Failure Scaling as Multiscale Instability in Defect Ensemble

Abstract

Fracture phenomena are some of the most intriguing processes in the nonlinear physics and material science. The nature of patterns derived from the failure processes have recently attracted a great interest. The fracture surface of quasi-brittle materials provides rich information about the structure evolution including the size, shape and localization of the critical flaw, mirror, mist, hackle and macroscopic crack branching [1]. The fracture patterns also reveal a well-defined fractal structure [2]. During the past decades a very important role of mesoscopic defects (microcracks, microshears) was established due to the study of transition from disperse accumulation of defects (damage) to fracture. Experimental data show that the defect ensemble exhibits pronounced features of the statistical multiparticle system with a strong interaction between defects and stress field, in particular, induced by macrocracks. To describe solid response to the defect growth, a statistical approach was developed in [3] using the experimental results from the direct study of microcrack evolution.The statistical approach allowed us to establish the specific features of the defect ensemble evolution depending on the characteristic size of structural heterogeneity (for instance, the size of grains in polycrystals) and, as the consequence, different modes of nonlinear solid response to the defect growth. Under loading conditions these nonlinearities are realized as specific forms of spatial-localized structures of defects. In dynamically loaded solids (shock wave loading, dynamic crack propagation) these structures have very legible structural pattern and their appearance are accompanied by a qualitative change of solid response to loading. The changes in the response occur in the form of the topological transition. The self-similarity of solid behaviour is caused by the excitation of spatial-time structures in the defect ensemble. These structures are related to the eigenfunction spectrum of the corresponding nonlinear problem which is determined by the nonlinearity (attractor) types of the equations developed in the framework of the statistical approach. The results of statistical analysis allow us to study the following phenomena:

• (i) crack formation caused by generation of collective modes, which develop as instabilities with the blow-up kinetics in the defect ensemble (microcracks) localized on the spectrum of spatial scales;

• (ii) self-similarity of failure kinetics under impact loading as the resonance excitation of collective modes in the defect system;

• (iii) self-similarity laws of failure caused by the crack propagation (steady-state, crack branching).