An Asymmetrical Self-Similar Dynamic Crack Model of Bridging Fiber Pull-Out in Unidirectional Composite Materials

Abstract

When composite materials produce a crack, their fibrous position will form bridges, moreover the crack usually propagates in the modality of asymmetrical self-similarity. In this paper an asymmetrical self-similar dynamic crack model of bridging fiber pull-out in unidirectional composite materials is built. Analytical solutions of the stresses, displacements, stress intensity factors and bridging fiber fracture speeds for this model under the action of moving loads and homogeneous loads, respectively, are acquired by self-similar measures. After those analytical solutions were utilized by superposition theorem, the solutions of arbitrary complex problems could be gained.

A dynamic asymmetrical crack model of bridging fiber pull-out in unidirectional composite materials

“…3. This variable current is similar to the result obtained by means of numerical solutions in the literature [41][42][43]; hence the obtained outcomes are proved to be right. The relative numerical value relationships are indicated in Table 1.…”

“…4. Such trends are homogeneous to the outcomes in the literature [36,41,[44][45][46][47]; therefore, it is correct. The correlative numerical value relations are illustrated in Table 2.…”

“…The limit of Eqs. (41) and (42) belongs to the shape ∞ ⋅ 0 , which should be translated into the modality of ∞ ∞ / , and then the aftermath of the two formulae can be calculated by the approaches of the L'Hospital theorem [39].…”

“…(23), (24), (41), (42) to easily plot K 1 (1) (t) and K 1 (2) (t) as a function of time t, respectively, and the numerical solutions of them are readily obtained. The following constants [40,41,36] are presumed: (t) and K 1 (2) (t) decay gradually to slow and trend to constants finally and have obvious singularity with the increase of time, because only variable t lies in the denominator of the two expressions; moreover the rest quantities are regarded as real constants. Such trends are expressed by the curves in Fig.…”

Dynamic Problem Concerning Mode I Semi-Infinite Crack Propagation

“…(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.…”