A phenomenological model of size-dependent hardening in crystal plasticity

Abstract

A phenomenological model of plastic deformation is proposed, which captures the size-dependence of plastic flow strength and work-hardening in pure FCC crystalline materials. Guided by discrete dislocation dynamics analyses, the treatment is based on two structural variables determining the mechanical state of the material. A complete description of plastic behaviour is achieved, giving two inherently different statements for the evolution of structure, supplemented by a new kinetic equation, which specifies the hardening law in differential form at fixed structure. Evolution of the first state variable is set by phenomenology; it accounts for the cardinal bulk phenomena of athermal hardening and dynamic recovery, in addition to geometric storage. The second state variable is kinematically determined so that an evolution equation need not be formulated explicitly in rate form. The model formulation leaves the classical treatment of dynamic recovery unaltered. However, since there is virtually no experimental data on the temperature and strain-rate dependence of plastic flow at the micron scale, emphasis is laid on athermal behaviour. In this limit, the model equations are integrated, following specified strain paths to give the flow strength at the current structure. Model predictions are assessed through comparison with results from discrete dislocation analyses of geometrically similar crystals subject to compression.

Keywords:

• dislocations
• plasticity
• size-effect
• work hardening
• Kocks-Mecking-Estrin model
• lattice rotations

Acknowledgements

Support from the National Science Foundation through the Faculty Early Career Development Program (CMMI-0748187) is gratefully acknowledged. The authors also acknowledge a grant from the Texas A&M University Supercomputing Facility.

Notes

Notes

1. Exceptionally, two realisations of the H = 0.2 µm specimen had ρ_G greater than 20% of the total density.

2. It is evident that if the dislocation density is obtained by integration of (4) with k ₀ = 0, as in the original KME model, then the Taylor equation would simply lead to a size-independent response.