Kapil K. Mathur

On modeling the development of crystallographic texture in bulk forming processes

Abstract A mathematical formulation is presented for modeling the evolution of deformation induced crystallographic texture in steady state bulk forming processes. The formulation treats the material response of the polycrystalline aggregate as a statistical function of the response of the individual grains. A viscoplastic relationship is assumed for deformation along the grain slip systems. Strain hardening on these slip systems is included. The viscoplastic stiffness matrix code is presented. A streamline technique has been used to integrate the evolution equation for this aggregate is derived and its implementation in a large deformation Eulerian finite element for the lattice rotation and the slip system hardness. As an application, the evolution of texture in a multipass aluminum rolling simulation has been modeled. The numerical predictions have been compared with reported experimental rolling textures.

A hybrid finite element formulation for polycrystal plasticity with consideration of macrostructural and microstructural linking

A hybrid finite element formulation for the plastic deformation of FCC metals with anisotropy is outlined. Polycrystal plasticity theory is used to develop the constitutive response. The hybrid approach facilitates introduction of the microscale stress in the macroscopic statement of equilibrium. Convergence of the hybrid formulation is contrasted with that of a velocity-pressure formulation. It is demonstrated that the hybrid formulation is well suited for studies where significant spatial variations in constitutive response result from having only one, or a very few, crystal orientations represented in each finite element. A simulation of channel die compression is made with one crystal per finite element. The resulting texture evolution is compared with other texture evolution models and experimental data for cold rolled aluminum. It is demonstrated that the brass texture component, observed in the experimental data, is developed through shear deformations arising from grain-to-grain interactions.

Application of polycrystal plasticity to sheet forming

Abstract A methodology for including anisotropy in metal forming analyses is presented. A finite element formulation is developed for the analysis of the inhomogeneous macroscopic deformations. Anisotropic material properties are derived from a microscopic description based on polycrystal plasticity theory. Efficient computation of the microscopic variables is achieved through massive data parallel computations. A procedure is set forth for initialization of the microscopic state variables from experimental measurement of the metal texture. The feasibility of initializing (from experimental data) and evolving (through massive computations) a detailed microscopic description for a complex deformation process is demonstrated through a predictive simulation. The predicted location and height of ears in the hydroforming of aluminium sheets are in good agreement with experiment.

On modeling anisotropy in deformation processes involving textured polycrystals with distorted grain shape

Abstract A mathematical formulation is presented which uses rate-dependent polycrystalline plasticity to model the development of plastic anisotropy in bulk forming processes. The formulation assumes that underlying a material point on a continuum scale is a collection of anisotropic, contiguous grains. The mechanical response at a continuum level is derived from the response of individual grains suitably averaged over all grains in the aggregate. The effects of preferred orientation (texture) and of the evolving grain shape on the directionality to the flow properties of the polycrystal are included. A general numerical framework is described for incorporating this complex material behavior in a finite element formulation. As an application, texture development during the flat rolling of aluminum sheets is presented. The simulation predictions have been compared with reported experimental data and with a previous study where the effects of grain shape were neglected.

On modeling damage evolution during the drawing of metals

Abstract A mathematical formulation for modeling the performance of a die design in a drawing operation is presented. The formulation uses internal state variable constitutive equations to predict the plastic flow and microstructure development of metals during a drawing operation. The shearing behavior of metals has been modeled by a version of Harts model appropriate for large strain deformations. Volumetric deformations are represented by the void growth model proposed by Cocks and Ashby. Decreases in the apparent density predicted using the formulation have been compared with the experimental results reported by Rogers and Coffin for the drawing of aluminum and copper strips.

Texture Development During Wire Drawing

The development of deformation induced anisotropy in wire drawing operations is modeled with a finite element formulation that incorporates a polycrystalline plasticity model to describe the metal anisotropy

Damage Evolution Modeling in Bulk Forming Processes

Abstract A mathematical formulation is presented for the analysis of metal forming operations which lead to accumulation of material damage by the nucleation and growth of voids. Two different approaches are introduced to model the accumulation of damage within the context of this formulation. Emphasis of the formulation is on the application of two state variable models to describe the strain hardening, rate-dependent plastic flow with plastic dilatancy. The numerical predictions have been compared with reported sheet drawing experiments. Good agreement between the numerical predictions and the experimental data demonstrates the success of the formulation. The application of the mathematical formulation in the design of manufacturing operations has been further demonstrated by studying the effect of die angle geometry, for a fixed thickness reduction, on the accumulation of material damage and on the evolution of the hardness.

Finite element modeling of polycristalline solids

ABSTRACT Anisotropy in the plastic flow of polycristalline solids can be computed based on the slip characteristics of individual crystals and included in finite element formulations as the constitutive description of the material. A variety of approaches exist for merging finite element formulations and polycrystal plasticity, and depending on the intended application the two may have different relationships to each other. We summarize two regimes that we refer to as large and small scale applications and outline a finite element formulation for each. Examples of both large and small scale applications are presented and some important issues associated with the implementation of each are discussed.