Plane stress yield function for aluminum alloy sheets—part 1: theory

Barlat, Frédéric; Brem, J. C.; Yoon, Jeong Whan; Chung, Kwansoo; Dick, Robert E.; Lege, D. J.; Pourboghrat, Farhang; Choi, Shi‐Hoon; Chu, Ernest H. Y.

doi:10.1016/s0749-6419(02)00019-0

Cited by 1,457 publications

(700 citation statements)

References 27 publications

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“…In this type of graphs, used for instance by Barlat et al (2003) In this chart, each point represents a different state of stress. Since the stress is normalized, all points of all time steps can be introduced in the same graph.…”

Section: Numerical Validationmentioning

confidence: 99%

“…In order to support this statement, the same VFM approach was employed to identify the parameters of the Yld2000-2D model (Barlat et al, 2003).…”

Section: Application Of the Yld2000-2d Criterionmentioning

confidence: 99%

“…The main limitation of the Hill48 model is that there is a fixed relation between the yield stress and Lankford parameter R in different directions. A popular model, which overtakes the main limitations of Hill48, is Yld2000-2D proposed by Barlat et al (2003) and Yoon et al (2004). Furthermore, Vegter and Van Den Boogaard (2006) use Bézier curves to describe the yield locus.…”

Section: Introductionmentioning

confidence: 99%

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Application of the virtual fields method to large strain anisotropic plasticity

Rossi

Pierron

Štamborská

2016

International Journal of Solids and Structures

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The identification of the plastic behaviour of sheet metals at severe deformation is extremely important for many industrial application such as metal forming, crashworthiness, automotive, aerospace, piping, etc. In this paper, the virtual fields method (VFM) was employed to identify the constitutive parameters of anisotropic plasticity models. The method was applied using the finite deformation theory in order to account for large strains. First the theoretical principles to implement the method are described in details, especially how to derive the stress field from the strain field. Afterwards a numerical validation was performed using the Hill48 model. Several aspects were studied with the numerical model: the effect of the used virtual fields, the minimum number of specimens required to identify the parameters, the stress distribution obtained from the specimen and its influence in the identification performance. A brief analysis on the influence of noise is also conducted. Finally a series of experiments was conducted on notched specimens of stainless steel, cut along different anisotropic directions. The displacement and strain fields were obtained by digital image correlation. Afterwards, the VFM was used to identify the parameters of the Hill48 model and the Yld2000-2D model. In this case, the Hill48 model was not able to correctly describe the material behaviour, while a rather good agreement was found with the Yld2000-2D model. The potential and the limitation of the proposed method are finally discussed.

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Section: Numerical Validationmentioning

confidence: 99%

“…In order to support this statement, the same VFM approach was employed to identify the parameters of the Yld2000-2D model (Barlat et al, 2003).…”

Section: Application Of the Yld2000-2d Criterionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Application of the virtual fields method to large strain anisotropic plasticity

Rossi

Pierron

Štamborská

2016

International Journal of Solids and Structures

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“…It is enough to mention only some of the most important: Mises [19], Burzyński [7], Hill [9][10][11][12][13], Logan and Hosford [18], Hoffman [14], Tsai-Wu [29], Karafillis-Boyce [15], Rychlewski [22], Barlat et al [1][2][3][4][5]8]. A great number and variety of different criteria make it questionable whether further propositions are really needed, especially when none of the previous ones has been definitely confirmed or rejected for a considerably broad scope of use.…”

Section: Motivationmentioning

confidence: 99%

Energy-Based Yield Criteria for Orthotropic Materials, Exhibiting Strength-Differential Effect. Specification for Sheets under Plane Stress State

Szeptyński

2017

Archives of Metallurgy and Materials

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A general proposition of an energy-based limit condition for anisotropic materials exhibiting strength-differential effect (SDE) based on spectral decomposition of elasticity tensors and the use of scaling pressure-dependent functions is specified for the case of orthotropic materials. A detailed algorithm (based on classical solutions of cubic equations) for the determination of elastic eigenstates and eigenvalues of the orthotropic stiffness tensor is presented. A yield condition is formulated for both two-dimensional and three-dimensional cases. Explicit formulas based on simple strength tests are derived for parameters of criterion in the plane case. The application of both criteria for the description of yielding and plastic deformation of metal sheets is discussed in detail. The plane case criterion is verified with experimental results from the literature.

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“…Most anisotropic yield functions are based on the associated flow rule (AFR) hypothesis obeying the normality rule. Accordingly, under the assumption of AFR with the light of material orthotropy, various phenomenological yield functions have been proposed to describe the initial anisotropy of metallic sheets including Hill's (1948), Barlat et al (1991Barlat et al ( , 2003Barlat et al ( , 2005Barlat et al ( , 2007, Karafillis and Boyce (1993), Barlat (2002, 2004), Bron and Besson (2004), Cazacu et al ( , 2006, Vegter and van den Boogaard (2006), Hu (2007), etc. Barlat et al (2011) proposed an alternative approach to consider kinematic hardening within the framework of anisotropic yield function under associated flow rule.…”

Section: Introductionmentioning

confidence: 99%

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

Safaei

Yoon

Waele

2014

International Journal of Plasticity

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a b s t r a c tAs opposed to associated flow rule (AFR) in which yield function and plastic potential are equal, the different definitions for them is an inherent characteristic of non-associated flow rule (non-AFR). This imposes a specific relation (but not equality) between equivalent plastic strain and plastic compliance factor. Unavoidably, this leads to a laborious effort for FE implementation of non-associated constitutive model specifically when several internal variables (such as kinematic hardening or damage parameters) are involved. This paper is mainly devoted to studying the conditions at which the non-AFR approach can be simplified so that the numerical implementation scheme is more convenient without loss of accuracy. It will be shown that by scaling the plastic potential function, the equality of equivalent plastic strain and compliance factor can be reserved. The effect of scaling of the non-AFR based on Barlat et al.'s (2003) anisotropic model (called Yld2000-2d) is comprehensively studied with FE simulation of tensile loading under uniaxial tensions along the different orientations as well as balanced biaxial stress condition. A fully implicit return-mapping scheme was introduced for stress integration of the constitutive model in a User-defined MATerial subroutine (UMAT). Cup drawing simulations of a highly textured aluminum alloy 2090-T3 were performed using simplified and original approaches. The results prove that the proposed simplified technique is a reliable alternative for the full expression.

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Plane stress yield function for aluminum alloy sheets—part 1: theory

Cited by 1,457 publications

References 27 publications

Application of the virtual fields method to large strain anisotropic plasticity

Application of the virtual fields method to large strain anisotropic plasticity

Energy-Based Yield Criteria for Orthotropic Materials, Exhibiting Strength-Differential Effect. Specification for Sheets under Plane Stress State

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

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