Tudor Balan

Non-quadratic yield criterion for orthotropic sheet metals under plane-stress conditions

The paper presents a new yield criterion for orthotropic sheet metals under plane-stress conditions. The criterion is derived from the one proposed by Barlat and Lian (Int. J. Plasticity 5 (1989) 51). Three additional coefficients have been introduced in order to allow a better representation of the plastic behaviour of the sheet metals. The predictions of the new yield criterion are compared with the experimental data for an aluminium alloy sheet and a steel sheet.

Prediction of Springback After Draw‐Bending Test Using Different Material Models

Within the framework of sheet metal forming, the importance of hardening models for springback predictions has been often emphasized. While some specific applications require very accurate models, in many common situations simpler (isotropic hardening) models may be sufficient. In these conditions, investigation of the impact of hardening models requires well defined test configurations and accurate measurements to generate the reference data. Specific draw-bend tests have been especially conceived for this purpose. In this work, such a draw-bending experimental device has been designed, for use on a biaxial tension machine. Three different steel sheets have been tested (one mild steel sheet and two HSS sheets) with thicknesses between 0.8 and 2 mm. Up to three different back-force levels were used for the tests. Wall curvatures and springback angles were measured. Finite element simulations of the tests were performed. A parameter sensitivity analysis has been carried out in order to determine the numerical parameters ensuring accurate springback results. The tests were simulated using an isotropic hardening model and a combined isotropic-kinematic hardening model. The impact of the hardening model is explored for the various test configurations and conclusions are drawn concerning their relative importance.

Investigation of Thick Sheet AHSS Springback in Combined Bending under Tension

This contribution investigates the springback behavior of several advanced high-strength sheet steels (TRIP, Dual-Phase, ferrite-bainite) with thicknesses up to 4 mm. Samples were tested by means of the bending-under-tension (BUT) test. This test proved very useful to discriminate constitutive models, while avoiding the interference of friction in the springback investigations [1,2]. However, the interpretation and numerical simulation of the test have to be carefully performed [3,4]. The applicability of several guidelines from the literature was investigated experimentally and numerically, in the context of thick AHS sheets. The monotonic decrease of springback as back force increased was confirmed for this category of sheet steels, and a general trend for the non-linear influence of the tool radius was observed. The influence of numerical factors on the predicted values of springback was investigated. Conclusions and simple guidelines are drawn from the analysis with industrial sheet forming applications in mind. References [1] T. Kuwabara, S. Takahashi, K. Akiyama, Y. Miyashita, SAE Technical paper 950691 (1995) 1-10. [2] I.N. Vladimirov, M.P. Pietryga, S. Reese, Prediction of springback in sheet forming by a new finite strain model with nonlinear kinematic and isotropic hardening, Journal of Materials Processing Technology 209 (2009) 4062-4075. [3] W.D. Carden, L.M. Geng, D.K. Matlock, R.H. Wagoner, Measurement of springback, International Journal of Mechanical Sciences 44 (2002) 79-101. [4] K.P. Li, W.P. Carden, R.H. Wagoner, Simulation of springback, International Journal of Mechanical Sciences 44 (2002) 103-122.

Plastic Instability Based on Bifurcation Analysis: Effect of Hardening and Gurson Damage Parameters on Strain Localization

Strain localization, which occurs in metallic materials in the form of shear bands during forming processes, is one of the major causes of defective parts produced in the industry. Various instability criteria have been developed in the literature to predict the occurrence of these plastic instabilities. In this work, we propose to couple a GTN-type model [1,2], known for its widespread use to describe damage evolution in metallic materials, to the Rice’s [3] localization criterion. The implementation of the constitutive modeling is achieved via a user material (UMAT) subroutine in the commercial finite element code ABAQUS. Large deformations are taken into account within a three dimensional co-rotational framework. The effectiveness of the proposed coupling for the prediction of the formability of stretched metal sheets is shown and Forming Limit Diagrams (FLDs) are plotted for different materials. References [1] Gurson, A.L., Continuum theory of ductile rupture by void nucleation and growth: Part I- yield criteria and flow rules for porous ductile media. Journal of Engineering Materials and Technology, 99(1):2–15 (1977). [2] Needleman A., V. Tvergaard, An analysis of ductile rupture in notched bars, Journal of the Mechanics and Physics of Solids, 32, 461-490 (1984). [3] Rice, J. R., The localization of plastic deformation. Theoretical and applied mechanics. Koiter ed., 207-227 (1976).

On the implementation of the continuum shell finite element SHB8PS and application to sheet forming simulation

In this contribution, the formulation of the SHB8PS continuum shell finite element is extended to anisotropic elastic-plastic behavior models with combined isotropic-kinematic hardening at large deformations. The resulting element is then implemented into the commercial implicit finite element code Abaqus/Standard via the UEL subroutine. The SHB8PS element is an eight-node, three-dimensional brick with displacements as the only degrees of freedom and a preferential direction called the thickness. A reduced integration scheme is adopted using an arbitrary number of integration points along the thickness direction and only one integration point in the other directions. The hourglass modes due to this reduced integration are controlled using a physical stabilization technique together with an assumed strain method for the elimination of locking. Therefore, the element can be used to model thin structures while providing an accurate description of the various through-thickness phenomena. Its performance is assessed through several applications involving different types of non-linearities: geometric, material and that induced by contact. Particular attention is given to springback prediction for a NUMISHEET benchmark problem.