Shekov Vitali, Kolesnikov Gennady
Institute of Geology, Karelian Research Centre, Russian Academy of Sciences, Pushkinskaya St. 11, IG KarRC RAS, 185610 Petrozavodsk, Russia.
Materials (Basel). 2023 Jul 7;16(13):4875. doi: 10.3390/ma16134875.
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.
本文讨论了脆性材料断裂行为的建模与预测。众多出版物表明，该领域的进展表现为出现了许多满足采矿业、建筑业和其他工程实践要求的新模型。作者仅关注一类模型，特别关注解的简单性与模型通用性之间的权衡。考虑到先前模型的优点，提出了该模型的一个新版本。我们提出了一个用于脆性断裂的微分能量准则，根据该准则，当耗散能量与储存（弹性）能量达到一定比例时发生断裂。断裂被视为变形过程的结束，初始几乎无裂纹的材料虚拟转变为有裂纹的真实材料。分别在应力 - 应变曲线的上升和下降分支上解析确定了最高和最低弹性模量。提出了一种用于确定应力 - 应变曲线峰值后分支上脆性断裂点的算法的图形版本。建模结果与文献中已知的实验数据一致。
