Study of FCC Single Crystals Elastic-Plastic Constitutive Relation

Guilherme Fiorin Fornel¹; Eduardo Bittencourt¹; Rafael Luis Moresco¹

¹ Universidade Federal do Rio Grande do Sul

doi:10.20906/CPS/CILAMCE2017-0379

Resumo

This work deals with two-dimensional elastic-plastic analysis of FCC (face-centered cubic) metallic single crystals in the context of small strains. The single crystal plastic behavior is a primal aspect in material behavior understanding at micro and submicroscopic scale. The study of such scales is important due to the expansion of nanotechnologies. Rate-independent behavior and the Hutchinson-Asaro's hardening are considered in this work. Three different functions for the hardening modulus are taken into account. In two of them, the effect of rapid decrease in hardening modulus observed in some alloy crystals is also regarded. The active slip system determination is based on Schmid criteria. This work presents a conditioning study of the constitutive equation system. It is demonstrated that the orientation of crystal lattice does not change the equation system conditioning. Uniform stress field examples are analyzed. The boundary conditions are parallel loading to (1-10) crystalline plane and strains are blocked in [1-10] direction, characterizing plane-strain. In these circumstances it is possible to adopt the simplified condition in which up to three slip systems are active: (001)[110], (-1-11)[112] and (-1-1-1)[-1-12]. It is shown that the numerical stability depends significantly on properties associated to the strain hardening.

Palavras-chave: Crystal plasticity; Crystal Hardening; Numerical stability