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

摘要

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.