The problem of the strength of a plate made of a brittle material with through mode I cracks is discussed. In contrast to the approach based on the singular solution of the classical theory of elasticity for a plane with a crack and on linear fracture mechanics, we propose to use nonsingular solutions obtained within the generalized elasticity theory and, as a result, to implement a method, conventional for the strength estimation of solids with stress concentration, based on the maximum stress criterion. The maximum stress is determined from a nonsingular solution of the generalized elasticity equations for a plane with a crack. The reported experimental results for plates with cracks under tension and bending confirm the solution obtained by the proposed method and allow it to be compared with a solution based on linear fracture mechanics. In fact, a new concept of fracture mechanics is put forward, which is free of singular solutions and allows the problems of fracture mechanics to be treated as problems of stress concentration. Comparison of the obtained analytical solutions with the experimental data has shown that the scale factor of generalized elasticity determines the critical state in fracture mechanics with no less accuracy than the critical stress intensity factor and therefore can be used as a fracture criterion. The resulting explicit nonsingular solutions allow the prediction of the stress concentration caused by a crack.

中文翻译：

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基于尺度相关广义弹性理论中最大应力准则的带裂纹板强度估计

讨论了具有贯穿式Ⅰ型裂纹的脆性材料板材的强度问题。与基于具有裂纹的平面的经典弹性理论的奇异解和线性断裂力学的方法相比，我们建议使用在广义弹性理论中获得的非奇异解，并因此实施一种方法, 常规用于具有应力集中的固体强度估计，基于最大应力准则。最大应力由具有裂纹的平面的广义弹性方程的非奇异解确定。所报告的受拉和弯曲裂纹板的实验结果证实了通过所提出的方法获得的解决方案，并允许将其与基于线性断裂力学的解决方案进行比较。事实上，断裂力学提出了一个新的概念，它没有奇异解，可以把断裂力学问题当作应力集中问题来处理。将得到的解析解与实验数据进行比较表明，广义弹性尺度因子决定断裂力学临界状态的精度不亚于临界应力强度因子，因此可作为断裂准则。由此产生的显式非奇异解允许预测由裂纹引起的应力集中。将得到的解析解与实验数据进行比较表明，广义弹性尺度因子决定断裂力学临界状态的精度不亚于临界应力强度因子，因此可作为断裂准则。由此产生的显式非奇异解允许预测由裂纹引起的应力集中。将得到的解析解与实验数据进行比较表明，广义弹性尺度因子决定断裂力学临界状态的精度不亚于临界应力强度因子，因此可作为断裂准则。由此产生的显式非奇异解允许预测由裂纹引起的应力集中。