The effect of work-hardening on plane strain crack growth under small scale yielding conditions

Abstract

Though highly idealized in character, the Dugdale-Bilby-Cottrell-Swinden (DBCS) line plastic zone model, gives essentially the same relation between theJ integral and the amount of crack growthΔc, as Rice, Drugan, and Sham's theoretical analysis for a crack growing in an elastic-perfectly plastic material under small scale yielding conditions. This paper extends the DBCS model analysis by incorporating work-hardening, and it is demonstrated that the relation betweenJ andΔc has the same form as for a nonwork-hardening material. Furthermore, it is predicted, for a high crack growth resistant material, that work-hardening decreases the steady-stateJ value, in accord with Dean and Hutchinson's numerical results, though it causes an increase in the initial slope of theJ —Δc curve, in accord with Sorensen's numerical results. These results are important as regards crack instability predictions under small scale yielding conditions.