Fracture dynamics problem on mode I semi-infinite crack

Abstract

By means of the theory of complex functions, fracture dynamics problems concerning mode I semiinfinite crack were studied. Analytical solutions of stress, displacement and dynamic stress intensity factor under the action of moving increasing loads Pt 3 /x 3 , Px 3 /t 2 , respectively, are very easily obtained using the ways of self-similar functions. The correlative closed solutions are attained based on the Riemann-Hilbert problems.

Dynamic Problem Concerning Mode I Semi-Infinite Crack Propagation

“…The values of D 1 (τ)/D(τ) can be ascertained from Appendix 1 of literatures [19,20,[23][24][25], indicated sole here: D 1 (τ)/D(τ) at the interval of the subsonic speeds is purely imaginary for the values which we are considering. Thus, elastodynamics problems for an orthotropic anisotropic body researched can be translated into seeking the single unknown function problems concerning F(τ) and W(τ) sufficing the boundary-value conditions.…”

“…(4) ~ (6) are the notation introduced [19,20,[23][24][25], and they are correlative variables which directly resolve displacements and stresses by the course of respective computations in Eq. (7).…”

“…(26), (37) to plot K 1 (t) as a function of time t, and their numerical solution is facilely obtained. The following constants are as follows [8,19,20,25,33,34] Known from Eq. (26), dynamic stress intensity factor K 1 (t) decreases tardily to slow and has evident singularity in virtue of unique variable t in the denominator, and the rest quantities are regarded as real constants.…”

“…At the initial moment t = 0 the halfplane is at rest. In these segments the loads and displacements are arbitrary linear combination of the following functions [1,17,19,20,[23][24][25]:…”

“…However, a lot of engineering machineries work under the conditions of dynamic loadings, and the statics studies can't virtually settle a series of dynamic problems appearing in the dynamic conditions, so it is essential to investigate their fracture dynamics problems. On account of the complexity, cockamamie and difficulty in mathematics, numerical solutions and half analytical solutions was attained by fewer researchers [9][10][11][12][13][14][15][16], moreover analytical solutions were attained much less [17][18][19][20]. So it is necessary to research semi-infinite crack dynamic propagation problem.…”