Sergey Lurie

Abstract:

We propose and elaborate a new concept of nonsingular cracks, the rationale for which is based on processing a large amount of experimental data taken from various scientific sources. It is important that the use of the gradient theory of elasticity is carried out simultaneously with the identification of the scale parameter and an indication of its physical meaning and fundamental role in fracture mechanics. We use the feature of the strain gradient elasticity theory (SGET) related to the regularization of classical singularity problems and show that structural analysis of the pre-cracked materials can be reduced to the failure analysis within SGET by using appropriate failure criteria formulated in terms of the Cauchy stresses. These stresses are workconjugated to strains and they have non-singular values in SGET solutions for the problems with cracks and sharp notches. Using experimental data for the samples made of the same material but containing different type of cracks we identify the additional length scale parameters within two simplified formulations of SGET. To do this we fitted the modeling results to the experimental data assuming that for the prescribed maximum failure load (known from the experiment) the chosen failure criterion should be fulfilled at the crack tip. For the most of the considered experiments with brittle and quasi-brittle materials (glass, ceramics, concrete) we found that the maximum principal stress criterion is valid.
The main peculiarity of the presented results is the proposed approach for the assessment of the material fracture. For the considered brittle and quasi-brittle materials we propose to use the failure criteria formulated with respect to the Cauchy stresses estimated within SGET. These stresses have the finite values in the whole domain and also at the crack tip. Due to this, we call the presented approach the "failure analysis" since the linear fracture mechanics approaches with singular fields do not involved here. Other words, we propose to transfer the standard approaches of the failure analysis to the bodies with cracks accounting for the strain gradient effects within SGET.
We confirm our suggestion based on the full-field numerical simulations and provide the examples of identification of SGET parameters for the known experimental data with pre-cracked brittle and quasi-brittle materials. It was shown that identified parameters allow us to predict the failure loads for the experimental samples with different type of cracks by using maximum principal Cauchy stress criterion.
As the main result, we show that identified values of the length scale parameters allows us to predict the maximum failure loads for the materials samples with different type of cracks (of different length, offset, inclination). Therefore, we show 1) that the length scale parameter of SGET can be treated as the shape independent material constant that controls the material fracture and 2) that the failure analysis of the structures with non-smooth geometry can be performed by using FEM simulations within SGET involving the failure criteria formulated in terms of the Cauchy stresses.
Presented approach can be treated as some type of the alternative to the classical LEFM among other known theories (theory of critical distances, cohesive zone models, Bazant theory of size effect, etc.). The main advantages of this approach is the possibility of the mesh-independent assessments for the material fracture and the caption of size effects
This work was supported by the Ministry of Science and Higher Education of the Russian Federation (Grant agreement 075-11-2020-023).