- English
- فارسی

# Hossein Shaarbaf

**Grade: ** Master

**Thesis Title:**

Micromechanical Modeling of Multi Phase Metals Using a Crystal Plasticity Model

**Year:** Sept. 2007- Feb. 2010.

**Abstract:**

In this thesis, the plastic deformation of single crystal, polycrystal and two phase polycrystal materials was studied by a FEM model calculation, taking into account anisotropic elasticity and crystal plasticity. Crystal plasticity methods represent a mesoscale, or grain level. These models use constitutive equations to model the behavior of single crystals to formulate a macroscopic response from the individual crystal responses. They allow simulation of the slip system strain hardening and internal stress development within the aggregate. Crystal plasticity allows each grain to be discretized into numerous finite elements or each grain may be composed of a single finite element. Balance laws are calculated for each individual crystal and the solution of these equations is used to partition the total deformation between the crystals. Once the applied deformation is known for each crystal, the condition of the crystal is evolved by numerically integrating the constitutive equations. The anisotropic material behavior of each single crystal is taken into account at every point in the finite element model. A FORTRAN subroutine called UMAT has been written particularly for the finite element code ABAQUS as a "user-material" subroutine for the constitutive model of single crystals. When simulating alloys, one must determine how the properties of each phase combine to form the macroscopic properties of the material and the ways in which the individual properties of one phase change due to the presence of the other phase. The different deformation characteristics of the separate phases cause interaction stresses and strains between them. The relationship of the phases to one another and the interactions between the grains under deformation must be taken into account since the internal interfaces between the phases can influence damage and internal stresses during plastic deformation. A composition of soft CU phase and hard FE phase is used for two phase polycrystal simulation. At first each phase of iron and copper was simulated individually as a single crystal model to obtain the effect of the grain direction on the mechanical behavior of single crystals. Then we consider a single phase polycrystal that consist of about 500 grains with independent orientation for iron and copper separately. The results from the FEM model calculation were compared with experimental results. The last simulation is a two phase iron-copper polycrystal with the various weight percent for each phase and about 500 independent orientations. The stress vs. strain dependence as obtained from this FEM-model appears to be in good accordance with experimental results.

**Keywords: **Crystal Plasticity; Single crystal; Two-phase polycrystal; FEM model.