{"title":"Structure and Relations of a Multi-Level Mathematical Model for Describing Microcracks Formation during Polycrystals Deformation","authors":"K. A. Kurmoiartseva, N. Kotelnikova, P. Volegov","doi":"10.26907/2541-7746.2021.2.197-213","DOIUrl":null,"url":null,"abstract":"The mechanical behavior of parts is significantly affected by the material’s internal defective structure and its evolution. The paper aims to build a complex physically based mathematical model for describing the behavior of metals in the deformation and destruction pro-cess. The main deformation mechanisms of metals and alloys are considered. The mechanism and criterion for the microcrack nucleation, as well as a method for microcracks describing, are outlined. The structure and main relations of the developed model are presented, inclu-ding a description of the most significant mechanisms carriers evolution implemented at each structural-scale level. A submodel of the evolution of dislocation densities during deformation due to such mechanisms as the new dislocations generation and opposite dislocations anni-hilation on close slipping systems is described. The algorithm for implementing the model and the results of modeling the dislocation structure evolution are presented. The multi-level approach based on the crystal plasticity and the introduction of internal variables is found to be sufficiently effective for describing both the propagation and nucleation of microcracks in metals.","PeriodicalId":41863,"journal":{"name":"Uchenye Zapiski Kazanskogo Universiteta-Seriya Fiziko-Matematicheskie Nauki","volume":"104 1","pages":""},"PeriodicalIF":0.1000,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Uchenye Zapiski Kazanskogo Universiteta-Seriya Fiziko-Matematicheskie Nauki","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.26907/2541-7746.2021.2.197-213","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0
Abstract
The mechanical behavior of parts is significantly affected by the material’s internal defective structure and its evolution. The paper aims to build a complex physically based mathematical model for describing the behavior of metals in the deformation and destruction pro-cess. The main deformation mechanisms of metals and alloys are considered. The mechanism and criterion for the microcrack nucleation, as well as a method for microcracks describing, are outlined. The structure and main relations of the developed model are presented, inclu-ding a description of the most significant mechanisms carriers evolution implemented at each structural-scale level. A submodel of the evolution of dislocation densities during deformation due to such mechanisms as the new dislocations generation and opposite dislocations anni-hilation on close slipping systems is described. The algorithm for implementing the model and the results of modeling the dislocation structure evolution are presented. The multi-level approach based on the crystal plasticity and the introduction of internal variables is found to be sufficiently effective for describing both the propagation and nucleation of microcracks in metals.