A non-associated constitutive model with mixed iso-kinematic hardening for finite element simulation of sheet metal forming

Study on the definition of equivalent plastic strain under non-associated flow rule for finite element formulation

“…Stoughton and Yoon (2009) proposed a non-AFR based anisotropic hardening model that resulted in excellent predictions of hardening curves for rolling, transverse and diagonal directions and for the balanced biaxial stress state. Improvements in prediction of cup height and springback of a U-bend specimen using non-AFR with mixed isotropic-kinematic hardening have been also reported by Taherizadeh et al (2010Taherizadeh et al ( , 2011. Gao et al (2011) showed the significance of the hydrostatic stress on plastic response with the non-associated flow rule.…”

“…(15) has been adopted by Stoughton (2002), Stoughton and Yoon (2006), Taherizadeh et al (2010 and Safaei et al (2013b) by simply making equal a uniaxial tension behavior along the rolling for yield function and plastic potential (called ''scaled simplified approach'' in this paper). This is because it results in a simpler implementation of the non-AFR constitutive model using a fully implicit backward Euler scheme.…”

“…Regarding the details of the integration scheme, Cvitanic et al (2008) presented a fully implicit scheme for a non-associated flow rule in the case of isotropic hardening based on multi-step return mapping method by Yoon et al (1999). Taherizadeh et al (2010) and Safaei et al (2013b) developed a fully implicit scheme for different mixed isotropickinematic hardening models. Due to the fact, only isotropic hardening is considered in this paper thus integration scheme is similar to that of Cvitanic et al (2008) so the reader is referred to that paper for further details.…”

Algorithmic Formulations of Evolutionary Anisotropic Plasticity Models Based on Non-Associated Flow Rule

“…In this forming process, the plastic anisotropy has important effect on the formation of undulative top edge of the finally drawn cup often termed as earing. Numerous phenomenological orthotropic yield functions with constant (fixed) anisotropy parameters under associated or non-associated flow rule have been tested in this forming process (Yoon et al, 1998(Yoon et al, , 1999(Yoon et al, , 2000Cvitanić et al, 2008;Taherizadeh et al, 2010Taherizadeh et al, , 2011Park and Chung, 2012;Safaei et al, 2013;Vrh et al, 2014;and others). These extensive numerical studies clearly indicate that the predicted earing trend (location of peaks and valleys) is the mirror image of the predicted r-value trend with the respect to the transverse direction, and that the prediction of the earing profile amplitude (the maximum difference in cup heights) is correlated to the prediction of the yield stress anisotropy amplitude.…”

Evaluation of stress integration algorithms for elastic–plastic constitutive models based on associated and non-associated flow rules

“…Stoughton and Yoon (2009) derived the stability conditions for the AFR plasticity. Advantages of using the non-AFR compared to the AFR for metal forming applications were discussed in works of Cvitanic et al (2008), Taherizadeh et al (2010), Park and Chung (2012) and Safaei et al (2013). Safaei et al (2014a) proposed an evolutionary anisotropic model based on non-AFR that excellently predicted distortional hardening and evolution of instantaneous r-values in seven uniaxial directions as well as balanced biaxial loading condition (tensile test at a cruciform specimen with identical force applied to each of the four sides).…”