A Strain Gradient Model for Fracture Prediction in Brittle Materials

In this paper, we present a new model to predict the fracture in brittle materials from a geometrical weakness presenting an arbitrary stress concentration. The main idea is to combine the strain gradient elasticity with a cohesive model that includes both the displacement and the rotation jumps between the cohesive surfaces in the separation law. Three material parameters were used in the establishment of the fracture criterion. The first two parameters are the commonly used $σc$⁠, the ultimate stress, and $Gc$⁠, the critical energy release rate. The third parameter is the characteristic length $l$ as in most of the strain gradient models. The proposed three-parameter model enables to take the different stress concentration levels into account, thus providing a criterion to predict fractures for any stress concentration, whether it is singular or not. Experimental results were selected to verify the accuracy and efficiency of the criterion. It was shown that the proposed model is physically reasonable, highly accurate, and easy to apply. It can be used in crack initiation prediction of engineering structures made of brittle materials.