On stress-state dependent plasticity modeling: Significance of the hydrostatic stress, the third invariant of stress deviator and the non-associated flow rule

Gao, Xiaosheng; Zhang, Tingting; Zhou, Jun; Graham, Stephen M.; Hayden, Matthew; Roe, Charles P.

doi:10.1016/j.ijplas.2010.05.004

Cited by 186 publications

(70 citation statements)

References 41 publications

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“…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. Park and Chung (2012) derived a symmetric stiffness modulus for the non-associated flow rule under the framework of the combined isotropic-kinematic hardening law.…”

Section: Introductionmentioning

confidence: 65%

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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Section: Introductionmentioning

confidence: 65%

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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“…It will be shown below that the majority of criteria met in the literature to predict onset of yield, failure or even phase transformation (Iyer [26], Pȩcherski et al [42], Gao et al [20], Iyer and Lissenden [27], Brünig et al [4], Raniecki and Mróz [46]) can be captured as the specific cases of this general format (9). If a = 0 and r = 1 whereas p is arbitrary, the Raniecki and Mróz cylindrical surface is recovered from (9),…”

Section: Remarks On Isotropic Yield/failure Criteria Accounting For Tmentioning

confidence: 99%

“…Note that the Huber-von Mises f (J 2s ), the Drucker-Prager f (J 1σ , J 2s ) and the Drucker f (J 2s , J 3s ) yield functions can be obtained as special cases. Assuming another combination of powers p/r = 1/2 and r = 6, we arrive at the Gao et al [20] yield function…”

Section: Remarks On Isotropic Yield/failure Criteria Accounting For Tmentioning

confidence: 99%

“…All cited criteria depend on both the first stress invariant and the second deviatoric invariant, but, additionally, they may also depend on the third deviatoric invariant. Criteria C1 Iyer [26], Gao et al [20] and C3 Iyer and Lissenden [27], Pȩcherski et al [42] are special cases of the general criterion C4, Eq. (9).…”

Section: Appendix C: Concise Review Of Isotropic and Anisotropic Explmentioning

confidence: 99%

“…However, some experimental evidences for pressure-sensitive metallic alloys show rather combined plastic/failure mechanism with pronounced tension/compression asymmetry effect of either isotropic nature (Nickel-base Inconel 718, Iyer [26], Pȩcherski et al [42]; 5083 aluminium alloy, Gao et al [20]) or anisotropic response (Ti-6Al-4V titanium alloy, Khan, Yu, Liu [30], Khan, Liu [29]; AA2008-T4 aluminium alloy; AZ31 magnesium alloy, Yoon et al [60]). …”

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confidence: 99%

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Constraints on the applicability range of pressure-sensitive yield/failure criteria: strong orthotropy or transverse isotropy

Skrzypek

Ganczarski

2016

Acta Mech

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Yield/failure initiation criteria discussed in this paper account for the three following effects: the hydrostatic pressure dependence, the tension/compression asymmetry, and isotropic or anisotropic material response. For isotropic materials, criteria accounting for pressure/compression asymmetry (strength differential effect) have to include all three stress invariants (Iyer and Lissenden in Int J Plast 19:2055-2081 Gao et al. in Int J Plast 27:217-231, 2011; Yoon et al. in Int J Plast 56:184-202, 2014; Coulomb-Mohr's, cf. Chen and Han in Plasticity for structural engineers. Springer, Berlin, 1995 criteria). In narrower case when only pressure sensitivity is accounted for, rotationally symmetric surfaces independent of the third invariant are considered and broadly discussed (Burzyński in study on strength hypotheses (in Polish). Akad Nauk Tech Lwów, 1928; Drucker and Prager in Q Appl Math 10:157-165, 1952 criteria). For anisotropic materials, the explicit formulation based on either all three common invariants (Goldenblat and Kopnov in Stroit Mekh 307-319, 1966; Kowalsky et al. in Comput Mater Sci 16:81-88, 1999) or first and second common invariants (extended von Mises-type Tsai-Wu's criterion in Int J NumerMethods Eng 38: [2083][2084][2085][2086][2087][2088] 1971) is addressed especially for the case of transverse isotropy, when difference between tetragonal versus hexagonal symmetry is highlighted. The classical Tsai and Wu criterion involves Hill's type fourth-rank tensor inheriting a possibility of convexity loss in case of strong orthotropy, as discussed by Ganczarski and Skrzypek (Acta Mech 225:2563-2582. In order to overcome this defect, in the present paper the new Mises-based Tsai-Wu's criterion is proposed and exemplary implemented for the columnar ice. A mixed way to formulate pressure-sensitive tension/compression asymmetric failure criteria-capable of describing fully distorted limit surfaces, which are based on both all stress invariants and the second common invariant (Khan and Liu in Int J Plast 38:14-26, 2012; Yoon et al. in Int J Plast 56:184-202, 2014), is revised and addressed to orthotropic materials for which the fourth-order linear transformation tensors are used to achieve extension of the isotropic criterion.

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Non‐normality and induced plastic anisotropy under fractional plastic flow rule: a numerical study

Sumelka

Nowak

2015

Num Anal Meth Geomechanics

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Summary In this paper, an implementation of fractional plastic flow rule in the framework of implicit and explicit procedures is under consideration. The fractional plastic flow rule is obtained from a generalisation of the classical plastic flow rule utilising fractional calculus. The key feature of this new concept is that in general, the non‐associative flow is obtained without necessity of additional potential assumption. If needed, the model can cover the anisotropy induced by plastic deformation. Illustrative examples showing the unusual flexibility of this model are also presented. Copyright © 2015 John Wiley & Sons, Ltd.

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On stress-state dependent plasticity modeling: Significance of the hydrostatic stress, the third invariant of stress deviator and the non-associated flow rule

Cited by 186 publications

References 41 publications

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

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

Constraints on the applicability range of pressure-sensitive yield/failure criteria: strong orthotropy or transverse isotropy

Non‐normality and induced plastic anisotropy under fractional plastic flow rule: a numerical study

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