Simulation of the deformation of polycrystalline nanostructured Ti by computational homogenization

Abstract

Computational homogenization by means of the finite element analysis of a representative volume element of the microstructure is used to simulate the deformation of nanostructured Ti. The behavior of each grain is taken into account using a single crystal elasto-viscoplastic model which includes the microscopic mechanisms of plastic deformation by slip along basal, prismatic and pyramidal systems. Two different representations of the polycrystal were used. Each grain was modeled with one cubic finite element in the first one while many cubic elements were used to represent each grain in the second one, leading to a model which includes the effect of grain shape and size in a limited number of grains due to the computational cost. Both representations were used to simulate the tensile deformation of nanostructured Ti processed by ECAP-C as well as the drawing process of nanostructured Ti billets. It was found that the first representation based in one finite element per grain led to a stiffer response in tension and was not able to predict the texture evolution during drawing because the strain gradient within each grain could not be captured. On the contrary, the second representation of the polycrystal microstructure with many finite elements per grain was able to predict accurately the deformation of nanostructured Ti.

Standard and strain gradient crystal plasticity models: application to Titanium

“…The validity of using only prismatic, basal and pyramidal c+a has been confirmed by the ability of the model to predict accurately both macroscopic stress-strain behavior and crystallographic texture evolution in nanostructured pure Ti after several passes of ECAP-C ( Segurado and LLorca, 2013).…”

“…However, the description of grains as cubes is very crude from the geometrical view, and the use of a single element for each grain is not capable to capture accurately in-grain fields and tends to give a stiffer response (Segurado and LLorca, 2013).…”

“…The periodic boundary conditions are set up according to the implementation presented by Segurado et al (Segurado and LLorca, 2013). …”

“…The saturation athermal strength s α a,s was taken equal to 1.1s α a,0 for each system, due to the fast saturation of the yield stress observed in the macroscopic experiments. The initial hardening rates h α 0 were taken, for simplicity, identical for the three active slip systems (Segurado and LLorca, 2013). The hardening was assumed to be isotropic and thus q αβ = 1.…”

“…Although some relevant deformation mechanisms occur at the nanometric scale, the influence of the polycrystalline microstructure on the macroscopic behavior can be accurately captured with a continuum micromechanical description. Particularly, continuum micromechanical homogenization models based on crystal plasticity have been successfully applied to predict the effect of grain orientation distribution and texture evolution in nano Ti (Segurado and LLorca, 2013). This approach can be extended also to include the effect of temperature and strain rate at the crystal level by an appropiate crystal plasticity formulation.…”