Energetic-statistical size effect in quasibrittle fracture
Jia-Liang Le
Department of Civil Engineering
University of Minnesota
Abstract
Modern engineering structures are often made of quasibrittle materials, which are brittle heterogeneous materials such as concrete, composites, toughened ceramics, etc. The salient feature of quasibrittle structures is that the failure behavior is strongly dependent on the structure size, which further leads an intricate scale effect on the structural strength. Un- derstanding this scale effect is critical for extrapolating the results of small-scale laboratory tests to predict the response of a full-scale structure. So far, two independent scaling theories have been developed for quasibrittle fracture: 1) statistical scaling derived from the weakest link model, and 2) energetic scaling derived from fracture mechanics. The statistical scaling theory is generally applicable to structures with a smooth boundary whereas the energetic scaling theory is applicable to structures with a large pre-existing crack. Nevertheless, many engineering structures are designed to have complex geometries and material mismatch, which could introduce stress singularities that are weaker than the conventional "-1/2" crack-tip singularity. To derive the scaling model for such structures, it is critical to understand how the weak stress singularities modify the classical energetic and statistical scaling theories. In this study, a new scaling model for quasibrittle fracture is derived, which explicitly relates the nom- inal structural strength to the structure size and the magnitude of the stress singularity. The theoretical analysis is based on a generalized weakest link model that combines the energetic scaling of fracture with the finite weakest link model. The model captures the transition from the energetic scaling to statistical scaling as the strength of the stress singularity diminishes. To verify the proposed scaling model, we perform finite element simulations of the size effect on fracture of both homogenous and bimaterial quasibrittle structures exhibiting different magni- tudes of stress singularities. It is shown that the new scaling law is in close agreement, for the entire range of stress singularities, with the numerically simulated size effect curves. In closing, extension of this model to scaling of fatigue lifetime is outlined.