Multiparametric full-field representations of the in-plane stress fields ahead of cracked components under mixed mode loading

In some cases of engineering interest, the contribution of the higher order stress terms (besides the stress intensity factors and the T-stress) is not negligible in the crack tip stress field. The main aim of the present investigation is to present a set of equations for accurately describing the crack tip stress components particularly for those cases where the modes I and II stress intensity factors used in combination with the T-stress component, are unable to capture with satisfying precision the complete stress field ahead the crack tip. The case of a plate with a central crack under mixed mode (I + II) loading is discussed to show the different contributions of the higher order terms in the overall stress field. The second example deals with a thin welded lap joint characterized by a jointing face width to thickness ratio d/t ranging from 0.5 to 5. The third example investigates the case of an inclined crack departing from the slit tip of a welded lap joint. The strain energy averaged over a control volume can be analytically evaluated with high precision by taking into account only four additional terms besides KI, KII and T. Finally, the averaged SED is used to provide a demarcation line between the elastic and the elastic–plastic behaviors as well as to create a possible bridging with the CJP (Christopher, James and Patterson) model.