Numerical Simulation Of Ubiquitiformal Fracture Surface In Heterogeneous Quasi-brittle Materials

It has been confirmed experimentally that fracture surfaces in various kinds of materials should be fractal in nature.Therefore,the emergent fractal fracture mechanics has been widely accepted as a powerful tool to describe the roughness and irregularities of fractured surfaces in heterogeneous quasi-brittle materials.However,it seems now that some inherent difficulties appear gradually with the development of fractal application especially when involving the fractal measure of the considered object.On the basis of a concept of ubiquitiform,the inherent difficulty in fractal application can be overcome,and it is possible to deeply discuss the extension of a ubiquitiform crack in quasi-brittle materials.In this thesis,based on the ubiquitiformal theory,the essential view that such a ubiquitiformal fracture surface should be resulted by the heterogeneity of the material properties is therefore proposed.And then,various models are adopted to research the ubiquitiformal fracture surfaces and the complexity in quasi-brittle materials,in which the heterogeneous material strength is characterized by the Weibull distribution.The main research work and achievements of paper are as following:(1)A simple statistical model is proposed to describe the configuration of a ubiquitiformal fracture surface in heterogeneous quasi-brittle materials.In the model,it is assumed that the crack propagates in the direction of the minimum dissipation of energyand the material properties conforms to the Weibull distribution.And then,the complexity of the ubiquitiformal crack is obtained by the box counting dimension.The numerical results of the complexity of the ubiquitiformal crack is found to be in good agreement with previous experimental data.Furthermore,it is also found that the complexity and the one-dimensional measure can be determined by the Weibull distribution parameters and independent of the spatial randomness of random variable.Finally,it can be concluded that the more heterogeneous materials the higher the complexity of the fracture surfaces.(2)Based on the ubiquitiformal theory,the boundary value problem for a ubiquitiformal crack is available due to that the normal of the ubiquitiformal crack surface can be defined.A numerical simulation on the propagation of a ubiquitiformal crack in quasi-brittle material is carried out by using the ABAQUS software,in which the XFEM-based cohesive segments model is used to simulate the crack propagation.The complexity of the fractured profile is also calculated by using the box counting dimension and is in good agreement with previous experimental data.The fracture energy which is related to the integral dimension measure is analyzed by the concept of ubiquitiform,which shows that ubiquitiformal fracture energy can be taken as an available fracture parameter of materials.(3)The meso-element equivalent method is used to investigate the effect of different inclusion size grade on the heterogeneity of materials.The relation between the inclusion size grade and the shape parameter of Weibull distribution is obtained,which provides a reasonable approach to use the above-mentioned numerical model and method in the engineering materials.And then,two samples of the experiment are carried out and the numerical results show the accuracy of the proposed relation.Meanwhile,the applicability which the heterogeneous material strength is characterized by the Weibull distribution is verified.(4)The effect of the inclusion strength,the spatial of distribution randonmness of inclusion and the maximum inclusion size on the ubiquitiformal fracture surface and complexity is studied by the numerical simulation of the concrete-like composite with different inclusion size grade.The analytical results indicate that: the correlation between the complexity and the fracture energy of concrete materials is related with fracture mode.For the transgranular fracture,a low complexity of ubiquitiformal crack in a high value of fracture energy,namely,the correlation between the complexity and the fracture energy is negative.On the contrary,however,the correlation between the complexity and the fracture energy is positive in the case of intergranular fracture.Moreover,the complexity increases with the maximum inclusion size.