Coupling of a crystal plasticity finite-element model with a probabilistic cellular automaton for simulating primary static recrystallization in aluminium

Abstract

The paper presents a two-dimensional approach for simulating primary static recrystallization, which is based on coupling a viscoplastic crystal plasticity finite-element model with a probabilistic kinetic cellular automaton. The crystal plasticity finite-element model accounts for crystallographic slip and for the rotation of the crystal lattice during plastic deformation. The model uses space and time as independent variables and the crystal orientation and the accumulated slip as dependent variables. The ambiguity in the selection of the active slip systems is avoided by using a viscoplastic formulation that assumes that the slip rate on a slip system is related to the resolved shear stress through a power-law relation. The equations are cast in an updated Lagrangian framework. The model has been implemented as a user subroutine in the commercial finite-element code Abaqus. The cellular automaton uses a switching rule that is formulated as a probabilistic analogue of the linearized symmetric Turnbull kinetic equation for the motion of sharp grain boundaries. The actual decision about a switching event is made using a simple sampling nonMetropolis Monte Carlo step. The automaton uses space and time as independent variables and the crystal orientation and a stored energy measure as dependent variables. The kinetics produced by the switching algorithm are scaled through the mesh size, the grain boundary mobility, and the driving force data. The coupling of the two models is realized by: translating the state variables used in the finite-element plasticity model into state variables used in the cellular automaton; mapping the finite-element integration point locations on the quadratic cellular automaton mesh; using the resulting cell size, maximum driving force, and maximum grain boundary mobility occurring in the region for determining the length scale, time step, and local switching probabilities in the automaton; and identifying an appropriate nucleation criterion. The coupling method is applied to the two-dimensional simulation of texture and microstructure evolution in a heterogeneously deformed, high-purity aluminium polycrystal during static primary recrystallization, considering local grain boundary mobilities and driving forces.

Modeling Microstructure Evolution of Ni Cermet Using a Cellular Automaton Approach

“…Generally speaking the transition rules used in the literature fall into two categories, based on either cell counting or free energy. The cell counting approach has been used for modeling microstructure changes that are driven only by interface curvature (15,29,32,33), whereas the free energy based approach has been employed in modelling microstructure changes driven by other driving forces, such as stored elastic energy, stored dislocation density and crystallographic orientation mismatch (28,34,35). The advantage of the free energy based approach is that the transition rule can be made scalable to any mesh size and to any combination of interface mobility and energy (34).…”

Linking plastic deformation to recrystallization in metals using digital microstructures

“…In [19], a 2D digital sample was meshed, mechanical testing was performed with crystal plasticity finite element simulations, and thermal treatment involving recrystallization was done subsequently using a CA approach [19]. A Monte Carlo (MC) approach can replace the CA approach, as done in [20][21][22][23].…”

Simulation of discontinuous dynamic recrystallization in pure Cu using a probabilistic cellular automaton

“…Each new nucleus is given the average orientation of the two boundary cells involved, cf. [41], and zero dislocation density. A zero initial dislocation density is here chosen for simplicity although it is noted from e.g.…”