Perturbation Analysis,Loading Trajectory Design And Forming Defects Study On Stretch-forming Process Based On Discrete Loading

Stretch-forming process has been widely used in aircraft skin manufacturing and other fields with high forming accuracy.The integral rigid clamps are used in conventional stretch-forming process,and the sheet metal is deformed under the overall movement of the integral rigid clamp,which may result in that the curved part can't be formed in the best way.It's difficult to form large-curvature and complex-shaped curved part,and the curved part is prone to appear forming defects such as noncontacting with the die,wrinkling and cracking.The integral rigid clamp is discretized into the discrete clamps arranged in array along the transverse direction,and the loading displacements of different discrete clamps can be calculated according to the die surface.By controlling the loading trajectory of each discrete clamp,different deformations are generated at different positions of the sheet metal,so as to obtain high-quality curved parts.Perturbation analysis,loading trajectory optimization,contact state analysis and forming defects study on stretch-forming process based on discrete loading are concluded in this paper.The main contents and conclusions in theoretical analysis,numerical simulation and experimental verification are as follows:The sheet metal of stretch-forming process can be be divided into the contacting area(the region contacting with the die)and the free area(the region noncontacting with the die),and the free area is constantly transformed into the contacting area during loading process.Perturbation analysis on the deformation of the free area,the plastic deformation of the free area is regarded as the superposition of uniform deformation and perturbation deformation.Meanwhile,the displacement,strain and stress increments in the free area are obtained on the basis of the uniform deformation,and the relationships between them are also established.Then,the equilibrium equation expressed by the displacement increment is established,and the trigonometric series solution of the displacement increment can be obtained by solving the partial differential equation.The undetermined coefficients in the series solution are determined by the boundary conditions of the stretch-forming process,and the theoretical strain and stress increments in the perturbation deformation are determined.Finally,the theoretical values of strain and stress in the free area are obtained by superimposing the stress and strain of the uniform deformation with the stress and strain increment of the perturbation deformation.When the curved part with small transverse curvature is stretched,the deformation of the contacting area is only slightly different from that of cylindrical part.Perturbation analysis on the deformation of the contacting area,the angle between the normal direction and the cross section of the curved part is taken as the perturbation angle,and the equilibrium equation in the form of strain increment is established in the contacting area.Then,taking the solution of stress and stain state in the free area as the boundary condition,the numerical solution of the stress and stain in the contacting area is calculated by the difference method.Finally,the accuracy of perturbation analysis is verified by comparing the numerical results and the theoretical values of spherical and saddle-shaped parts formed by stretch-forming process.From the perspective of space geometry,when the sheet metal is transformed into the specific shape of three-dimensional surface by stretch-forming process based on discrete loading,in theory,there are countless possible loading trajectories for the discrete clamps.Among many loading trajectories,finding the optimal loading trajectory is the key to stretch-forming process based on discrete loading.The deformation degree of the sheet metal can be expressed by equivalent plastic strain,when the sheet metal is deformed into the desired shape by generating the minimum equivalent plastic strain,the minimum equivalent plastic strain criterion is proposed,and the optimized trajectory stretch-forming process based on discrete loading is designed,meanwhile,the formulas of loading displacement and speed at each discrete clamp are given.Finally,the finite element models of conventional stretch-froming process and optimized trajectory stretch-forming process based on discrete loading are established by using Abaqus software.By comparing the sticking degree and stress-strain distribution of the formed parts,for the curved part formed by loading optimized trajectory,it is found that the effective forming area can fully fit with the die surface,the stress and strain distribution is more uniform,and the forming effect is better.Different loading trajectories have the great impact on the forming results of stretched curved parts.In this paper,the evolution of contact state between sheet metal and die and its influence on forming accuracy and wrinkling defects are compared between conventional stretch-froming process and optimized trajectory stretch-forming process based on discrete loading.In conventional stretch-forming process,the spherical and saddle-shaped parts firstly contact with the center and edge regions of the die,and the approximate ellips of the contacting area of spherical part extends to the edge region of the sheet metal,and the approximate arc of the contacting area of saddle-shaped part extends to the central region of the sheet metal,respectively.Meanwhile,the edge region of spherical parts is difficult to fit with the die,which could cause the large shape error;when the transverse compressive stress in the central region is too large,the saddle-shaped part may be easy to produce wrinkling defect.In optimized trajectory stretch-forming process based on discrete loading,the contacting areas of spherical and saddle-shaped part extend to the end of the sheet metal in the approximate rectangular,and the sheet metal can simultaneously contact with the die from the central region to edge region in the transverse direction,which can make the sheet metal deform more stable,and the curved part without any defects and with high forming accuracy can be obtained.In order to more accurately analyze the fracture defects in stretch-forming process,the M-K model based on the original measured stress-strain data is proposed,and the theoretical prediction method of necking forming limit curve(FLC)is introduced in detail.However,because there is no obvious necking phenomenon before fracture for some aluminum alloy sheets,the predicted method of fracture forming limit curve(FFLC)is studied based on ductile fracture criterion(DFC).The uniaxial tensile,plane strain and shear specimens with different shapes and sizes are designed,and the undetermined material parameters in DFC are calibrated by the combination method of experiment and numerical simulation.The best specimen combination and theoretical FFLC are determined by the orthogonal experiment,and the effects of each material parameter on stress triaxiality-fracture strain curve and FFLC are compared and analyzed.Finally,the fracture tendency of the curved part during stretch-forming process is judged by quantitatively analyzing on the distributions of major and minor strains of the formed part on FLC and FFLC.The maximum strain of the formed part is above the ultimate strain,which may result in that the sheet metal is prone to fracture.However,when the maximum strain of the formed part is below the ultimate strain,the sheet metal will not produce fracture defect.