Abstract

Although fracture mechanics offers a way to assess the probability of fracture in materials with critically stressed notches, its criteria can hardly account for complex configurations of structures (e.g., welded ones), residual stresses, and inhomogeneity of material properties. Besides, the use of strength criteria accounting for local plasticity requires special tests. Therefore, strength criteria based on physical deformation and fracture models are developed. Here, for analyzing the strength of a cracked material based on a generalized brittle fracture criterion, we propose a mathematical model of the elastoplastic stress state of its prefracture zone ahead of the crack tip. The model proceeds from several assumptions on plastic strains under simplified loading conditions, and its coefficients as well as characteristic load dependences of stresses and strains are found from extensive finite element data on materials with edge and surface cracks. From comparison with numerical data it follows that the proposed method of estimation gives an error of about 10%. The model provides an analytical description of the first principal stress in prefracture zones under loading, and its use in the brittle fracture criterion opens the way to assess to the strength of a wide range of structures.

中文翻译：

---

裂纹尖端区域弹塑性应力状态的建模

摘要

尽管断裂力学提供了一种评估具有临界应力缺口的材料的断裂概率的方法，但其标准很难解释结构的复杂配置（例如焊接结构）、残余应力和材料特性的不均匀性。此外，考虑局部塑性的强度标准的使用需要特殊测试。因此，开发了基于物理变形和断裂模型的强度标准。在这里，为了基于广义脆性断裂准则分析裂纹材料的强度，我们提出了裂纹尖端之前的预断裂区弹塑性应力状态的数学模型。该模型源自对简化加载条件下塑性应变的几个假设，及其系数以及应力和应变的特征载荷依赖性是从具有边缘和表面裂纹的材料的广泛有限元数据中找到的。从与数值数据的比较可以看出，所提出的估计方法给出了大约 10% 的误差。该模型提供了载荷作用下预断裂区的第一主应力的分析描述，它在脆性断裂准则中的使用为评估各种结构的强度开辟了道路。