Application of a Thermo-Viscoplastic Model to the Analysis of Defects in Warm Forming Conditions

Abstract

Summary When deformation takes place at warm temperature (from 350°C up to 750°C), material properties can vary considerably with the variation of temperature and strain rate. Our main concern here is the analysis of plastic deformation processes in warm regime, including alterations of the flow resistance of metal, such ductile fracture and bifurcation of plastic deformation. In the first part of the paper, we give some details about constitutive laws used in the thermo-viscoplastic range. Experimental results are presented, they concern 1038 and 4142 steels, used at warm temperature, in an annealed state. In order to evaluate the limits to formabality in bulk forming, we have also measured the strains at fracture in using the notched tensile test of round bars and the compression test of axisymmetric specimens. The experimental result obtained are expressed in a diagram that relates effective plastic strain at fracture and hydrostatic stress ratio (σ m /σ). In the second part of the paper, we describe a simple one step implicit-explicit integration method for analyzing the quasi-static deformations of solids, in the elastic-viscoplastic range, including damage and temperature effects. Numerical applications are given in the case of upset cylinders, and an industrial problem is treated concerning axisymmetrie forward extrusion. The examples presented illustrate well the newness and the industrial relevance of the analysis.