Transient motion of an interfacial line force or dislocation in an anisotropic elastic bimaterial

et al. 2011

An elastic analysis of an internal crack with bridging fibers parallel to the free surface in an infinite orthotropic anisotropic elastic plane is studied, and asymmetrical dynamic fracture model of bridging fiber pull-out of unidirectional composite materials is presented for analyzing the distributions of stress and displacement with the internal asymmetrical crack under the loading conditions of an applied nonhomogenous stress and the traction forces on crack faces yielded by the bridging fiber pull-out model. Thus the fiber failure is ascertained by maximum tensile stress, the fiber ruptures and hence the crack propagation should also appear in the modality of selfProject supported by the postdoctoral foundation of China (No. 2005038199), HeiLongJiang provincial nature science foundation of China (ZJG04-08).

Section: Resultsmentioning

confidence: 99%

Asymmetrical dynamic fracture model of bridging fiber pull-out of unidirectional composite materials

et al. 2011

“…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.…”

Section: Resultsmentioning

confidence: 99%

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

et al. 2011

By means of the theory of complex functions, fracture dynamics problems of mode I semiinfinite crack for anisotropic orthotropic body were researched. Analytical solutions of stress, displacement, and dynamic stress intensity factor under the action of moving increasing loads P x 3 /t 3 , P t 4 /x 3 , respectively, are very easily obtained utilizing the approaches of self-similar functions. In the light of relevant material's coefficients, the alterable rule of dynamic stress intensity factor was depicted very well. The correlative closed solutions are attained based on the Riemann-Hilbert problems. After those analytical solutions were applied by the superposition principle, the solutions of discretional complex problems could be attained.

“…The variable law of dynamic stress intensity factor K 1 (t)versus time is similar to that of different boundary conditions [31,32,37,[45][46][47][48][49][50][51][52][53], therefore it is proved to be correct. The measures of self-similar functions are still applicable in researches of mode semi-infinite I crack [31], mode III crack [54][55][56][57][58] and mode III interface crack [19,[59][60][61][62][63][64][65], as well as axially symmetrical crack, detailed in [1,30,66]. Using corresponding representationf (x, y, t) = t n f (x/t, y/t), where n is an integral number, the problem discussed can be easily translated into homogeneous function of x and t of zeroth dimension, namely self-similar function.…”

Section: Resultsmentioning

confidence: 99%

Analytical solutions of dynamic mode I crack under the conditions of displacement boundary

et al. 2011

By the approaches of the theory of complex variable functions, the problems of dynamic mode I crack under the condition of displacement boundary are investigated. For this kind of dynamic crack extension problems with arbitrary index of self-similarity, the universal representations of analytical solutions are facilely deduced by the methods of self-similar functions. Analytical solutions of the stresses, displacements and stress intensity factors are readily acquired using the methods of self-similar functions. The problems studied can be very easily translated into Riemann-Hilbert problems and their closed solutions are gained rather straightforward in terms of this technique. According to corresponding material properties, the mutative rule of stress intensity factor was illustrated very well. Using those solutions and superposition theorem, the solutions of arbitrarily complex problems can be attained.