Large plastic deformation of crystalline aggregates. CISM course, Udine, Italy, July 15--19, 1996
[The articles of this volume will not be indexed individually.] This book presents in a nicely written text of lectures delivered at a CISM session organized in Udine, Italy (1996) by the editor C. Teodosiu. In a rather concise form it succeeds to present various and rich facets of the modelling of plastic deformations in crystalline aggregates, in contrast, or complement, to the finite-strain theory of single crystals. The presentation develops in a logical way from experimental aspects to numerical simulations. The first contribution by \textit{H. P. Stüwe} (Leoben, Austria) gives in a few pages the main experimental observations concerning crystal plasticity, that is, the notions of glide, dislocations, cold and hot workings, and rate sensitivity. The second, and central contribution by \textit{C. Teodosiu} (University of Paris-Nord, France) is devoted to the dislocation modelling in crystalline plasticity. The author, a well-known contributor to the field, has largely contributed to bridging the gap between the dislocation level of description and the phenomenological thermomechanics of finite strains. He delivers here a masterly exposition which helps one to relate the microdynamics of viscoplastic flows and the engineering approach (viscoplastic potential and dislocation-based hardening laws). This is made more concrete by an illustration of the finite element simulation of the plastic deformation of multicrystals and by its comparison to experimental evidence. The author rightly emphasizes forthcoming studies on the role played by the texture and the needed modelling of interaction between texture and microstructural evolution. \textit{C. Stolz} (Ecole Politechnique, Paris, France), in a dense and clearly written contribution, exposes the general technique (homogenization) of passing from micro- to macro-quantities in the plastic case. This follows the tradition set forth by R. Hill and J. Mandel and the more recent works of P. Suquet. This is achieved in both small- and large-strain descriptions. The final results concern the evolution law and the rate boundary value problem in polycrystals. The next contribution, by \textit{L. Anand} et al. (M.I.T., USA), concentrates on the constitutive modelling of polycrystalline metals. This is also presented in the required finite-strain framework. Special attention is paid to f.c.c. crystals. The polycrystal description makes use of G. I. Taylor's ideas and exploits a simple averaging scheme. Applications are given to cut-drawing and the high-rate deformation of tantalium. This contribution is richly illustrated by thirty three figures. The rather long contribution by \textit{A. Molinari} (Metz, France) is certainly the more mathematical one among those presented in this book, but this is done with an extreme clarity which should avoid any obstacle for non-mathematically oriented readers. The contribution concerns the so-called self-consistent modelling of plastic and viscoplastic polycrystalline materials following the works of E. Kröner, A. Zaoui and M. Berveiller. Particular points that receive special emphasis are the presentation of the grain-matrix interaction law, and the evolution of the crystallographic structure and of the morphology of grains in order to model the development of the overall anisotropy of the polycrystal. The contribution starts with an exposition of Eshelby's (now classical) treatment of the ellipsoidal heterogeneity embedded in an infinite matrix -- but this for a linear viscous case and then for a nonlinear case -- and it also concludes with a useful appendix devoted to Eshelby's problems in linear elasticity and with two other appendices on the self-consistent scheme itself and on convexity properties. In the meantime, the self-consistent method is explained and implemented in the case at hand, and applications are given to the torsion textures of copper, stress-strain relations of polyethylene, and the texture development in zirconium alloys. The final contribution, by \textit{P. R. Dawson} (Cornell, USA) and \textit{A. Kumar} (Brown, Providence, USA), is an extremely interesting discussion of numerical simulations of deformation processes in polycrystal plasticity. In these simulations, the aggregate behaviour is based on models for crystallographic slip in single crystals and on appropriate hypotheses for computing the average response of crystals comprising the aggregate. Approaches are in fact presented for accounting for the orientations of individual crystals, for describing distributions of crystal orientations, and for updating these distributions with deformation. The rolling of f.c.c. and hexagonal close-packed metals is considered as an illustration. In all, this book, both a pedagogical aid and a monography indicating research trends, is a must for all those, graduate students and professional researchers alike, who deal with the difficult endeavour presented by the modelling of the mechanical behaviour of polycrystalline materials.
scientific article; zbMATH DE number 1128596