{"title":"A General Axisymmetric Elastic-Plastic Solution for an Arbitrary Isotropic Yield Criterion under Plane Stress","authors":"E. A. Lyamina","doi":"10.1134/S0025654424603100","DOIUrl":null,"url":null,"abstract":"<p>Plane stress solutions in plasticity have qualitative features not inherent to other deformation modes. Examples are a particular condition of the non-existence of solutions and the necessity to verify that the conditions under which the assumption of plane stress is acceptable are satisfied. Therefore, analytical and semi-analytical solutions are advantageous over numerical solutions, even though the former require simplified constitutive equations. A typical approach for deriving analytical and semi-analytical solutions to axisymmetric problems is to assume Tresca’s yield criterion or another yield criterion represented by linear equations in terms of the principal stresses. Such yield criteria are piecewise linear, and the solution to a boundary value problem usually involves several plastic regimes, making it cumbersome. Moreover, using piecewise linear yield criteria may significantly affect predicted strain distributions compared to smooth yield criteria, which are more accurate for most metals. The present paper provides a general axisymmetric elastic perfectly plastic solution for an arbitrary isotropic yield criterion under plane stress conditions. The flow theory of plasticity based on the associated plastic flow rule is used. Obtaining quantitative results requires evaluating ordinary integrals by a numerical method. The solution is especially simple if one of the boundary conditions requires that the stress components are constant on a surface surrounded by a plastic region. A numerical example of using the solution is presented.</p>","PeriodicalId":697,"journal":{"name":"Mechanics of Solids","volume":"59 1","pages":"541 - 554"},"PeriodicalIF":0.6000,"publicationDate":"2024-06-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mechanics of Solids","FirstCategoryId":"5","ListUrlMain":"https://link.springer.com/article/10.1134/S0025654424603100","RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MECHANICS","Score":null,"Total":0}
引用次数: 0
Abstract
Plane stress solutions in plasticity have qualitative features not inherent to other deformation modes. Examples are a particular condition of the non-existence of solutions and the necessity to verify that the conditions under which the assumption of plane stress is acceptable are satisfied. Therefore, analytical and semi-analytical solutions are advantageous over numerical solutions, even though the former require simplified constitutive equations. A typical approach for deriving analytical and semi-analytical solutions to axisymmetric problems is to assume Tresca’s yield criterion or another yield criterion represented by linear equations in terms of the principal stresses. Such yield criteria are piecewise linear, and the solution to a boundary value problem usually involves several plastic regimes, making it cumbersome. Moreover, using piecewise linear yield criteria may significantly affect predicted strain distributions compared to smooth yield criteria, which are more accurate for most metals. The present paper provides a general axisymmetric elastic perfectly plastic solution for an arbitrary isotropic yield criterion under plane stress conditions. The flow theory of plasticity based on the associated plastic flow rule is used. Obtaining quantitative results requires evaluating ordinary integrals by a numerical method. The solution is especially simple if one of the boundary conditions requires that the stress components are constant on a surface surrounded by a plastic region. A numerical example of using the solution is presented.
期刊介绍:
Mechanics of Solids publishes articles in the general areas of dynamics of particles and rigid bodies and the mechanics of deformable solids. The journal has a goal of being a comprehensive record of up-to-the-minute research results. The journal coverage is vibration of discrete and continuous systems; stability and optimization of mechanical systems; automatic control theory; dynamics of multiple body systems; elasticity, viscoelasticity and plasticity; mechanics of composite materials; theory of structures and structural stability; wave propagation and impact of solids; fracture mechanics; micromechanics of solids; mechanics of granular and geological materials; structure-fluid interaction; mechanical behavior of materials; gyroscopes and navigation systems; and nanomechanics. Most of the articles in the journal are theoretical and analytical. They present a blend of basic mechanics theory with analysis of contemporary technological problems.