An examination of the neutral loading condition in plasticity theory

Abstract

An examination is made of a number of neutral loading experiments according to classical plasticity theory. For work hardening materials the question as to whether plastic deformation occurs during neutral loading depends strongly upon the deformation produced from initial loading. Initial elastic loading with a subsequent stress path that follows the boundary of the initial vield surface is truly neutral with a wholly elastic response. However, when plastic strain is produced from initial loading then plastic flow is produced from a subsequent stress path that follows the boundary of a surface that is an isotropic expansion of the initial yield surface. Since this violates the assumption of isotropic hardening the usefulness and limitations of the rule of kinematic hardening are examined. It is further shown that the results from recent experiments are particularly relevant to the appraisal of modern developments to plasticity theory.Neutral loading without work hardening will produce plastic flow. It is shown that the corresponding Prandtl—Reuss theoretical solutions are representative of observed behaviour for both severely pre-strained materials and for others that do not harden appreciably.The concept is introduced of lower and upper bounds on the deformation that can be expected from neutral loading. These correspond to the extreme purely elastic and non-work-hardening solutions, respectively.