Session: 13-03-01: General: Mechanics of Solids, Structures and Fluids I

Paper Number: 172562

Non-Schmid Continuum Slip Crystal Plasticity With Implications for Dissipation Rate 

Within the context of continuum slip crystal plasticity, Schmid’s law states that the slip rate on a slip system (defined by a slip direction and a slip plane normal) is governed by the resolved shear stress on that system. However, under many circumstances, stresses other than the Schmid resolved shear stress can play a significant role. For example, even in fcc crystals, cross-slip can activate mechanisms influenced by non-Schmid stresses. Deviations from Schmid’s law have also been observed in a wide variety of crystalline solids, including intermetallics, MAX phases, and several bcc crystals.

In line with these observations, non-Schmid stress effects have been incorporated into discrete dislocation plasticity formulations, where their inclusion was found to be critical for achieving consistency with experimental observations. Similarly, for rate-independent continuum slip crystal plasticity, yield criteria involving non-Schmid stresses have been developed.

Here, we formulate a rate-dependent continuum slip crystal plasticity constitutive relation that incorporates a non-Schmid shear stress term. In this formulation, non-Schmid stresses enter the driving force for slip and act to reduce plastic deformation on the affected slip system(s). This can result in a change in active slip mode. More fundamentally, the inclusion of non-Schmid stresses in the plastic flow rule may lead to negative dissipation rates for certain deformation histories (a behavior that violates a common requirement in continuum plasticity, namely, that dissipation should be non-negative for all possible deformation histories).

This non-negative dissipation requirement is analogous to the Coleman-Noll postulate (which mandates that the Clausius–Duhem inequality be satisfied for all deformation histories). However, from a statistical mechanics perspective, the Clausius-Duhem inequality holds only in the limit of large systems and long times (it may be violated during discrete events over short timescales).

Because a non-Schmid slip system flow rule allows for the possibility of negative dissipation, several fundamental questions arise: (i) What are the implications, within a continuum slip crystal plasticity formulation, of the dissipation rate being negative (either on a subset of the active slip systems or on all active slip systems)? (ii) What is the effect on stability if a negative dissipation rate does occur? (iii) Can stability be ensured by imposing additional conditions?

Beyond the sign of the dissipation rate, further questions concern the overall mechanical behavior: (i) How does non-Schmid stress-governed plastic flow affect the overall stress-strain response? (ii) How does it influence the evolution of slip (particularly the onset and development of strain localization)?

To address these questions, we investigate the implications of non-Schmid-governed plastic flow within the framework of quasi-static plane strain tension of a planar single crystal with two potentially active slip systems. The crystal is oriented for symmetric double slip, with the slip rate on one or both systems influenced by a non-Schmid stress term. For simplicity, this term is taken to depend on the Schmid resolved shear stress of the other slip system.

Finite deformation, finite element analyses are carried out for planar tensile bars with an initial geometric imperfection (to promote nonuniform deformation). The overall stress-strain response (including the onset of stress drop due to localized deformation) and the evolution of the plastic dissipation rate (both pointwise and integrated over the bar) are computed for various characterizations of the non-Schmid stress term. This problem setup provides a simplified context in which to examine the possible consequences of a negative plastic dissipation rate.

Presenting Author: Ankit Srivastava Texas A&M University

Presenting Author Biography: Ankit is an Associate Professor in the Department of Materials Science and Engineering at Texas A&M University, College Station, TX.

Authors:

Ankit Srivastava Texas A&M University
Alan Needleman Texas A&M University