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  • NASA/TP—2013–217480

    Elastic-Plastic J-Integral Solutions for Surface Cracks in Tension Using an Interpolation Methodology P.A. Allen and D.N. Wells Marshall Space Flight Center, Huntsville, Alabama

    April 2013

    National Aeronautics and Space Administration IS20 George C. Marshall Space Flight Center Huntsville, Alabama 35812

    https://ntrs.nasa.gov/search.jsp?R=20130012740 2020-03-13T13:05:20+00:00Z

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    NASA/TP—2013–217480

    Elastic-Plastic J-Integral Solutions for Surface Cracks in Tension Using an Interpolation Methodology P.A. Allen and D.N. Wells Marshall Space Flight Center, Huntsville, Alabama

    April 2013

    National Aeronautics and Space Administration

    Marshall Space Flight Center • Huntsville, Alabama 35812

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    Available from:

    NASA Center for AeroSpace Information 7115 Standard Drive

    Hanover, MD 21076 –1320 443 –757– 5802

    This report is also available in electronic form at

    TRADEMARKS

    Trade names and trademarks are used in this report for identification only. This usage does not constitute an official endorsement, either expressed or implied, by the National Aeronautics and Space Administration.

    Acknowledgments

    The authors would like to acknowledge James C. Newman, Jr. (Mississippi State University) and Ivatury S. Raju (NASA Langley) for their pivotal work on the linear-elastic stress intensity factor equations for surface cracks. The work of Dr. Newman and Dr. Raju has provided the foundation for a wealth of study into the fracture behavior of surface cracks. The authors would also like to thank Preston McGill (NASA Marshall Space Flight Center) for his thorough review of this paper. Finally, the authors would like to especially thank Robert H. Dodds Jr. (University of Illinois at Urbana- Champaign Professor Emeritus) for reviewing this paper and for his continual guidance, mentoring, and encouragement.

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    EXECUTIVE SUMMARY

    No closed form solutions exist for the elastic-plastic J-integral for surface cracks due to the nonlinear three-dimensional (3D) nature of the problem. Traditionally, each surface crack case must be analyzed with a unique and time-consuming nonlinear finite element analysis (FEA). Addition- ally, knowledge of nonlinear FEA, plasticity theory, and elastic-plastic fracture mechanics is required to reliably execute this type of analysis. To simplify this process, the authors have developed and ana- lyzed an array of 600 3D nonlinear finite element models for surface cracks in flat plates under ten- sion loading. The solution space covers a wide range of crack shapes and depths (shape: 0.2 ≤ a/c ≤ 1, depth: 0.2 ≤ a/B ≤ 0.8) and material flow properties (elastic modulus to yield ratio: 100 ≤ E/sys ≤ 1,000, and hardening: 3 ≤ n ≤ 20). The solution of this large array of nonlinear models was made practical by computer routines that automate the process of building the finite element models, running the nonlinear analyses, post-processing model results, and compiling and organizing the solution results into multidimensional arrays. The authors have developed a methodology for interpolating between the geometric and material property variables that allows the user to estimate the J-integral solution around the surface crack perimeter as a function of loading condition from the linear-elastic regime through the elastic-plastic regime. In addition to the J-integral solution, the complete force versus crack mouth opening displacement (CMOD) record is estimated. The solution space and interpo- lation routines have been extensively verified throughout the range of applicable geometries and materials. The user of this interpolated solution space need only know the crack and plate geometry and the basic material flow properties to reliably evaluate the full surface crack J-integral and force versus CMOD solution; thus, a solution can be obtained very rapidly by users without elastic-plastic fracture mechanics modeling experience. Enabling a convenient surface crack solution in the fully elastic-plastic domain, which up to now was only available for linear-elastic conditions, will signifi- cantly reduce the costs typically associated with evaluating elastic-plastic surface crack behavior. The authors hope this will promote advanced surface crack testing methodologies in the elastic-plastic regime and simplify aspects of surface crack structural assessment using the elastic-plastic J-integral.

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    TABLE OF CONTENTS

    1. INTRODUCTION ............................................................................................................. 1

    2. COMPUTATIONAL PROCEDURES ............................................................................... 4

    2.1 Constitutive Model ....................................................................................................... 4 2.2 Solution Space .............................................................................................................. 5 2.3 Finite Element Models .................................................................................................. 9 2.4 Automation Methods ................................................................................................... 11 2.5 Interpolation Methodology .......................................................................................... 12 2.6 Solution Space Interpolation ........................................................................................ 16

    3. REVIEW AND VERIFICATION ..................................................................................... 30

    3.1 Representative Model Results ....................................................................................... 30 3.2 Verification Process ....................................................................................................... 35 3.3 Elastic-Plastic Solution Comparison to Benchmark Data Set ....................................... 38 3.4 Interpolated Solution of the Round Robin Surface Crack Set ...................................... 42

    4. CONCLUSIONS ................................................................................................................ 52

    APPENDIX A—WIDTH EFFECTS SUBSTUDY ................................................................ 53

    APPENDIX B—COLLECTION OF BENCHMARK MODELS COMPARISON PLOTS ............................................................................... 56

    APPENDIX C—FINITE ELEMENT MODELS SOLUTION DATABASE ......................... 82

    APPENDIX D—BENCHMARK FINITE ELEMENT MODELS SOLUTION DATABASE ..........................................................