Fully plastic crack-tip fields for CCP and DECP specimens under tension in non-hardening materials

Detailed ®nite element analyses are performed for center cracked plate (CCP) and double edge cracked plate (DECP) in non-hardening materials under plane strain conditions. The objective is to systematically investigate the e€ects of deformation level, loading type, crack depth and specimen dimension on crack-tip ®elds and constraints of these two specimens. Special attention is placed on (a) under what conditions the slip-line ®elds can be present near the crack tip, and (b) determining what deformation mechanism makes the crack-tip ®elds signi®cantly di€erent in the two specimens at fully plastic state. The results reveal that (a) at load levels much smaller than the limit load (i.e., small-scale yielding) the crack-tip ®elds are close to the Prandtl ®eld for both specimens, (b) the e€ects of crack depth a/W on the crack-tip ®eld is not remarkable for CCP, but signi®cant for DECP at the limit load, (c) as L/Wr2.4 for CCP and L/Wr2 for DECP, the crack-tip ®elds are independent of the specimen length L/W, (d) at the limit load, the crack face is under compression for all CCP, and (e) a compression (tensile) zone exists at the crack face of shallow (deep) cracked DECP. Moreover, it is found that there exist tensile and compressive stresses along the vertical centerline of specimen for both CCP and DECP which result in a bending moment MVL. The di€erence between MVL and the moment generated by the applied far-®eld loads makes the crack opening stress non-uniform along the remaining ligament. Recall that the slip-line ®elds for both the CCP and DECP have uniform opening stress along the ligament. At the limit load, therefore, the numerical crack-tip stress ®elds can only approach to, but cannot attain to, the slip-line ®elds for both CCP and DECP specimens. In addition, through comparison of the di€erent limit loads given for DECP specimens, the present results indicate that the limit load formula given by Kumar et al. (EPRI, 1981) is valid only for 0.4R a/W R0.7, whereas the formula of Ewing and Hill (1967) can be used for any crack depth