Strain-energy density and fracture-process zone. Report 1. Theoretical premises

Abstract

A representation is proposed for the total strain-energy density (SED) in dimensionless form. The θ-distribution of the elastic and plastic parts of the total SED, and also the strain-energy-density factor S for the full range of mixed fracture modes under plane strain and a plane stress state are presented. Differences, as defined by the strain-energy-density factor, are established between fracture conditions under plane strain and a plane stress state. A general relationship between strain-energy density and a material parameter (the size of the fracture-process zone) is brought to light in dimensionless form. The relationship obtained predicts the pattern of continuous variation in the size of the fracture-process zone from static to cyclic material fracture. A material constant can be considered one of the consequences of fracture. Equations are proposed for calculation of the size of the fracture-process zone under a plane stress state and plane strain over the full range of mixed deformation modes with respect to standard mechanical properties of the materials.