Pressure dependence of yielding and associated volume expansion in tempered martensite

Spitzig, W.A.; Sober, R. J.; Richmond, O.

doi:10.1016/0001-6160(75)90205-9

Cited by 285 publications

(99 citation statements)

References 11 publications

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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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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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“…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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“…Based on experimental results of uniaxial tension under a superimposed hydrostatic pressure for aluminum and steel alloys, Spitzig et al [12] and Spitzig and Richmond [13] formulated the pressure sensitivity of metals by adding the first stress invariant to the von Mises stress as below:…”

Section: A General Yield Function For the Tension Compression Asymmetmentioning

confidence: 99%

“…This general yield function assumes a linear dependence of yielding on the first invariant according to experimental results of Spitzig et al [12] and Spitzig and Richmond [13] and preserves the asymmetry of the third stress invariant to model SD effect of pressure insensitive metals. The material constants of b and c modulate the influence of the pressure and the third invariant on yielding of metals while the material parameter a is determined by experiments used to characterize the strain hardening behavior of metals.…”

Section: A General Yield Function For the Tension Compression Asymmetmentioning

confidence: 99%

Development of Plasticity Model Using Non Associated Flow Rule for HCP Materials Including Zirconium for Nuclear Applications

Glazoff¹,

Yoon²

2013

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In this report (prepared in collaboration with Prof. Jeong Whan Yoon, Deakin University, Melbourne, Australia) a research effort was made to develop a non-associated flow rule for zirconium. Since Zr is a hexagonally close packed (HCP) material, it is impossible to describe its plastic response under arbitrary loading conditions with any associated flow rule (e.g. von Mises). As a result of strong tension-compression asymmetry of the yield stress and anisotropy, zirconium displays plastic behavior that requires a more sophisticated approach.Consequently, a new general asymmetric yield function has been developed which accommodates mathematically the four directional anisotropies along 0°, 45°, 90°, and biaxial, under tension and compression. Stress anisotropy has been completely decoupled from the r-value by using non-associated flow plasticity, where yield function and plastic potential have been treated separately to take care of stress and r-value directionalities, respectively. This theoretical development has been verified using Zr alloys at room temperature as an example as these materials have very strong SD (Strength Differential) effect. The proposed yield function reasonably well models the evolution of yield surfaces for a zirconium clock-rolled plate during in-plane and through-thickness compression. It has been found that this function can predict both tension and compression asymmetry mathematically without any numerical tolerance and shows the significant improvement compared to any reported functions.

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Pressure dependence of yielding and associated volume expansion in tempered martensite

Cited by 285 publications

References 11 publications

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

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

Development of Plasticity Model Using Non Associated Flow Rule for HCP Materials Including Zirconium for Nuclear Applications

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