EFFECT OF STRESS-STRAIN CURVE OF MATERIAL ON SOLUTION OF PLANE-STRESS PROBLEMS WITH LARGE PLSTIC DEFORMATION
-
摘要:
本文首先将以前所得到的关于两个轴对称塑性平面应力问题(薄圆环和旋转盘)的有关方程和计算结果作了一个简单的叙述.这些计算结果是根据两种不同硬化特性的材料和一种理想塑性材料的应力应变曲线在不同负荷下计算得到的.这些结果指出这三种不同材料的应力应变曲线和负荷对于这两个问题的主应力比值和比例应变的影响很小,而对于比例应力的影响则很大.之后,分析了二维的塑性平面应力问题的方程;这些方程考虑了大应变,但不包括体积力(body force).分析这些方程中的包括材料应力应变曲线项和载荷数项的结果,认为假若在边界上的主应力的比值和比例应变不变,则材料的应力应变曲线和载荷对于主应力比值和比例应变的分布的影响可能不大,而对于比例应力的影响则很大.这种边界条件在实际问题中的普通加减下,满足的可能想是很大的.薄圆环和旋转盘的边界条件及所得的结果和这分析的结果是完全一致的.从这些结果并可提出一个简单而相当准确的近似解,最后并将本文所得的结果和依留辛(Ильюшии)的理论——关于小应变下三维问题形变理论的应用条件——作了比较.
Abstract:A brief review of author's previous work on the plastie plane stress problems with axial symmetry is first made. Results obtained for two of such problems, which show that the effeets of τ(γ) of the material and of loading on the distributions of the proportionate strains and of the ratios of principal stresses are very samll, are summmarized. An analysis of the equations is then made and the preceding ersults are explained. Equations of equilibrium in terms of the principal stresses and of the principal strains are derived for the two-dimensional plane stress problems without body force but considering finite strains. An analysis of these equations leads to the surmise that the effects of τ(γ) of the material on the distributions of the proportionate strains and of the ratios of the principal stresses are samll, provided that the proportionate strains and the ratios of the principal stresses at the boundary remain the same at different loads. On the other hand, the effects of τ(γ) of the material and of the load on the distributions of proportionate stresses are large. A simple approximate method of solution is obtained by using these results. The results obtained in this paper are compared with Ilyushin's theory of small elastic-plastic deformation.
-
Nadni, A., Plastic Behavior of Metals in the Strain-Hardening Range. Part I. Jour. Appl. Phys., 8, No. 3, pp.205-213(March 1937). Ильюшин, А. А., Связь между теорией Сен-Венана, Деви, Миаеса и теорией яаориеп Яаяцх Упруго-пласти-чееких Деформадии, IEMM,9(1945),207-218 Ильюмип, А. А., К теории матых улруго-пластических деформации, IEMM,10(1946),347-356. Handelman, G. H., Lin,C. C. & Prager, W., On the Mechanical Behavior of Metals in the Strain-Hardening Range, Quarterly of Applied Mathematics, 4,1947,pp.397-407 Drueker, D. C., A Reconsideration of Deformation Thcorica of Plaotieity. A. S. M. E. Trano., 71, No. 5, pp. 587-592(July 1939). Nadai, A., Plasticity. 1931, McGraw-Hill Book Co., Ine. Nadai A., and Donnell, L H., Stress Distribution in Rotating Disks of Ductilc Material after the Yield Point has been Reached. A. S. M. E. Trans., 51,pt. I, APM-51-16,1929,pp.173,180;Discussion,PP.180-181 Gjeyzal, A., Plastie Deformation of a Circular Diaphragm under Pressure. Jour. Appl. Mech., 15,No,3,pp.288-296(Sept. 1948). Millenson, M. B. and Manson, S. S. Determination of Stresses in Gas-Turbine Disks Subjected to Plastic Flow and Oreep, NACA Rep, 906,1948(Formerly NACA TN 1636). Stowell, Elbridge Z., Stress and Strain Concentration at a Circular Hole in an Infinite Plate, NACA TN 2073,1950 李敏华(Lee-Wu, M. H.), Analysis of Plune-plastie-Stress Problems with Axial Symmetry in Strain-Hardening Range, NACA Rept. 1021,1951(Supersedes NACA TN 2217,1950. Presented at the Third Symposium on Plasticity, Brown University, 1950). 李敏华(Lee-Wu, M. H.), Linearized Solution and General Plastic Behavior of Thin Plate with Oiroular Hole in Strain-Hardoning Range, NACA TN 2301, March, 1951. 李敏华(Lee-Wu, M. H.), General Plastic Behavior and Approximate Solutions of Rotating Disk in Strain-Hardening Range, NACA TN 2367, May, 1951. 李敏华(Lee-Wu, M. H.), A Simple Method of Determining Plastic Stresses and Strains in Rotating Disks with Non-Uniform Metal Properties. Trans, A. S. M. E., of Appl, Mech., 19, No. 4,pp.489-495,Dec.1952. -
点击查看大图
计量
- 文章访问数: 1671
- HTML全文浏览量: 45
- PDF下载量: 543
- 被引次数: 0
下载:
