A unified method to solve higher order asymptotic crack-tip fields of mode I, mode II and mixed mode I/II crack in power-law creeping solids

•A unified method is proposed to solve higher order asymptotic solutions based on the concept of second order mixity factor.•The characteristics of higher order asymptotic solutions are studied which can encompass mode I, mode II and mixed mode.•The possibly existed mathematical solutions for higher order term asymptotic solutions are discussed. A higher order asymptotic analysis with separable variable form is presented in this paper for crack tip mechanics fields under mixed mode creep conditions. By defining a second order mode mixity factor, higher order term solutions are investigated by solving the boundary value problem. The solution procedure is validated first and then the characteristics of various kinds of second order asymptotic solutions for mixed I/II creep crack tip field are presented and discussed. The angular distribution functions of the second order stress and the stress exponent for various cases are given. Detailed relations between the amplitudes of the second order term and the first order term are also discussed. The method and solutions given in this paper encompass the higher order term solutions of pure mode I, pure mode II and mixed mode I/II.