The Solution Of Complex Variable Function And The Numerical Simulation Of Stress Intensity Factor At Crack Tips

As a new branch of solid mechanics,fracture mechanics mainly studies the law of crack growth in materials and engineering structures,and has been applied more and more in the neighborhood of structure,machinery,rock and soil,and earthquake resistance.In fracture mechanics,the most important mechanical parameter is the stress intensity factor at the crack tip.It controls the stress and displacement fields near the crack tip.The main work of this paper is as follows:1)based on the theory of linear elastic fracture mechanics,the three point bending edge straight crack stress intensity factor at the crack tip,the first attempt to use the theory of complex function-Christopher mapping,Schwartz will be mapped to the upper half plane polygon area,thus it is concluded that the problem of the conformal mapping function,and USES this mapping function to calculate the three point bending edge crack under pressure in the distance the value of the point at the crack tip stress intensity factor and the calculation results and test data are compared in the existing literature,the results show that the calculation results of this paper are in good agreement with the test data,and especially the pressure is small,the result is close to are the same.The analysis method in this paper is feasible.In addition,the relationship between the value of the stress intensity factor and the load and size of the model can be obtained from the results in this paper.2)the herringbone straight crack in frozen soil test sample,this paper,by using ANSYS finite element analysis software for modeling and calculation,the herringbone finite element calculation model was established,and the effect on five different dimensions,load and stress intensity factor of the meshing density situation to carry on the numerical simulation,and the calculated results with existing literature provided by the standard pattern,comparing the calculation results the results showed that the calculation results of this paper is very good,the maximum relative error is only 0.47%.At the same time,the relation between the value of the stress intensity factor and the model size,the load,the density of finite element mesh and the temperature is also analyzed.3)finally in this paper,the semi-infinite crack in the crack of the narrow body under the action of stress and the shear stress at the crack tip stress intensity factor,using ANSYS finite element software modeling and calculation,and will get the result of the complex functions in the existing literature and analyzed,the results show that when the crack surface under the action of stress,in this paper,the calculation results with the literature results of relative error is only 2.41%,when the load increases,in this paper,the calculation results and the relative error of the results in the literature can also gradually increase,When the crack surface is subjected to shear force,the relative error between the calculated results in this paper and theresults in the literature is only 1.63%.When the load increases,the relative error between the calculated results in this paper and the results in the literature is still no more than 2%.