The effect of pressure on the flow stress of metals

Spitzig, W.A.; Richmond, O.

doi:10.1016/0001-6160(84)90119-6

Cited by 314 publications

(141 citation statements)

References 12 publications

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“…Barlat et al (2003) used two linear transformations on the Cauchy stress tensor to propose a new plane stress yield function for aluminum alloy sheets to consider the anisotropy effects. Stoughton and Yoon (2004) proposed a non-AFR based on a pressure sensitive yield description with isotropic hardening to account the strength differential effect (SDE) that was consistent with the Spitzig and Richmond (1984) results. Lee et al (2008) developed a continuum plasticity model to consider the unusual plastic behavior of magnesium alloy in finite element analysis.…”

Section: Introductionmentioning

confidence: 60%

Combination of modified Yld2000-2d and Yld2000-2d in anisotropic pressure dependent sheet metals

Moayyedian

Kadkhodayan

2015

Lat. Am. j. solids struct.

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A bstract In the current research to model anisotropic asymmetric sheet metals a new non-AFR criterion is presented. In the new model, Modified Yld2000-2d proposed by Lou et al. (2013) is considered as yield function and Yld2000-2d proposed by Barlat et al. (2003) is considered as plastic potential function. To calíbrate the presented criterion, the yield function which is a pressure dependent criterion requiers ten directional yield stresses such as uniaxial tensile stresses in three directions of 0°, 45°, 90°, uniaxial compressive yield stresses in six directions of 0°, 15°, 30°, 45°, 75°, 90° from the rolling direction along with biaxial yield stress. Moreover, the plastic potential function which is a pressure indepedent criterion needs eight experimental data points such as tensile R-values in seven directions of 0°, 15°, 30°, 45°, 60°, 75°, 90° from the rolling direction and also biaxial tensile R-value. Finally with comparing the obtained results with experimental data points, it is shown that the presented non-AFR criterion predicts compressive yield stress, biaxial tensile yield stress and R-values more accurately than Modified Yld2000-2d and it would be considered as a new criterion for anisotropic asymmetric metals. KeywordsYld2000-2d, Modified Yld2000-2d, Anisotropic asymmetric yield functions, Non-associated flow rule, Downhill Simplex Method.

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Section: Introductionmentioning

confidence: 60%

Combination of modified Yld2000-2d and Yld2000-2d in anisotropic pressure dependent sheet metals

Moayyedian

Kadkhodayan

2015

Lat. Am. j. solids struct.

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“…As is indicated by experiments, yield surface is often well described by a proper quadric surface which provides a description of the strength-differential effect [24][25][26] in uniaxial states. According to (2.2), each energy component Φ i is proportional to |σ i | 2 .…”

Section: Yield Conditionmentioning

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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“…Equation (19) is in fact an extension of Drucker's equation (12), by use of an additional term linear with respect to the first invariant J 1σ , according to experimental results by Spitzig et al [53] as well as Spitzig and Richmond [54]. This format inherits after Drucker's trigonal symmetry that enables to describe the SD effect, but the presence of first invariant J 1σ leads to a conical surface, instead of a cylindrical in Drucker's case.…”

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

confidence: 99%

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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The effect of pressure on the flow stress of metals

Cited by 314 publications

References 12 publications

Combination of modified Yld2000-2d and Yld2000-2d in anisotropic pressure dependent sheet metals

Combination of modified Yld2000-2d and Yld2000-2d in anisotropic pressure dependent sheet metals

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

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

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