towards an accurate springback prediction - experiments and modeling
Ali Torkabadi is a PhD student in the department of Mechanics of Solids, Surfaces & Systems (MS3). His supervisor is prof.dr.ir. A.H. van den Boogaard from the faculty of Engineering Technology (ET).
Finite element (FE) simulations are used extensively during the tool design stage to predict the springback; it can then be compensated for by adapting the tool’s geometry. The tool is adapted in such a way that the formed product takes the intended shape after springback. In order to accurately predict springback and compensate for it correctly, constitutive models are needed to accurately describe the material mechanics.
In this thesis, specific attention has been paid to the unloading behavior of advanced high strength steels (AHSS). Springback is governed by the stress–strain behavior of the material during unloading when the forming forces are removed. Therefore, modeling the unloading behavior of the material is of a great importance to springback prediction.
It is generally accepted that the springback of the deformed material is driven solely by the recovery of elastic strain upon unloading; however, experimental evidence has shown that this is an invalid assumption. It has widely been observed that a plastically deformed material shows a nonlinear unloading/reloading behavior. Considering that the springback is governed by the total recovered strain upon unloading of the deformed part, modeling the unloading behavior is essential for an accurate springback prediction.
In this research, the main mechanisms responsible for the observed nonlinear unloading/reloading behavior are studied. This is carried out by performing a combination of theoretical, experimental and numerical studies on DP600 and DP800 from the family of AHSS.
To understand the physics of the nonlinear unloading/reloading behavior, uniaxial tensile tests are conducted. It is observed that the unloading/reloading behavior of the material is complex, showing direction dependency, time dependent behavior and sensitivity to baking treatment.
Based on the experimental results, it is concluded that there are two potential mechanisms behind the nonlinear unloading/reloading behavior: 1. dislocation driven anelasticity and 2. inhomogeneous deformation at the microscale. According to the theory of dislocation driven anelasticity, the reversible motion of the dislocation bow-outs contributes to an additional strain on top of elastic strain during unloading and reloading. This additional strain, known as anelastic strain, results in the observed nonlinear unloading/reloading behavior. A mixed physical-phenomenological model is proposed to describe the observed nonlinearity for different levels of pre-strain. The proposed model is generalized to a 3D constitutive model incorporating elastic, anelastic and plastic strains. The model is shown to be capable of predicting the stress–strain response of a DP800 steel subjected to unloading/reloading cycles.
An alternative theory is established on the inhomogeneous deformation at the microstructure. To this end, the stress and strain partitioning in a dual phase microstructure are analyzed using the crystal plasticity finite element modeling (CPFEM) approach. The model shows that some fractions of the material re-yield in compression during unloading. Based on the insight obtained from CPFEM, a model based on the elasto-plastic self-consistent (EPSC) homogenization scheme is proposed. In this model, the material inhomogeneity is modeled by considering a distribution in yield stress of material fractions. The EPSC model is shown to capture the nonlinear unloading/reloading behavior and Bauschinger effect simultaneously.
Draw-bend experiments are used as a benchmark for evaluating the performance of the developed models in predicting the springback of DP800. The draw-bend setup was designed and built during this research and represents a realistic forming process. The draw-bend experiments are simulated using the newly developed models and the results are compared with the classical E-modulus degradation model and the case where the E-modulus is taken as a constant. The results show that modeling the nonlinear unloading/reloading behavior results in a more accurate springback prediction in comparison with the classical approaches.