An asymptotic analysis of stationary and moving cracks with frictional contact along bimaterial interfaces and in homogeneous solids

Abstract

The plane strain and plane stress problem of a stationary or steadily moving crack with frictional sliding crack surface contact is investigated, with emphasis on the asymptotic structure of the crack tip fields. The crack is assumed to lie along the interface of an elastic anisotropic bimaterial with an aligned plane of symmetry, which covers special cases where the bimaterial is orthotropic or isotropic, or where the bimaterial becomes homogeneous. A full representation of the asymptotic fields around the interface crack is derived in terms of several arbitrary analytic functions, with explicit expressions for the singular crack tip stress and displacement fields given for a steadily propagating interface crack in an isotropic bimaterial, which are used to predict the direction of possible crack deviation from the interface. For a stationary crack, the singularity of the stresses can be, in general, stronger or weaker than r−½ (where r is the distance to the crack tip) depending on the loading history, while for a steadily growing crack, the singularity must be weaker than r−½, resulting in zero energy release rate at the crack tip. For bimaterials with orthotropic symmetries, the form of the singular stress field is found somewhat similar to that of the classic mode II problem. When these types of materials become homogeneous, and irrespective of the amount of friction between the contacting crack faces, the singular crack tip fields are identical to those of the classic mode II problem. Hence, the solutions are also governed by the conventional stress intensity factor KII, implying a nonzero crack tip energy release rate, which is related to KII in the usual manner. Implications of the above findings will be discussed.