This book explains how plane elastostatic crack problems may be formulated and solved in terms of hypersingular integral equations. The unknown functions in the hypersingular integral equations are the crack opening displacements. Once the hypersingular integral equations are solved, the crack tip stress intensity factors, which play an important role in fracture analysis, may be easily computed.

Cite as:
W. T. Ang, Hypersingular Integral Equations in Fracture Analysis, Woodhead Publishing, Cambridge, 2013.

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Table of contents and preface
FORTRAN codes for Kaya and Erdogan technique in Section 3.2
FORTRAN codes for the crack element method in Section 3.3
Errata sheet
Additional note on Chapter 1 (Section 1.4)
Notes on Cauchy principal and Hadamard finite-part integrals

Chapter 1 
Elastic crack problems, fracture mechanics, equations of elasticity and finite-part integrals
DOI: 10.1533/9780857094803.1
Abstract: This chapter gives a brief account on the linear theory of fracture mechanics and the importance of the crack tip stress intensity factors in predicting crack extension, lays down the mathematical equations in linear elasticity needed in subsequent chapters, and provides basic definitions of the Hadamard finite-part integrals which appear in hypersingular integral equations for crack problems. 

Chapter 2
Hypersingular integral equations for coplanar cracks in anisotropic elastic media
DOI: 10.1533/9780857094803.25
Abstract: This chapter shows how Fourier integral representations for plane elastostatic displacements and stresses may be used to derive hypersingular integral equations for coplanar cracks in an elastic full space, an infinitely long elastic slab and between two dissimilar elastic half spaces. Formulae for the stresses near the crack tips are given in this chapter.

Abstract: This chapter presents two different numerical methods for solving a general system of hypersingular integral equations in linear crack problems. The first method approximates the unknown crack opening displacements globally over each crack by using Chebyshev polynomials of the second kind. In the second method, the cracks are discretised into small elements and the crack opening displacements are approximated locally over each crack element using simple spatial functions. In both methods, the hypersingular integral equations are approximately reduced to linear algebraic equations. Complete FORTRAN 77 programmes for the numerical methods are listed.
FORTRAN codes for Kaya and Erdogan technique in Section 3.2
FORTRAN codes for the crack element method in Section 3.3

Chapter 4
Hypersingular boundary integral equation method for planar cracks in an anisotropic elastic body
DOI: 10.1533/9780857094803.77
Abstract: This chapter shows how the boundary integral equations in linear elasticity may be employed to obtain hypersingular boundary integral equations for the numerical solution of a plane elastostatic problem involving arbitrarily located planar cracks in a two-dimensional body of finite extent. The boundary integral equations are also used together with special Green's functions to derive hypersingular integral equations for arbitrarily located planar cracks in an elastic full space, an elastic half space and an infinitely long elastic slab.

Chapter 5
A numerical Green's function boundary integral approach for crack problems
DOI: 10.1533/9780857094803.107
Abstract: This chapter describes the numerical construction of an elastostatic Green's function for arbitrarily located traction free planar cracks in an elastic full space. The Green's function, which is constructed by solving numerically a suitable system of hypersingular integral equations, is used to formulate a plane elastostatic crack problem in terms of boundary integral equations that do not contain any integral over the cracks.

Chapter 6
Edge and curved cracks and piezoelectric cracks
DOI: 10.1533/9780857094803.123
Abstract: This chapter explains how the analyses in the earlier chapters may be extended to include edge and curved cracks and plane electro-elastostatic crack problems.