THE DETERMINATION METHOD OF WILLIAMS ELEMENT WITH GENERALIZED DEGREES OF FREEDOM FOR EQUIVALENT ANALYSIS OF SIFS AT THE CURVED CRACK TIP

The Williams element with generalized degrees of freedom (W element) for stress intensity factors (SIFs) analysis of the linear crack tip of plane elastic continuum based on Williams series must satisfy the boundary conditions that σ_θ=0 and τ_ρθ=0(θ=±π) on a crack surface, but the curved crack surface does not meet it. Therefore, the application of the W element is limited to a curved crack. The local region of the curved crack tip of a plane elastic continuum is equivalently treated to solve the problem, where the crack tip is taken as the center to establish an equivalent region by selecting an appropriate radius, that is, the curved micro-segments where the slope changes monotonously is intercepted, the end of which the tangent line is guided to cross over into broken line that will approximately replace the curved micro-segment. The analysis of examples show that when the size of the equivalent region takes are commended value, the calculation of this method has high precision, which proves that the improved method is reasonable in analyzing the SIFs of curved cracks. Meanwhile, the recommended value of equivalent region size is developed, that is, ψ_min=5π/6, and the length of the curve intercepted by the equivalent region should be greater than 1/5 length of the original curve.