Weight functions and stress intensity factor solutions

Weight functions and stress intensity factor solutions Xue-Ren Wu and A. Janne Carlsson Pergamon, Oxford, 1991, £50.00 hbk ISBN 0-08-041702-7 This book is a welcome addition to the literature on theoretical fracture mechanics. As the title suggests the book deals almost exclusively with the calculation of stress intensity factors using (crack-line) weight functions, a versatile and efficient technique. The reader is assumed to be familiar with the basic ideas and principles of linear elastic fracture mechanics. The authors, who have been active researchers in this field for many years, have based the book on the results of this research, much of it previously unpublished. The book is substantial, more than 500 pages, and contains a wealth of data. The book starts off with a short User Guide (two pages only). It is worthwhile to read this, because it clearly sets out the following: the aims of the book; the method of presentation; the reasons why the chapters are structured in the way they are; and how the techniques are used. The main body of the book is divided into three parts. Part I, consisting of Chapter 1, gives the theoretical background and an overview of the weight function technique. Part II, consisting of Chapters 2 to 16 is the bulk of the book and contains the results for weight functions and stress intensity factors for various geometries, one geometry per chapter. Part III, consisting of Chapter 17, deals with the determination of crack opening displacement, Dugdale model solutions and crack opening areas. Chapter 1, entitled 'Theoretical Background and Overview' contains an exact derivation of the generalized crack-line weight function, which is based on Betti's reciprocal theorem and the principle of superposition. A necessary requirement in order to define the weight function is the knowledge of a reference solution, for the body in question, consisting of a known stress intensity factor and a

Int J Fatigue July 1992

known displacement field on the crack faces. This enables the stress intensity factor to be obtained for any arbitrary loading from an integral of the product of the applied crack face pressure and the crack-line weight function. It is rare for a reference stress intensity factor and a displacement field to be known exactly. This has led the authors to develop approximate unified analytical representations of the crack opening displacements from a minimum of data. Since it is obvious that the crack opening displacement fields are very different for the centre cracks (closed at both ends) and edge cracks (closed at one end only), the authors consider these two cases separately. They develop two distinct dosed-form weight functions for the two cases, before discussing the choice of reference load cases. Finally in this chapter they consider some special techniques for the numerical integration if the stress intensity factor integral cannot be evaluated analytically. The weight function procedures defined in the first chapter are then used to obtain stress intensity factors for central cracks in finite rectangular plates (Chapter 2); central cracks in circular discs (Chapter 3); and a periodic array of collinear cracks in an infinite sheet (Chapter 4). Each chapter follows the same pattern of using the weight function to determine the stress intensity factor for several basic load cases; the value of the results is demonstrated with some applications. In most cases the values of the normalized stress intensity factors are presented in both tabular and graphical form. The next section of the book, which constitutes the major part (Chapters 5 to 16) deals with edge cracks. The same format is followed as for the central cracks. The first three

Chapters (5, 6 and 7) consider edge crack(s) in semi-infinite bodies. Chapter 8 considers an edge crack in a square sheet and Chapter 9 the compact-tension specimen. The remaining chapters in Part II consider edge cracks in circular bodies on the edge of circular holes or notches. Chapters 10 and 11 consider crack(s) in solid discs (cylinders) and Chapter 12 a crack at the edge of a semicircular notch in a finite plate. Chapters 13 to 15, which occupy nearly half of the book, contain the weight functions and stress intensity factors that will have the most apphcations. They concern radial crack(s) at holes in both finite and infinite plates, with many examples and comprehensive results. The important problems of radial crack(s) in a circular ring (hollow cylinder) are studied in Chapter 15, which is the largest chapter. Several cases of circumferential cracks in pipes are considered in Chapter 16. The final chapter demonstrates the use of weight functions in the determination of other, often neglected, crack parameters such as crack opening displacements, solutions to the Dugdale model and crack opening areas. The book is based on the authors' own research and hence it contains very little information about other techniques for obtaining weight functions on the crack or any other boundary. The need for a reference solution and the desire for simple semianalytical techniques necessarily imposes limitations on the geometric configurations that can be studied; but many of those in the book are of practical importance. I look forward to future attempts to extend these techniques to more general geometries in two dimensions, and perhaps even three dimensions. D.P. Rooke

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