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摘要: 材料结构强度的准确预报是工程结构设计与优化的关键, 也是固体力学的核心问题之一. 传统强度理论主要依赖于经验公式, 虽种类繁多, 但适用的材料和工况有较大的局限性. 为确保安全, 工程结构设计往往采用较大的安全系数, 造成了极大的材料浪费, 且依然无法杜绝恶性事故的发生. 如何从普适的原理出发, 突破传统强度理论的经验桎梏, 发展新的材料结构强度评估理论, 是一个亟待解决的科学与工程难题. 本文简要总结了传统强度理论所存在的问题, 概述了一些基于能量思想预报材料结构失效行为的方法, 并重点介绍了作者提出的热力学强度理论体系. 该理论体系将材料结构视为一个热力学系统, 把材料结构失效强度的预报纳入被广泛认可的热力学框架. 原则上, 该理论对材料结构的失效模式没有限制, 适用于多种失效模式的强度预报. 以几个代表性实例来说明理论的正确性和广泛适用性, 体现了极好的工程应用前景.Abstract: The accurate prediction of structural strength of materials is the key issue to the design and optimization of engineering structures and is one of the core problems in solid mechanics. Traditional strength theories mainly rely on empirical formulas, which are largely limited by the applicable materials and working conditions. To ensure safety, engineering structural design often adopts large safety factors, resulting in a significant waste of materials and still can not eliminate the occurrence of catastrophic accidents. How to break through the empirical shackles of traditional strength theories and develop a new theory of structural strength assessment of materials from universal principles is an urgent scientific and engineering problem to be solved. This article briefly summarizes the problems with traditional strength theories, outlines some methods for predicting the failure behavior of the material structures based on the energy theory, and highlights the thermodynamic strength theory proposed by the author. In this theory we treat the material structure as a thermodynamic systems and establish the relationship between the prediction of the failure strength of a material structure with the thermodynamic stability analysis. In principle, this theory has no restrictions on the failure modes of material structures and is applicable to strength prediction for a wide range of failure modes. Several representative examples are used to demonstrate the correctness and wide applicability of the theory, which reflects excellent prospects for engineering applications.
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Key words:
- Strength theory /
- Thermodynamics /
- Failure criterion /
- Stability analysis
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图 2 外载作用下初始裂纹为a0的薄板
$ {G_I} = {{2\pi \sigma _{}^2ah} \mathord{\left/ {\vphantom {{2\pi \sigma _{}^2ah} {{E_{\text{e}}}}}} \right. } {{E_{\text{e}}}}} $ ,$ R = 4h\gamma + 4ah{{\partial \gamma } \mathord{\left/ {\vphantom {{\partial \gamma } {\partial a}}} \right. } {\partial a}} $ 与裂纹长度的关系图. (a)$ \gamma $ 与裂纹长度无关, R阻力是定值. 当荷载为$ \sigma _1^{} $ 时, 裂纹不扩展; 当荷载增加至$ \sigma _2^{} $ 时, 裂纹失稳扩展. (b) R阻力曲线单调递增, 当荷载为$ \sigma _1^{} $ 时, 裂纹稳定扩展; 当荷载增加至$ \sigma _2^{} $ 时, 裂纹失稳扩展
图 3 (a)单轴荷载作用下无限板上的圆孔示及虚拟裂纹意图, (b) 岩石的轴向临界载荷与孔洞半径的关系, 实验数据 (黑点) 取自文献(Carter 1992)
图 4 (a) 不同模量玻璃纤维增强聚合物压缩实验所得的临界荷载与Euler公式结果的对比(AlAjarmeh et al. 2019), (b) 压杆直构型态和合力偏心态示意图
图 5
$ f\left( {kL} \right) = kL\cos kL + \sin kL $ 的函数图,$ f\left( {kL} \right) = 0 $ 的首个大于零的解为$ kL = {\text{2}}{\text{.03}} $ 表 1 LiNbO3单晶样品结构信息和实验结果
样品编号 S/mm W/mm B/mm a/mm Pmax/N a/W 1-1 16 3.90 1.76 0.8 66.52 0.21 1-2 16 4.00 1.71 1.0 60.38 0.25 1-3 16 4.03 1.73 1.3 50.83 0.32 1-4 16 4.20 1.76 1.6 47.20 0.38 1-5 16 4.13 1.70 2.0 32.85 0.48 1-6 16 4.20 1.73 0.8 77.52 0.19 1-7 16 4.10 1.70 1.5 46.49 0.37 1-8 16 4.30 1.73 1.7 47.11 0.40 
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