Calculation method of stress intensity factor based on the three-dimensional stress field at the crack tip

An approach for calculating stress intensity factors was proposed based on the first several items of the theoretical polynomial solution of the elastic crack tip stress field in infinite body, and the stress intensity factors were calculated by fitting the finite element solution of elastic crack tip stress field in actual crack bodies. This method did not need assuming the stress and strain state at crack tip in calculated of stress intensity factors, and the calculated results were more in line with the actual stress and strain state in the three-dimensional crack bodies. First, the availability of this method was validated based on the theoretical solution of center-through-crack stress field in a two-dimensional infinite plate, and the fitting item of the polynomial function to determine the stress intensity factors was explored. Then by calculating the stress intensity factors of center through crack in two-dimensional infinite plate, embedded circle crack in three-dimensional infinite body and center through crack in three-dimensional finite thickness plate, the validity and rationality of the proposed method had been verified by comparative analysis with theoretical solutions of the infinite plate and infinite body, and also with the finite element solutions based on displacement extrapolation method and 1/4 point opening displacement method. Studies show that this method can reasonably reflect the actual stress and strain state of crack tip in three dimensional crack bodies, and the calculated stress intensity factors are more reasonable.