Effect of material’s randomness on scaling of crack propagation in ceramics

Abstract

Crack propagation in real (quasi)brittle materials demonstrates various signs of stochasticity; a tortuous character of fracture surfaces, multiple cracking and crack branching observed in experiments are a vivid confirmation of it. Traditional approaches of fracture mechanics represent cracks as geometrically smooth objects with straight (or curved) crack fronts, thus usually neglecting morphology of real cracks. An introduction of a direct account for stochastic features of brittle materials into modelling schemes leads to a more adequate description of real fracture processes. The effect of the material's randomness on crack propagation in ceramics is studied based on the approach, combining these random features with continuum damage mechanics (CDM) and fracture mechanics. CDM describes a macroscopic manifestation of various failure processes developing at lower length scales. The numerical mode-I fracture analysis, based on discretization of a specimen's cross-section, containing a sharp notch, into rectangular elements, provides detailed information on slow crack propagation. A necessity to describe a crack with its length changing along the front presupposes a transition from a unique stress-intensity factor to a set of its local values. A computational procedure for simulation of crack-damage interaction and crack propagation in alumina specimens at tension is suggested on the basis of a modification of a lattice scheme unified with ideas of CDM and local stress-intensity factors. Inhomogeneity of material properties is modelled in terms of various random spatial distributions of the initial damage in the specimen's cross-section. Characterization of complicated morphology of cracks is implemented by means of scaling analysis of the crack-front shape.

From nucleation to percolation: the effect of system size when disorder and stress localization compete

“…Though through heat treatment one can tune the length scale of disorder in phase-separated glasses [25]. Earlier experiments also studied the role of a varying disorder strength during pattern formation in random spring network [26,27], study of roughness of a fracture surface [28], transition from nucleation to damage mechanics in random fuse network [29,30], etc. Linear elastic fracture mechanics, on the other hand, predicts the load distribution around an Inglis crack [31,32] to be 1/r 2 -type where r is the distance from the crack tip.…”

Modes of failure in disordered solids

“…While experimentally it is not easy to tune the strength of disorder precisely, heat treatment can tune the length scale of disorder in phaseseparated glasses [9]. There have been many other experiments and simulations describing the effect of increased disorder on roughness [10], pattern formation in spring networks [11,12], damage nucleation and percolation in random fuse models [13,14] etc. As for the range of stress redistribution, linear elastic fracture mechanics predict a 1/r 2 type load redistribution around an Inglis crack [15,16].…”

Low-temperature thermally modified fir-derived biomorphic C–SiC composites prepared by sol-gel infiltration

“…Compared with the above methods, the solgel infiltration method has some advantages including lower material costs, a simpler production process, and the ability to maintain the structure and morphology of the initial template integrally [20,21]. The mechanical properties of biomorphic SiC composites prepared by MI have been reported, while those produced by CVI, Sol-gel and SI have barely been reported, probably owing to the inhomogeneous microstructure [7,11,13,16,20,[22][23][24][25].…”