1st Edition

Stress Concentrations in Laminated Composites

By Seng C. Tan Copyright 1994
    482 Pages
    by CRC Press

    482 Pages
    by CRC Press

    From the Author's Preface

    The objective of this book is to provide a thorough and systematic study of the problem of laminated composites containing stress concentrations. Stress concentrations are introduced in laminated plates in the forms of circular holes, elliptical openings and straight cracks. These forms of cutouts have many practical applications, and are familiar to most engineers. Stress concentrations exist in all known structural components. Stress concentrations have great practical importance because they are normally the cause of failure.
    In addition to stress analyses of laminated composites, we need more fundamental understanding of the failure mode, the failure criterion, the effects on global laminate response, and the design of composites in the presence of stress concentrations.
    In this book, all the subjects studied are closely related to the problem of stress concentrations in laminated composites . . . . All the models are verified with many experimental results. The underlying objective of this comprehensive study is to give the readers an in-depth and thorough understanding of the problem of stress concentrations in composites.
    This book is the first to address the problem of laminated composites containing stress concentrations in a systematic way.

    Each chapter ends with a Discussion and Conclusion section and a References section.

    I. Background

    1. Introduction to Composite Materials
    Introduction - Classifications - Properties - Problems of Stress Concentration - Current Applications - Stress-Strain Relations - Laminated Plate Theory

    2. Test Methods
    Introduction - Tension Tests - Compression Tests - Shear Tests - Tests of Open Hole Specimens - Methods for Damage Detection

    3. Failure Criteria
    Introduction - Guidelines - Classical Failure Criteria - Discussions - New Failure Criteria - Failure Criteria in the Presence of Stress Gradient - Appendix: Transformation of Principal Stresses

    II. Finite-Width Solutions

    4. Finite-Width Correction Factor for Anisotropic Plate
    Introduction - Fundamental Theory - Improved Theory - Experimental and Numerical Comparisons - Anisotropic Plate with an Elliptical Opening

    5. Strain and Stress Concentrations
    Introduction - Stresses and Displacement Fields - Definition of Stress and Strain Concentration Factors - Anisotropic Plate with Circular Hole - Correction Factor for Finite-Width - Experimental Procedure - Experimental Results - SCF( and SCF( for Damaged Laminates - Appendix: Parametric Studies

    III. Laminate Failure Models (Analytical)

    6. Approximate Stress Analyses and Stress Failure Models
    Introduction - Stress Analysis - Numerical Examples and Comparisons - Stress Failure Models - Applications

    7. Experiment and Modified Failure Models
    Introduction - Experiment for Tensile Tests - Results for Data Reduction - Prediction for Modified Models - Results of the Modified Models

    IV. Lamina Failure Models (Analytical)

    8. Point Strength and Minimum Strength Models
    Introduction - Stress Analysis - Strength Models - Crack Simulation - Experimental Observation - Predictions and Comparisons - Characteristic Length as a Function of Opening Construction

    9. Lamina-Based Fiber Failure Criteria and Effective Stress Failure Models
    Introduction - Fracture Models - Unnotched Ultimate Strength - Results for Laminates with an Elliptical Opening - Baseline Characteristic Length - Comparison of Compression with Tension - Fracture Toughness

    10. Notched Strength of Thermoplastic Composites
    Introduction - Strength Models - Finite-Width Correction Factor - Experimental Investigation - Comparison of Data - Results

    11. Shear Loading of Composites Containing an Opening
    Introduction - Stress Analysis - Minimum Strength Model - Examples of Stress Distribution - Experimental Program - Comparisons

    12. Multiaxial Loading of Multidirectional Laminates
    Introduction - Stress Distribution - Failure Criteria, Mechanisms and Models - Unnotched Ultimate Strength - Uniaxial Loading of Laminates with a Slanted Crack - Fracture Under Multiaxial Loading

    13. Mixed-Mode Fracture of Unidirectional and Off-Axis Laminates
    Tensile Loading - Introduction - Stress Analysis - Complex Roots - Failure Models - Finite-Width Correction Factors - Experiment and Results - Correlation of Theory with Experiment

    14. Mixed-Mode Fracture of Unidirectional and Off-Axis Laminates
    Compressive Loading - Introduction - Strength Analysis - Strength Models - Finite-Width Correction Factors - Experimental - Discussion and Conclusion

    15. Correlation of Damage Mechanisms and Characteristic Lengths
    Introduction - Theoretical Background - Experimental Procedures - Results and Discussion - Comparison of Ultimate Strength

    Progressive Failure Models (Numerical)

    16. A Progressive Failure Model for Laminates with Cutouts
    Introduction - Finite Element Analysis - Damaged Lamina Formulation - Failure Criteria - Computation Procedures - Parametric Studies - Comparison with Experiment

    17. Damage Accumulation, and Accumulation due to Compressive Loading
    Introduction - Formulation of the Damage Problem - Finite Element Analysis - Damaged Lamina Formulation - Failure Criteria - Computation Procedures - Parametric Studies - Results - Limitations of the Model

    VI. Design Methodology

    18. Design of Composite Laminates by a Ranking Method
    Introduction - Design Considerations and Objective - Stress and Strength Analysis - Design Methodology using Strength - Development of Computer Program RANKHO - Varying Thickness Ratios of Laminates - Laminates Generated by Rigid-Body Rotation - Designing Laminates with a Crack - Discussion and Conclusions

    19. Optimal Design with an Iterative Method
    Introduction - Statement of the Problem - Design Methodology - Strength Ratio - Allowable Stress - Iterative Method - Results of the Iterative Method

    20. Mechanical Response and Design of Laminates with a Reinforcement
    Introduction - Stress Analysis - Strength Models - Theoretical Results and Predictions - Design Methodology

    Appendix: Unit Conversion Tables - Index - 80 tables, 277 figures


    The numerous schematics and X-ray radiographs in this volume illustrate stress concentrations, materials design and test methods. Here is a small sampling of this illustrative material: - An example of stress concentration problems in a typical wing structure for composite airplane - Deformations of a composite ply subjected to extensional and bending loads - A typical specimen for tension test - Schematic diagram of minisandwich specimen - Anti-buckling device for compression test of off-axis specimens - Methods of evaluating the stress interaction coefficient by Tsai and Wu - A finite-width anisotropic laminate containing a central elliptical opening - Measuring the strain concentration factor of anisotropic plates - The coordinates and characteristic length of a composite laminate with an opening - Compression-failed specimens of the AS4/APC-2 layup containing a hole - The distribution of tangential stress in a graphite/epoxy AS4/3502 laminate with a crack under shear loading - A three-rail shear specimen in testing fixture - Failed specimen of a graphite/PEEK AS4/APC-2 laminate containing a slanted 45ΓΈ crack

    Reference Data

    More than 100 tables and graphs provide reference data on stress concentrations and failure. Here is a small sampling: - Elastic properties and specific gravity of typical isotropic and unidirectional composites - Ratios of specific tensile strength of typical materials and steel - Elastic properties of typical graphite/epoxy laminae - Predicted and experimental effective laminate properties - Data for Gr/Ep AS4/3502 laminates containing a circular hole - Strength properties - Ultimate strength of AS4/APC-2 laminates containing a central hole - Comparison of the experimental shear modulus and the prediction using laminated plate theory - Experimental results for the ultimate shear strength of Gr/Ep AS4/3502 laminates containing cracks - Comparison of the predicted and experimental notched strength for laminates containing a central hole - The top 15 laminates for the Stress Vector (0, 2, 0)


    Seng C. Tan