Role of Disorder in the Size Scaling of Material Strength

Abstract

We study the sample size dependence of the strength of disordered materials with a flaw, by numerical simulations of lattice models for fracture. We find a crossover between a regime controlled by the fluctuations due to disorder and another controlled by stress-concentrations, ruled by continuum fracture mechanics. The results are formulated in terms of a scaling law involving a statistical fracture process zone. Its existence and scaling properties are only revealed by sampling over many configurations of the disorder. The scaling law is in good agreement with experimental results obtained from notched paper samples.

Emergent patterns of localized damage as a precursor to catastrophic failure in a random fuse network

“…Similar to the process zones in Ref. [12], the damage accumulation zone surrounding the failure nucleation point becomes visible only after statistical averaging, while it cannot be identified in a single realization [compare Fig. 2(a) and 2(d)].…”

“…This procedure of studying localized damage accumulation in terms of conditional averages is similar to the approach used in Ref. [12] where damage patterns around preexisting cracks were studied in order to establish statistical signatures of the fracture process zone surrounding the crack tips. This emergent damage pattern also occurs for the critical nucleation process.…”

“…To this end, we perform extensive simulations of the random fuse model (RFM) [6,7], probably the simplest model where disorder, stress enhancements, and stress interactions can be incorporated. The model has been successfully used to study fracture size effects arising from a random microcrack distribution [8][9][10][11] and from large notches [12]. In both cases it is possible to relate the geometrical and statistical properties of the cracks existing before failure to the actual value of the fracture stress.…”

Fracture size effects from disordered lattice models

“…At fixed disorder, a c increases with L since notchless specimens get weaker. The fracture toughness G c (since in the models E = 1) seems in our simulations to be proportional to the average model element strength at weak disorder at least, and perhaps gets reduced with strong disorder (15). More numerical work in this direction might be interesting.…”

“…A brief account of the results for the RFM has been published in Ref. (15). In more detail, we consider the random fuse model (RFM), the random spring model (RSM) and the random beam model (RBM).…”