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Zusammenfassung:
The report presents an 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
which 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 which 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 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.
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 occuring 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 simulation of
texture and microstructure evolution in a heterogeneously deformed high purity
aluminum polycrystal during static primary recrystallization considering local grain
boundary mobilities and driving forces.
