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Top2. Literature Review
In sheet metal forming process, cyclic loading occurs due to bending and unbending of material in the die such as when the sheet is drawn over a die corner (Sanchez, 2010; Yoshida, Uemori, & Fujiwara, 2002). This is shown in Figure 1.
Figure 1. Description of Cyclic Loading (A) Draw-Bend (B) Springback (C) Stress-Strain Path (Yoshida et al., 2002)
Yoshida and Uemori(Yoshida & Uemori, 2003) described this cyclic process as having four distinct features: load reversal and Bauschinger point, transient behaviour, work-hardening stagnation and permanent softening. To improve sheet metal forming simulation, there is a need to incorporate an appropriate constitutive equation capable of describing the Bauschinger effect and so-called cyclic transient, which describes transition between the elastic and elastic-plastic state during repeated loading. A combination of isotropic and nonlinear kinematic hardening has been considered as one of the best material models, as the former has been associated with the capability to improve cyclic transient and the latter with the capability to take care of the Bauschinger effect (Chun, Jinn, & Lee, 2002). The Chaboche nonlinear kinematic hardening model as described by Equation 1 was chosen for kinematic hardening in this work. A combination of this hardening model and Voce isotropic hardening models in Equation 2 was selected to represent the mixed hardening model as shown by Equation 3.
The parameters involved are: Q, b, C and 
. Q defines the maximum change in the size of the yield surface and b is the rate of the changes. C is a kind of kinematic hardening modulus and 
defines the rate at which the kinematic hardening modulus decreases as the plastic deformation develops. This is a widely accepted model in sheet metal forming simulation (Chun et al., 2002) and has been applied in finite element software, such as Abaqus (Abaqus, 2000). Identification of material parameters in this and other cyclic hardening models requires a proper cyclic loading experiment to be developed and carried out.