A continuum model for slip transfer at grain boundaries

Claude Fressengeas,Manas V Upadhyay

doi:10.1186/s40323-020-00145-6

Abstract

Using a continuous representation of dislocations in elastoplastic polycrystals, we investigate slip transfer at grain boundaries by assessing the compatibility of the slip system shear rates with tangential continuity of the plastic distortion rate tensor at these interfaces. Fulfillment of this tangential continuity condition is needed for consistency of the continuous description of dislocations in polycrystals. We show that, in f.c.c. materials at moderate temperatures, this condition unequivocally translates into constraints on the slip rates on both sides of grain boundaries. Appended to the elastoplastic boundary value problem, it allows a complete determination of the slip system shear rates. An algorithm enabling the implementation of compatible slip transfer in both the finite element methods and the spectral methods based on Fast Fourier Transforms is provided in both standard crystal plasticity and the mechanics of dislocations fields.

Highlights

Grain boundaries have a significant impact on plasticity mediated by dislocation glide
Incrementing α through steps (1, 2) and ignoring steps (3–7), as commonly practiced in standard crystal plasticity simulations to provide an evaluation of the dislocation density field, yields an α-field localized in the vicinity of the interfaces and associated with undue tangential discontinuity of the plastic distortion rate
Concluding remarks The present analysis of slip transfer is made in the generic context of a field theory of dislocations [1,2,27]

Summary

Introduction

Grain boundaries have a significant impact on plasticity mediated by dislocation glide. Tangential continuity constraints along interfaces Material properties and/or field variables, such as the elastic/plastic displacement and distortion/distortion rate fields or the dislocation density field may encounter discontinuities across surfaces such as grain boundaries in polycrystals.

Results

Conclusion