Solutions of the second elastic–plastic fracture mechanics parameter in test specimens under biaxial loading

• Elastic–plastic finite element analyses were conducted to obtain A-term for three test specimens under biaxial loading.
• Solutions cover wide range of crack depth, material nonlinearity and from small scale yielding to large scale yielding.
• It is demonstrated that biaxial loading has significant effect on crack tip constraint.
• Three estimation methods were used to obtain empirical equations of A for engineering applications.
• Solutions of A can be easily converted to get Q and A2 solutions.

Extensive finite elements analyses have been conducted to obtain solutions of the A-term, which is the second parameter in a three-term elastic–plastic asymptotic expansion, for test specimens under biaxial loading. Three mode I plane-strain test specimens, i.e. single edge cracked plate (SECP), center cracked plate (CCP) and double edge cracked plate (DECP) were studied. The crack geometries analyzed include shallow to deep cracks, and the biaxial loading ratios analyzed are 0.5 and 1.0. Solutions of A-term were obtained for materials following the Ramberg–Osgood power law with hardening exponent of n = 3, 4, 5, 7 and 10. Remote tension loading was applied which covers from small-scale to large-scale yielding. Based on the finite element results, effects of biaxial loading on crack tip constraint were discussed. Empirical equations to predict the A-term under small-scale yielding to fully-plastic condition were developed using estimation methods developed earlier. Based on the relationships between A and other commonly-used second fracture parameter Q and A2, the present solutions can be used to calculate parameters Q and A2 as well. The results presented in the paper are suitable to determine the second elastic–plastic fracture parameters for test specimens for a wide range of crack geometries, material strain hardening behaviors under biaxial loading conditions.