Papers by Keyword: Anisotropic Yield Function

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Authors: A. Pradeau, Sandrine Thuillier, Jeong Whan Yoon
Abstract: The work associated to this abstract is focused on the modelling of an aluminium alloy under the shape of sheet. It characterizes the mechanical behaviour up to rupture of an AA6016 alloy, taking into account the anisotropy and the hardening of the metal. The mechanical tests on which the model is based on consist of uniaxial tension, simple shear and hydraulic bulging performed at room temperature up to rupture, except for the simple shear. The numerical model is constituted of three parts. The choice of the model is suited for ductile fracture and allows for high flexibility, thanks to a total of 21 material parameters. The material parameter identification is realised through an inverse methodology. The objective of such an approach is to minimize iteratively the gap between the experimental and numerical outputs. Validation of the results is then done with the help of bending tests. The bending tests are performed with and without pre-strain in tension prior to the air-bending. Different amplitudes of pre-strain allows to reach rupture or not in bending, thus giving the possibility to find the value of the parameter controlling the non-linear accumulation of the damage. The correlation between experiments and simulations is proved to be successful and gives a very good representation of the mechanical behaviour of the aluminium alloy studied.
Authors: Kazuo Okamura, Toshiya Suzuki, Yuya Ishimaru, Hiroshi Hamasaki, Fusahito Yoshida
Abstract: In this study, the circular hole expansion process of high-strength steel sheet is numerically simulated using FE analysis with Hill48 quadratic, Gotoh’s fourth order, Yld2000-2d and Yoshida’s sixth order polynomial yield function. The effects of anisotropic yield functions on local reduction of thickness are evaluated. The thickness distribution around the circular hole edge at just before necking depends on the initial hole diameter. When the initial hole diameter is relative large, the simulation results give almost same thickness distribution among different yield functions. While the initial hole is relative small, individual characteristics of yield function becomes clear and the sixth order yield function gives the best prediction.
Authors: Shigeru Nagaki, Kenichi Ohsita, Takeshi Hayashida
Authors: Mohsen Safaei, Wim De Waele, Shun Lai Zang
Abstract: In this paper the capabilities of Associated Flow Rule (AFR) and non-AFR based finite element models for sheet metal forming simulations is investigated. In case of non-AFR, Hill’s quadratic function used as plastic potential function, makes use of plastic strain ratios to determine the direction of effective plastic strain rate. In addition, the yield function uses direction dependent yield stress data. Therefore more accurate predictions are expected in terms of both yield stress and strain ratios at different orientations. We implemented a modified version of the non-associative flow rule originally developed by Stoughton [1] into the commercial finite element code ABAQUS by means of a user material subroutine UMAT. The main algorithm developed includes combined effects of isotropic and kinematic hardening [2]. This paper assumes proportional loading cases and therefore only isotropic hardening effect is considered. In our model the incremental change of plastic strain rate tensor is not equal to the incremental change of the compliance factor. The validity of the model is demonstrated by comparing stresses and strain ratios obtained from finite element simulations with experimentally determined values for deep drawing steel DC06. A critical comparison is made between numerical results obtained from AFR and non-AFR based models
Authors: Hiroshi Hamasaki, Fusahito Yoshida, Takeshi Uemori
Abstract: This paper describes fully implicit stress integration scheme for Yoshida’s 6th order yield function combined with Yoshida-Uemori kinematic hardening model and its consistent tangent matrix. Cutting plane method was employed for accurate integrations of stress and state variables appeared in Yoshida-Uemori model. In the present scheme, equivalent plastic strain, stress tensor and all the state variables are treated as independent variables in order to handle the 6th order yield function which is not the J2 yield function, and the equilibriums for each variables are solved for the stress integration. Subsequently, exact consistent tangent matrix which is necessary for implicit static finite element simulation was obtained. The proposed scheme was implemented into finite element code LS-DYNA and deep drawing process for aluminum alloy sheet was calculated. The earing appearance after drawing was compared with the experiment.
Authors: Hirotaka Kano, Jiro Hiramoto, Toru Inazumi, Takeshi Uemori, Fusahito Yoshida
Abstract: Yoshida-Uemori model (Y-U model) can be used with any types of yield functions. The calculated stress strain response will be, however, different depending on the chosen yield function if the yield function and the effective strain definition are inappropriate. Thus several modifications to Y-U model were proposed in the 10th International Conference on Technology of Plasticity. It was ascertained that in the modified Y-U model, the same set of material parameters can be used with von Mises, Hill’s 1948, and Hill’s 1990 yield function. In this study, Yld2000-2d and Yoshida’s 6th-order polynomial type 3D yield function were examined and it was clarified that the same set of Y-U parameters can be used with these yield functions.
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