Plasticity of Cold Worked Metals A Deductive Approach

Plasticity Theory is a basic tool of Structural Engineering to evaluate the ultimate strength of structures and their behaviour under large loads. Any modern computing code in structural analysis makes use of it to model the response of a structure beyond the elastic range –often by exploiting very sophisticated computational analysis and advanced kinematics for large deformations. Yet all this valuable effort has its Achille's heel: the evolution law of the yield surface of the material, also referred to as work-hardening rule.The work-hardening rules that are usually introduced to model this phenomenon are the kinematic rule, the isotropic rule and some combinations –more or less linear– of them. None is capable of reproducing the dramatic shape changes of the elastic domains shown in the picture. Other work-hardening rules are also available. They are invariably more complicated than the former and possibly even less adequate to represent the post-elastic behaviour of real materials when it comes to general three-dimensional elastic-plastic processes. Still these processes are within the reach of many commercially available computing codes, which in principle should enable us to make general elastic-plastic analyses as needed. The lack of more realistic work-hardening rules, however, sets serious doubts about the validity of the results that can thus be obtained. As a consequence we often have to restrict the applications to particular classes of processes, reduce the range of admissible deformations and make frequent recourse to experimental validation.The book approaches the work-hardening problem in a deductive way, starting from elementary hardly questionable facts, working out their inescapable consequences and following them until a practical solution is obtained.