Abstract
The fracture behaviors of quasi-brittle materials are commonly specimen size (size effect) and crack size (boundary effect) dependent. In this study, a new failure model is developed for characterizing the size and boundary effects. The derivative of the energy release rate is firstly introduced to predict the nominal strength dominated by the strength mechanism. Combined with the energy criterion for the energy mechanism, an asymptotic model is developed to capture the effect of any crack size on the nominal strength, and its expression for geometrically similar specimens is also established, which is able to characterize the size effect. Detailed comparisons of the proposed model with the size effect law and the boundary effect model are performed, respectively. The nominal strength predictions based on the proposed model are validated with the experimental results of cracked three-point bending beam specimens made of concrete, of limestone and of hardened cement paste and compared with the model predictions given by the size effect law and the boundary effect model.
Highlights
Nominal strengths of quasi-brittle materials, like concretes, rocks, some types of ceramics, etc., are commonly specimen size [1,2,3,4] and crack size dependent [5,6,7,8].(FPZ) around the tip of the defect
The boundary effect is determined by the size of a fully-developed Fracture Process Zone (FPZ), its distance to the front boundary measured by the crack length and its distance to the back boundary measured by the un-cracked ligament
The fitted tensile strength is much higher than the direct measurement, which indicates that the predictions of the strength mechanism in the boundary effect model are inappropriate
Summary
Nominal strengths of quasi-brittle materials, like concretes, rocks, some types of ceramics, etc., are commonly specimen size (size effect) [1,2,3,4] and crack size dependent (boundary effect) [5,6,7,8]. Combined with the LEFM criterion that predicts the nominal strength based on the energy mechanism, an asymptotic model is developed to capture the full process of crack initiation and crack propagation. Based on this information, the proposed model is established and compared with the boundary effect model and the Type 2 size effect law.
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