The analysis of crack tip fields in ferroelastic materials

Abstract

The stress and strain fields near a stationary crack in a ferroelastic material are analyzed.The constitutive response of the material is taken to be characteristic of a polycrystallinesample assembled from randomly oriented tetragonal single crystal grains. The constitutivelaw accounts for the strain saturation, asymmetry in tension versus compression,Bauschinger effects, reverse switching, and strain reorientation that can occur inthese materials due to the non-proportional loading that can arise near a cracktip. Detailed finite element calculations are carried out to determine the stressand strain fields in the vicinity of the crack tip, and to compute values for theJ-integral on various integration paths around the tip. The results of the calculations arediscussed in relation to results for growing cracks and for stationary cracks in standardelastic–plastic materials.