The Variation of the Elliptic Paraboloid Failure Locus Beyond the Elastic Limit

Abstract

A method is presented by defining an isotropic hardening plasticity through an appropriate sequence of an isotropic problems. Assuming a stepwise form of loading or unloading, we measure the instantaneous tension and compression yield stresses along the transient principal-stress directions. These parameters completely define the instantaneous state of anisotropy of the body for the corresponding loading step, by applying the theory of elliptic paraboloid failure locus (EPFS). The parameter identification problem is formulated on the constitutive expressions for this most general failure criterion, and by applying convenient constraints derived from the EPFS theory, which are serving as filters throughout the whole procedure of evaluating the characteristic values of terms defining the variable components of the failure tensor polynomial, as the material is continuously loaded from the elastic into the plastic region and up to the ultimate failure load.

Accurate simple tests in uniaxial tension and compression yield sufficient data for defining the yield loci of the material for the loading step considered. These data were used as input values for establishing the mode of plastic deformation of the body during a particular loading path. It was shown that the prediction or the eventual correction of either extrapolated or interpolated yield surfaces are reasonable and concordant with experimental evidence.

Since the method allows the separate complete definition of the particular values of the coefficients of the failure tensor H and the strength differential effect tensor h at each loading step, it presents the important advantage over other experimental methods of clearly indicating the parts contributed either by plasticity, or by strength differential effect of elastically and plastically deformed materials and their evolution during the development of plastic deformation.