Orthotropic strip with central semi-infinite crack under arbitrary loads applied far apart from the crack tip

Abstract

The exact analytical solution has been obtained for a problem of orthotropic strip with central semi-infinite crack loaded normally with self-balanced system of forces applied far enough from the crack tip to be considered as applied at infinity. The general solution is expressed as a superposition of solutions for two modes of loading: (i) symmetrically applied moments; (ii) symmetrically applied transverse forces with compensating moments. The exact expressions for stress intensity factor (SIF) have been obtained. Due to symmetry only the opening mode of SIF is present for each case of loading. For both cases of loading the stress states are determined by two dimensionless parameters composed by four elastic constants. Expression for SIF for the case of loading with symmetrically applied moments is obtained in terms of elementary functions and coincides with the elementary solution due to beam theory. Expression for SIF for the case of loading with symmetrically applied transverse forces with compensating moments has been obtained in terms of one function of one of the parameters expressed as a single integral, multiplied by a power function of the second parameter. The solution for this case demonstrated good agreement with the existing numerical solution for the range of parameters, for which the latter had been obtained. The obtained solution covers all possible range of parameters.