Abstract
The use of a stress-strain constitutive relation for the undamaged material and a traction-separation cohesive crack model with softening for cracking has been demonstrated to be an effective strategy to predict and explain the size-scale effects on the mechanical response of quasi-brittle materials. In metals, where ductile fracture takes place, the situation is more complex due to the interplay between plasticity and fracture. In the present study, we propose a multi-scale numerical method where the shape of a global constitutive relation used at the macro-scale, the so-called hardening cohesive zone model, can be deduced from meso-scale numerical simulations of polycrystalline metals in tension. The shape of this constitutive relation, characterized by an almost linear initial branch followed by a plastic plateau with hardening and finally by softening, is in fact the result of the interplay between two basic forms of nonlinearities: elasto-plasticity inside the grains and classic cohesive cracking for the grain boundaries.
Highlights
The cohesive zone model (CZM) is widely applied in the computational mechanics community to model cracking in quasi-brittle materials at the macro-scale [1,2,3,4]
A limit analysis approach based on the proposed constitutive laws can provide asymptotic approximation to the post-peak response, which can be relevant in the analysis of ductile-to-brittle transitions
In the present study it has been shown that the shape of the hardening cohesive crack model can be deduced by the fundamental interplay between the following forms of nonlinearity at the meso-scale: grain plasticity and intergranular cracking in the polycrystalline microstructure of metals
Summary
The cohesive zone model (CZM) is widely applied in the computational mechanics community to model cracking in quasi-brittle materials at the macro-scale [1,2,3,4]. This softening, impossible to be explained as the result of purely plastic deformations, is the physical result of the formation of small micro-cracks and micro-cavities that coalesce, grow and lead to specimen failure Another interesting problem where there is a strong interplay between plasticity of the continuum and grain boundary decohesion is represented by the MgCa0.8 alloy investigated in [9]. The presence of these interfaces along grain boundaries promotes brittle intergranular cracking in addition to ductile plastic deformation of the grains These experimental evidences suggest that the interplay between the two elementary forms of nonlinearity related to grain boundary decohesion and plasticity inside the grains is responsible for the failure behavior of the material at the meso-scale. Meso-Scale Simulations of Ductile Polycrystalline Materials Based on the Cohesive
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
