Comparison of constraint analyses with global and local approaches under uniaxial and biaxial loadings

Fracture toughness is an important material property used to perform the integrity assessment of engineering components containing cracks. Due to the difference in crack tip constraint, specimens may show different fracture toughness. The constraint difference for cruciform specimen with shallow crack, compact tension (CT) specimen and three point bending specimen with shallow and deep cracks are investigated. Both linear elastic and elastic-plastic fracture mechanics are applied to study the constraint effect based on two-parameter fracture criterion. Crack tip constraint depends on the applied loading. J-A2 method is used to precisely capture the crack tip constraint and crack tip stress distributions. Local approach to fracture can be applied to transfer the fracture toughness among different specimens under uniaxial and biaxial loadings. In case of positive T-stress, T-stress increases with KI. In the case of negative T-stress, T-stress decreases with KI. Q-stress generally decreases with applied loading for both deep crack and shallow crack cases. Loss of constraint occurs for the single-edged bending (SEB) specimen with deep crack and thus raises the question whether the SEB specimen is proper to be used to obtain material toughness. For the cruciform bending (CRB) specimen, the constraint at the crack tip surface shows a least constraint while the deepest point has a relatively higher constraint. At a fracture probability of 10%, the fracture toughness difference between CT specimen and CRB specimen is about 50 MPa m0.5, i.e 200% of the fracture toughness. This big difference demonstrates the importance of considering the constraint effects in the integrity analysis.