In the investigation described in this book, extensive finite element analyses are performed to obtain numerical solutions of constraint parameter A for two-dimensional (2D) and three-dimensional (3D) crack geometries under both uniaxial and biaxial loading condition through a least-square fitting method. Based on the determined numerical solutions of constraint parameter A, constraint effect at cracK-Tip (-front) of 2D and 3D cracked specimens are analyzed under both uniaxial and biaxial loading condition.

Three sets of methodologies for estimating constraint parameter A of elastic-plastic fracture mechanics are developed in the current investigation. They are: (1) estimating constraint parameter A by curve shape similarity, (2) predicting A values directly from the T-stress, and (3) determining parameter A based on the fully plastic solutions of A. With the obtained numerical solutions of constraint parameter A, estimate formulas for A values corresponding to the three sets of newly-developed estimate methodologies are developed for 2D and 3D cracked structures under both uniaxial and biaxial loading. It is shown that all three sets of methods can be used to predict A values with good accuracy.

In the current investigation, it is validated that, the obtained solutions of constraint parameter A (whether estimate methods/formulas or numerical solutions) can be utilized to predict other two commonly-used constraint parameters Q and A2 (a different normalized form of A) through the relationships between A and Q as well as A and A2.

In addition, in the research described in this book, characters of near crack-front fields of 3D cracked structures under mixed-mode (mode I and mode II) loading are investigated for various crack constraints through a modified boundary layer (MBL) formulation with various T-stress values applied at the outer boundary of MBL respectively, which simulate the variation of remote constraint in the crack front region.

Chapter 1: Introduction

 

  1.1. Historical Background of Research

  1.2. Research Objectives

  1.3. Outline of the Book

 

Chapter 2: Theoretical Background and Literature Review

 

  2.1. Characterization of CracK-Tip (-Front) Fields

  2.2. One-Parameter Approach

   2.2.1. One-Parameter Approach of Linear Elastic Fracture Mechanics (LEFM)

   2.2.2. One-Parameter Approach of Elastic-Plastic Fracture Mechanics (EPFM)

  2.3. Two-Parameter Approach of Linear Elastic Fracture Mechanics (LEFM)

   2.3.1. K-T Two-Parameter Approach

  2.4. Two-Parameter Approach of Elastic-Plastic Fracture Mechanics (EPFM)

   2.4.1. J-T Two-Parameter Approach

     2.4.1.1. J-T approach

     2.4.1.2. Modified Boundary Layer (MBL) Problem

   2.4.2. J-Q Two-Parameter Approach

   2.4.3. J-A Two-Parameter Approach

   2.4.4. Application of Two-Parameter Elastic-Plastic Fracture Mechanics Approach

  2.5. Methods for the Determination of Dominant Fracture Mechanics Parameters

   2.5.1. Solution of Stress Intensity Factor K

   2.5.2. Solution of J-integral

  2.6. Methods for the Determination of Constraint Fracture Mechanics Parameters

   2.6.1. Solution of T-stress

     2.6.1.1. Determination of T-stress

     2.6.1.2. Prediction of T-stress by Weight Function Method

   2.6.2. Solution for Q Parameter

     2.6.2.1. Determination of Q Parameter

     2.6.2.2. Prediction of Q Factor through Q-T Relationship

     2.6.2.3. Prediction of Q Parameter under Large-Scale Yielding

   2.6.3. Solution of Parameter A

     2.6.3.1. Numerical Determination of Parameter A

     2.6.3.2. Possibility of Predicting Parameter A through Curve Shape Similarity

   2.6.4. Relationships among Constraint Parameters

     2.6.4.1. Relationship between the Constraint Parameters Q and T

     2.6.4.2. Relationship between the Constraint Parameters A and A2

     2.6.4.3. Relationship between the Constraint Parameters A and Q

  2.7. Three-Dimensional Aspects of Fracture Analysis

  2.8. Mixed Mode Loading

   2.8.1. Modified Boundary Layer (MBL) Formulation under Mode II Loading

   2.8.2. Fields under Mixed Mode Loading

  2.9. Closing Remarks

 

Chapter 3: The Development of Estimation Methods

  3.1. Prediction of Constraint Parameter A Based on Curve Shape Similarity

   3.1.1. Formulating Curve Shape Similarity of Parameter A

   3.1.2. Predicting Parameter A through Curve Shape Similarity

  3.2. Prediction of Constraint Parameter A Based on T-stress

   3.2.1. Determining Parameter A under Small-Scale Yielding

   3.2.2. A-T Relationship

     3.2.2.1. Existence of A-T Relationship

     3.2.2.2. Modified Boundary Layer Formulation for Parameter A

     3.2.2.3. Determination of A-T Relationship

   3.2.3. Predicting Parameter A through T-stress

  3.3. Prediction of Constraint Parameter A Based on Fully-Plastic Solution

   3.3.1. Parameter A under Fully-Plastic State

   3.3.2. Determining Coefficient a1

   3.3.3. Determining Parameter A through Fully Plastic Solution

  3.4. Application of Estimation Methods on Three-Dimensional Cracked Structures

  3.5. Closing Remarks

 

Chapter 4: Solution of Constraint Parameter A for 2D Specimens under Uniaxial Loading

  4.1. Finite Element Analysis of Modified Boundary Layer Formulation

   4.1.1. Problem Definition

   4.1.2. Finite Element Analysis and Parameter A Determination

     4.1.2.1. Finite Element Modeling

     4.1.2.2. Determining Parameter A Based on Finite Element Analysis

   4.1.3. Results and Discussion

     4.1.3.1. Verification of FEA Model and Analysis Procedure

     4.1.3.2. Numerical Solution of Parameter A

  4.2. Finite Element Analysis of Test Specimens

   4.2.1. Problem Definition

   4.2.2. Finite Element Analysis and Parameter A Determination

     4.2.2.1. Finite Element Modeling

     4.2.2.2. Determining Parameter A Based on Finite Element Analysis

   4.2.3. Results and Discussion

     4.2.3.1. Verification of FEA Model and Analysis Procedure

     4.2.3.2. Numerical Solution of Parameter A and Discussion for Constraint Effect

  4.3. Solution of Parameter A by Curve Shape Similarity

  4.4. Solution of Parameter A by T-stress

   4.4.1. Determination of A-T Relationship

   4.4.2. T-stress Solution by Weight Function Method

   4.4.3. Parameter A Solution by T-stress

  4.5. Solution of Parameter A by Fully Plastic Analysis

   4.5.1. Fully-Plastic Solution of Parameter A

   4.5.2. Determination of Coefficient a1

   4.5.3. Parameter A Solution by Fully-Plastic Analysis

  4.6. Estimating Other Constraint Parameters from A Solutions

   4.6.1. Estimating Constraint Parameter A2 from Parameter A

   4.6.2. Estimating Constraint Parameter Q from Parameter A

  4.7. Concluding Remarks

 

Chapter 5: Solution of Constraint Parameter A for 2D Specimens under Biaxial Loading

  5.1. Finite Element Analysis of Test Specimens

   5.1.1. Problem Definition

   5.1.2. Finite Element Analysis and Parameter A Determination

     5.1.2.1. Finite Element Modeling

     5.1.2.2. Determining Parameter A Based on Finite Element Analysis

   5.1.3. Results and Discussion

     5.1.3.1. Verification of FEA Model and Analysis Procedure

     5.1.3.2. Numerical Solution of Parameter A and Discussion for Constraint Effect

  5.2. Solution of Parameter A by Curve-Shape Similarity

  5.3. Solution of Parameter A by T-stress

   5.3.1. T-stress Solution by Weight Function Method

   5.3.2. Parameter A Solution by T-stress

  5.4. Solution of Parameter A by Fully Plastic Analysis

   5.4.1. Determination of Coefficient a1

   5.4.2. Parameter A Solution by Fully Plastic Analysis

  5.5. Concluding Remarks

 

Chapter 6: Solution of Constraint Parameter A for 3D Specimens

  6.1. Finite Element Analysis of 3D Modified Boundary Layer Formulation

   6.1.1. Problem Definition

   6.1.2. Finite Element Analysis and Parameter A Determination

     6.1.2.1. Finite Element Modeling

     6.1.2.2. Determining Parameter A Based on Finite Element Analysis

   6.1.3. Results and Discussion

     6.1.3.1. Verifications

     6.1.3.2. Numerical Solutions of Parameter A

  6.2. Finite Element Analysis of 3D Test Specimens

   6.2.1. Problem Definition

   6.2.2. Finite Element Analysis and Parameter A Determination

     6.2.2.1. Finite Element Modeling

     6.2.2.2. Determining Parameter A Based on Finite Element Analysis

   6.2.3. Results and Discussion

     6.2.3.1. Verification

     6.2.3.2. Numerical Solutions of Parameter A and Discussion for Constraint Effect

  6.3. Solution of Parameter A by Curve Shape Similarity

  6.4. Solution of Parameter A by T-stress

   6.4.1. Determination of A-T Relationship for 3D Cases

   6.4.2.T-stress Solution by Finite Element Method

   6.4.3. Parameter A Solution by T-stress

  6.5. Solution of Parameter A by Fully Plastic Analysis

   6.5.1. Fully Plastic Solution of Parameter A

   6.5.2. Determination of Coefficient a1

   6.5.3. Parameter A Solution by Fully Plastic Analysis

  6.6. Concluding Remarks

 

Chapter 7: Crack-Front Fields of 3D Carck Structures under Mixed-Mode Loading

  7.1. Finite Element Analysis of 3D Modified Boundary Layer Formulation under Mixed-Mode Loading

   7.1.1. Problem Definition

   7.1.2. Finite Element Modeling and Analysis

   7.1.3. Results and Discussion

     7.1.3.1. Verifications

     7.1.3.2. Results and Discussion

  7.2. Concluding Remarks

 

Chapter 8: Conclusions and Recommendations

  8.1. Conclusions

  8.2. Recommendations for Further Investigation

NOMENCLATURE

Appendix