The Physics and Mathematics of Adiabatic Shear Bands

This book is a research monograph on the material instability known as adiabatic shear banding which often occurs in a plastically deforming material as it undergoes rapid shearing. Plastic deformation generates heat, which eventually softens most materials with continued straining, a process which is usually unstable. In this case the instability results in thin regions of highly deformed material, which are often the sites of further damage and complete failure. Divided into three parts, the book first reviews the physical phenomena and the standard methods of testing and characterization. It then establishes a general theory of isotropic plasticity with finite deformations as a setting for the simpler, but still nonlinear and highly coupled, equations of adiabatic shearing and the idealizations that are necessary to establish them. The main body of the book examines a series of one-dimensional problems of increasing complexity. In this way a comprehensive and quantitative picture of the complete phenomena is built up. Particular care is taken to use well established asymptotic techniques to find simple, but universal, analytic expressions or scaling laws that encapsulate various aspects of the dynamic formation and the final morphology of shear bands. The last two chapters review recent two-dimensional experiments and analyses. A fully developed mechanics of shear is just beginning to emerge as a major companion to fracture mechanics, this book may speed the process along.