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高江平, 杨华, 蒋宇飞, 吴鹏阁, 孙世界. 三剪应力统一强度理论研究. 力学学报, 2017, 49(6): 1322-1334. DOI: 10.6052/0459-1879-17-081
引用本文: 高江平, 杨华, 蒋宇飞, 吴鹏阁, 孙世界. 三剪应力统一强度理论研究. 力学学报, 2017, 49(6): 1322-1334. DOI: 10.6052/0459-1879-17-081
Gao Jiangping, Yang Hua, Jiang Yufei, Wu Pengge, Sun Shijie. Study of three-shear stress unified strength theory. Chinese Journal of Theoretical and Applied Mechanics, 2017, 49(6): 1322-1334. DOI: 10.6052/0459-1879-17-081
Citation: Gao Jiangping, Yang Hua, Jiang Yufei, Wu Pengge, Sun Shijie. Study of three-shear stress unified strength theory. Chinese Journal of Theoretical and Applied Mechanics, 2017, 49(6): 1322-1334. DOI: 10.6052/0459-1879-17-081

三剪应力统一强度理论研究

STUDY OF THREE-SHEAR STRESS UNIFIED STRENGTH THEORY

  • 摘要: 材料强度理论研究是高等材料力学的一个重要研究领域,200多年来,各国学者提出了许多强度理论及试验研究结果. 这些理论都是从不同的假设和力学模型出发,推导出不同的数学表达式,但一般只适用于某一类特定的材料. 各种强度理论之间是否有联系?是否可能建立一个广泛适用的统一强度理论?自19世纪末以来,世界各国学者都在努力寻求建立统一强度理论,但一直没有成功. 本文应用理论研究和试验验证相结合的方法,提出并验证了三剪应力统一强度理论。认为当作用于菱形十二面单元体上的三个主剪应力及其作用面上的三个正应力的函数达到某一极限值时,材料发生破坏. 三剪应力统一强度理论是全应力理论,它用一个统一的线性表达式包含或逼近了现有的和其他新的各种单一和统一、线性和非线性、外凸和非凸的强度理论,形成了以单剪强度理论为下限、而以三剪应力强度理论为上限的一系列强度理论的新体系,实现了外凸强度理论和非凸强度理论的高度统一,使强度理论从适用于某一类材料、某种应力状态的单一强度理论发展为可以适用于各种材料及不同应力状态的统一强度理论,并能更大程度地发挥材料的强度潜力. 通过与大量试验结果的对比分析表明:三剪应力统一强度理论可以广泛适用于各种材料及其不同的应力状态.

     

    Abstract: The strength theory is an important research subject in advanced mechanics. Many strength theories and important experimental results have been put forward by the scholars all over the world since 200 years ago. Different mathematical expressions were deduced based on different assumptions and mechanical models in these theories which can only be applied to some specific materials. What is the relationship among various strength theories? Can we propose a unified strength theory that adapted to more kinds of materials? Considerable effort has been devoted to this important problem by many scientists all over the world since the end of the 19th century, but it has not been solved. The three-shear stress unified strength theory has been put forward and verified by the method of combining the theoretical study with the experimental verification in this paper. It is considered that the material will failure when the function of the three principal shear stresses and their corresponding three normal stresses which acting on the main shear planes of the dodecahedron element reaches a magnitude. The three-shear stress unified strength theory is the whole force theory, it uses a unified linear expression to contain or approximate the existing and other newly various single and unified, linear and unlinear, convex and non-convex strength theory, it forms a new strength theory system which the inner boundary is the single-shear strength theory and its external boundary is the three-shear stress strength theory, it brings about the highly unity of the strength theory, it develops the unified strength theory which can suitable for different kinds of materials under various stress states from the single-shear strength which only suitable for some specific materials under specific stress states, and it can make full use of the potential strength of the materials. It is shown that the three-shear stress unified strength theory can be widely suitable for different kinds of materials under various stress states from the fact that a large number of experimental results of materials are in agreement with this theory.

     

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