Numerical Study Of Fracture Surface Properties Of Random Fuse Model

Investigating the microscopic dynamic process of fracture in disordered heterogeneous materials is significant important in the regions of scientific research and technology application,which can help us to theoretically study the macroscopic law and microscopic mechanism of material fracture better.The random fuse model(RFM)is one of the important theoretical models that can describe the fracture process of heterogeneous materials,and the study on its scaling behaviors and statistical properties of fracture surface can help us to understand it better.Based on the scale behaviors and extremum statistical properties,the properties of the fracture surfaces of RFM in two-dimensional diamond and triangular lattice has been investigated using numerical simulations.The main works are as follows:The statistical behaviors of roughness exponent and height distributions of fracture surfaces of RFM in two-dimensional diamond with different substrate scales has been studied.In our paper,the surface roughness of fracture exhibits excellent dynamic scaling behavior,and the well-estabilished Family-Vicsek is still satisfied.The values surface roughness exponent is ?= 0.752 ±0.008 and the value of local surface roughness is ?loc=0.758±0.012,which satisfied the approximate equality???loc within the range of allowable error.The obtained values of surface roughness are in the range of observed experimental values.Also,maximal-and minimal-height distribution can not satisfy the three kinds of usual extreme statistical distribution,which are Weibull,Gumbel and Frechet extreme value statistical distribution,but fit the Asym2 Sig distribution.The statistical behaviors of roughness exponent and height distributions of fracture surfaces of RFM in two-dimensional triangular with different substrate scales has been studied.In our work,the surface roughness of fracture exhibited excellent dynamic scaling behavior,and the values surface roughness exponent is?=0.772±0.013 and the value of local surface roughness is ?loc=0.776±0.003,which satisfied the approximate equality ???loc within the range of allowable error.The obtained values of surface roughness are in the range of observed experimental values.Also,maximal-and minimal-height distribution exhibits excellent dynamic scaling behavior,which can satisfy the Asym2 Sig distribution.Within the range of allowable error,the values of surface roughness of two-dimensional diamond and triangular lattice are deemed to be identical,and theyhave similar properties of the fracture surfaces,which can well describe the fracture process of materials.The results of this paper indicates that the RFM is a very effective theoretical model in the numerical analysis of the scaling properties of rough fracture surfaces.