AN ABSTRACT OF THE THESIS OF PING CHENG for the degree of Master of Science in ForestProducts presented on May 8 1996. Title: Assessing Biaxial Strength Characteristicsof Wood-Based Structural Panels. A / Signature redacted for privacy. Abstract Approved: Dr. Robert J. Leichti Biaxial strength characteristics of wood-based structural panels wereevaluated by using analytical and experimental methods. Cruciformplywood specimens were tested under biaxial tensile-tensile, compressive-compressive loadingsin a symmetrically- jointed-arm test fixture, which was mounted on a universal testingmachine. Performance of the test fixture was also evaluated during the tests. Electricalresistance strain gauges were used to measure strain values at apoint of interest, and brittle coatings were also used to analyze strain distributions over the test section. Finite-elementanalysis was employed to develop an analytical tool. The basic configurations, detail alternatives,and the influence of reinforcement orientation on the uniformity of the biaxialstress/strain distributions in the test section of the cruciform specimen wereexamined by using the finite-element method. The experimental strain values and those fromfinite-element analysis were found in close agreement. The Tsai-Wu Tensor Polynomial Strength Theory was used to construct a predicted biaxial strength envelope in stress space. Comparisons were made between the experimental data and the theoretical predictions in quadrants I and III of stress space, as well as between the finite-element results and the theoretical predictions in quadrants II and IV of stress space. Good agreements were found in quadrants I, II and IV at a load value that corresponded with audible cracking. In quadrant III of stress space, compressive-compressive stress space, the experimental failure stress condition did not agree with the analytical solution for the strength theory envelope in that quadrant. With respect to testing method, the jointed-arm test fixture worked well in tension-tension tests. However, a method of special lateral support was needed for the compression-compression biaxial condition. Results also indicated that reinforcement orientation in the arms may influence ultimate load capacity and failure mode of the biaxial specimen. °Copyright by Ping Cheng May 8, 1996 All rights reserved Assessing Biaxial Strength Characteristics of Wood-Based Structural Panels by Ping Cheng A THESIS submitted to Oregon State University in partial fulfillment of the requirements for the degree of Master of Science Presented May 8, 1996 Commencement June 1996 Master of Science thesis of Ping Cheng presented on May 8, 1996. APPROVED: Signature redacted for privacy. Major Professor, representing Forest Products Signature redacted for privacy. Head of Department of Forest Products Signature redacted for privacy. Dean of Graduate School I understand that my thesis will become part of the permanent collection of Oregon State University libraries. My signature below authorizes release of my thesis to any reader upon request. Signature redacted for privacy. Ping Cheng, Author ACKNOWLEDGMENT This thesis could not be completed successfully without the input and support of many individuals whom I am sincerely indebted to. Now, I would like to take this opportunity to show my gratefulness to them. I wish to extend a very special thank-you to my major professor, Dr. Robert J. Leichti of the Forest Products Department for your years of patience, consistent support, and encouragement throughout the studies. Dr. Leichti has been invaluable in this research process, and without him I could never finish this thesis. I am forever appreciative of his support. I also would like to thank my committee, Dr. Terence D. Brown of the Forest Products Department, Dr. John Peterson of the Civil Engineering Department, and Dr. Eldon D. Olsen of the Forest Engineering Department for their helpful suggestions; Dr. Milan Vatovec for his assistance in setting-up the testing equipment. My gratitude is extended to my parents, my sister for their human support so vitally necessary to finishing the thesis. Further acknowledgment goes to my friends for their help. Funding for this research was provided by the Center of Wood Utilization Research. Forest Research Laboratory, Oregon State University. Table of Contents Page INTRODUCTION 1 The Multiaxial Stress State 3 Objectives 4 LITERATURE REVIEW 6 Biaxial Testing Systems 6 Geometry of Test Specimen 9 Testing Methods for Various Materials 14 Measuring Methods for Strain 20 Strength Theories for Composite Materials 26 Tsai-Wu Tensor Polynomial Strength Theory 29 The Generalized Hooke's Law 35 Finite-Element Analysis Method 37 MATERIAL AND MATERIAL CHARACTERIZATIONS 41 The Material 41 Data Acquisition System 41 System Software 42 Load and Deflection Measurement 42 Uniaxial and Elastic Material Properties 43 Uniaxial and Bending Tests 44 Objectives of Uniaxial and Bending Tests 44 Tensile Tests 44 Table of Contents (continued) Page Compressive Tests 47 Five-Point Bending Tests 52 IV. BIAXIAL EVALUATION METHODS 60 Objectives of Biaxial Evaluations 60 Biaxial Specimen Optimizations 61 Basic Geometry Development 61 Reinforcement 64 Finite-Element Evaluation of the Cruciform Specimen 65 ANSYS® Finite-Element Program 65 Development of Finite-Element Model 67 Element Type 67 Finite-Element Model 68 Element Mesh 68 Boundary Conditions 69 Elastic Properties 69 Loadings 73 Expected Stress Distributions 73 Methods of Biaxial Testing 83 The Test Fixture 83 Loading Method 85 Rate of Loading 85 Measurement and Data Storage 88 Biaxial Stress Analysis Methods 88 Strain Gauges 88 Brittle Coatings 93 Table of Contents (continued) Page Evaluations of Mechanical Testing and Modeling 94 Performance of the Fixture 94 Tensile-Tensile Results 98 Compressive-Compressive Results 101 Effects of Reinforcement Orientations on Biaxial Strength Characteristics 103 Effect on Load Capacity 103 Effect on Failure Mode 103 STRENGTH THEORY ANALYSIS 104 Calculation of Strength Tensors 105 Calculation of Stress Components 106 Strength Envelope 108 Comparison of Results -- Experimental v. Strength Theory 109 Summary 117 CONCLUSIONS 119 BIBLIOGRAPHY 121 APPENDICES 129 Appendix A:ANSYS® Finite-Element Program 130 Appendix B: ANSYS® Element Type--Solid46 133 Appendix C: Sample of ANSYS® Input 135 Appendix D: Design of Test Fixture 141 Appendix E: Calculations of Expected Maximum Load 147 Appendix F: Strain Gauge Characteristics 148 Appendix G:Load-Strain Data for Biaxial Tests 149 List of Figures Figure Page 1.1 Failure envelope in a biaxial stress state 5 2.1 Symmetrically-jointed-arm test fixture for biaxial tests 10 2.2 Perspective view of the biaxial extensiometer (Makinde et al., 1992) 23 3.1 Dimensions and shape of specimen for uniaxial tensile test 46 3.2 Dimensions and shape of compressive test specimenbased on the work of Lee and Biblis (1980) 50 3.3 Photograph of compressive test set-up for large plywood specimen 51 3.4 Quarter-point load case and the corresponding shear and moment diagrams 56 3.5 Five-point load case and the corresponding shear and moment diagrams 57 3.6 Five-point bending test set-up 58 4.1 Cruciform plywood specimen for biaxial tests 62 4.2 Single-layer finite-element model including boundary conditions and loading 70 4.3 Reduced finite-element model showing thickness transition away from central test section 71 4.4 Full finite-element model showing thickness, showing transition at the boundary of the central test section 72 4.5 Normal stress ax for 0-degree reinforcement 75 4.6 Normal stress ay for 0-degree reinforcement 76 4.7 Shear stresstxyfor 0-degree reinforcement 77 4.8 Normal stress ax for 90-degree reinforcement 78 List of Figures (continued) Figure Page 4.9 Normal stress ay for 90-degree reinforcement 79 4.10 Shear stresstxyfor 90-degree reinforcement 80 4.11 Stress distributions for ax and ay on the line OX at various load ratios a) Py:Px=0, b) Py:Px=0.5, c)Py:Px=0.75 81 4.12 Stress distributions for ax and ay on the line OY at various load ratios a) Py:Px=0, b) Py:Px=0.5, c) Py:Px=0.75 82 4.13 Biaxial test fixture mounted between the traversing crosshead and the weighing platform for biaxial tensile tests 86 4.14 Biaxial test fixture mounted between the stationary and traversing crossheads for biaxial compressive tests 87 4.15 Wheatstone bridge circuit with temperature compensation 90 4.16 Strain gauge rosette at the point of interest on the cruciform specimen 92 4.17 Schematic diagram of the calculation of load acting on the specimen 97 4.18 Biaxial tensile test load-strain data, showing different strain values on specimen PA02 with OORF and adjacent arms of the test fixture 98 5.1 Predicted biaxial strength envelope for plywood 112 5.2 Comparisons of theoretical predictions (solid triangle points) with both experimental biaxial test data and finite-element results (solid square points) at load level P=4500 lb (20 lcN) for the specimens having 0-degree reinforcement; experimental results are shown in quadrants, I and III; finite-element results are shown in quadrants, II and W 115 5.3 Comparisons of theoretical predictions (solid diamond points) with experimental biaxial test data (solid square points) at load level P=4500 lb (20 lcN) for the specimens having 90-degree reinforcement 116 List of Tables Table Page 2.1 Steps in finite-element analysis 40 3.1 Calculated strengths X and Y and stiffness 47 3.2 Calculated strengths X' and Y' and stiffness 52 3.3 Calculated elastic material properties from