{"title":"Mixed Scheme of the Finite Element Method as a Basis for Computational Analysis of Model Crack Mechanics Problems","authors":"O. Yu. Chirkov","doi":"10.1007/s11223-024-00601-3","DOIUrl":null,"url":null,"abstract":"<p>The application and comparison of different fracture mechanics concepts are discussed to be used in computing stress intensity factors (SIF) from the numerical solutions of model crack theory problems with a mixed scheme of the finite element method. Approximation of displacements rests on piecewise-linear interpolation functions with triangular elements, and strain and stress distributions are approximated by the linear combination that includes the piecewise-linear interpolation and interior bell function. The latter ensures the stability and convergence of the approximate discrete problem solution. The solution results for linear elastic and elastoplastic model plane central mode I crack-strip tension problems under different loading and plane strain state conditions are presented. Elastoplastic calculations were made with an ideal elastoplastic material model. The application of the energy balance and <i>G</i>-integral concepts to the calculation of the specific work of fracture at the stationary crack tip is substantiated. It is shown that on condition of uniform plate partition in the vicinity of the crack tip, the application of those concepts to SIF calculation for one loading stage is consistent with the Irwin plastic zone correction, maintaining this approach in further mesh thickening. Elastoplastic calculations on repeated loading demonstrated that tensile stresses ahead of the crack tip were about the same as on the initial one, but the opening at the crack tip on the former was larger than on the latter, and this effect was most pronounced for the first half of active loading values. Several aspects of SIF calculations on repeated loading are presented.</p>","PeriodicalId":22007,"journal":{"name":"Strength of Materials","volume":"26 1","pages":""},"PeriodicalIF":0.7000,"publicationDate":"2024-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Strength of Materials","FirstCategoryId":"88","ListUrlMain":"https://doi.org/10.1007/s11223-024-00601-3","RegionNum":4,"RegionCategory":"材料科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATERIALS SCIENCE, CHARACTERIZATION & TESTING","Score":null,"Total":0}
引用次数: 0
Abstract
The application and comparison of different fracture mechanics concepts are discussed to be used in computing stress intensity factors (SIF) from the numerical solutions of model crack theory problems with a mixed scheme of the finite element method. Approximation of displacements rests on piecewise-linear interpolation functions with triangular elements, and strain and stress distributions are approximated by the linear combination that includes the piecewise-linear interpolation and interior bell function. The latter ensures the stability and convergence of the approximate discrete problem solution. The solution results for linear elastic and elastoplastic model plane central mode I crack-strip tension problems under different loading and plane strain state conditions are presented. Elastoplastic calculations were made with an ideal elastoplastic material model. The application of the energy balance and G-integral concepts to the calculation of the specific work of fracture at the stationary crack tip is substantiated. It is shown that on condition of uniform plate partition in the vicinity of the crack tip, the application of those concepts to SIF calculation for one loading stage is consistent with the Irwin plastic zone correction, maintaining this approach in further mesh thickening. Elastoplastic calculations on repeated loading demonstrated that tensile stresses ahead of the crack tip were about the same as on the initial one, but the opening at the crack tip on the former was larger than on the latter, and this effect was most pronounced for the first half of active loading values. Several aspects of SIF calculations on repeated loading are presented.
本文讨论了不同断裂力学概念的应用和比较,这些概念可用于利用有限元法的混合方案从模型裂纹理论问题的数值解中计算应力强度因子(SIF)。位移的近似依赖于三角形元素的片断线性插值函数,应变和应力分布则通过包括片断线性插值和内部钟形函数的线性组合来近似。后者确保了近似离散问题解的稳定性和收敛性。文中给出了不同荷载和平面应变状态条件下线性弹性和弹塑性模型平面中心模 I 裂缝带拉伸问题的求解结果。弹塑性计算采用理想的弹塑性材料模型。能量平衡和 G 积分概念在静止裂纹尖端断裂比功计算中的应用得到了证实。结果表明,在裂纹尖端附近板块均匀分隔的条件下,将这些概念应用于一个加载阶段的 SIF 计算与欧文塑性区修正是一致的,在进一步加厚网格时保持这种方法。对重复加载进行的弹塑性计算表明,裂纹尖端前方的拉应力与初始加载大致相同,但前者裂纹尖端的开口大于后者,而且这种影响在有效加载值的前半部分最为明显。本文介绍了重复加载 SIF 计算的几个方面。
期刊介绍:
Strength of Materials focuses on the strength of materials and structural components subjected to different types of force and thermal loadings, the limiting strength criteria of structures, and the theory of strength of structures. Consideration is given to actual operating conditions, problems of crack resistance and theories of failure, the theory of oscillations of real mechanical systems, and calculations of the stress-strain state of structural components.