fracture in a material, the microstructural level is examined. Metals and ceramics that are used in engineering applications are comprised of crystalline grains, which are separated by grain boundaries and results in a crystalline material. Both the grains and grain boundaries, contain defects or impurities that are created during manufacturing. Material properties are a direct result of the molecular bond strength of the grains and grain boundaries [11]. Cracks begin their life in a slip band of a single grain within the microstructure. The slip in the grain begins in the most favorable slip system for a given crystal structure. It is this slip band that propagates from grain to grain, which leads to the initial crack growth. Grain orientation plays a significant role in this slip propagation, but so do other microstructural features such as dislocations, inclusions, notches, porosity, grain clustering, neighboring grains, grain boundaries, and average grain size [11][20].
When discussing microstructural influences on macrostructure mechanical properties, it is important to touch on the effects of grain size, shape, and orientation. A material is said to be isotropic if it is homogeneous and has the same mechanical properties in all directions. This is appropriate at the macroscopic level, but at the microscopic level, various sizes and shapes of tiny grains are randomly oriented. Isotropic properties are typical of metals that have relatively small and consistent grains, such as low carbon steels. Raw materials however, are never perfectly isotropic, but is often assumed to be if the directional properties are almost the same. Assuming isotropicity reduces the complexity of solving the constitutive equations, which define the stress- strain relationship. Anisotropic materials, have directional properties that cannot be satisfied by using an isotropic assumption [11]. Anisotropic metals have an oriented grain structure that is the
result of rolling, extrusion or forging manufacturing processes. As the size of the oriented gains
increases, the effective directional mechanical properties become more pronounced. When
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quantifying mechanical properties in a material, especially anisotropic materials, it is important to quantify the properties in each microstructural orientation.
Figure 2.10: Material extraction orientation from parent material [11]
ASTM notation for specimens extracted from a plate or forging is relative to the geometry associated with manufacturing processes, as illustrated in Fig. 2.10. Material specimen orientations are denoted using the letters: L, S and T. The designation L, refers to the length or the longitudinal direction and depending on the manufacturing method, either the rolling direction, extrusion direction or the axis for forging. The designation S, refers to the thickness of the parent material and is called the short transverse direction. The designation T, refers to the width and is called the long transverse direction. ASTM utilizes a specimen orientation consisting of two of the geometric designations separated by a hyphen, where the first letter represents the direction of loading and the second represents the direction of primary crack growth. For example: L-T refers to a specimen being loaded in the longitudinal direction and having a crack growing in the long transverse direction. Similarly, a T-S specimen would be loaded in the long transverse direction and have a crack grow in the short transverse direction. It can be thought of as Cartesian coordinate system where x, y, and z are replaced by directions L, T and S. If the two directions are given and not separated by a hyphen, then it is referring to a plane that is formed by
the axes of the two directions or a plane parallel to it. For example, the plane TS is defined by the
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long transverse and short transverse axes and is the plane the of primary crack growth for an L-T
specimen, as shown in Fig. 2.10.
The purpose of this orientation system is to relate specimen geometry to microstructure
grain orientation resulting from the material manufacturing process. Grains in the microstructure
are longest in the longitudinal direction, flattest in the thickness direction from the rolling process
and less flat in the long transverse direction, depicted in Fig. 2.11. A cross-sectional view of a
grain, using the TS plane, would have an elliptical cross-section, where the short transverse is the minor axis and the long transverse is the major axis.
Figure 2.11: Microstructure orientation [10]
Crack growth occurs through the microstructure of the material in three distinct modes or micromechanisms: ductile fracture, cleavage fracture, and intergranular fracture, as illustrated in
Fig. 2.12.
(a) Ductile fracture (b) Cleavage (c) Intergranular fracture
Figure 2.12: Three micromechanisms of fracture in metals [12]
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Ductile fracture is the result of void nucleation, growth, and coalescence caused by reoccurring plastic strain occurring at the crack tip, as shown in Fig. 2.13. Ductile fracture often takes on the form of a zig-zag pattern, where voids coalesce as a result of internal shear forces [12].
(a) Initial state (b) Void growth at the crack tip (c) Coalescence of voids with crack tip
Figure 2.13: Mechanism for ductile crack growth [12]
Cleavage fracture, also called intragranular fracture, occurs when a crack path cuts through individual grains and typically result in macroscopic straight cracks in the plane perpendicular to the loading direction. Since cleavage fracture involves breaking bonds, the local stress must be sufficient to overcome the cohesive strength of the material. The angle of cleavage fracture through each grain changes as the crack moves and crosses boundaries of grains, as shown in Fig.
2.14.
Figure 2.14: River patterns form as a result of a cleavage crack crossing a twist boundary between grains [12]
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Intergranular cracking occurs when a crack path follows the grain boundary of the microstructure and passes around the individual grains. Intergranular fracture is not typically a fracture mechanism for ductile metals, which usually fail by a coalescence of voids. There are however, certain situations that can lead to cracking along the grain boundary, such as: precipitation of a
brittle phase on the grain boundary, hydrogen embrittlement, intergranular corrosion and grain
boundary cavitation, and cracking at high temperatures [12].
In metallic alloys, grains typically have higher fracture toughness than the grain
boundaries, It is preferable at the material macroscopic level, to orient the long grain direction in-
line with the loading direction to promote intragranular growth. Despite orienting the
microstructure with the direction of loading, crack fronts may still propagate in unexpected
directions as they traverse through the microstructure. There are weak planar grain boundaries
that may interact with the crack tip and cause it to deviate from the primary crack path, as
illustrated in Fig. 2.15.
Figure 2.15: Schematic illustration of crack interactions with weak planar grain boundaries: (a) L-S/T-S orientations, ‘crack arrest’, (b) S-L/S-T orientations, ‘crack delamination/splitting’, and (c) L-T/T-L orientations, ‘crack divider’ [9]
This project focuses primarily on fatigue branching mechanisms that manifest from
exploiting one or more of these weak planar grain boundary interactions, causing the crack to
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deviate from the primary crack path. Crack branching is defined as crack growth occurring in multiple directions at the same time. Branching occurs in three configurations that are dependent on loading direction and the primary crack direction, as shown in Figs. 2.15 and 2.16.
Figure 2.16: Crack branching configurations with respect to the rolling axes [8]
Crack turning is defined as a gradual change in the direction of the primary crack. Crack deviation occurs when the crack growth continues in a direction and deviates from the expected crack path, i.e., the plane perpendicular to the loading direction.
These branching mechanisms are well documented in high strength 2xxx and 7xxx series aluminum alloys, which are prone to intergranular crack propagation [9]. Branching is most prominent under mode I loading in L-S and T-S orientations, particularly the crack arrest/blunting
(L-S/T-S) and the crack splitting/delamination (S-T/S-L) branching configurations [9]. In L-S and
T-S configurations, delaminations can develop across the grain boundaries that are normal to and just ahead of the approaching primary crack tip, and can give the appearance of mini crack arresters [8]. They are thus termed the “arrestor” or “blunting” branching configuration, due to the increased apparent macroscopic toughness inferred of the main crack front, introduced by this
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phenomena. A similar increase of apparent macroscopic toughness manifests in the L-T and T-L
“divider” configuration. The opposite is true of the “splitting” configuration, found in S-L and S-
T orientations, which has been shown to reduce the marcoscopic toughness [6][8][9][10][20].
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CHAPTER III
TESTING PROCEDURES
The purpose of this chapter is to discuss testing standards, equipment and procedures used in the process of conducting fatigue crack growth testing on Al 7085-T7452 specimens.
3.1 Fatigue Specimens Details
Fatigue specimens were fabricated from two different forms of Al 7085-T7452. The first
form of specimens were extracted from a parent material of a large hand forged monolithic
unitized aircraft structural member, and grain orientations were extracted with respect to the
original forging. The second form of specimens were extracted from an aircraft monolithic
unitized bulkhead that had undergone a die forging process (Al 7085-T7452, treated post-forging with ALCOA SSR™ residual stress relief), grain orientations were extracted with respect to the original forging. The majority of the specimens consisted of hand forged material, due to the limited supply of material that could be extracted from the die forged parent component. Two test specimen geometries, Middle-crack Tension (M(T)) and Compact Tension (C(T)), were used for characterizing the fatigue crack growth rate properties in Al 7085-T7452.
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X X – X X – X X – X Replicate Load Ratio Material Form Material Specimen Type Specimen Grain Orientation
Material Coded Grain Coded Coded Coded Specimen Coded Load Ratio Replicate Type Value Form Value Orientation Value Value Value Hand Forged H L-S LS 0.1 01 1 A M(T) M Die Forged D T-S TS 0.5 05 2 B C(T) C L-T LT 0.7 07 3 C S-L SL -0.1 11 1 N/A S-T ST -0.5 15 2 _02 -0.9 19 3 _03
Figure 3.1: Specimen naming convention
3.1.1 M(T) Specimens
For the purpose of this test, there were a total of eighteen M(T) specimens, of which fifteen were hand forged and three were die forged. Hand forged specimens were machined into
4.00” wide M(T) specimens by ALCOA and arrived with a small hole at the location of the started notch, as shown in Fig. 3.2. The die forged material was received from foundry in the form of rough cut sections with the grain orientations marked. The rough cut slabs of die forged material were machined to 4.00” wide M(T) specimen dimensions to match the hand forged specimens. Images of the die forged material, prior to machining, can be seen in Figs. B.1-B.3.
M(T) specimens required a starter notch machined with wire EDM and tapped holes placed for mounting knife edges Clip On Displacement (COD) gages. The starter notches were cut using wire Electrical Discharge Machining (EDM), using a 0.006” diameter wire at low power settings to cut both sides of the through thickness hole to a length of 0.020”, as shown in Fig. 3.3. C(T) specimens were extracted from the fractured M(T) specimens. M(T) fracture surfaces were
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photographed, cut-off and retained for later examination, and the remainder of the material from the M(T) specimen was used to machine C(T) specimens.
Figure 3.2: M(T) specimen with through thickness center hole
Figure 3.3: Notched hole diagram for M(T) specimens (X.XXX = ± 0.005”)
3.1.2 C(T) Specimens
For the purpose of this test, there were a total of twenty-nine C(T) specimens extracted from M(T)s, twenty-three from hand forged and six from die forged specimens. C(T) specimen geometry is shown in Fig. 3.4. Various examples of C(T) extraction orientations are illustrated in
Fig. 3.5. M(T) fracture surfaces were photographed, cut-off and retained for later examination, and the remainder of the material from the M(T) specimen was used to machine C(T) specimens.
Of the extracted C(T)s, six hand forged and three die forged were set aside as specimens for conducting KR curve determination testing in accordance with ASTM standards at a later date
[21]. KR curve testing is used as an alternate method for finding a material’s resistance to fracture,
25
which is not limited by the thickness requirements of traditional fracture toughness test methods.
Of the remaining twenty C(T)s, seventeen were hand forged and three were die forged. The origin
of parent M(T) specimens were tracked for all extracted C(T) specimens for comparison at a later
date, if necessary.
Figure 3.4: Drawing of 3W C(T) specimen with starter notch
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Figure 3.5: Diagram of C(T) specimen extraction orientations from parent M(T) material
3.1.3 Polishing Procedure
To ensure a smooth and uniform finish of the specimen surface, over the area where the cracking is expected to occur, each specimen was polished. This will reduce the likelihood that
27
surface flaws from the machining process will influence the path the crack to change its path due to stress concentrations. The polishing provides the consistent material thickness throughout the
test area and allows for a more precise visual crack measurements to be taken. The mirror like
surface provides a means to observe ductile fracture on the surface through the distortion of
reflections.
Both types of fatigue specimens were polished using the same procedure, the only
difference being the location which was polished. The process began with 600 grit sanding paper
and a wet sanding polishing technique, with isopropanol alcohol as the liquid medium, in the
direction perpendicular to the EDM notch and the intended cracking direction. This process was
continued with subsequent 800/1000/1200/2000 grit sanding papers, using the same wet sanding
technique. A manual sanding technique was chosen over powered mechanical means, to avoid
any damage that could result from excessive heat buildup. The final step of the procedure was
using Never-Dull polishing compound until a surface roughness of 1.9 Ra was achieved.
Polishing was completed for both sides of each specimen.
Figure 3.6: Polishing region for M(T) specimens
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Figure 3.7: Polishing region for C(T) specimens
3.2 Testing Standards
The purpose of this section is to provide a brief of overview of the automated crack
length measurement method used during testing, as well as, the testing validity criteria outlined in
the testing standard. The primary document outlining fatigue crack growth testing is ASTM
testing standard E647-15e1, which was followed for all testing procedures, data reduction
techniques, and results contained in this report [16].
3.2.1 Compliance Based Crack Calculation Method
The compliance based method for monitoring crack length is an automated approach that utilizes high speed data acquisition and processing systems. This method uses compliance relationship between v, the crack opening displacement and P, the force applied to the test specimen. Further compliance relationships and calculation techniques are explained in section
2.1.3. Compliance based crack length calculations use normalized values of compliance and crack length that have been analytically derived for a number of standard specimen geometries. Values are normalized using specimen thickness, B, and elastic modulus, E.
The relationships for calculating crack length use dimensionless values of compliance,
EvB/P (or ECB where C is v/P) and normalized crack length, a/W. E is the elastic modulus, B is
29
the thickness of the specimen, a is the crack length, and W is the width of the specimen. Further nomenclature relating to specimen geometries are given in Figs. 3.8 and 3.9. It is possible to empirically develop a compliance relationship for any specimen type used in fatigue crack growth testing, aside from the analytically derived ones given in the testing standard [16]. The equations governing these relationships for the M(T) and C(T) geometries are explained in detail in section
4.1.
a = crack length B = specimen thickness W = specimen width C = compliance 𝑣𝑣⁄ E = Young’s𝑃𝑃 modulus y = half gage length ɳ = 2𝑦𝑦 = nondimensional gage length �𝑊𝑊
Figure 3.8: M(T) specimen dimension nomenclature [16]
Figure 3.9: C(T) specimen nomenclature
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3.2.2 Validity Criteria
This section focuses on the validity criteria that will used during testing. All validity
requirements were derived from the ASTM E647 testing standard for fatigue crack growth. The
standard specifies criteria that applies to all specimen types, as well as, specimen specific validity
requirements. When discussing validity requirements, it is important to mention that M(T)
specimens are subjected to additional requirements. At each visual crack length measurement, a
total of four measurements are taken for M(T) specimens, two on the front surface and two on the
back. C(T) specimen only require two crack tip measurements, one on the front surface and one
on the back.
Figure 3.10: Out-of-plane cracking limits [16]
As a general requirement, data becomes invalid if the crack deviates more than ± 20° from the plane of symmetry for a distance of 0.1W or greater at any point during the test, as seen in Fig. 3.10. In addition, if the crack deviates more than 10° during testing, the crack turning must be reported. Crack symmetry must also be maintained to ensure the quality of the fatigue data. All specimen geometries must maintain crack symmetry about the mid-plane of the thickness, located at B/2. If the crack sizes measured on the front and back surfaces differ by more than 0.25B. For
M(T) specimens, the average of the front M(T) specimens also require crack symmetry about the mid-plane in the width direction, located at the specimen centerline (W/2). The data is invalid for an M(T) specimen if the average crack lengths, about the centerline, differ by more than 0.025B.
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The cracks for each side should be the average of the cracks on the front and back surface, i.e.,
the average of the left front and left rear compared to the average of the right front and right rear
[16].
3.3 Test Setup
This section outlines the components that made up the test setup for all results presented
in this report. All tests were conducted in Air Force Research Laboratory’s (AFRL) FIRST Lab at
Wright-Patterson Air Force Base. There was a desire to automate the testing as much as possible
and eliminate the number of visual measurements taken per fatigue specimen. The compliance
crack length calculation by the crack opening displacement method, through the use of
extensometers, was determined as the best approach for this testing. To automate the fatigue
crack growth testing procedure, an existing crack tracking program named ACORN, was received
from the Materials Directorate from AFRL. This program was debugged and modified to
accommodate negative load ratio testing to increase functionality and improve its robustness.
ACORN was verified to conform to all requirements set forth in the testing standard [16].
ACRON crack tracking program was used as an external controller for the fatigue testing,
performed data logging, and provided a closed loop feedback controller signal to the load frame.
The ACORN software is described in further detail throughout section 3.3.
3.3.1 Load Frame and Control Systems
A 55 kip MTS load frame was used for testing all M(T) fatigue specimens and a 22 kip
MTS load frame was used for testing all C(T) fatigue specimens. MTS Station Manager software
was used for load frame control, sensor management, calibration, signal management, overload
protection, active interlock control, and external command control. The MTS Station Manager
software was used to tune the test frames for the desired load ranges to more responsively hit the
desired force commands and reduce any over or under-shooting dynamic responses.
3.3.2 Sensors, External Command and Data Acquisition
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Two identical COD gages were used for testing M(T) specimens, MTS 632.05E-60 COD gages with a fullscale range of ±0.020” and a 1.040” gage length. Both gages were calibrated
using MTS Station Manager, according to manufacturer’s instructions, using a MTS dial-type
displacement gage calibrator and the provided knife edge alignment/mounting fixture. COD
gages are spring loaded and attach to the outer surface of the specimen, spanning the expected
cracking plane, via metallic knife edges. One COD gage was mounted on each side of the M(T)
specimen on knife edges, so to be centered about the starter notch. Knife edges were fastened to
the specimen using four #4-40 tapped holes thru thickness, centered about the notched hole and centerline of the M(T) specimens. Refer to Fig. A.1 for MTS COD data sheet with dimensions and spacing of tapped holes. Both COD gages were input signals to the MTS Station Manager where the mathematical average of the two displacements was taken and the resulting calculated value and sent as an output parameter to ACORN. This was determined as the best practice to capture the opening displacement of the crack in the presence of uneven crack lengths. It is also noted that the displacement parameter v, outlined in the testing standard [16], is a single value and
as a best practice, the average of the two displacements was used. The difference between gages
was monitored periodically throughout testing each M(T) specimens to ensure the fidelity of the
practice.
For the testing of C(T) fatigue specimens, a single clip-on COD gage was used, MTS
632.02E-20 COD gage with fullscale range of +0.100” / -0.05” and a gage length of 0.200”. The
gage was calibrated in the same manner as the gages for the M(T) specimens. The gage was
clipped onto the sharp edges that were cut into the C(T) specimen at the opening of the starter
notch using wire EDM, as illustrated in Fig. 3.4. COD measurement was outputted to ACORN in
the same manner as the averaged signal for the M(T) specimens.
Both the 55 kip and 22 kip load frames had integrated load cells to acquire force data and
head displacement sensors for measuring the location of the hydraulic head. The force signal was
outputted to ACORN for calculations. Upper and lower force thresholds were set in MTS Station
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Manager to avoid any unintentional overloads that could damage the specimen. If either of the force thresholds were achieved, the force would immediately ramp down to zero pounds and hold until reset. The displacement of the hydraulic head was also used as an interrupt and in the case where the displacement was above the threshold, as would be the case at the final failure of a specimen, the interlock feature would be triggered and the hydraulics would be disabled.
3.3.3 ACORN Fatigue Crack Growth Software
The ACORN crack tracking program is was designed and operated using National
Instruments LabView. ACORN uses the specimen dimensions that the user inputs and the cycle- by-cycle force and COD data to solve the appropriate equations in ASTM E647 [16], in real-time.
The operator must manually enter the lbf/volt or inches/volt for the associated load and displacement signals to mirror those setup in the MTS Station Manager. ACORN has a real-time load compensator that can be used to adjust the commanded load signal to achieve the target load, and the operator can set the max error threshold to begin compensating and the speed to execute the correction. This ensures that the target Pmax and Pmin are within the desired percent error
bounds, by using a feedback loop for the outputted load command waveform and reading the
analog signal for comparison to the force waveform from the MTS Station Manager.
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Figure 3.11: ACORN main dashboard, load vs. displacement plot
ACORN uses the user defined bounds of percent of load range, between which, it calculates the slope of the force-displacement curve. It calculates the slope by using a best-fit line through the points of the specified range. This slope is referred to as open-crack compliance, Co,
and is the compliance value that in used to calculate crack length. It is noted from section 2.1.3,
that the lower bound must be above the crack opening force, Pop, to avoid capturing crack closure effects and for the compliance to be accurately calculated, see Fig. 2.7. The upper and lower bounds the compliance calculation are represented on the force vs. displacement plot as green horizontal lines in Fig. 3.11.
The operator can specify the number of cycles over which to average the open compliance value. This can be useful to avoid the calculated crack length from oscillating ±
0.001” at smaller crack lengths, where the crack opening displacement is a smaller portion of the
COD sensors’ full-range displacement is used. A value of fifteen or twenty cycles was found to be an appropriate number of cycles to use for this setting.
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At the start of testing a new specimen, the operator can use the integrated effective
Young’s modulus (Eeff) calculator to determine an approximation for Young’s modulus to use
during testing. The iterative modulus calculation method is expanded upon in section 4.2. The Eeff calculator utilities an iterative solver that uses an initial guess for E and the user inputted actual initial crack length (measured length of starter notch, an), and begins cycling the specimen to the target loads to obtain open-crack compliance, Co. The solver then uses the initial guess of
Young’s modulus (Eguess) and opening compliance to calculate a crack length, compares it to the
actual crack length, adjusts Eguess and continues iterating until its find the Eguess that results in the
actual crack length. The final value of Eguess is the Eeff for that particular specimen and becomes a fixed value that will be used in all further calculations for the specimen. ACORN simultaneously records the initial open compliance value Co as Coi, for later use and likewise calculates the initial
calculated secant compliance value Cs as Csi.
ACORN exports data at every crack length interval, Δa, that is requested by the operator.
The data at each Δa increment is logged in two different data types: calculated and raw. The calculated data from each cycle gets added to the text file of existing data points and the raw data is saved to its own unique data file. The calculated data that is saved include values such as: data point number, cycle count, crack length, Pmax, Pmin, ΔK, and da/dN. The raw data is saved to a file named after the corresponding data point number, which contains a single cycle (loading and unloading) of force and crack opening displacement data points, of the cycle when the Δa increment triggered the data export. This raw data can be useful in post processing for verification and calculating additional useful parameters ACORN has a built in error threshold in the compliance calculator, which automatically aborts the test if the best-fit line for the data points if, the coefficient of determination, R2 < 0.96.
3.3.4 Test Fixtures and Measuring Instruments
M(T) specimens were loaded into the 4” MTS wedge grips of the 55 kip load frame, with
hydraulic controls set to ~3500 psi. M(T) specimens were centered with the wedge grips and
36
aligned in the longitudinal direction. M(T) specimens tested at negative load ratios of R = -0.5 and R = -0.9 required additional buckling guide fixture to prevent the 0.25” thick specimen from buckling at high compressive loads. A custom “free-floating” buckling guide system was designed for these tests. It consisted of two machined 0.5” steel plates separated by a 3D printed spacer made from VeroWhite® material, to allow for a small air gap around specimen. Steel buckling guide plates were lined on the inward facing side with polytetrafluoroethylene (PTFE)
adhesive tape to reduce friction between the guide and the M(T) specimen, as well as, to reduce
the risk of scratching the polished aluminum surface. The spacers were sandwiched between the
steel plates and secured using a row of fasteners on each side of the guide. Brackets were
fabricated to bolt onto the MTS wedge clamps to keep the buckling guide in place during testing.
A 0.25” thick strip of rubber was placed between the brackets and the bottoms of the steel plates
to dampen the oscillating motion of the buckling guide and eliminate hard contact.
Figure 3.12: Orthogonal view of buckling guide mounted on M(T) specimen
37
Figure 3.13: Buckling guide on M(T) specimen with mounted COD gages during test
C(T) specimens were loaded into a clevis and pin fixture and tested on a 22 kip load frame. Clevis and pin fixture assembly was designed according to ASTM E647 [16] specifications for a 3W C(T) fatigue test specimen, as seen in Fig. 3.14. Threaded loading rods were manufactured from 4” long 7/8”-14 UNC bolts, modified by removing the head from the shank. MTS 2” v-shaped wedge grips were used to grip along 2” of the bolt shank, clevises were then threaded on and secured in place with a jam nut.
38
Figure 3.14: Clevis and pin assembly for gripping C(T) specimens [16]
The tolerance stack up between the clevis, pin and C(T) specimens prevents the specimen from
accidently being loaded in compression. The tips the upper and lower clevis touch before the
specimen can be loaded, preventing potential damage when load frame ramps to 0 lbf hold condition.
39
Figure 3.15: 22 kip MTS load frame pictured during fatigue test of C(T) specimen
Figure 3.16: C(T) specimen loaded in test fixture. COD gage mounted at the mouth of starter notch (left) and taking initial measurements at starter notch with travelling microscopes (right).
40
Visual crack length measurements were taken periodically for all specimens during testing using two travelling microscopes, one to track crack growth on the front face and the other for the back. Microscopes were mounted on digital Vernier slides and attached to the respective load frame using laboratory clamps and booms. Microscope position along slides were adjusted by a worm screw mechanism. All measurements were taken by approaching from the same direction to avoid measurement error resulting backlash of the worm screw.
3.4 Testing Methods
This section provides an overview of the testing practices and procedures used during the
duration of fatigue testing.
3.4.1 Precracking
M(T) specimens were precracked using constant load ratio and maintaining constant Kmax
≈ 9 ksi√in through load shedding, by incrementally decreasing the load amplitude according to
E647 [16], to a crack length (2a) of 0.5”.The remainder of the testing was conducted using constant amplitude loading (constant ΔP). C(T) specimens were precracked and tested using constant amplitude loading, to capture FCG data at lower Kmax values than during M(T) testing.
Pmax was selected, such that Kmax at the desired precrack length of 0.65” would be between 8.0 and 9.0 ksi√in.
3.4.2 M(T) Testing and Data Collection
Prior to loading specimens into the 55 kip load frame, six thickness measurements were
taken with a micrometer along the uncracked ligament and averaged. The specimen width was
measured in the same manner, but with Vernier calipers. Knife edges were placed on both sides
of the specimen using the provided gage length block to achieve the proper spacing and collinear
placement, then fastened into place with #4-40 cap head screws.
The specimen was guided into the load frame grips with the aid of indexing brackets to ensure proper alignment and positioned the top 1.5” of the specimen into the upper wedge grip.
The upper grip was engaged and hydraulic pressure set to 3500 psi. The head of the frame was
41
then raised or lowered to a position, such that the starter notch was vertically centered in the crosshairs of the travelling microscopes. COD gages were clipped onto knife edges, one on each side, and manually adjusted until they were centered and secured in place. The force and COD values were zeroed in MTS Station Manager with the specimen was suspended from the upper
grip. The lower head was then raised up toward the specimen until it was overlapping the
specimen by 1.5”, then the lower grip was engaged and hydraulic pressure set to 3500 psi. The
force was then set to a 0 lbf hold condition in MTS Station Manager, followed by enabling safety interlocks and setting thresholds for force and displacement parameters.
Figure 3.17: Front and side views of M(T) specimen during test
Travelling microscopes were then zeroed about the centerline of the starter notch and recorded initial starter notch lengths for each of the four crack tips (two on each face of the specimen). ACORN software was booted and initial specimen dimensional parameters, laboratory environment testing conditions, and senor parameters were entered into their appropriate fields.
42
Testing loads, frequency (10 Hz), mode, bounds for compliance measurement, crack interval, limits and error bounds were also specified in ACORN. The external command function was enabled in MTS Station Manager and load control authority was passed to external controller.
ACORN was placed in load shedding mode and triggered to stop testing once the specified precrack length was achieved. The test start command was initiated and the test ran until precrack length was achieved, at which point the lengths of all crack four crack tips were record and the test resumed. Visual crack measurements were taken periodically throughout the testing of each specimen.
Each M(T) specimen was controlled by ACORN until fracture or to the crack length where ACORN aborts the test due to compliance data correlation thresholds, whichever came first. In cases where ACORN aborted because of below threshold compliance data correlation, the
COD gages were removed and data collection ceased. The MTS Station Manager would then be
used to command the same load and frequency parameters as is ACORN, until the M(T)
specimen failed and separated into two pieces.
3.4.3 C(T) Testing and Data Collection
Prior to loading C(T) specimens into the 22 kip load frame, nine thickness measurements
were taken with a micrometer along the uncracked ligament and averaged. Due to the uniqueness
of how notch length an, is measured, from the perpendicular centerline that connects the loading
holes, it is not accurately measured using mechanical metrology instruments. A backlit
microscope equipped with a 2-axis measurement table was used. Each C(T) specimen was placed
on the table and rotated until the line connecting the center-points of both holes were parallel with
the y-axis of the table. The displacement values were zeroed at the midpoint of the aforementioned line, then proceeded to measure the dimensions of the initial notch length an, and
specimen width W.
C(T) specimens were loaded into the clevis suspended from the upper grip, by inserting
one of the hardened steel pins. The lower head of the test frame was manually raised using MTS
43
Station Manager until the clevis thru hole aligned with the lower mounting hole of the C(T) specimen, and second steel pin inserted. At this point the COD gage was clipped onto the sharp edges at the mouth of the starter notch and adjusted until centered and secured. COD gage displacement value was then zeroed within MTS Station Manager. It is worth noting, that at this point, no tension load has been applied to the specimen. The lower head displacement was slowly adjusted until the point where contact was made, the displacement was back off a few thousands of an inch, and the load cell force value was zeroed. The MTS controller was then placed in load control mode and set to 5 lbf. If a 0 lbf is commanded, the controller would cause the head
displacement to wander. This was due to the suspended nature of the specimen and the fact that a
wide range of head displacements would yield 0 lbf, between the bounds of the clevises touching and load being applied to the specimen. It was decided to have the MTS Station Manager software override the lower bound of the external controller so that the specimen always stayed in tension and avoiding a condition where the clevises touch and trigger an interlock shutdown. The
5 lbf offset of the force value would be handled by ACORN’s built-in compensator, and would adjust the commanded load signal to achieve the desired loads.
ACORN software was booted and initial parameters set, in a similar fashion to that of the
M(T) specimens. All C(T) specimens were precracked and tested with constant amplitude loading with a constant Pmax of 800 lbf. For all specimens tested at load ratio R = 0.1, Pmax = 800 lbf and
Pmin = 80 lbf and specimens tested at R = 0.5 received Pmax = 800 lbf and Pmin = 400 lbf.
The external control feature on MTS Station Manager was enabled with a 5 lbf target set point offset and load control authority was given to ACORN. The traveling microscopes were zeroed at the end of the EDM machined notch. The test start command was initiated and testing ran continuously until specimen failure or test abort triggered by ACORN for below threshold compliance data correlation, whichever occurred first. In the case where the latter occurred, C(T) specimens were taken to final fracture using the same procedure as M(T) specimens and MTS
Station Manager. Visual crack measurements were able to be taken on C(T) specimens during
44
testing. Measurements were periodically taken during the test and would be aligned with a point in time that ACORN logged a data point at the end of a crack length interval. The length to the
crack tip from the traveling microscope display, was added to the initial notch length to obtain
crack length for each visual measurement.
45
CHAPTER IV
DATA REDUCTION
Data reduction methods were derived from ASTM E647 recommendations [16]. Raw cycle data files, captured at each data point, and ACORN output files of calculated values were used in conjunction to post process the data. The approach to reducing the data into the desired components, required the raw cycle-by-cycle data points and its associated cycle count value to be exclusively used to calculate all results contained in this report. All results were generated using various MATLAB codes that were internally developed and tested by AFRL. The recalculation of ACORN results was conducted to extract additional parameters of interest that were not within the capabilities of the software. It also provided the opportunity for transparency and full-control over the equations and constraints used in compliance based crack length calculation methods.
4.1 Calculation Methods
Compliance based COD crack calculation methods were used for all crack length measurements. For the M(T) specimen geometry, crack length a, can calculated using the
following:
2𝑎𝑎 2 3 4 (17) �𝑊𝑊 = 1.06905𝑥𝑥 + 0.588106𝑥𝑥 − 1.01885𝑥𝑥 + 0.361691𝑥𝑥 where:
𝐶𝐶 ⎛− (𝐸𝐸𝐸𝐸𝐶𝐶𝑜𝑜+ ɳ)�𝐸𝐸𝐸𝐸𝐸𝐸− ɳ+𝐶𝐶1ɳ + 𝐶𝐶2ɳ 3�⎞ ⎜ � ⎟ (18) ⎜ 2.141 ⎟ 𝑥𝑥 = 1 − 𝑒𝑒⎝ ⎠ where Co is open-crack compliance and C1, C2, and C3 = 0 for the case of uniform stress
distribution where L/W = 2.0. Eqs. (17) and (18) are valid for a state of plane stress. A wide range
46
of positive and negative load ratios were used when testing M(T) specimens. Since it is not
possible to have a negative stress intensity factor, it is necessary that Pmin ≥ 0 and ΔP is calculated as:
> (19) ∆𝑃𝑃 = 𝑃𝑃𝑚𝑚𝑚𝑚𝑚𝑚 − 𝑃𝑃𝑚𝑚𝑚𝑚𝑚𝑚 for 𝑅𝑅 0
∆𝑃𝑃 = 𝑃𝑃𝑚𝑚𝑚𝑚𝑚𝑚 for 𝑅𝑅 ≤ 0 where the stress intensity range for all load ratios can be found using:
∆𝑃𝑃 𝜋𝜋𝜋𝜋 𝜋𝜋𝜋𝜋 (20) ∆𝐾𝐾 = 𝑠𝑠𝑠𝑠𝑠𝑠 𝐵𝐵 �2𝑊𝑊 � 2 � where α = 2a/W and α is the normalized crack length. This expression is accurate to within 1% for 2a/W ≤ 0.8 for M(T) specimens with clamped ends [16].
For the C(T) specimen geometry, crack length a, can calculated using the following:
( ) 𝑃𝑃 2 + 2 3 4 (21) 𝐾𝐾 = ( )3/2 0.886 + 4.64 − 13.32 + 14.72 − 5.6 𝐵𝐵∆ 𝑊𝑊 1 − 𝛼𝛼 ∆ � 𝛼𝛼 𝛼𝛼 𝛼𝛼 𝛼𝛼 � where α = a/W and α is√ the normalized𝛼𝛼 crack length; expression valid for a/W ≥ 0.2 [16]
Figure 4.1: C(T) specimen possible extensometer measurement locations [16]
𝑎𝑎 2 3 4 5 (22) = = 𝐶𝐶0 + 𝐶𝐶1𝑢𝑢𝑥𝑥 + 𝐶𝐶2𝑢𝑢𝑥𝑥 + 𝐶𝐶3𝑢𝑢𝑥𝑥 + 𝐶𝐶4𝑢𝑢𝑥𝑥 + 𝐶𝐶5𝑢𝑢𝑥𝑥 𝑊𝑊 𝛼𝛼 where the constants C0, C1, C2, C3, C4 and C5, can be found in Table 4.1, for the extensometer
measurement location V0, depicted in Fig. 4.1. And where ux is given by:
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1 −1 𝐸𝐸𝐸𝐸𝐸𝐸 2 (23) 𝑢𝑢𝑥𝑥 = + 1 �� 𝑃𝑃 � � where v/P is open-crack compliance, Co, and Eqs. (22) and (23) are valid for 0.2 ≤ a/W ≤ 0.975.
Table 4.1: Coefficients for C(T) crack calculation for possible measurement locations [16]
Meas. X/W C C C C C C Location 0 1 2 3 4 5
VX1 −0.345 1.0012 −4.9165 23.057 −323.91 1798.3 −0.345
V0 −0.250 1.0010 −4.6695 18.460 −236.82 1214.9 −0.250
V1 −0.1576 1.0008 −4.4473 15.400 −180.55 870.92 −0.1576
VLL 0 1.0002 −4.0632 11.242 −106.04 464.33 0
Crack growth rates for all specimens were calculated using the Incremental Polynomial
Method for calculating da/dN, as outlined in ASTM E647 Appendix (X1) [16].
4.2 Crack Length Correction Methods
A linear regression was performed on calculated crack lengths for all specimens, in accordance with the correction technique described in E647, using the initial and final visual crack lengths as endpoints. Initial visual crack measurement were taken for each specimen and the final crack length was only able to be taken if the crack tip had not deviated so much that it was no longer visible through traveling microscope. If the final visual crack length measurement
was not able to be taken, then the final calculated crack length was assumed correct and
regression bounds were initial visually measured crack length and the final calculated crack
length.
The compliance crack length calculation method was found to be less accurate at short
crack lengths in M(T) specimens. This is supported by Appendix A2 in ASTM E647-15e1, which recommends that you use a notch length 2an, of at least 0.2W (an of at least 0.1W). For the 4.00”
wide M(T) specimens used, it recommends an of at least 0.40”. It was found to be less accurate than claimed by ASTM E647. During testing, short visually measured crack lengths were not
48
tracking with the visually measured calculated crack lengths. This was noticed when the effective modulus calculation was taken at the start of a test by ACORN, as described in section 3.3.3, and was approximately 30% lower than the actual modulus of the material. This was thoroughly investigated and the root cause was identified as a mathematical sensitivity, in Eqs. (17) and (18), to the variables: E and Co. The open-crack compliance, Co, was ruled out as the cause after verifying the linearity of the COD gages, determined that the calibrated range for the COD gages was appropriate for the displacements and that it was not the result of a signal-to-noise related issue.
A relationship was found between the actual crack length obtained from the visual measurements and what the value of E, in Eq. (18), would be to obtain the correct crack length.
The values of E were calculated using the visual crack lengths for several specimens and their corresponding open-crack compliance values, calculated from the raw data files, and iteratively solving Eqs. (17) and (18) for each measurement. The calculated effective modulus Ecalc, was
found to have an increasing nonlinear relationship with the visually measured crack length avis, as
seen in Fig. 4.2. The literature modulus value for 7xxx series Aluminum is approximately 10.1
Msi.
49
11.0
10.5 )
Msi 10.0 ( calc
E 9.5
9.0
8.5
8.0
7.5 y = 2.051x3 - 8.579x2 + 12.129x + 4.198 7.0 R² = 0.976 Calculated Young’s modulus, modulus, Young’s Calculated 6.5
6.0 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8
Visually measured crack length, avis (in.) Figure 4.2: Sensitivity relationship identified between visual crack lengths and calculated effective modulus for M(T) specimen geometry.
The identification of the existence and strong correlation of the relationship between modulus and crack length, associated with Eqs. (17) and (18), provided sufficient justification to
use calculated effective modulus values Ecalc, as a replacement for E, as a means to correct the crack lengths calculations for M(T) specimens in addition to the linear regression correction
technique. The modulus correction was implemented by iteratively solving for Ecalc at each data point associated with a visual crack length measurement, then used a linear spacing technique to obtain effective modulus values for the data points that occurred between the visual crack length measurements.
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CHAPTER V
RESULTS
The purpose of this chapter is to report the results of post processed fatigue crack growth rate data and illustrate trends discovered between microstructure orientation, load ratio, and specimen type. Results for crack turning, branching, and crack deviation are summarized for each specimen tested and reported with corresponding Kmax values at which minor and major deviations occurred, Kmax-dev. For the purpose of this report, all values of stress intensity factors
are expressed in units of ksi√in. Reported values of ΔK will refer to full-range applied stress
intensity factor and may be denoted as ΔK or ΔKapp. Values reported as ΔKeff were calculated
using the normalized ACR method, Eqs. (15) and (16). Results are presented in order of
microstructure orientation, followed by forging method and test specimen type. For crack growth
rate plots, stress intensity factor may be expressed in terms of ΔK, ΔKACR or Kmax to illustrate
various relationships.
Two metrics were established for quantifying the magnitude of crack branching and
deviation, as well as the concern that these unique fracture mechanisms create with respect to
structural integrity and unpredictability. The first metric captures the max stress intensity factor
Kmax-dev, at which branching or deviation is visible on the surface. To further clarify, the lower
bound metric, Kmax-dev (Minor), are reported when these branching mechanisms are visible with the naked eye, although small branches were observed at shorter crack length when viewing under magnification. The upper bound metric, Kmax-dev (Major), is reported at a point when the
branching crack tips are 2 or more in number over a crack length range of 0.200” and/or longer
than 0.100” in length. The upper limit is typically visible in growth rate plots as either a sharp
51
drop-off in da/dN or the origin at which widening of scatter occurs. These sudden changes are indicators that the energy driving crack growth is being diverted to multiple crack tips and the
point at which the data becomes invalidated for current fatigue and fracture testing methods and
standards.
5.1 L-S and S-L Orientations
This section contains the results for all test specimens with L-S and S-L microstructure orientations. Crack branching and/or deviation were the primary fracture mechanisms of interest that were observed in the L-S material specimens. There was only one occurrence of crack turning across all L-S specimens. A summary of crack branching and turning behavior for all specimens with L-S orientation can be found in Table 5.1. Crack growth rate data for L-S and S-L orientations are shown in Figs. 5.1-5.10. The fracture surfaces of the L-S M(T) specimens are given in Fig. 5.11. The corresponding crack lengths for the Kmax values of Kmax-dev (Minor), Kmax-dev
(Major), and starting point of the sinusoidal behavior in the crack growth rate in Table 5.1, were mapped onto the fracture surfaces of the L-S M(T) specimens, as seen in Fig. 5.12.
52
Table 5.1: Summary of crack branching and turning results in L-S orientation
Crack Start of K K Specimen Crack Deviation max-dev max-dev Sinusoidal Minor Major Notes ID Turning or Behavior (ksi√in) (ksi√in) Branching (ksi√in)
INVALID due to MH-LS-01 - - - - - overload during precracking
Asymmetric @ MH-LS-01_02 N Y 20.9 25.7 14.3 Kmax = 17 ksi√in MH-LS-05 N Y 20.9 27.7 11.0 MH-LS-07 N Y 20.5 29.5 9.9 MH-LS-11 N Y 17.2 24.0 11.5 MH-LS-15 N Y 22.0 30.2 12.7 MH-LS-19 N Y 20.7 27.0 11.8 CH-LS-01-A N Y 17.6 22.6 - CH-LS-01-B N Y 18.1 23.6 - CH-LS-01-C N Y - 21.7 - CH-LS-05-A N Y 23.1 26.6 - CH-LS-05-B N Y 17.9 22.3 - CH-LS-05-C N Y 21.6 26.5 - MD-LS-01 Y Y 15.3 20.0 11.2 CD-LS-01 N Y 26.1 33.7 -
53
1.0E-04 MD-LS-01 MH-LS-01_02 MH-LS-05 MH-LS-07 MH-LS-11 MH-LS-15 MH-LS-19 1.0E-05 (in./cycle) dN da/ 1.0E-06
1.0E-07 1 10 100 ΔKACR (ksi√in.)
Figure 5.1: Growth rate plot of all L-S M(T) specimens f(ΔKACR)
1.0E-04 MD-LS-01 MH-LS-01_02 MH-LS-05 MH-LS-07 MH-LS-11 1.0E-05 MH-LS-15 MH-LS-19 (in./cycle) dN da/ 1.0E-06
1.0E-07 1 10 100 ΔK (ksi√in.) Figure 5.2: Growth rate plot of all L-S M(T) specimens f(ΔK)
54
1.0E-04 MD-LS-01 MH-LS-01_02 MH-LS-05 MH-LS-07 MH-LS-11 MH-LS-15 1.0E-05 MH-LS-19 (in./cycle) dN da/ 1.0E-06
1.0E-07 1 10 100 Kmax (ksi√in.)
Figure 5.3: Growth rate plot of all L-S M(T) specimens f(Kmax)
1.0E-04 CH-LS-01-A CH-LS-01-B CH-LS-01-C CD-LS-01 CH-LS-05-A CH-LS-05-B CH-LS-05-C 1.0E-05 CH-SL-01-A CH-SL-01-B (in./cycle) dN da/ 1.0E-06 Stunted growth ΔKACR ~12 ksi√in.
1.0E-07 1 10 100 ΔKACR (ksi√in.)
Figure 5.4: Growth rate plot of L-S and S-L C(T) specimens f(ΔKACR)
55
1.0E-04 CH-LS-01-A CH-LS-01-B CH-LS-01-C CD-LS-01 CH-LS-05-A CH-LS-05-B CH-LS-05-C 1.0E-05 CH-SL-01-A CH-SL-01-B (in./cycle) dN
da/ 1.0E-06
1.0E-07 1 10 100 ΔK (ksi√in.) Figure 5.5: Growth rate plot of L-S and S-L C(T) specimens f(ΔK)
1.0E-04 CH-LS-01-A CH-LS-01-B CH-LS-01-C CD-LS-01 CH-LS-05-A CH-LS-05-B 1.0E-05 CH-LS-05-C (in./cycle) dN da/ 1.0E-06
1.0E-07 1 10 100
Kmax (ksi√in.)
Figure 5.6: Growth rate plot of L-S C(T) specimens f(Kmax)
56
5.0E-05 MD-LS-01 MH-LS-01_02 MH-LS-05 MH-LS-07 MH-LS-11 MH-LS-15 MH-LS-19
5.0E-06 (in./cycle) dN da/
5.0E-07 5 10 15 20 25 30 ΔK (ksi√in.) Figure 5.7: Sinusoidal pattern in growth rate as f(ΔK) in L-S orientation for M(T) specimens of varying load ratios
5.0E-05 MD-LS-01 MH-LS-01_02 MH-LS-05 MH-LS-07 MH-LS-11 MH-LS-15 MH-LS-19
5.0E-06 (in./cycle) dN da/
5.0E-07 10 12 14 16 18 20 22 24 26 28 30 Kmax (ksi√in.)
Figure 5.8: Sinusoidal pattern in growth rate as f(Kmax) in L-S orientation for M(T) specimens of varying load ratios
57
5.0E-05
5.0E-06 (in./cycle) dN da/ CH-LS-01-A CH-LS-01-B CH-LS-01-C CD-LS-01 CH-LS-05-A CH-LS-05-B CH-LS-05-C 5.0E-07 5 7 9 11 13 15 17 19 21 23 25 ΔK (ksi√in.) Figure 5.9: Sinusoidal pattern in growth rate as f(ΔK) in L-S orientation for C(T) specimens of varying load ratios
5.0E-05
5.0E-06 (in./cycle) dN da/ CH-LS-01-A CH-LS-01-B CH-LS-01-C CD-LS-01 CH-LS-05-A CH-LS-05-B CH-LS-05-C 5.0E-07 10 12 14 16 18 20 22 24 26 28 30 Kmax (ksi√in.)
Figure 5.10: Sinusoidal pattern in growth rate as f(Kmax) in L-S orientation for C(T) specimens of varying load ratios
58
Hand Forged 0.50” L-S R = 0.7
Hand Forged 0.50” L-S R = 0.5
Hand Forged 0.50” L-S R = 0.1
Hand Forged 0.50” L-S R = -0.1
Hand Forged 0.50” L-S R = -0.5
Hand Forged 0.50” L-S R = -0.9
Die Forged 0.50” L-S R = 0.1
Die Forged 0.50” L-T R = 0.1
Figure 5.11: Fracture surfaces of L-S and L-T M(T) specimens
59
Hand Forged 0.50” L-S R = 0.7
Hand Forged 0.50” L-S R = 0.5
Hand Forged 0.50” L-S R = 0.1
Hand Forged 0.50” L-S R = -0.1
Hand Forged 0.50” L-S R = -0.5
Hand Forged 0.50” L-S R = -0.9
Die Forged 0.50” L-S R = 0.1
Die Forged 0.50” L-T R = 0.1
K (Minor) K (Major) Start of Sinusoidal Behavior max-dev max-dev Figure 5.12: Fracture surfaces of L-S and L-T M(T) specimens marked overlaid with locations of values: Kmax-dev (Minor), Kmax-dev (Major), and the start of sinusoidal behavior in the growth rate plot
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5.2 T-S and S-T Orientations
This section contains the results for all test specimens with T-S and S-T microstructure orientations. A summary of crack branching and turning behavior for all specimens with T-S orientation can be found in Table 5.2. Crack growth rate data for L-S and S-L orientations are shown in Figs. 5.13-5.19. The fracture surfaces of the T-S M(T) specimens are given in Fig. 5.20.
The corresponding crack lengths for the Kmax values of Kmax-dev (Minor), Kmax-dev (Major), and starting point of the sinusoidal behavior in the crack growth rate in Table 5.2, were mapped onto the fracture surfaces of the T-S M(T) specimens, as seen in Fig. 5.21.
It should be noted, that all hand forged C(T) type specimens for the T-S orientation experienced crack turning at some point during testing, however the majority exhibited curving soon after precracking. Crack curvature correction techniques, such as those introduced by Forth
[22], were not implemented in the post processing procedure due to the angle of out-of-plane growth and the rapid transition from pure mode I loading to mode II dominated mixed mode loading. ASTM E647 does not recommend using C(T) specimens for materials with highly anisotropic fatigue and fracture properties [16] and studies have demonstrated the amplification effect of positive T-stress on crack path deviation for C(T) specimens in mode I loading, particularly in anisotropic materials [8][23][24]. Kmax values reported in the notes column of
Table 5.2, are the stress intensity at which ASTM E647 specifies as the invalid criteria of for
deviation angles θ > 20°, for a crack length L ≥ 0.1W, see Fig. 3.10. Significant branching was in observed in C(T) specimens for R = 0.1 and R = 0.5 load ratios, before severe crack turning occurred.
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Table 5.2: Summary of crack branching and turning results in T-S orientation
Crack Start of K K Specimen Crack Deviation max-dev max-dev Sinusoidal Minor Major Notes ID Turning or Behavior (ksi√in) (ksi√in) Branching (ksi√in)
10+ branches on back MH-TS-01 Y Y 14.6 17.8 10.4 face alone
7+ branches on back MH-TS-05 Y Y 15.2 19.0 10.3 face alone MH-TS-07 N Y 22.7 27.3 20.3 MH-TS-11 N Y 13.9 22.3 9.2
INVALID due to MH-TS-15 - - - - - asymmetry during precracking MH-TS-15_02 N Y 18.9 24.6 9.2 MH-TS-15_03 N Y 18.8 22.6 9.2 MH-TS-19 N Y 17.2 20.9 8.45
Severe crack turning CH-TS-01-A Y Y 13.4 - - @ Kmax = 18.1 ksi√in Severe crack turning CH-TS-01-B Y N - - - @ Kmax = 19.5 ksi√in Severe crack turning CH-TS-01-C Y Y 12.3 12.3 - @ Kmax = 14.7 ksi√in Severe crack turning CH-TS-05-A Y Y 10.9 12.6 - @ Kmax = 14.9 ksi√in Severe crack turning CH-TS-05-B Y Y 11.1 - - @ Kmax = 13.7 ksi√in Severe crack turning CH-TS-05-C Y N - - - @ Kmax = 13.6 ksi√in 7+ branches on back MD-TS-01 N Y 14.7 18.5 11.0 face alone
Shear lips and canted CD-TS-01 Y Y 19.3 - - fracture surface post branching
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1.0E-04 MD-TS-01 MH-TS-01 MH-TS-05 MH-TS-07 MH-TS-11 MH-TS-15_02 1.0E-05 MH-TS-15_03 MH-TS-19 (in./cycle) dN
da/ 1.0E-06
1.0E-07 1 10 100 ΔKACR (ksi√in.)
Figure 5.13: Growth rate plot of all T-S M(T) specimens f(ΔKACR)
The da/dN vs. ΔKACR plot for T-S M(T)s, Fig. 5.13, depicts two distinct groups, each containing
specimens that share growth rate trends. The upper group of T-S M(T) specimens in Fig. 5.13,
consists of die forged of R = 0.1 and hand forged of R = -0.5 and R = -0.9. This group of specimens share a similar growth rate and a distinct trend as a function of ΔKACR. The lower
group consists of hand forged T-S specimens, with load ratios of R = -0.1, R = 0.1, R = 0.5, and
R = 0.7.
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1.0E-04 MD-TS-01 MH-TS-01 MH-TS-05 MH-TS-07 MH-TS-11 MH-TS-15_02 1.0E-05 MH-TS-15_03 MH-TS-19 (in./cycle) dN da/ 1.0E-06
1.0E-07 1 10 100 ΔK (ksi√in.) Figure 5.14: Growth rate plot of all T-S M(T) specimens f(ΔK)
1.0E-04 MD-TS-01 MH-TS-01 MH-TS-05 MH-TS-07 MH-TS-11 MH-TS-15_02 1.0E-05 MH-TS-15_03 MH-TS-19 (in./cycle) dN da/ 1.0E-06
1.0E-07 1 10 100 Kmax (ksi√in.)
Figure 5.15: Growth rate plot of T-S M(T) specimens f(Kmax)
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CD-TS-01 1.0E-04 CH-TS-01-A CH-TS-01-B CH-TS-01-C CH-TS-05-A CH-TS-05-B 1.0E-05 CH-TS-05-C (in./cycle) dN da/ 1.0E-06
1.0E-07 1 10 100 ΔKACR (ksi√in.)
Figure 5.16: Growth rate plot of T-S C(T) specimens f(ΔKACR)
CD-TS-01 1.0E-04 CH-TS-01-A CH-TS-01-B CH-TS-01-C CH-TS-05-A CH-TS-05-B 1.0E-05 CH-TS-05-C (in./cycle) dN da/ 1.0E-06
1.0E-07 1 10 100 ΔK (ksi√in.) Figure 5.17: Growth rate plot of T-S C(T) specimens f(ΔK)
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CD-TS-01 1.0E-04 CH-TS-01-A CH-TS-01-B CH-TS-01-C CH-TS-05-A CH-TS-05-B 1.0E-05 CH-TS-05-C (in./cycle) dN da/ 1.0E-06
1.0E-07 1 10 100 Kmax (ksi√in.)
Figure 5.18: Growth rate plot of T-S C(T) specimens f(Kmax)
MD-TS-01 MH-TS-01 1.0E-04 CH-TS-01-A CH-TS-01-B CH-TS-01-C CD-TS-01 CH-ST-01-A CH-ST-01-B CH-ST-01-C (in./cycle) 1.0E-05 dN da/
1.0E-06 1 10 100 ΔKACR (ksi√in.) Figure 5.19: Comparison between T-S and S-T for R = 0.1
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Hand Forged 0.50” T-S R = 0.7
Hand Forged 0.50” T-S R = 0.5
Hand Forged 0.50” T-S R = 0.1
Hand Forged 0.50” T-S R = -0.1
Hand Forged 0.50” T-S R = -0.5
Hand Forged 0.50” T-S R = -0.5
Hand Forged 0.50” T-S R = -0.5
Hand Forged 0.50” T-S R = -0.9
Die Forged 0.50” T-S R = 0.1
Figure 5.20: Fracture surfaces of T-S M(T) specimens
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Hand Forged 0.50” T-S R = 0.7
Hand Forged 0.50” T-S R = 0.5
Hand Forged 0.50” T-S R = 0.1
Hand Forged 0.50” T-S R = -0.1
Hand Forged 0.50” T-S R = -0.5
Hand Forged 0.50” T-S R = -0.5
Hand Forged 0.50” T-S R = -0.5
Hand Forged 0.50” T-S R = -0.9
Die Forged 0.50” T-S R = 0.1
K (Minor) K (Major) Start of Sinusoidal Behavior max-dev max-dev Figure 5.21: Fracture surfaces of T-S M(T) specimens marked overlaid with locations of values: Kmax-dev (Minor), Kmax-dev (Major), and the start of sinusoidal behavior in the growth rate plot
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5.3 L-T Orientation
The fatigue data for die forged Al 7085-T7452 tested in the L-T orientation is shown in Figs.
5.22-5.24. The fracture surface of the M(T) specimen is located in the bottom of Fig. 5.11. There
was no legacy data to compare the L-T growth rate date to. This makes it difficult to ascertain whether the significant difference in growth rate at lower stress concentrations is a statistical anomaly or an artifact of an unidentified fracture mechanism. A tensile residual stress of ~2 ksi√in was found in the C(T) specimen using the ACR method, which can be seen when comparing Figs. 5.23 and 5.24. Despite the difference in growth rate at low stress intensity levels, the two curves converged at Kmax ≈ 15 ksi√in. The C(T) specimen experienced a gradual crack turning that began at Kmax ≈ 17 ksi√in on one side and on the other side, experienced branching at
Kmax ≈ 29 ksi√in.
MD-LT-01 1.0E-04 CD-LT-01 (in./cycle) 1.0E-05 dN da/
1.0E-06 1 10 100 Kmax (ksi√in.)
Figure 5.22: Growth rate plot of die forged L-T f(Kmax)
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MD-LT-01 1.0E-04 CD-LT-01 (in./cycle) 1.0E-05 dN da/
1.0E-06 1 10 100 ΔK (ksi√in.) Figure 5.23: Growth rate plot of die forged L-T f(ΔK)
MD-LT-01 1.0E-04 CD-LT-01 (in./cycle) 1.0E-05 dN da/
1.0E-06 1 10 100 ΔKACR (ksi√in.)
Figure 5.24: Growth rate plot of die forged L-T f(ΔKACR)
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CHAPTER VI
DISCUSSION AND CONCLUSIONS
6.1 Discussion
The material system, Al 7085-T7452, has exhibited unique fatigue and fracture properties
for each microstructure loading orientation tested. Aerospace Material Specifications (AMS)
provide minimum KIC fracture toughness values for hand forged and die forged Al 7085-T7452 in the L-T, T-L and S-L orientations [4][5]. The standards do not specify fracture toughness values for the L-S or T-S orientations. Test specimens in both the L-S and T-S orientations were found to exhibit subsurface damage on the interior of the specimen before showing any indication of such damage on the surface. The subsurface damage was discovered only after testing to failure and examining the fracture surfaces, as seen in Figs. 5.11 and 5.20. Branching was typically found to appear on the surface, at the point, where the subsurface damage grew through the thickness and reached the surface.
Fracture surface roughness onset and severity differ for various load ratios, as seen in
Figs. 5.11 and 5.20. The fracture surface roughness appears to be a function of ΔK and Pmin relative to Pop. Specimens that were exposed to higher positive load ratios, appear to have fracture roughness onset at larger Kmax values. The black deposits on the fracture surface, appear to be the
result of closure effects, where the fracture surfaces were repeatedly in hard contact with one
another. The specimens in Figs. 5.11 and 5.20, which were tested at a load ratio of R = 0.7, did not have any black deposits over the fracture surface. These specimens were always cycled above their crack opening force, which appears the have prevented the fracture surfaces from contacting
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or “rubbing” against each other, and further points to friction between fracture surfaces as the likely cause of these black deposits.
Figure 6.1: Sinusoidal pattern in growth rate data from Schubbe’s investigation into branching in Al 7050-T7451 [10]
Sinusoidal patterns emerged from the expected sigmoidal shape in the growth rate plots of both L-S and T-S orientations, and took on the appearance of two distinct forms. A similar sinusoidal behavior was documented in Schubbe’s study of crack branching in the L-S orientation of Al 7050-T7451 [10], as seen in Fig. 6.1. The first form, was a pattern of sinusoids, relatively small in amplitude and short in period. These smaller sinusoidal patterns in the growth rate, were often found at stress intensity levels lower than those found to exhibit crack branching or deviation. The small sinusoids point to some combination of subsurface fatigue mechanisms, not visible at the surface crack tips at the time of occurrence, as a potential cause. These appeared consistently in specimens tested at loading ratios, R = 0.5 and R = 0.7, and also in other load ratios at relatively low values of ΔK.
The second form of sinusoids, were larger in amplitude and longer in period than the first form, and were inconsistent in size and shape. These larger and inconsistent wave forms, were often found to appear in the growth rate data, at crack lengths, where one or more branches
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appeared on the specimen surface. The peak of the wave form was consistently found to occur at crack lengths corresponding to the base of a branching crack. A quick drop in growth rate followed these peaks, then continued while the crack driving force energy was being diverted to multiple crack tips. This behavior continued until the branching of at least one of the multiple crack tips retards and ceased growing. The relationship between suppressed growth rate events observed in da/dN vs. stress intensity plots, and particular instances of crack tip splitting and branching along the crack path, was observed in a die forged C(T) specimen, with an L-S orientation and load ratio R = 0.1, as illustrated in Fig. 6.2.
Figure 6.2: Correlation of abrupt change in crack growth rate events with specific occurrences of crack tip splitting and branching, illustrated on CD-LS-01. Primary crack path is from right to left.
A unique series of subsurface to surface cracking events were observed in die forged
M(T) specimen, with L-S orientation and load ratio R = 0.1. Photographs were taken periodically when visual crack length measurements were recorded. Images were time stamped and synced with data points from the raw data file. Cracks emerged from the subsurface at various points
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throughout the test and remained unconnected with adjacent crack tips for portions of or the
remainder of the test (until specimen failure). The images of the events and their corresponding
location on the fatigue plot are illustrated in Figs. 6.3-6.5. Fig. 6.3a shows the puckering of the
crack surface where a subsurface crack is about to break through from the interior of the
specimen. Fig. 6.3b pictures the subsurface crack from (a) after emerging to the surface and two
unconnected crack tips. Fig. 6.3c depicts a second crack emerged from below and behind the
crack pictured in (b). There are at the time of event (c), three unconnected crack tips.
1.00E-04
c
= 17 ~ 0.375 inch 퐾푚푎푥 푘푠𝑚𝑚 𝑚𝑚𝑚𝑚
1.00E-05 (in./cycle) dN da/ b a
= 15.1 ~ 0.375 inch = 15.6 ~ 0.375 inch _ =15.1 푚푎푥 푚푎푥 1.00E-06 퐾 퐾 𝑚𝑚푎푥 푘푠𝑚𝑚 𝑚𝑚𝑚𝑚 퐾 푘푠𝑚𝑚 𝑚𝑚𝑚𝑚 1 푘푠𝑚𝑚√𝑚𝑚𝑚𝑚 10 100 ΔK (ksi√in.) Figure 6.3: Subsurface-to-surface cracking events (a),(b), and (c) impact growth rate for die forged MD-LS-01
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1.00E-04
e
= 20 ~ 0.375 inch 퐾푚푎푥 푘푠𝑚𝑚 𝑚𝑚𝑚𝑚
1.00E-05 (in./cycle) dN da/
d f
= 18.3 = 21.2 ~_ 0.375 inch=15.1 ~ 0.375 inch 푚푎푥 푚푎푥 1.00E-06 퐾 𝑚𝑚푎푥 퐾 푘푠𝑚𝑚 𝑚𝑚𝑚𝑚 퐾 푘푠𝑚𝑚 𝑚𝑚𝑚𝑚 1 푘푠𝑚𝑚√𝑚𝑚𝑚𝑚 10 100 ΔK (ksi√in.) Figure 6.4: Subsurface-to-surface cracking events (d),(e), and (f) impact growth rate for die forged MD-LS-01
Fig. 6.4d pictures the growth of the third crack tip that has grown in length and developed a small split. Fig. 6.4e depicts yet another crack tip that has emerged from the subsurface, above and behind the crack tip in (d). The third subsurface crack remains unconnected with the existing three. Fig. 6.4f shows the progression of the crack, which emerged in (e), grow both backwards and forwards, while remaining independent of the neighboring cracks on the surface.
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1.00E-04
i
~ 0.375 inch = 27 퐾푚푎푥 푘푠𝑚𝑚 𝑚𝑚𝑚𝑚
1.00E-05 j (in./cycle) ~ 0.375 inch dN da/ g h
= 23.2 ~ 0.375 inch = 25.6 _ =15.1 ~ 0.375 inch 푚푎푥 퐾 푘푠𝑚𝑚 𝑚𝑚𝑚𝑚 푚푎푥 1.00E-06 퐾 𝑚𝑚푎푥 퐾 푘푠𝑚𝑚 𝑚𝑚𝑚𝑚 1 푘푠𝑚𝑚√𝑚𝑚𝑚𝑚 10 100 ΔK (ksi√in.) Figure 6.5: Subsurface-to-surface cracking events (g),(h), (i), and (j) impact growth rate for die forged L-S specimen (MD-LS-01)
Fig. 6.5g shows the progression of the forward most crack tip as it continues to curve upward.
The crack then turns and continues on a horizontal path, parallel to the original crack plane, as seen in Fig. 6.5h. It also grew backwards, and connected with the split crack tip formed in (d), increasing the total of unconnected crack tips to three. Fig. 6.5i shows the further progression of
the foremost crack tip in the horizontal direction. A split later occurred at the point where the
crack had transitioned to the horizontal earlier, and is pictured just before final failure in Fig. 6.5j.
The region of the fatigue plot, indicated by the green dashed oval in Figs. 6.3-6.5, is a sharp drop
in growth rate. This stunted growth occurs at a time before any indications are visible on the
surface of the specimen, and that out-of-plane subsurface crack growth began at or before Kmax =
13.1 ksi√in. This example demonstrates the importance of characterizing the onset of subsurface crack splitting and branching that occurs within the interior of the material.
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Branching was observed in all hand and die forged material specimens with L-S orientation. Branching was observed in all M(T) specimens with T-S orientation and in the majority of T-S C(T) specimens. The branching behavior was found to be unique from specimen to specimen, and appears to be an artifact of the random alignment of grain boundaries at the crack front. Fig. 6.6, shows a rare occurrence of a symmetric branching crack in a hand forged
C(T) specimen with L-S orientation. From the randomness of branching behaviors observed throughout testing, it appears that it is unlikely to accurately predict the size, shape, quantity or direction of branching cracks in either the L-S or T-S orientations.
The fracture surfaces of the M(T) specimens L-S and T-S orientations shown in Figs.
5.12 and 5.21, which are respectively overlaid with the locations of the stress intensity values in
Tables 5.1 and 5.2, provide insight into the relationship between the observed sinusoidal behavior and the initiation of subsurface branching. The blue vertical lines, representing the start of
moderate sinusoidal behavior in the growth rate, appear to be located almost on top of the
location where fracture surface roughness begins for specimen of L-S and T-S orientations. There
is not a strong relationship that can be observed in specimens subjected to load ratios R ≥ 0.5,
which further alludes to the possible role of crack closure effects and its impact on subsurface
branching mechanisms. It is difficult to determine the existence of a similar behavior on the L-S
and T-S die forged specimens, due to the asymmetry in the visual appearance of the fracture surface about the specimen centerline. In L-S and T-S specimens with loading ratio R < 0.5, there is a strong relationship between the sinusoidal growth rate behavior and subsurface branching. It becomes quite apparent, when looking at the distance (Δa) between the blue and yellow indicator lines, that subsurface branching occurs well before any indication is visible on the surface of the material. It is also evident, that the distance (Δa) between the yellow and red indicator lines is relatively smaller than the Δa between the blue and yellow. The window of time to detect the appearance of branching on the surface, before the crack path is no longer predictable is quite
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short, when compared to window of time which spans from the initiation of interior branching to the first appearance of branching on the surface.
~0.50 inch
Figure 6.6: Symmetric branching in hand forged L-S C(T) specimen. Crack path is right to left.
Although many researchers [6][8][9][10][25] have agreed that branching mechanisms impact and slow the growth rate of the primary crack front, as they have deemed them crack
“arrestors,” it is paramount to understand that the unpredictable microstructure composition is what drives the size, direction, and quantity of macroscopic branching cracks. To attempt to exploit and rely on the energy dissipating characteristics of crack arresting branches, would appear to be a dangerous practice, given the lack of general understanding of these mechanisms, in conjunction with the unknowns introduced by complex part geometries and residual stress fields.
It appears that the best approach for designing with material that possess branching characteristics, in one or more orientations, is to use an identified range of stress intensities as a design limit. The value, from within the range, which the designer chooses may depend on the how critical the component is and whether the component could be easily accessed for Non-
Destructive Evaluation (NDE), to detect early signs of subsurface damage.
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When testing materials, such as Al 7085-T7452, that have been known to have crack
branching mechanisms, it may be difficult to fully leverage traditional automated testing
techniques, which do not have the capability of capturing the sequence of branching events.
Unique sequential branching behavior, such as the behavior shown in Figs. 6.3-6.6, would go
undocumented and undiscovered. It is apparent that modifications or an additional appendix to
the current testing standard may be necessary to standardize testing procedures and validity
criteria for similar alloy systems.
6.2 Conclusions
The potential for delamination events creates a significant challenge for designers to
leverage the many advantages of Al 7085-T7452 when designing monolithic primary aircraft
structure. Even though a stress intensity range for crack branching delamination has been
identified, no quantitative description of these delamination mechanisms within the subsurface is
currently available. Instances of sustained macroscopic deviation, by means of substantial branching of crack turning, from the primary crack plane, invalidate current material testing methods, for mode I loading, and may affect conventional lifing procedures. An appendix to the current testing standard may be necessary to standardize procedures and validity criteria for alloy systems with similar branching mechanisms.
Fracture surfaces of hand and die forged M(T) specimens indicate that subsurface branching cracks typically begin forming at Kmax of 10-14 ksi√in. in the L-S orientation and Kmax
of 9-11 ksi√in. in the T-S orientation, for load ratios R ≤ 0.5. Branching became visible on the surface at Kmax of 15-26 ksi√in. in both hand and die forged specimens with L-S orientation and at
Kmax of 11-19 ksi√in. in the T-S orientation, for load ratios R ≤ 0.5. Crack growth eventually became dominated by branching mechanisms and resulted in the inability to predict the direction of the primary crack front, for all specimens in the L-S orientation. The same unpredictable behavior was found in all hand and die forged M(T) specimens with T-S orientation and in 40% of C(T) specimens with T-S orientation. Specimens in the L-S orientation exhibited crack path
79
instability within a Kmax range of 20-30 ksi√in., while T-S specimens exhibited the same crack path instability within a Kmax range of 12-27 ksi√in. Specimens in the T-S orientation were found to exhibit visible branching behavior at a lower Kmax range than specimens in the L-S orientation.
A detailed summary of the results is located in Table 6.1.
Table 6.1: Summary of stress intensity ranges associated with the onset of crack branching and turning mechanisms
Kmax-dev Kmax-dev Subsurface Material Minor Major Branching Orientation Load Ratio Form ~ Range ~ Range ~ Range, Kmax (ksi√in) (ksi√in) (ksi√in) L-S HAND ALL TESTED 17 – 23 22 – 30 10 – 16 L-S HAND R ≤ 0.5 17 – 23 22 – 30 10 – 16 L-S HAND R < 0.5 17 – 21 22 – 30 10 – 14 L-S DIE R = 0.1 15 – 26 20 – 34 11 T-S HAND ALL TESTED 11 – 23 12 - 27 9 – 20 T-S HAND R ≤ 0.5 11 – 19 12 – 24 9 – 10 T-S HAND R < 0.5 12 – 19 12 – 24 9 – 10 T-S DIE R = 0.1 15 – 19 19 11
Even though minimum allowable KIC values are available for the L-T, T-L, and S-L orientations at various depths in the forging in AMS4403 and AMS4414 [4][5], there is very little publically available growth rate data for any material orientation to compare to. If the aerospace community wants to leverage Al 7085-T7452, then it must be committed to fully defining the properties of the material system, to learn how and where to utilize its strength and understand its weaknesses. It is necessary that these branching mechanisms are taken into account during the preliminary design process, to ensure performance and accurately predict sustainment cost and schedule, when using Al 7085-T7452 for structural components.
6.3 Future Work
For future efforts, it would be beneficial to examine the effects of branching mechanisms within the subsurface. Branching mechanisms could be further characterized by using Scanning
80
Electron Microscopy (SEM) on fracture surfaces to check for delaminations, and correlating
delamination density with Kmax. It would also be of interest to determine if these delaminations
are preventing full crack closure from occurring during compressive load cycles. This may be
supplemented by performing Computer Tomography (CT) imaging on specimens with significant
branching behavior of any unique artifacts.
Polarized light imaging (with a chemical etching), should be conducted on surfaces and
mid-plane (B/2) to find the initial onset of subsurface branching. Establish a more simplified
method for correcting modulus sensitivity in the compliance based crack calculation method,
particularly at shorter crack lengths. Accurate crack length calculations at short crack lengths are
important for researching branching mechanisms over a large range of stress intensities and when
limited quantities of material are available for testing. It may prove useful to conduct constant ΔK
testing at several values of ΔK that are in the range of subsurface branching behavior. The data
produced from constant ΔK testing would help narrow the range if stress intensities responsible
for the initiation of branching mechanisms, as well as confirm correlation with branching and
Kmax or ΔK.
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[25] Bush, R. W., Bucci, R. J., Magnusen, P. E., Kuhlman, G. W., (1993), "Fatigue Crack Growth Rate Measurements in Aluminum Alloy Forgings: Effects of Residual Stress and Grain Flow," Fracture Mechanics: Twenty Third Symposium, ASTM STP 1189, Ravinder Chona, Ed., American Society for Testing and Materials, Philadelphia, pp. 568-589.
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APPENDIX A
Testing Setup and Procedures
Figure A.1: Drawing of 1.04” gage knife edge placement for MTS 623 extensometers
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Table A.1: Test matrix
Specimen Specimen Forging Load Testing Parent Orientation Notes Name Type Type Ratio Order Specimen
MH-TS-01 M(T) Hand T-S 0.1 3 MH-TS-05 M(T) Hand T-S 0.5 4 MH-TS-07 M(T) Hand T-S 0.7 6 MH-TS-11 M(T) Hand T-S -0.1 9 MH-TS-15 M(T) Hand T-S -0.5 11 INVALID MH-TS-15_02 M(T) Hand T-S -0.5 14 MH-TS-15_03 M(T) Hand T-S -0.5 15 MH-TS-19 M(T) Hand T-S -0.9 13 MH-LS-01 M(T) Hand L-S 0.1 1 INVALID MH-LS-01_02 M(T) Hand L-S 0.1 2 MH-LS-05 M(T) Hand L-S 0.5 5 MH-LS-07 M(T) Hand L-S 0.7 7 MH-LS-11 M(T) Hand L-S -0.1 8 MH-LS-15 M(T) Hand L-S -0.5 10 MH-LS-19 M(T) Hand L-S -0.9 12 MD-LS-01 M(T) Die L-S 0.1 16 MD-TS-01 M(T) Die T-S 0.1 17 MD-LT-01 M(T) Die L-T 0.1 18 CH-TS-01-A C(T) Hand T-S 0.1 19 MH-TS-19 CH-TS-01-B C(T) Hand T-S 0.1 21 MH-TS-11 CH-TS-01-C C(T) Hand T-S 0.1 23 MH-TS-11 CH-TS-05-A C(T) Hand T-S 0.5 34 MH-TS-05 CH-TS-05-B C(T) Hand T-S 0.5 35 MH-TS-05 CH-TS-05-C C(T) Hand T-S 0.5 30 MH-TS-15_03 CH-ST-01-A C(T) Hand S-T 0.1 25 MH-TS-07 CH-ST-01-B C(T) Hand S-T 0.1 26 MH-TS-15 CH-ST-01-C C(T) Hand S-T 0.1 28 MH-TS-15_03 CH-LS-01-A C(T) Hand L-S 0.1 24 MH-LS-19 CH-LS-01-B C(T) Hand L-S 0.1 20 MH-LS-01_02 CH-LS-01-C C(T) Hand L-S 0.1 22 MH-LS-01 CH-LS-05-A C(T) Hand L-S 0.5 31 MH-LS-05 CH-LS-05-B C(T) Hand L-S 0.5 32 MH-LS-05 CH-LS-05-C C(T) Hand L-S 0.5 33 MH-LS-11 CH-SL-01-A C(T) Hand S-L 0.1 27 MH-LS-07 CH-SL-01-B C(T) Hand S-L 0.1 29 MH-LS-15 CD-LS-01 C(T) Die L-S 0.1 37 MD-LS-01 CD-TS-01 C(T) Die T-S 0.1 38 MD-TS-01 CD-LT-01 C(T) Die L-T 0.1 36 MD-LT-01
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APPENDIX B
Specimen Photographs
Figure B.1: Die forged L-S raw material as received
Figure B.2: Die forged T-S raw material as received
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Figure B.3: Die forged L-T raw material as received
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