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Park, Namsu,Stoughton, Thomas B.,Yoon, Jeong Whan Elsevier 2019 International journal of plasticity Vol.121 No.-
<P><B>Abstract</B></P> <P>An accurate description of the material yielding behavior is of great importance for a trustworthy prediction of complicated forming processes via numerical analysis. For metal sheets, the work hardening rate, in general, varies according to the loading directions and conditions due to the texture developed during cold rolling processes, and accordingly, the yield surface evolves with a variation of its shape and size during plastic deformation. The non-uniform evolution of the yield surface becomes a non-negligible issue especially for the materials showing the severe tension/compression asymmetry on the yielding behavior with respect to the loading direction. A primary concern here is that the advanced yield criteria previously developed normally feature an isotropic expansion of the yield surface which is determined at an initial yielding stage and thereby neglect the evident changes in the shape of the yield surface as implied by experimental tests. In this paper, a solution to the challenge of modeling a general criterion, which accurately describes the evolution of the anisotropy/asymmetry-induced distortional yielding behavior, is proposed using neither any interpolation nor optimization techniques for the calibration of the yield surface. The new criterion is proposed based on the Stoughton and Yoon (2009) criterion, which features non-associated flow rule, with the multiplication of two additional terms referred to as scaling and asymmetry functions. The proposed criterion was successfully applied to various types of metallic materials to validate its noticeable flexibility and general applicability in describing the anisotropic/asymmetric yielding behavior. An extensive comparison of the experimental results with the predictions from the proposed criterion reveals that the proposed criterion provides sufficient predictability on the subsequent evolution of the anisotropy/asymmetry-induced distorted yield surface for various metallic materials over a broad range of plastic strain level, strain rate, and temperature.</P> <P><B>Highlights</B></P> <P> <UL> <LI> The evolution of the anisotropy/asymmetry-induced distortional yielding behavior is proposed. </LI> <LI> The new criterion is proposed based on the Stoughton and Yoon (2009) criterion, which features non-associated flow rule. </LI> <LI> The proposed criterion was successfully applied to various types of metallic materials. </LI> <LI> The proposed criterion provides sufficient predictability on the subsequent evolution of the distorted yield surface. </LI> </UL> </P>
A new strategy to describe nonlinear elastic and asymmetric plastic behaviors with one yield surface
Lee, E.H.,Stoughton, T.B.,Yoon, J.W. Pergamon Press ; Elsevier Science Ltd 2017 International journal of plasticity Vol.98 No.-
This paper proposes a new strategy to describe both nonlinear elastic and asymmetric plastic behaviors (early re-yielding, transient Bauschinger effect, permanent softening, and work-hardening stagnation) only with one yield surface. There have been the popular models, such as Yoshida-Uemori and Quasi-Plastic-Elastic (QPE) models, that have led to remarkable improvements in describing material's behavior and predicting springback. Although the Yoshida-Uemori model describes the asymmetric plastic behavior, it is challenging to follow the nonlinear elastic response. On the other hand, the QPE model does not capture the work-hardening stagnation though it follows the nonlinear elastic behavior. Besides, the above models have multiple surfaces leading to a complex mathematics and, then leading to increased computation time. In this study, a new one surface method incorporates state of strain change or state of energy change as well as the stress state in determining the deformation mode, so that it is possible to keep only one yield surface. In order to capture the work-hardening stagnation, the one surface method traces the equivalent plastic strain, then compares the change in the incremental equivalent plastic strain of the current path to the accumulated one up to the previous path when the loading direction reverses. This way makes the computation time much faster than an existing method which employs an additional surface to capture the work-hardening stagnation. The one surface method has been implemented into a user-defined material (UMAT) subroutine, and validated by comparing it with the experimental results and the results from Yoshida-Uemori and QPE models with cycling loading conditions and U-draw bending test. This work shows that the one surface method can describe both nonlinear elastic and asymmetric plastic behaviors with the reduction of complexity and computation time.
Lee, E.H.,Stoughton, T.B.,Yoon, J.W. Pergamon Press ; Elsevier Science Ltd 2017 International journal of plasticity Vol.99 No.-
This paper proposes a simple coupling of quadratic and non-quadratic yield functions with a non-associated flow rule to describe the evolution of yield surface (or anisotropic hardening). The non-quadratic part is an isotropic function and is supposed to control curvature of the whole model. The quadratic part takes a role to describe anisotropic hardening throughout a deformation history by employing the hardening functions of different loading conditions. The new yield model just multiplies a quadratic and non-quadratic parts, and it does need neither any interpolation nor optimization at a discrete level of equivalent plastic strain. The new model is compared with several material models with four different material data in order to validate advantages of the new model in capturing anisotropic hardening and controlling its curvature of yield surface. In addition, artificial material cases are applied to the new model to study sensitivity of the model.
Kinematic hardening model considering directional hardening response
Lee, Eun-Ho,Stoughton, Thomas B.,Yoon, Jeong Whan Elsevier 2018 International journal of plasticity Vol.110 No.-
<P><B>Abstract</B></P> <P>This paper proposes a kinematic hardening model to capture both asymmetric plastic behavior (early-reyielding, transient Bauschinger effect and permanent softening) and directional hardening (anisotropic hardening) response at the same time. The previously reported kinematic hardening models have brought significant improvements of ability to describe the asymmetric plastic behavior of sheet metal in cycling loading conditions at fixed one angle from the rolling direction (RD). However, their inability to cover the anisotropy in the directional hardening response has a limitation to describe the anisotropic hardening behavior because material constants of general kinematic hardening models are only fitted to one reference axis. In order to capture the anisotropic hardening with a kinematic hardening model, this work proposes a scheme to combine a kinematic hardening model with a function, which is called the condition function in this paper, to account for the change of the mechanical property with respect to the RD. The condition function should explicitly capture four independent hardening data in different directions, 0°, 45°, 90° to the RD and the equal biaxial (EB) condition in order to gain an appropriate parameter set. The new model is validated with four tests and the results are compared with other material models to clearly show that the new model can capture both the anisotropic hardening response and the asymmetric plastic behavior for monotonic and cycling loading conditions.</P> <P><B>Highlights</B></P> <P> <UL> <LI> This paper proposes a kinematic hardening model to capture both asymmetric plastic behavior and directional hardening response at the same time. </LI> <LI> This work proposes a scheme to combine a kinematic hardening model with the condition function to account for the change of the mechanical property with respect to the rolling direction. </LI> <LI> The condition function should explicitly capture four independent hardening data in different directions, 0°, 45°, 90° to the RD and the equal biaxial (EB) condition. </LI> <LI> The new model is validated with three tests and the results are compared with other material models. </LI> </UL> </P>