Abstract
The numerical simulation of shear localization under high strain rates can be modeled by a system of four partial differential equations including conservation of momentum, conservation of energy, elastic, and inelastic constitutive relations. This article introduces the gradient terms of the equivalent plastic strain to the inelastic equation based on the implicit gradient theory of plasticity to preserve the ellipticity for the shear band modeling. The model is constructed by the mixed finite element formulation with B-bar to reduce shear locking effects considering displacement, stress, equivalent plastic strain, and temperature as the solution field and thereafter solving the entire nonlinear governing system simultaneously. The performance of the gradient plasticity model is verified by two benchmark shear band problems, and the obtained numerical results are tested with the high-rate experimental results.
Highlights
Shear band is a dynamic failure, common to be observed in metallic materials as a highly localized zone of intense plastic deformation when subjected to the high strain rates.[1,2]
As the fact that shear band is considered as a material instability propagating at the time scale of microseconds and its width is on the order of tens of microns,[3] modeling shear band problems can be a hard core in these aspects
Plastic flow models derived from experimental results dependent on strain rate, strain rate hardening, and temperature are recommended to describe the formation of shear localization.[7,8]
Summary
Shear band is a dynamic failure, common to be observed in metallic materials as a highly localized zone of intense plastic deformation when subjected to the high strain rates.[1,2] As the fact that shear band is considered as a material instability propagating at the time scale of microseconds and its width is on the order of tens of microns,[3] modeling shear band problems can be a hard core in these aspects. Different mechanisms such as strain hardening, strain rate hardening, and thermal softening are competing which results in three distinct stages in the process of shear band formation.[5,6] For numerical modeling, plastic flow models derived from experimental results dependent on strain rate, strain rate hardening, and temperature are recommended to describe the formation of shear localization.[7,8]. Higher order gradients of the EQPS are considered in the inelastic constitutive relation which preserve the ellipticity for the simulation of shear band problems.[30] The weak form of the governing equations is discussed as well . The gradient plasticity theory introduces the higher order plasticity terms into the conventional governing differential equations together with the intrinsic length scales to characterize the microstructure behavior.
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