Influence of Evolution in Anisotropy During Strain Path Change on Failure Limits of Sheet Metals
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Influence of Evolution in Anisotropy During Strain Path Change on Failure Limits of Sheet Metals Kaushik Bandyopadhyay1 · Shamik Basak2 · Hongjin Choi2 · Sushanta K. Panda3 · Myoung‑Gyu Lee2 Received: 23 July 2020 / Accepted: 2 October 2020 © The Korean Institute of Metals and Materials 2020
Abstract Effects of evolution in anisotropy during plastic deformation under strain path changes on the formability and failure were investigated in the present study. The evolution in anisotropic property of the extra deep drawing steel was considered by implementing the non-quadratic anisotropic yield function Yld2000-2d as a function of effective plastic strain, and the corresponding forming behaviour in two-step forming processes was analysed. For the strain path effect, pre-strain was applied under biaxial mode using Marciniak in-plane stretch forming set-up, followed by the secondary deformation using the outof-plane stretch forming tool. For failure prediction of the proposed two-step forming, different failure limit approaches were investigated. First, a strain based forming limit diagram (FLD), proposed as the Marciniak–Kuczynski model was modified to include the evolution in anisotropic yield function. The dynamic shift in FLD was also determined by taking strain path change into consideration. In addition, the influence of evolution of yield function on the strain path independent failure limit criteria was also assessed in terms of stress based forming limit diagram. Finally, the prediction accuracy of the failure limit criteria was compared among different models in terms of failure location and limiting dome height (LDH). It was observed that the incorporation of evolution in anisotropic yield surface improved the prediction of formability in terms of the LDH and strain distribution for the investigated material. Keywords MK model · Evolutionary yield function · Yld2000-2d · Forming limit diagram · Multi-step forming
1 Introduction Over the decade strain based forming limit diagram (FLD) is the predominant failure criterion for sheet metal forming. These FLDs can either be evaluated following different experimental procedures such as Nakazima test [1], Hasek test [2] and Hecker test [3] or by following various theoretical approaches. One of the initial formulations for calculating localised necking in material under plane stress state was proposed by Hill [4]. Keeler-Brazier proposed empirical equation to determine FLD spanning over drawing to biaxial region. There are different other theoretical models * Myoung‑Gyu Lee [email protected] 1
Department of Mechanical Engineering, IIT Bhilai, Raipur 492015, India
2
Department of Material Science and Engineering and RIAM, Seoul National University, Seoul 08826, Republic of Korea
3
Department of Mechanical Engineering, IIT Kharagpur, Kharagpur 721302, India
to predict the FLD of a sheet material, and among these Marciniak–Kuczynski (MK) model [5, 6], Gurson–Tvergaard–Needleman model (GTN) [7], and Storen Rice vertex theory [8] were rigorously used
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