Asymptotic representation of the stress field near the crack tip of an infinite plate with two semi-infinite symmetrical edge notches: theoretical study and computational experiment

This article is aimed at theoretical study of the stress-strain state of an infinite plate with two semi-infinite symmetrical edge notches. The analytical solution is obtained by means of decomposition in the M. Williams series expansion and subsequent calculation of the amplitude coefficients of the expansion using the complex representation of stresses. An analysis of the multiparametric expansion of the stress field and a computational experiment with different number of terms are carried out. A comparison of the complex representation of the stress field with the asymptotic series of M. Williams obtained shows the need for an accurate estimate of the number of terms keeping in the expansion series depending on the distance from the crack tip.