Hocine Chalal

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.

Efficient solid–shell finite elements for quasi-static and dynamic analyses and their application to sheet metal forming simulation

Thin structures are commonly designed and employed in engineering industries to save material, reduce weight and improve the overall performance of products. The finite element (FE) simulation of such thin structural components has become a powerful and useful tool in this field. For the last few decades, much attention and effort have been paid to establish accurate and efficient FE. In this regard, the solid–shell concept proved to be very attractive due to its multiple advantages. Several treatments are additionally applied to the formulation of solid–shell elements to avoid all locking phenomena and to guarantee the accuracy and efficiency during the simulation of thin structures. The current contribution presents a family of prismatic and hexahedral assumed-strain based solid–shell elements, in which an arbitrary number of integration points are distributed along the thickness direction. Both linear and quadratic formulations of the solid–shell family elements are implemented into ABAQUS static/implicit and dynamic/explicit software to model thin 3D problems with only a single layer through the thickness. Two popular benchmark tests are first conducted, in both static and dynamic analyses, for validation purposes. Then, attention is focused on a complex sheet metal forming process involving large strain, plasticity and contact.

Quadratic Solid–Shell Finite Elements for Geometrically Nonlinear Analysis of Functionally Graded Material Plates

In the current contribution, prismatic and hexahedral quadratic solid–shell (SHB) finite elements are proposed for the geometrically nonlinear analysis of thin structures made of functionally graded material (FGM). The proposed SHB finite elements are developed within a purely 3D framework, with displacements as the only degrees of freedom. Also, the in-plane reduced-integration technique is combined with the assumed-strain method to alleviate various locking phenomena. Furthermore, an arbitrary number of integration points are placed along a special direction, which represents the thickness. The developed elements are coupled with functionally graded behavior for the modeling of thin FGM plates. To this end, the Young modulus of the FGM plate is assumed to vary gradually in the thickness direction, according to a volume fraction distribution. The resulting formulations are implemented into the quasi-static ABAQUS/Standard finite element software in the framework of large displacements and rotations. Popular nonlinear benchmark problems are considered to assess the performance and accuracy of the proposed SHB elements. Comparisons with reference solutions from the literature demonstrate the good capabilities of the developed SHB elements for the 3D simulation of thin FGM plates.

Prediction of necking in thin sheet metals using an elastic–plastic model coupled with ductile damage and bifurcation criteria:

In this paper, the conditions for the occurrence of diffuse and localized necking in thin sheet metals are investigated. The prediction of these necking phenomena is undertaken using an elastic–plastic model coupled with ductile damage, which is then combined with various plastic instability criteria based on bifurcation theory. The bifurcation criteria are first formulated within a general three-dimensional modeling framework, and then specialized to the particular case of plane-stress conditions. Some theoretical relationships or links between the different investigated bifurcation criteria are established, which allows a hierarchical classification in terms of their conservative character in predicting critical necking strains. The resulting numerical tool is implemented into the finite element code ABAQUS/Standard to predict forming limit diagrams, in both situations of a fully three-dimensional formulation and a plane-stress framework. The proposed approach is then applied to the prediction of diffuse and localized necking for a DC06 mild steel material. The predicted forming limit diagrams confirm the above-established theoretical classification, revealing that the general bifurcation criterion provides a lower bound for diffuse necking prediction, while the loss of ellipticity criterion represents an upper bound for localized necking prediction. Some numerical aspects related to the prestrain effect on the development of necking are also investigated, which demonstrates the capability of the present approach in capturing the strain-path changes commonly encountered in complex sheet metal forming operations.

Explicit dynamic analysis of sheet metal forming processes using linear prismatic and hexahedral solid-shell elements

Purpose The purpose of this paper is to propose two linear solid-shell finite elements, a six-node prismatic element denoted SHB6-EXP and an eight-node hexahedral element denoted SHB8PS-EXP, for the three-dimensional modeling of thin structures in the context of explicit dynamic analysis. Design/methodology/approach These two linear solid-shell elements are formulated based on a purely three-dimensional (3D) approach, with displacements as the only degrees of freedom. To prevent various locking phenomena, a reduced-integration scheme is used along with the assumed-strain method. The resulting formulations are computationally efficient, as only a single layer of elements with an arbitrary number of through-thickness integration points is required to model 3D thin structures. Findings Via the VUEL user-element subroutines, the performance of these elements is assessed through a set of selective and representative dynamic elastoplastic benchmark tests, impact-type problems and deep drawing processes involving complex non-linear loading paths, anisotropic plasticity and double-sided contact. The obtained numerical results demonstrate good performance of the SHB-EXP elements in the modeling of 3D thin structures, with only a single element layer and few integration points in the thickness direction. Originality/value The extension of the SHB-EXP solid-shell formulations to large-strain anisotropic plasticity enlarges their application range to a wide variety of dynamic elastoplastic problems and sheet metal forming simulations. All simulation results reveal that the numerical strategy adopted in this paper can efficiently prevent the various locking phenomena that commonly occur in the 3D modeling of thin structural problems.

On the use of solid–shell elements for thin structures: Application to impact and sheet metal forming simulations

A family of linear and quadratic assumed-strain based solid–shell elements (SHB) is presented in this paper to simulate 3D thin structural problems including both quasi-static and dynamic analyses. The SHB solid–shell elements are based on a three-dimensional formulation, with only displacements as degrees of freedom, and a reduced integration technique with an arbitrary number of integration points along the thickness direction, which enables them to model 3D thin structures with only one layer of elements through the thickness. All SHB elements have been successfully implemented into ABAQUS dynamic/explicit and static/implicit codes. Several static and dynamic benchmark tests as well as sheet metal forming process simulations, involving large strain, material nonlinearity and contact, have been conducted to assess the performance of the SHB elements.

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.