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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.
E-Book Content
SOLUTION OF CRACK PROBLEMS SOLID MECHANICS AND ITS APPLICATIONS Volume 44 Series Editor: G.M.L. GLADWELL Solid Mechanics Division, Faculty of Engineering University of Waterloo Waterloo, Ontario, CanadaN2L3Gl Aims and Scope of the Series The fundamental questions arising in mechanics are: Why?, How?, and How much? The aim of this series is to provide lucid accounts written by authoritative researchers giving vision and insight in answering these questions on the subject of mechanics as it relates to solids. The scope of the series covers the entire spectrum of solid mechanics. Thus it includes the foundation of mechanics; variational formulations; computational mechanics; statics, kinematics and dynamics of rigid and elastic bodies; vibrations of solids and structures; dynamical systems and chaos; the theories of elasticity, plasticity and viscoelasticity; composite materials; rods, beams, shells and membranes; structural control and stability; soils, rocks and geomechanics; fracture; tribology; experimental mechanics; biomechanics and machine design. The median level of presentation is the first year graduate student. Some texts are monographs defining the current state of the field; others are accessible to final year undergraduates; but essentially the emphasis is on readability and clarity. For a list of related mechanics titles, see final pages. Solution of Crack Problems The Distributed Dislocation Technique by D.A.HILLS Department ofEngineering Science, University of Oxford, Oxford, U.K. P. A. KELLY The Oxford Orthopaedic Engineering Centre, Nuffield Orthopaedic Centre, Oxford, U.K. D.N.DAI Department of Engineering Science, University of Oxford, Oxford, U.K. and A. M. KORSUNSKY Department of Materials Science and Metallurgy, University of Cambridge, Cambridge, U.K. Springer-Science+Business Media, B.V. Library of Congress Cataloging-in-Publication Data Solution of crack problems; the distributed disc location technique by D. A. Hi I Is. .. [et a 1. l. p. cm. -- (Solid lIIechanics and its appl ications ; v. 44) Includes bibliographical references and index. I 1. Fracture mechanics. 2. Stresses and strains--Mathematical models. I. Hills, D. A. 0 in Figure 1.8, i.e. the crack front is curved forward a