Solution of Crack Problems

The Distributed Dislocation Technique
1. Auflage. Softcover version of original hardcover Auflage 1996
ISBN: 978-90-481-4651-2
Verlag: Springer Netherlands

Buch, Englisch, Band 44, 308 Seiten, Paperback, Format (B × H): 155 mm x 235 mm, Gewicht: 493 g

Reihe: Solid Mechanics and Its Applications

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.

Zielgruppe

Research

Autoren/Hrsg.

Hills, D. A.

Korsunsky, A. M.

Kelly, P.A.

Dai, D. N.

Fachgebiete

• Technische Wissenschaften Technik Allgemein Mathematik für Ingenieure
• Mathematik | Informatik EDV | Informatik Professionelle Anwendung Computer-Aided Design (CAD)
• Technische Wissenschaften Technik Allgemein Computeranwendungen in der Technik
• Mathematik | Informatik Mathematik Mathematische Analysis Differentialrechnungen und -gleichungen
• Mathematik | Informatik Mathematik Mathematische Analysis Reelle Analysis
• Technische Wissenschaften Maschinenbau | Werkstoffkunde Technische Mechanik | Werkstoffkunde Festigkeitslehre, Belastbarkeit
• Naturwissenschaften Physik Mechanik Klassische Mechanik, Newtonsche Mechanik
• Mathematik | Informatik EDV | Informatik Angewandte Informatik Computeranwendungen in Wissenschaft & Technologie

Inhaltsverzeichnis

1 Introduction to Fracture Mechanics.- 2 Distributed Dislocation Fundamentals.- 3 Further Topics in Plane Crack Problems.- 4 Interface Cracks.- 5 Solution of Axi-Symmetric Crack Problems.- 6 Three-Dimensional Cracks: An Introduction.- 7 Three-Dimensional Cracks: Further Concepts.- 8 Concluding Remarks.- A Dislocation Influence Functions.- A.1 Notation.- A.2 A Dislocation Outside a Circular Inclusion.- A.2.1 A Dislocation Near a Circular Hole.- A.3 A Dislocation Near a Straight Interface.- A.3.1 A Dislocation in a Half-Plane.- A.4 The Interfacial Dislocation.- A.4.1 Interfacial Stresses.- A.5 A Dislocation on the Boundary of a Circular Inclusion.- A.6 Displacements Due to a Dislocation.- A. 7 Transformation Rules for the Dislocation.- A.8 Dundurs’ Parameters.- B Numerical Solution of SIEs with Cauchy Kernel.- B.l The Standard Gaussian Quadrature Formulae.- B.2 Gaussian Quadrature for SIEs with Cauchy Kernel.- B.3 SIEs Arising in Surface-Breaking Crack Problems.- B.3.1 The Method of Boiko and Karpenko.- B.3.2 Expansion Method.- B.3.3 Series Expansion.- B.4 Numerical Quadrature: Generalised Cauchy Kernel.- C Plane and Ring Dipole Influence Functions.- C.1 Plane Influence Functions.- C.2 Plane Dipole Transformation Rules.- C.3.1 Asymptotic Behaviour of the Integrals.- C.3.2 Numerical Considerations.- C.4 Finite Part Integrals.- D Contour Integral and Kernel Function.- D.1 Closed-Form of Certain Contour Integrals.- References.