Constitutive Models, Physically Based Models for Plasticity

Synonyms

Mechanism-based plasticity

Definition

Physically based models for the plastic behavior of crystalline, metallic materials are discussed. However, deformation by twinning and phase transformations as well as the evolution of texture are omitted.

Overview

Slip of dislocations is the main cause for plastic deformation. Additional mechanisms are formation of twins and phase transformations (mainly austenite to martensite). Several models for deformation hardening have been proposed and most of them depict proportionality between the flow stress in shear, τ, and the square root of the total dislocation density, ρ, giving the relationship

$$ \tau =\alpha Gb\sqrt{\rho } $$

(1)

where α ~ 0.2 for fcc and α ~ 0.4 for bcc metals (Chapter 1 in [1]). G is the shear modulus and b is the magnitude of Burgers vector. Moving dislocations are the cause of the plastic shear rate expressed by the Orowan equation

$$ {{\dot{\gamma}}^p}=\frac{{d{\gamma^p}}}{dt }={\rho_m}bv $$

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