This paper addresses the apparently disparate views of fracture in brittle materials with the purpose of demonstrating the interrelationship of the fracture process at all length scales. Experimental measurements have shown that the fractal dimension is directly proportional to the fracture energy, gamma _c, during the fracture process, i.e., gamma _c=1/2 E a_0 D~* where E is the elastic modulus, a_0 is a structural parameter and D~* is the fractal dimensional increment. Molecular dynamics modeling shows that the fractal nature of hte fracture surface can be explained by the molecular motion induced during fracture. Quantum mechanical molecular orbital calculations suggests that the most likely reaction pathway to brittle fracture is a series of ring contractions, which are related to a_0 and form the basis for further propagation. Thus, we have identified a reasonable atomic level foundation for the structural parameter, a_0. Based on a comparison of atomic and molecular modeling with macroscopically measured values of D~*, we can calculate a_0. The value of a_0 can be related to the strained structure of the materials whether amorphous or crystalline. As a result of the combination of experimentation and modeling, we suggest that the brittle fracture process is a percolation of a series of ring contractions along the crack front, which result in the observed fracture surfaces for several brittle materials.
展开▼
机译：本文阐述了脆性材料中断裂的明显不同观点，目的是证明在所有长度尺度上断裂过程的相互关系。实验测量表明，在断裂过程中，分形维数与断裂能γ_c成正比，即γ_c= 1/2 E a_0 D〜*，其中E为弹性模量，a_0为结构参数， D〜*是分形维数增量。分子动力学建模表明，断裂表面的分形性质可以用断裂过程中引起的分子运动来解释。量子力学分子轨道计算表明，脆性断裂最可能的反应途径是一系列环收缩，这些环收缩与a_0有关，并为进一步传播奠定了基础。因此，我们为结构参数a_0确定了合理的原子能级基础。根据原子和分子模型与宏观测量值D〜*的比较，我们可以计算a_0。 a_0的值可以与材料的应变结构有关，无论是非晶的还是晶体的。通过实验和建模相结合的结果，我们认为脆性断裂过程是沿着裂纹前沿的一系列环收缩的渗滤，这导致观察到几种脆性材料的断裂表面。
展开▼
