Forming Limit Of Sheet Metal Under Nonlinear Strain Path

Sheet metal stamping is a plasticity forming processes widely used for production of components and parts in the field of automobile, aerospace and equipment manufacturing industry. Forming limit curve(FLC) is a vital index for quality evaluation of formed part and processes design. Its accuracy is very important to the design of forming processes. Traditional forming limit diagram(FLD) is obtained by theoretical calculation or experimental test on the basis of linear strain path assumption. However, the practical strain path of the formed material is always nonlinear in forming processes. According to the theory of crystal plasticity deformation, the plasticity deformation in one crystal slip direction will influence the subsequence deformation in other direction under complex nonlinear loading path condition. Strain path change has a marked effect on the material behavior, especially on the hardening characteristic and forming limit. Thus, the investigation on the material constitutive model and forming limit under nonlinear strain path change, exploring the forming limit theory with pre-strain loading condition, analyzing the transient forming limit at evaluated temperature, have a vital significance to accuracy improvement of the formability evaluation and its engineering application in sheet metal forming processes by plasticity deformation.This thesis is focused on the issue of formability for sheet metal under non-linear strain path change. The theoretical calculation for forming limit determination with pre-strain loading condition, experimental test method and numerical analysis for forming limit under the condition of continuous strain path change, and the transient FLD at elevated temperature and its application in hot stamping processes are investigated. The detailed content and major results are as follows:(1) To the constraint condition of linear strain path assumption in Swift diffuse and Hill localized neck theory, a constraint equation for material neck under strain path change condition was proposed. Based on the proposed constraint equation, a theory and analytical approach for forming limit calculation under bi-linear strain path condition with pre-strain were developed. In the theoretical approach, it is difficult to obtain directly the analytical result when a complex constitutive model is used. Hence, it is a reasonable alternative choice to using the well-known M-K model, which is based on the assumption of groove defect, to predict the forming limit under non-proportional loading condition. However, the high order yield function in material constitutive model caused a no-converging problem in solution to the nonlinear systems of equations of force equilibrium and geometric compatibility condition in M-K model. And the plastic strain ratio between the groove area and normal area can’t converge to the prescribed critical value. To overcome this problem, a backtracking operation was introduced in the iterative solution to the nonlinear equations. A scale technique for iteration step length has been implemented, which effectively suppressed and eliminated the no-converging problem in the iterative procedure. And it makes the M-K model based forming limit calculation easier to obtain convergent results. Meanwhile, the approaches developed in this work were used to predict the forming limit for Aluminum alloy sheet Al 2008-T4 under bi-linear strain path. It is showed that the predicted results are in good agreement with the experimental ones. The effect of pre-strain on the material FLC can be predicted accurately.(2) A novel formability index Fsp accounted for the strain path history is put forward, which can promote the application of more accurate formability evaluation for sheet metal under continuous strain path change condition. In order to verify current proposed formability index, a drawing-reverse drawing forming limit experiment setup was developed, which is based on the material deformation mode in drawing processes. The acquiring method for real strain path using DIC technique and the criterion for forming limit strain state were explored. The measured strain path results of initial failure location in sample showed that the representative strain path changes in sheet metal forming process are successfully obtained by the developed experiment setup. And the strain path change modes include: uniaxial tension to plane strain, biaxial tension to plane strain, and plane strain to biaxial tension to plane strain. Based on the deformation characteristic of sheet in the drawing-reverse drawing processes, the limit dome height(LDH) evaluation index was modified. And the influence of sample shape and processes condition on the strain path and modified LDH evaluation index in drawing-reverse drawing processes are quantitatively analyzed. Based on the measured strain path history data at the initial failure location in sample, the accuracy of the proposed formability index for sheet metal forming under continuous strain path change condition was verified.(3) The standard isotropic-kinematic combined hardening model does not account the latent hardening effect induced by no-proportional loading path change, and the influence of nonlinear strain path on the material characteristic can’t be fully described. Hence, the internal variables representing the loading path change during material deformation processes were introduced, and the latent hardening effect caused by nonlinear strain path was taken into account in the extended anisotropy constitutive model. The effect of microstructure change during nonlinear strain path loading on the modulus of isotropic and kinematic hardening was considered, respectively. And the Bauschinger effect and the cross-hardening effect during reverse loading and orthogonal strain path change loading can be characterized with this constitutive model. A material subroutine UMAT was programmed for its numerical implementation and integrated in the finite element code LS-DYNA. The numerical simulation for the drawing reverse-drawing forming limit experiment processes and the twist springback in advanced high strength steel was investigated with the anisotropy constitutive model. And the comparison between the simulated results with the corresponding experimental ones showed that the advanced anisotropy yield criterion combined with the hardening model accounted the latent hardening effect improved the accuracy of numerical simulation for sheet metal forming.(4) The effect of temperature and strain rate on the material characteristic and mechanical behavior of ultra-high strength steel 22 Mn B5 was analyzed. A Logistic equation was introduced to describe the temperature dependence of plasticity anisotropy. The anisotropy constitutive model for hot forming processes is constructed. The material flow behavior at high temperature Austenite state described by the model is found in good agreement with the experimental data. Based on the M-K model, the FLC under constant temperature and strain rate are predicted. It is showed that the formability improved when temperature and strain rate increase. Furthermore, a three-dimension forming limit surface(3D-FLS) is constructed on the condition that the FLC under equilibrium isothermal condition are obtained. The thermal-mechanical coupled finite element analysis for hot forming of a B pillar was modeled. Comparing the predicted results with experimental ones showed that the section thickness distributions are in good agreement with the measured data, and the neck location of B pillar after forming was successfully predicted. The results validated the accuracy of the material constitutive model and the thermal-mechanical coupled model. And the validity of the developed 3D-FLSapplication in hot forming processes is also verified. The developed prediction method for transient FLD at elevated temperature provided an important guide for formability analysis in thermo forming processes.