A General Axisymmetric Elastic-Plastic Solution for an Arbitrary Isotropic Yield Criterion under Plane Stress

IF 0.6 4区 工程技术 Q4 MECHANICS Mechanics of Solids Pub Date : 2024-06-04 DOI:10.1134/S0025654424603100
E. A. Lyamina
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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.

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平面应力下任意各向同性屈服准则的一般轴对称弹塑性解法
摘要 塑性中的平面应力解具有其他变形模式所不具备的定性特征。例如,解不存在的特殊条件,以及必须验证平面应力假设可接受的条件是否满足。因此,分析和半分析解法比数值解法更有优势,尽管前者需要简化的构成方程。推导轴对称问题的分析和半分析解法的典型方法是假设 Tresca 屈服准则或其他由主应力线性方程表示的屈服准则。这种屈服准则是片断线性的,而边界值问题的求解通常涉及多个塑性状态,因此非常麻烦。此外,与平滑屈服准则相比,使用片断线性屈服准则可能会严重影响预测的应变分布,而平滑屈服准则对大多数金属而言更为精确。本文提供了平面应力条件下任意各向同性屈服准则的一般轴对称弹性完全塑性解。本文使用了基于相关塑性流动规则的塑性流动理论。要获得定量结果,需要用数值方法求常积分。如果边界条件之一要求被塑性区域包围的表面上的应力分量恒定,那么求解就特别简单。本文介绍了一个使用该解法的数值示例。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
Mechanics of Solids
Mechanics of Solids 医学-力学
CiteScore
1.20
自引率
42.90%
发文量
112
审稿时长
6-12 weeks
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.
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