Solution of Crack Problems

1. Front Matter

   Pages i-xii

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2. Introduction to Fracture Mechanics

   • D. A. Hills, P. A. Kelly, D. N. Dai, A. M. Korsunsky

   Pages 1-27

3. Distributed Dislocation Fundamentals

   • D. A. Hills, P. A. Kelly, D. N. Dai, A. M. Korsunsky

   Pages 29-68

4. Further Topics in Plane Crack Problems

   • D. A. Hills, P. A. Kelly, D. N. Dai, A. M. Korsunsky

   Pages 69-106

5. Interface Cracks

   • D. A. Hills, P. A. Kelly, D. N. Dai, A. M. Korsunsky

   Pages 107-136

6. Solution of Axi-Symmetric Crack Problems

   • D. A. Hills, P. A. Kelly, D. N. Dai, A. M. Korsunsky

   Pages 137-169

7. Three-Dimensional Cracks: An Introduction

   • D. A. Hills, P. A. Kelly, D. N. Dai, A. M. Korsunsky

   Pages 171-210

8. Three-Dimensional Cracks: Further Concepts

   • D. A. Hills, P. A. Kelly, D. N. Dai, A. M. Korsunsky

   Pages 211-230

9. Concluding Remarks

   • D. A. Hills, P. A. Kelly, D. N. Dai, A. M. Korsunsky

   Pages 231-233

10. Back Matter

    Pages 235-306

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This book is concerned with the numerical solution of crack problems. The techniques to be developed are particularly appropriate when cracks are relatively short, and are growing in the neighbourhood of some stress raising feature, causing a relatively steep stress gradient. It is therefore practicable to represent the geometry in an idealised way, so that a precise solution may be obtained. This contrasts with, say, the finite element method in which the geometry is modelled exactly, but the subsequent solution is approximate, and computationally more taxing. The family of techniques presented in this book, based loosely on the pioneering work of Eshelby in the late 1950's, and developed by Erdogan, Keer, Mura and many others cited in the text, present an attractive alternative. The basic idea is to use the superposition of the stress field present in the unfiawed body, together with an unknown distribution of 'strain nuclei' (in this book, the strain nucleus employed is the dislocation), chosen so that the crack faces become traction-free. The solution used for the stress field for the nucleus is chosen so that other boundary conditions are satisfied. The technique is therefore efficient, and may be used to model the evolution of a developing crack in two or three dimensions. Solution techniques are described in some detail, and the book should be readily accessible to most engineers, whilst preserving the rigour demanded by the researcher who wishes to develop the method itself.

• cracks
• fracture
• fracture mechanics
• mechanics
• transformation

• Department of Engineering Science, University of Oxford, Oxford, UK

  D. A. Hills, D. N. Dai

• The Oxford Orthopaedic Engineering Centre, Nuffield Orthopaedic Centre, Oxford, UK

  P. A. Kelly

• Department of Materials Science and Metallurgy, University of Cambridge, Cambridge, UK

  A. M. Korsunsky

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