Gorti B. Sarma

Modeling the kinetics and microstructural evolution during static recrystallization : Monte Carlo simulation of recrystallization

The kinetics of microstructure and texture evolution during static recrystallization of a cold-rolled and annealed f.c.c. material is simulated by coupling a finite element model of microstructural deformation with a Monte Carlo simulation of recrystallization. The salient features of the simulations include a nucleation model for recrystallization based on subgrain growth and the modeling of simultaneous recovery during recrystallization. The simulation results quantify the effects of non-uniform stored energy distribution and orientation gradients present in the cold-worked microstructure on recovery by subgrain growth, and hence on the spatial distribution of nuclei and their orientations. The growth of these recrystallized nuclei in the presence of continued recovery of the substructure has been simulated for initial cold-work levels of e=0.7 and 1.1 obtained by plane strain compression. The simulations are shown to be potentially capable of capturing the formation and evolution of cube texture commonly observed in cold-rolled and annealed f.c.c. materials.

Finite element simulations of cold deformation at the mesoscale

Abstract The deformation of polycrystalline aggregates is modeled using the finite element method. Explicit discretization at the single crystal level is employed to study the inhomogeneous deformations of individual crystals. Plastic deformation by crystallographic slip is treated using a constitutive model based on crystal plasticity. The formulation is used to predict the non-uniform nature of strain hardening and texture evolution in the crystals subjected to plane strain compression. The capability of the simulations to capture the inhomogeneous deformation of individual grains during plastic deformation of polycrystals is demonstrated. The hardness and orientation values of elements from the same grain evolve to different final values due to local inhomogeneities and interactions with neighbors. The simulations provide a means to obtain quantitative information on the inhomogeneous distributions of stored energy and orientations among the different crystals comprising the microstructure.

Integration algorithm for modeling the elasto-viscoplastic response of polycrystalline materials

Abstract An integration scheme is presented for modeling the texture evolution and stress–strain response of elasto-viscoplastic polycrystalline materials. Single crystal kinematics based on a multiplicative decomposition of the deformation gradient is used to obtain an evolution equation for the crystal elastic deformation gradient. An implicit scheme to integrate this equation is presented which is stable and efficient. The reorientation of the crystal as well as the elastic strain can then be obtained from a polar decomposition of the elastic deformation gradient. Numerical studies are presented using material parameters for aluminum (FCC crystals) and zircaloy (HCP crystals) to demonstrate the general nature of the model. Predictions of the model are also compared with those obtained using a rigid-viscoplastic polycrystal model which neglects the elastic response. Retaining the elastic response makes the model useful for large deformation analyses where both anisotropy due to texture as well as elastic effects such as springback and residual stresses are important.

Simulations of deformation and recrystallization of single crystals of aluminium containing hard particles

The deformation of a single crystal of aluminium in the Goss orientation {011}100 containing a coarse particle of silicon was modelled by using a finite-element (FE) code based on the crystal plasticity approach. The simulations clearly captured the heterogeneous deformation of the aluminium matrix, resulting in a region of high deformation in the vicinity of the hard particle, surrounded by a region where the amount of deformation was significantly lower. The evolution of the corresponding deformation substructure during annealing was simulated using a Monte Carlo technique. The simulations clearly demonstrated the discontinuous evolution of the subgrains in the deformation zone to form recrystallization nuclei around the hard particle, and the subsequent growth of these nuclei to consume the matrix region around the particle. For plane strain compression up to ezz = -0.4 that was used in this study, the deformation texture components near the particle consisted of rotations up to 20° from the initial Goss orientation about the transverse direction. Recrystallization simulations captured the formation and growth of nuclei from the deformation heterogeneities existing near the hard particle and predicted a significant strengthening of the orientations present in the particle deformation zone. The simulation results are shown to capture many of the experimentally observed features of deformation and recrystallization textures in aluminium single crystals containing coarse particles of silicon.

Monte Carlo simulation of deformation substructure evolution during recrystallization

Recently, a microstructure and texture evolution model was presented for static recrystallization by coupling a Monte Carlo (MC) simulation of recrystallization with a finite element (FE) simulation of microstructural deformation based on crystal plasticity. The crystal plasticity model provided a quantitative description of the orientation distributions in the deformed microstructure. In this paper, a new model for recrystallization is presented where recrystallization is modeled as a one-step, heterogeneous subgrain growth process. The simulations indicate how existing prior high angle boundaries as well as the high angle boundaries produced by the deformation process migrate to sweep through the deformed regions to produce typical recrystallized microstructures and kinetics. The simulations also capture the heterogeneous growth of subgrains induced by long-range orientation gradients present in the deformation substructure. The simulations are used to evaluate the recrystallization kinetics, microstructure and texture evolution for deformed fcc polycrystals.

Influence of residual stress on thermal expansion behavior

We demonstrate that the thermal expansion behavior of a material can be substantially modified by the presence of residual stresses. In the case of a composite tube made of two layers of dissimilar steels, in situ neutron diffraction measurements revealed a significant difference in the coefficients of thermal expansion along the radial and tangential directions. It is shown that the observed difference in thermal expansion is due to the change of residual stresses with temperature.

Modelling the deformation of face centred cubic crystals to study the effect of slip on {110} planes

The deformations of single crystals and polycrystals of aluminium have been modelled using the finite-element method. The constitutive behaviour is modelled using crystal plasticity to account for the plastic deformation by slip, and to track the hardening and reorientation of the material. By discretizing each crystal with a large number of elements, the non-uniform deformations due to local inhomogeneities and interactions with neighbouring crystals are modelled. Simulations of plane strain compression of (001)[110] oriented single crystals are used to demonstrate the ability of the model to capture shearing in the rolling-normal plane, and the consequent reorientation of the crystal to the {112}111 copper components. The simulations are used to examine the effect of including {110}110 slip systems in addition to the usual {111}110 systems for face centred cubic metals on the stability of the cubic orientation. The results indicate that slip on {110} planes greatly enhances the stability of the cubic orientation, while having little contribution in the deformation of most other orientations.

Using high performance Fortran for parallel programming

Abstract A finite element code with a polycrystal plasticity model for simulating deformation processing of metals has been developed for parallel computers using High Performance Fortran (HPF). The conversion of the code from an original implementation on the Connection Machine systems using CM Fortran is described. The sections of the code requiring minimal inter-processor communication are easily parallelized, by changing only the syntax for specifying data layout. However, the solver routine based on the conjugate gradient method required additional modifications, which are discussed in detail. The performance of the code on a massively parallel distributed-memory Intel PARAGON supercomputer is evaluated through timing statistics. Published by Elsevier Science Ltd.

Modeling Studies to Predict Stresses in Composite Floor Tubes of Black Liquor Recovery Boilers

The results of finite element modeling studies to analyze the composite floor tubes of recovery boilers used by the pulp and paper industry are presented. Thermal and mechanical analyses have been carried out to examine the changes in the stresses during a normal operating cycle. Three different materials for the clad layer have been studied-304L stainless steel and alloys 625 and 825. The results show that the coefficient of thermal expansion and the strength of the clad layer play a significant role in the stress variation due to the heating and cooling associated with an operating cycle, with implications for the development of cracks in the tubes clue to stress corrosion cracking. The analyses also show that axial stress in the carbon steel layer is compressive at the fireside tube crown and tensile in the membrane, which provides a possible explanation for the commonly observed differences in crack propagation in tubes and membranes.

Mesoscale Simulations of Microstructure Evolution in a Temperature Gradient

The evolution of pore and grain structure in a nuclear fuel environment is strongly influenced by the local temperature, and the temperature gradient. The evolution of pore and grain structure in an externally imposed temperature gradient is simulated for a hypothetical material using a Potts model approach that allows for porosity migration by mechanisms similar to surface, grain boundary and volume diffusion, as well as the interaction of migrating pores with stationary grain boundaries. First, the migration of a single pore in a single crystal in the presence of the temperature gradient is simulated. Next, the interaction of a pore moving in a temperature gradient with a grain boundary that is perpendicular to the pore migration direction is simulated in order to capture the force exerted by the pore on the grain boundary. The simulations reproduce the expected variation of pore velocity with pore size as well as the variation of the grain boundary force with pore size.