In-plane and out-of-plane crack-tip constraint effects under biaxial nonlinear deformation

In-plane and out-of-plane constraint effects on crack-front stress fields under both elastic–plastic and creep conditions are studied by means of three-dimensional numerical analyses of finite thickness boundary layer models and plane strain reference solutions. This investigation is an extension of the plane strain solution obtained by Shlyannikov and Boychenko in 2008, with special attention on what constraint parameters existed in the nonlinear crack-tip fields in a finite thickness solid. Characterization of constraint effects is given by using the non-singular T-stress, the local triaxiality parameter, the factor of the stress-state in 3D cracked body and the second order term amplitude factor. The influence of nominal stress load biaxiality and creep time on the behavior of constraint factors is considered. Stresses and constraint factors from FEA at the crack-front on different planes in the thickness direction of the plate are compared with plane strain reference solutions. The results show that 3D-stress fields can be characterized in common with the local triaxiality parameter and factor of the stress-state in 3D solid by the three-term solution throughout the thickness even in the region near the free surface. It is found that there is a distinct relationship between the in-plane and the crack-front out-of-plane constraint factors which can be well captured using the relation between the second order term amplitude factor and remote boundary layer stress.