Weight Function Method for computations of crack face displacements and stress intensity factors of center cracks

The weight function method provides a powerful and reliable tool for the determination of the stress intensity factor around the crack tip in a linearly elastic cracked solid subjected to arbitrary loading conditions. However, it is difficult to exactly compute the crack face displacement whose partial derivative is responsible for the weight function calculation. In the present paper, only one reference stress intensity factor is used for the purpose of establishing a general expression of the crack face displacement. Then, the generalized and simple expression is applied to calculate the weight function and the stress intensity factor of the center crack configuration. The calculation of the weight function is reduced to the simple integration of the correction function and of the partial derivative of the crack face displacement. It is shown that the present expressions for the computations of the crack face displacement and its partial derivative are in good agreement with their exact solutions