Iowa State University Capstones, Theses and Retrospective Theses and Dissertations Dissertations 1989 Study of mixed mode stress intensity factor using the experimental method of transmitted caustics Nasser Soltani Iowa State University Follow this and additional works at: https://lib.dr.iastate.edu/rtd Part of the Applied Mechanics Commons Recommended Citation Soltani, Nasser, "Study of mixed mode stress intensity factor using the experimental method of transmitted caustics " (1989). Retrospective Theses and Dissertations. 9182. https://lib.dr.iastate.edu/rtd/9182 This Dissertation is brought to you for free and open access by the Iowa State University Capstones, Theses and Dissertations at Iowa State University Digital Repository. It has been accepted for inclusion in Retrospective Theses and Dissertations by an authorized administrator of Iowa State University Digital Repository. For more information, please contact [email protected]. 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University Microfilms international A Bell & Howell Information Company 300 North Zeeb Road, Ann Arbor, Ml 48106-1346 USA 313/761-4700 800/521-0600 Order Number 9014957 Study of mixed mode stress intensity factor using the experimental method of transmitted caustics Soltani, Nasser, Ph.D. Iowa State University, 1989 UMI 300N.ZeebRd. Ann Ait)or, MI 48106 study of mixed mode stress intensity factor using the experimental method of transmitted caustics by Nasser Soltani A Dissertation Submitted to the Graduate Faculty in Partial Fulfillment of the Requirements for the Degree of DOCTOR OF PHILOSOPHY Department: Engineering Science and Mechanics Major: Engineering Mechanics Approved: Signature was redacted for privacy. In Charge of Major Wd Signature was redacted for privacy. For the Major Detriment Signature was redacted for privacy. For the Graduate College Iowa State University Ames, Iowa 1989 Copyright (c) Nasser Soltani, 1989. All rights reserved. ii TABLE OF CONTENTS CHAPTER 1. INTRODUCTION 1 CHAPTER 2. LITERATURE REVIEW 7 Energy Balance Approach 7 Griffith Theory 7 Modified Griffith Theory 12 Stress Intensity Factor Approach 13 Numerical Works 16 Experimental Works 21 CHAPTER 3. THEORY OF THE METHOD OF CAUSTICS ... 29 Introduction 29 Physical Principle of the Method 30 Mathematical Principle of the Method 34 Data Processing Techniques 45 Three-point Deterministic Method 45 The Multi-point Over-deterministic Method 48 CHAPTER 4. EXPERIMENTAL TECHNIQUE 55 Model Material 55 iii Model Geometry 56 Procedure 57 Calibration of Stress-optical Constants 62 Data Collection Method 65 Three-point Method 68 Multi-point Method 70 CHAPTER 5. RESULTS AND DISCUSSION 74 The Effect of the AppHed Load 74 Three-point Deterministic Results 77 Multi-point Over-deterministic Results 78 CHAPTER 6. CONCLUSION AND DISCUSSION 88 ACKNOWLEDGEMENTS 92 BIBLIOGRAPHY 93 APPENDIX A. PROGRAM DIGITIZE 102 APPENDIX B. PROGRAM TCAUSTIC 121 APPENDIX C. PROGRAM BACKPLOT 130 iv LIST OF TABLES Table 4.1: Properties of plexiglas at room temperature . 56 Table 4.2: Geometrical parameters of specimens 60 Table 5.1: Experimental and numerical results (three-point method) . 79 Table 5.2: Results of computer generated caustic 79 Table 5.3: Experimental and numerical results (multi-point method) . 81 V LIST OF FIGURES Figure 2.1: Through thickness crack in a large plate 8 Figure 2.2: Variation of energy with crack length 10 Figure 2.3: Three basic modes of crack deformations 13 Figure 2.4: Polar crack tip coordinate and stress systems 16 Figure 3.1: Optical arrangement for caustic analysis 31 Figure 3.2: Change of light path for transmission and reflection 32 Figure 3.3: The principle of the transmitted method of caustics 33 Figure 3.4: Caustics from (a) transmitted light and (b) reflected light . 35 Figure 3.5: Transmitted light-ray deflection 36 Figure 3.6: Change in optical path length 38 Figure 3.7: Caustics for fi =0, and 1 44 Figure 3.8: Mixed mode transmitted caustics 46 Figure 3.9: Definition of different caustic diameters 47 Figure 3.10: Variation of the ratio # = ^raax—^rnm versus u — . 49 JJmax A J Figure 3.11: Variation of the factor 6 = ^ versus 50 Figure 3.12: Caustic curve associated with multipoint method 52 Figure 4.1: Model geometry 58 VI Figure 4.2: Unloaded model observed through transmitted light 59 Figure 4.3: Experimental set up 61 Figure 4.4: Loading apparatus (a) Loading frame (b) Load cell 63 Figure 4.5: Theoretical caustic image of a circular hole in a plate (a) Transmitted (b) Reflected 66 Figure 4.6: Experimental caustic images of a circular hole in a plate (a) transmitted (b) reflected 67 Figure 4.7: Distances used in three-point method 69 Figure 4.8: Computer setup 71 Figure 4.9: Block diagram of data analysis programs 72 Figure 5.1: Transmitted caustic band 75 Figure 5.2: Caustic pattern due to use of an area light source 76 Figure 5.3: The effect of the applied load 77 Figure 5.4: Computer generated Caustics 80 Figure 5.5: Experimental and numerical Kj/Kj^ versus h/a for model A 82 Figure 5.6: Experimental and numerical versus h/a for model A 83 Figure 5.7: Experimental and numerical Kj/Kj^ versus h/a for model B tip 1 84 Figure 5.8: Experimental and numerical Kjj/Kj^ versus h/a for model B tip 1 85 Figure 5.9: Experimental and numerical Kj/Kj^ versus h/a for model B tip s 86 vii Figure 5.10: Experimental and numerical versus h/a for model B tip s 87 1 CHAPTER 1. INTRODUCTION Structural studies which consider crack extension behavior as a function of ap­ plied loads is called fracture mechanics. The objective of fracture mechanics is to provide quantitative answers to specific problems concerning structures containing pre-existing flaws which causes cracks to initiate in service. In addition, fracture mechanics is used to analyze the rate at which small cracks grow to critical size. Materials fracture in many different ways and for many different reasons. A wide variety of defects can be found to some degree in all structures. These flaws may exist as a result of material imperfections, defects generated during service life or defects introduced by design. The fracture of a structure or material, caused by presence of cracks or flaws, occurs at loads much lower than those that would cause yielding of the material. In these situations a strength of material analysis is not sufficient to guarantee the safe operation of the structure under loading conditions. The classification of fracture in a simple meaningful manner is not an easy task, although many such classifications have been proposed. Some of these have been based on the stress state, others upon such considerations as the test temperature, the strain rate, the environment, the energy absorbed, the amount of plastic flow, and the fracture path. In looking for simplifying coordinating features, it is helpful to keep two significant facts in mind. The first is that there are only two ways in 2 which a material can be fractured: they can be pulled apart, or they can be sheared. The second fact of importance is that all fractures are two stage processes involving crack nucleation and crack growth. Among fracture theories proposed, linear elastic fracture mechanics (LEFM) which is the result of considerable investigations during the past two decades, is well developed and now can be used to solve many engineering problems in fracture analysis and material selection. Linear fracture mechanics can also be extended to solve problems with moderate plasticity. In linear fracture mechanics formulation, the most important parameter used to distinguish cracks and which measures the severity of a crack is called the stress intensity factor. Stress intensity factors can be obtain from the stress field near the crack tip. In general, the stress intensity factor is linearly proportional to the external or applied load and contains a factor which describes the configuration of the body including the crack length. The usefulness of stress intensity factors in the analysis of problems of residual static strength, fatigue crack growth and stress corrosion is now well established. The power of stress intensity factor method of analysis lies in the assumption that the behavior of a sharp crack is determined by the stress field at the tip; it is thus necessary to determine the stress intensity factors only.