Anisotropic material modelling with application to sheet metal forming

Springback is one of the major problems in the sheet metal forming industry, and is characterized by the elastically-driven change of the end shape of a work piece after unloading and removal from tooling. During forming, sheet metal is subjected to stretching, bending and reverse bending, and this makes kinematic hardening indispensable for the modelling of springback. The accurate prediction of springback requires the use of an appropriate material model, which is capable of describing typical metal hardening phenomena, such as ratchetting and the Bauschinger effect. The present dissertation discusses the realistic modelling of springback in sheet metal forming by means of a new finite strain anisotropic material model. The derivation of the constitutive equations of the model is based on the multiplicative split of the deformation gradient in the context of hyperelasticity. The model incorporates nonlinear Armstrong- Frederick kinematic hardening, nonlinear Voce-type isotropic hardening and Hill-type plastic anisotropy. A new form of the exponential map algorithm, which preserves the plastic volume and the symmetry of the internal variables, has been developed. The detailed comparison of the exponential map algorithm to two modified backward Euler algorithms which also fulfil plastic incompressibility shows that the exponential algorithm is very accurate and robust. The main focus of the thesis is the simulation of springback and earing formation in sheet metal forming. Due to the combination of nonlinear kinematic and nonlinear isotropic hardening the material model is capable of correctly predicting the springback of DP600 steel strips in the draw bend test. The simulation results are in a very good agreement with the experimental data. The model is also successfully applied to the S- rail benchmark test where the springback of IF steel sheets is simulated. Due to the fact that Neo-Hooke-type hyperelasticity is present in the formulation, it can also be used for the simulation of the thermoforming process of thermoplastic blends, where large elastic strains occur. In addition, the capability of the model of simulating the formation of earings during the cup drawing of circular blanks is verified by conducting deep drawing simulations and comparison with experiments.