New approach to failure of pre-cracked brittle materials based on regularized solutions of strain gradient elasticity

In this paper, we use the feature of the strain gradient elasticity theory (SGET) related to the regularization of classical singularity problems. We suggest that the structural analysis of pre cracked materials can be reduced to failure analysis within SGET by using the appropriate failure criteria formulated in terms of the Cauchy stresses. These stresses are work-conjugated to strains, and they have non-singular values in SGET solutions for the problems with cracks and sharp notches. We confirm our suggestion based on the full-field numerical simulations and provide examples of identification of the length scale parameters of SGET for the known experimental data with pre-cracked brittle and quasi-brittle materials. We show that the identified length scale parameters allow us to predict the failure loads for the experimental samples with different type of cracks by using the maximum principal Cauchy stress criterion. In the experiments with a mixed-mode fracture of the quasi-brittle material (PMMA with inclined cracks), we found that there may arise a transition between the failure determined by the maximum principal stress criterion and the criterion related to the second invariant of the Cauchy stress tensor that can be explained by the change of the stress state triaxiality.

Automated summary

This paper simplifies the structural analysis of pre-cracked materials by utilizing the features of strain gradient elasticity theory and suggests appropriate failure criteria based on Cauchy stresses. By identifying length scale parameters through numerical simulations and experimental data, the failure loads for different types of cracks in experimental samples can be predicted. Furthermore, a transition between failure criteria determined by maximum principal stress and the second invariant of the Cauchy stress tensor is observed in experiments with quasi-brittle materials, possibly due to changes in stress state triaxiality.