Numerical Simulation Of Cupping Test Based On Material Point Method

Metal cupping test is a performance test of stamping process,which is used to measure the deep drawing performance of metal.The forming process of metal cupping test which involves geometry nonlinearity and material nonlinearity is a process of large deformation.The simulation of traditional finite element has the mesh distortion,which needs to undertake the grid subdivision.The computational efficiency and precision will be reduced.The material point method which combines particle point and background mesh is a new kind of meshless method,which effectively avoids the problem of mesh distortion when the finite element method simulates the large deformation of sheet metal.In this paper,the material point method is applied to simulate the research of cupping test in order to explore the influence of different lubrication situation,the thickness of sheet and stamping speed on cupping test.The simulation result of MPM is compared with that of the traditional finite element method to verify the effectiveness and feasibility of material point method in cupping forming.Specific contents are as follows:The discrete format of governing equation and the weak form of material point method is deduced by using the weighted residual method,and then the display calculation procedure of material point method is given.Based on the material point method,the program of cupping test is written by using FORTRAN language.The cup drawing test is simulated by using respectively the programs based on material point method and the commercial finite element software ABAQUS,and the simulation results of the material point are compared with that of the finite element method and experimental results in the literature from the equivalent strain of sheet metal,the cupping test value and time efficiency.The results show that the simulation results of material point method are in good agreement with the experimental results,and the calculation precision of material point method is the same as that of finite element method.A numerical simulation study on cupping test was carried out based on the material point method.The effect of sheet thickness,friction coefficient and stamping speed on sheet deformation in the process of cupping test is discussed respectively.The displacement nephogram,cupping test value and equivalent strain nephogram are obtained with different stamping speed,friction coefficient and the thickness of the sheet metal.The results show that the displacement nephogram is relatively uniform,and the change of metal sheet thickness is similar.There is a trough at the neck of the ring where the thickness thinning is bigger and the sheet is prone to cracking.It is consistent with the experimental results.The cupping test value decreases and the equivalent strain increases with the increase of stamping speed and friction coefficient.The cupping test value increases and the equivalent strain decreases with the increase of sheet thickness.The maximum equivalent strain appears in the ring neck near the center of sheet.This study in this paper provides a new simulation method for the numerical simulation of cupping test.It also provides some guidance for the stamping of metal sheet.