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

Abstract

Detailed finite 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 effects of deformation level, loading type, crack depth and specimen dimension on crack-tip fields and constraints of these two specimens. Special attention is placed on (a) under what conditions the slip-line fields can be present near the crack tip, and (b) determining what deformation mechanism makes the crack-tip fields significantly different 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 fields are close to the Prandtl field for both specimens, (b) the effects of crack depth a/W on the crack-tip field is not remarkable for CCP, but significant for DECP at the limit load, (c) as L/ W≥2.4 for CCP and L/ W≥2 for DECP, the crack-tip fields 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 M VL . The difference between M VL and the moment generated by the applied far-field loads makes the crack opening stress non-uniform along the remaining ligament. Recall that the slip-line fields for both the CCP and DECP have uniform opening stress along the ligament. At the limit load, therefore, the numerical crack-tip stress fields can only approach to, but cannot attain to, the slip-line fields for both CCP and DECP specimens. In addition, through comparison of the different 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 0.4≤ a/ W≤0.7, whereas the formula of Ewing and Hill (1967) can be used for any crack depth.