Fracture Load Predictions in Additively Manufactured ABS U-Notched Specimens Using Average Strain Energy Density Criteria

Differential Energy Criterion for Brittle Fracture: Conceptualization and Application to the Analysis of Axial and Lateral Deformation in Uniaxial Compression of Rocks

This paper discusses modeling the behavior and prediction of fracture of brittle materials. Numerous publications show that progress in this area is characterized by the emergence of a number of new models that meet the requirements of the mining industry, construction and other engineering practices. The authors focus only on one class of models, paying special attention to the compromise between simplicity of solution and versatility of the model. A new version of the model is proposed, taking into account the advantages of previous models. We present a differential energy criterion for brittle fracture substantiated, according to which, fracture occurs at a certain ratio of dissipated and stored (elastic) energy. Fracture is considered as the end of the deformation process with a virtual transformation of the initial material almost without cracks into a real material with cracks. The highest and lowest elastic moduli are analytically determined, respectively, on the ascending and descending branches of the stress-strain curve. A graphical version of the algorithm for determining the brittle fracture point on the post-peak branch of the stress-strain curve is proposed. The modeling results are consistent with the experimental data known from the literature.

Analytical Model with Independent Control of Load–Displacement Curve Branches for Brittle Material Strength Prediction Using Pre-Peak Test Loads

The relevance of problems related to the fracturing of engineering materials and structures will not decrease over time. Fracture mechanics methods continue to be developed, which, combined with numerical methods of computer modeling, are implemented in software packages. However, this is only one facet of the complex of actual problems related to modeling and analyzing the behavior of brittle materials. No less important are the problems of developing not only numerical, but also new analytical models. In this paper, analytical models of only one class are considered, the distinguishing feature of which is that they describe the full load–strain curve using only one equation. However, the determination of model parameters requires tests for which the destruction of the test object is necessary, which may be unacceptable if controlled destruction is technically impossible or economically unreasonable. At the same time, in practice, it is possible to obtain values of stresses and strains caused by loads smaller than the peak load. Pre-peak loads can be used to predict strength using numerical methods, but it is desirable to have a suitable analytical model to extend the capabilities and to reduce the cost of applied research. Such a model was not found in the known literature, which motivated this work, which aims to modify the analytical model to predict strength and the full load–displacement (or stress–strain) curve using only pre-peak loading. This study is based on the analysis of known data and synthesis using mathematical modeling and fracture mechanics. The input data for the model do not include the particle size distribution and other physical and mechanical properties of the components of the material under study. These properties may remain unknown, but their influence is taken into account indirectly according to the “black box” methodology. Restrictions of the scope of the model are defined. The simulation results are consistent with experiments known from the literature.