Re-Meshing in Finite Element Simulations of Hot Working Including a Microstructural Evolution Model

Abstract

Material models that couple the evolution of flow stress to the evolution of the microstructure are important for the simulation of hot working processes in which the microstructure undergoes large changes. Among the microstructural evolution mechanisms in hot working, dynamic recrystallization (DRX) plays a central role as it occurs during deformation. When the workpiece deforms, the element shape may deteriorate, which makes re-meshing necessary. At the same time, certain regions of the finite element mesh undergo DRX and a sharp interface between recrystallized and non-recrystallized portions of the workpiece develops. Elements of the old mesh that are cut by the interface contain nodes with a non-zero recrystallized volume fraction and nodes where the recrystallized volume fraction is zero. During re-meshing, when the microstructural data is transferred to the new mesh, nodes or integration points that are actually in region of the workpiece that is not yet recrystallized may be assigned a non-zero recrystallized volume fraction. As a consequence, the interface moves, which is unwanted and may produce large errors when re-meshing is frequently done. In this paper, the problem of the propagation of the DRX interface during re-meshing is treated. It is shown that the propagation occurs with standard data mapping algorithms and produces a large error at the interface. A re-meshing scheme is proposed that uses a smooth mesh-free interpolating function based on radial basis functions to interpolate the recrystallized volume fraction. The interface is the zero level set of this interpolant. Performing the mapping as a least squares fit of the interpolant allows for a substantial reduction of the mapping error and suppresses the propagation of the DRX front.