Physics and Mathematics of Adiabatic Shear Bands

5R21. Physics and Mathematics of Adiabatic Shear Bands. - TW Wright (US Army Res Lab, Aberdeen Proving Ground MD). Cambridge UP, Cambridge, UK. 2002. 241 pp. ISBN 0-521-63195-5. $60.00.Reviewed by P Perzyna (Inst of Fund Tech Res, Polish Acad of Sci, Swietokrzyska 21, Warsaw, 00-049, Poland).This little book is based on a course of lectures given by the author on visits to the University of California at San Diego in 1990 and 1995. The topics were chosen primarily because of the author’s particular research interests, but also to fill a gap of research monographs in the field of the material instability known as adiabatic shear banding. TW Wright has a reputation of long standing as a particularly lucid and methodical expositor, both when writing and lecturing. This book also is a model of clarity (with, however, some exceptions to be mentioned), and it is a pleasure to read. Adiabatic shear banding is a new and very important field of mechanics. In dynamic loading plastic flow processes in solid bodies failure may arise as a result of an adiabatic shear band localization which is generally attributed to a plastic instability generated by thermal softening during dynamic deformation. This is why the investigations of adiabatic shear banging now have a crucial role. The contents of a book can be divided into three parts. The first four chapters set the physical and mathematical foundations for detailed study of adiabatic shearing. Chapters 5, 6, and 7 explore the dynamics of band formation in a one-dimensional (1D) setting. The last two chapters extend the discussion to two dimensions. The references not complete, but representative, are chosen according to the author taste. The most important first part of the book is written very superficially. In the first chapter, the physical foundations and experimental observations of adiabatic shear banding are treated only as introductory considerations. The author does not consider the fundamental problems of adiabatic shear banding in single crystals. Chapters 2 and 3 bring a brief summary of balance laws, and fundamental description of thermoelasticity and thermoplasticity. In Chapter 4, several flow models for thermoviscoplasticity are presented. The author has privilege concerning the choice of models in description and application, however, he considered mostly the 1D models of thermoviscoplasticity and omitted such important 3D models like the Duvant-Lions model, the consistency model, and the model based on the overstress function (this last one has a long tradition, cf, Bingham 1922, Hohenemser and Prager 1932, Sokolovsky 1948, Malvern 1950, Perzyna 1963). It is noteworthy to add that these three models have been recently broadly used in study of the problems of adiabatic shear banding (for the review articles of presented results in these fields, cf, P Perzyna (ed), Localization and Fracture Phenomena in Inelastic Solids, Springer-Verlag, Wien, New York, 1998). The second part of the book (Chs 5, 6, and 7) recapitulates the notable contributions to description of adiabatic shear banding by the author. Several 1D initial boundary value problems are solved, and major features of band formation are discussed. These features for the linear differential equations include the timing of localization, the morphology of fully developed bands, and the quantitative role of various physical properties, such as thermal conductivity, heat capacity, work hardening, thermal softening, and strain rate sensitivity. Without heat conduction and strain rate sensitivity, the dynamic governing equations in a 1D problem may show a change of type from wave propagation phenomena to instability phenomenon. It is very strange and very difficult to understand the result obtained by the author that strain rate sensitivity (viscosity) has the effect of delaying only, but not eliminating instability phenomenon. For the three models of the theory of thermo-elastoviscoplasticity mentioned earlier (namely, the Duvant-Lions model, the consistency model, and the model based on the overstress function), it has been proved that viscosity has the effect of regularization of the mathematical problem, so that the solution may have diffuse localization of plastic deformation but the instability phenomenon is avoided. Very good example of this proof for two models (Duvant-Lions model and the model based on overstress function) may be found in the monograph by JC Simo and TJR Hughes, Computational Inelasticity (Springer-Verlag, New York, 1998). It is noteworthy to stress that the regularization property is accomplished because viscosity introduces implicitly a length-scale parameter into the dynamical initial-boundary value problem, ie, l=αcτ, where τ is the relaxation time for mechanical disturbances, c denotes the velocity of the propagation of the elastic waves in the material, and α is the proportionality factor which depends on the particular initial-boundary value problem. The final part of the book (Chs 8 and 9) is concerned with discussion of the results obtained by 2D experimental observations and the principal known solutions of 2D problems with propagating shear bands. In Chapter 8, the author focuses the discussion on three kinds of 2D experiments. The discussion of solutions presented in Chapter 9 is confined to local analysis near the tip of a propagating shear band or to boundary layer and similarity solutions. We conclude that the author disregarded many important problems that recently have been very well developed. For instance, he did not consider analytical methods for investigation criteria for adiabatic shear band formation (initiation). There exist two very well-known methods that are broadly used in the investigation criteria for shear band localization for both single crystals and polycrystalline solids. The first method is based on the analysis of acceleration waves. In this investigation the instantaneous adiabatic acoustic tensor plays a fundamental role. The second is called the standard bifurcation method (cf, JR Rice, The localization of plastic deformation, Theoretical and Applied Mechanics (WT Koiter, ed), North-Holland, Amsterdam, 1976, 207-220). The author did not discuss the softening effect generated by microdamage mechanisms within the material during plastic flow processes. It is a very well-known fact that this kind of softening in many practical cases may have decisive importance in the formation process of shear bands. Interaction of stress waves and dispersion effects has a very important role in the development of adiabatic shear bands. These problems need also to be considered more deeply. Very recently, experimental observations have been performed to investigate the initiation and propagation characteristics of dynamic shear bands in several kinds of steel, (cf, PR Gudurn, AJ Rosakis, and G Ravichandran, Dynamic shear bands: An investigation using high speed optical and infrared diagnostics, Mechanics of Materials, 33 (2001), 371-402). These investigations open a new branch of research works focusing on dynamics of shear bands as the problems of mesomechanics. This reviewer’s opinion is that no attempt has been made to do more than touch on a small fraction of the subject of adiabatic shear banding. Thus, Physics and Mathematics of Adiabatic Shear Bands can be treated as a very introductory course on adiabatic shear banding. The book should be purchased by individuals as well as by libraries.