Yc. Gao et G. Rousselier, NEAR-TIP QUASI-STATIC CRACK-GROWTH BEHAVIOR IN STRAIN-HARDENING AND SOFTENING MATERIAL, Theoretical and applied fracture mechanics, 20(3), 1994, pp. 149-155
Analyzed in this work is a semi-infinite crack that grows slowly in a
steady-state. The assumed constitutive relation for the material permi
ts strain hardening and softening as it is damaged in time. Four disti
nct regions divided angularly are identified for the asymptotic expres
sions of the quasi-static crack-tip stress field. They refer to materi
al degraded in front of the crack; undergone elastic unloading; reload
ing of degraded material; and material completely exhausted in its loa
d carrying capacity.