The study is aimed at experimental and computational determination of the coefficients in crack tip asymptotic expansions for a wide class of specimens under mixed mode loading conditions. Multiparametric presentation of the stress filed near the crack tips for a wide class of specimens is given. Theoretical, experimental and computational results obtained in this research show that the isochromatic fringes in the vicinity of the crack tip require to keep the higher order stress terms in the asymptotic expansion of the stress field around the crack tip since the contribution of the higher order stress terms (besides the stress intensity factors and the $T$-stress) is not negligible in the crack tip stress field. One can see that the higher – order terms of the asymptotic expansion are important when the stress distribution has to be known also farther from the crack tip and it is necessary to extend the domain of validity of the Williams solution. It is shown that at large distances from the crack tips the effect of the higher order terms of the Williams series expansion becomes more considerable. The knowledge of more terms of the stress asymptotic expansions will allow us to approximate the stress field near the crack tips with high accuracy.