A criterion for description of anisotropy and yield differential effects in pressure-insensitive metals

Cazacu, Oana; Barlat, Frédéric

doi:10.1016/j.ijplas.2003.11.021

Cited by 464 publications

(190 citation statements)

References 22 publications

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“…Applying consistently a system of the first stress invariant and the second and the third stress deviator invariants, Eq. (7) can also be written as (6). The other stress invariant systems are broadly discussed by Haigh [22], Westergaard [59], Novoshilov [39],Życzkowski [61], and summarized by Altenbach et al [2] in a recent important monograph.…”

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

confidence: 99%

“…This isotropic equation is also extended to material anisotropy in order to properly describe various metals of AA 2008-T4, high-purity α-titanium and the AZ31 magnesium alloy. In case if pressure sensitivity is ignored (b = 0 and a = k), the Cazacu and Barlat [6] format is recovered,…”

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

confidence: 99%

“…Hill [24], Sayir [50], Betten [3],Życzkowski [62]), can be shown in a general fashion f = f (0) , (2) : σ , σ : (4) : σ , σ : (6) : σ : σ , . .…”

mentioning

confidence: 99%

“…(1) uses unspecified representation of an unlimited number of common invariants. In such a case, initiation of plastic flow is governed by the structural tensors of plastic anisotropy of even-ranks: (0) = Π, (2) , (4) , (6) , . .…”

mentioning

confidence: 99%

“…Indeed, the majority of the pressure-insensitive metallic materials shows rather plastic yield initiation mechanism of either isotropic nature (NiTi shape memory alloys, Raniecki and Mróz [46]; Mg, Mg-Th or Mg-Li alloys, Cazacu and Barlat [6]; 4Al-1 4 O 2 titanium alloy, Cazacu et al [7]) or anisotropic nature (Al 6061-T6511 alloy, Cazacu and Barlat [6]; Ti-6Al-4V titanium alloy, Khan et al [28]; Al 6260-T4 alloy, Korkolis and Kyriakides [33]). …”

mentioning

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

confidence: 99%

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

confidence: 99%

“…Hill [24], Sayir [50], Betten [3],Życzkowski [62]), can be shown in a general fashion f = f (0) , (2) : σ , σ : (4) : σ , σ : (6) : σ : σ , . .…”

mentioning

confidence: 99%

mentioning

confidence: 99%

mentioning

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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Modeling Plastic Anistropy and Strength Differential Effects in Metallic Materials

Cazacu¹,

Barlat²

2008

Multiscale Modeling of Heterogenous Materials

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Deformation Behavior of Mg from Micromechanics to Engineering Applications

Lilleodden¹,

Mosler²,

Homayonifar³

et al. 2011

Magnesium Technology 2011

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A criterion for description of anisotropy and yield differential effects in pressure-insensitive metals

Cited by 464 publications

References 22 publications

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

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

Modeling Plastic Anistropy and Strength Differential Effects in Metallic Materials

Deformation Behavior of Mg from Micromechanics to Engineering Applications

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