Characterization Of Crack Propagation Fracture Parameters Based On The Ubiquitiform Theory

Fractal geometry,as an important tool to investigate complex irregular configurations,provides an important theoretical basis for solving non-linear problems.In the field of fracture,the fractal fracture mechanics based on fractal theory has become a new important subject because the fracture surfaces of many materials have fractal characteristics confirmed by experiments.However,when studying the fractal fracture mechanics deeply,it is found that there are unreason and many confusions in the measurement problems.The ubiquitiform theory is a fundamental way to solve the difficulties in fractal application and is reasonable in the characterization of fracture problems.Based on the ubiquitiform theory,in this paper the fracture of cracked members is investigated.The main contents are as following:Firstly,consider the ubiquitiformal characteristics of the crack propagation path and introduce the ubiquitiform complexity and the scale invariance which are two key parameters of ubiquitiform theory to the theoretical derivation of the fracture parameters for mode I crack propagation.Besides,the influence of the complexity on the stress intensity factor and the crack propagation force are analyzed by numerical examples.Secondly,the uniaxial tensile failure behaviors of cast iron with different crack were studied experimentally.The results suggest that crack is an important cause of component failure,and the longer the crack is,the worse the tensile performances of components is.In addition,the cross-section morphology of tensile specimens was measured by laser confocal microscopy.The box counting method was utilized to calculate the complexity of cross-section contour and the statistical self-similarity scale.The accuracy of the expressions of ubiquitiformal fracture stress and ubiquitiformal fracture energy were verified by experimental data.Finally,the ubiquitiformal characteristics of the fracture sections are caused by the inhomogeneity of the materials.Based on Weibull statistical distribution and the extended finite element method,we described the inhomogeneity of the material and numerically simulated the crack propagation process of the specimens with cracks.The complexity of the simulation path was calculated.The simulation results are in good agreement with the experimental results,which indicates the rationality of the model.In addition,the simulation results of crack growth in inhomogeneity models under different Weibull homogeneity distributions show that the more homogeneous the material is,the less complex the crack path is.It verifies the basic idea that the inhomogeneous characteristics of the material will lead to the ubiquitiform crack in the components.