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

Abstract

A cellular automaton algorithm with probabilistic cell switches is employed in the simulation of dynamic discontinuous recrystallization. Recrystallization kinetics are formulated on a microlevel where, once nucleated, new grains grow under the driving pressure available from the competing processes of stored energy minimization and boundary energy reduction. Simulations of the microstructural changes in pure Cu under hot compression are performed where the influence of different thermal conditions are studied. The model is shown to capture both the microstructural evolution in terms of grain size and grain shape changes and also the macroscopic flow stress behavior of the material. The latter gives the expected transition from single-to multiple-peak serrated flow with increasing temperature. Further, the effects on macroscopic flow stress by varying the initial grain size is analyzed and the model is found to replicate the shift towards more serrated flow as the initial grain size is reduced. Conversely, the flow stress is stabilized by larger initial grain sizes. The extent of recrystallization as obtained from simulations are compared to classical JMAK theory and proper agreement with theory is established. In addition, by tracing the strain state during the simulations, a post-processing step is devised to obtain the macroscopic deformation of the cellular automaton domain, giving the expected deformation of the equiaxed recrystallized grains due to the macroscopic compression.

Mesoscale modeling and simulation of microstructure evolution during dynamic recrystallization of a Ni-based superalloy

“…The reason for such a difference may be because that the elongated grain boundaries provide more potential nucleation sites for recrystallization due to a higher ratio of the grain boundary volume to grain volume. At the same time, the newly formed recrystallized grains impinge earlier with support of the morphology change of the matrix, resulting in a smaller average grain size as compared to the conventional CA simulation [5][6][7][8][9][10][11][12][13][14][15][16][17][18]. In addition, it can be also found that the grain morphology deformation has a decreased effect on the critical strain for DRX.…”

“…In this case, initial grain size, initial grain orientation and dislocation density are used as input data to the CA model; the flow curve, dislocation density, finial grain size and orientation and recrystallized fraction are the output data. Hallberg et al [11] employed the CA model with probabilistic cell switches in simulating DRX of pure Cu. Ding et al [12] investigated the hot compression behavior of the Mg-9Al-1Zn alloy using EBSP analysis and the CA method.…”

Approaches to Modeling of Recrystallization

“…Plotting Equation (1) in a double-logarithmic diagram allows convenient identification of the parameters B and n A . The Avrami exponent n A , given by the slope of the plot, gives some indication of the character of the nucleation process, i.e., if site-saturated or continuous nucleation takes place, and changes if two-or three-dimensional results are considered [2,6,19]. Limitations and modifications of the KJMA model are discussed in [20][21][22].…”

“…The formulation in Equation (5) corresponds to the proportional nucleation model in [30,31]. Expressions for the nucleation rate as in Equation (5) have been used in Monte Carlo modeling of recrystallization in [35,36] and in cellular automata models in [19,37,38]. Once nucleated, the recrystallized grains can grow due to a driving pressure p acting on the grain boundary.…”

“…The pre-exponential term m 0 can be viewed as a function of both temperature and of the crystallographic misorientation across the grain boundary [55]. A grain boundary mobility formulation like in Equation (11) has been employed analytically in [56] and in cellular automata in [19,38].…”