Two Dynamic Propagation Problems of Symmetrical Mode III Crack

Abstract

By the approaches of the theory of complex functions, two dynamic propagation problems of symmetrical mode Ⅲ crack were researched. The problems considered can be very facilely changed into Riemann-Hilbert problem by means of self-similar functions, and the general representations of analytical solutions of the stress, the displacement and dynamic stress intensity factor under the conditions of moving variable loads Pt and Px2/t2 which were applied the edges of mode Ⅲ crack, respectively, were readily acquired.

Fracture dynamics problems of mode I semi-infinite crack for anisotropic orthotropic body

“…This method can be used not only in elastodynamics [16][17][18][27][28][29], but also in elastostatics [15,24,36,37] and even in other scopes [15,37,38]. The measures of self-similar functions are still applicable in researches of mode III crack [39][40][41][42][43][44][45] and mode III interface crack [46][47][48][49][50][51][52][53] as well as axially symmetrical crack, detailed in [1,6,13,54]. η is substituted by τ , and hence At τ 2 > C 2 d , when a < 0, b < 0; presumed C 66 < C 11 , from the (A.2), the following results is obtained: are both positive real, therefore, all of the four roots of (A.1) are real.…”

Asymmetrical Dynamic Propagation Problem on the Edges of Mode III Interface Crack Subjected to Superimpose Loads

“…This approach can utilize not only in elastodynamics [15][16][17][18][19][20][21][22][23][24][27][28][29][30][31][32][33]39,46,47], but also in elastostatics [25,37,48,49] and even in other domains [25,49,50]. The approaches of selfsimilar functions are still applicable in researches of mode I crack [23,24,28,[30][31][32][33]39,46,47,[51][52][53][54] and mode III crack [55][56][57][58][59][60] as well as axially symmetrical crack, detailed in [30,32,61].…”

Dynamic Problem Concerning Mode I Semi-Infinite Crack Propagation

“…This technique can be used not only in elastodynamics [19,20,22-25, 33,34], but also in elastostatics [21,30,42,43] and even in other domains [21,43,44]. The measures of selfsimilar functions are still applicable in researches of mode III crack [45][46][47][48][49][50][51] and mode III interface crack [52][53][54][55][56][57][58][59] as well as axially symmetrical crack, detailed in [1,6,21,60].…”