Influence of plastic anisotropy on the limit load of highly under-matched scarf joints with a crack subject to tension

A new semi-analytical plane strain upper bound limit load solution for highly under-matched scarf joints with a crack subject to tension is provided. It is assumed that plastic deformation is fully confined to the soft weld material. A numerical technique is only necessary to evaluate ordinary integrals. Distinguished features of the solution are that (i) plastic anisotropy of the weld material is taken into account and (ii) the asymptotic behavior of the chosen kinematically admissible velocity field in the vicinity of the bi-material interfaces coincides with that of the real velocity field. This ensures that the stress boundary condition is satisfied at these interfaces. Hill's quadratic yield criterion is adopted. It is shown that the effect of plastic anisotropy on the limit load is significant. Therefore, this material property can affect the accuracy of predictions of conventional flaw assessment procedures. The accuracy of the solution at a certain set of parameters is verified by comparison with a numerical slip-line solution.