Elastoplastic three dimensional crack border field-II. Asymptotic solution for the field

The distributions of crack border stresses and strains in strain hardening materials under a triaxial stress constraint Tz ε{lunate}[0,0.5] are studied. It is found that at Tz = 0 and 0.5, the singularity of stresses is most serious and coincident with the HRR solution. When 0 < Tz < 0.5, however, the singularity and angular distributions of the field change with Tz. It is shown clearly that in the layers near the free surface the variation of the singularity of stresses is strongest. Finally, theoretical investigation of the characterization of the 3D crack border field is made and it is proved that single parameter dominance is lost and a two parameter system including Tz should be adopted to describe the 3D crack border field.