基于相场模型的准脆性材料的断裂统计研究

在非均质材料损伤断裂过程中, 材料内部的无序性是影响其力学性质的关键因素。混凝土作为一种在工程中被广泛使用的准脆性的非均质材料, 其损伤断裂问题也被重点关注。文章在统一相场理论的框架下, 运用非均质材料相场内聚裂缝模型, 将相关性引入二维随机场建模, 对二维非均质材料的断裂过程的特征量进行统计分析。结果表明: 在断裂过程中, 裂缝的起始、发展和最终断裂形态与微观无序性高度相关; 材料内部的相关长度越小, 随机场的均质度越大, 固体的宏观抗拉强度就越强。通过定量分析发现, 材料微观随机强度分布的相关长度对宏观抗拉强度的影响可以表示为 $ f_{t} \sim l_{c}^{-1/2} $, 类似固体材料破坏的尺寸效应规律。该研究结果可为混凝土等非均质材料的断裂行为提供新的理论视角。

The mechanical properties of heterogeneous materials are significantly influenced by internal disorder during the process of damage and fracture. Concrete, as a widely used quasi-brittle heterogeneous material in engineering, has garnered increased attention from researchers regarding its damage and fracture behavior. Under the framework of unified phase field theory with cohesive crack model of heterogeneous materials, this paper introduces correlation into two-dimensional random field modeling, and statistically analyzes the characteristic quantities of the fracture process of two-dimensional heterogeneous materials. The study reveals a strong correlation between the initiation, propagation, and final morphology of cracks and the microscopic disorder in the fracture process. It is observed that smaller correlation lengths and greater homogeneity of the random field lead to higher macroscopic tensile strength of the solid. Furthermore, quantitative analysis demonstrates that the influence of correlation length of microscopic random strength distribution on macroscopic tensile strength can be expressed as $ f_{t} \sim l_{c}^{-1/2} $, similar to the size effect in failure of solid materials. The findings offer new insights into fracture behavior in heterogeneous materials like concrete.