Zur Flie�bedingung der Plastizit�tstheorie

Sayir, Mahir

doi:10.1007/bf00538762

Cited by 53 publications

(26 citation statements)

References 9 publications

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“…Hence, these criteria are strongly exposed to a possible convexity loss, see Eq. (50). To avoid the aforementioned deficiency of convexity lack, the new von Mises-Tsai-Wu failure criterion, which is free from the possibility of inadmissible degeneration of the single convex, simply connected elliptical surface into two concave hyperbolic surfaces as shown in Eq.…”

Section: Discussionmentioning

confidence: 99%

“…The authors are convinced of the conventional approach, which is based on rigorous application of common invariants formalism, see Goldenblat and Kopnov [21], Sayir [50], and others.…”

Section: Discussionmentioning

confidence: 99%

“…The second invariant ensures energy-based interpretation of the limit criterion, whereas the third common or transformed invariant is optional. The most general form D1, originated by Goldenblat and Kopnov [21], Sayir [50], etc., is written in a polynomial format, where the exponents α, β, γ , . .…”

Section: C7mentioning

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%

“…Hence, the general form (1) is usually specialized for engineering needs. In a particular case, Goldenblat and Kopnov [21], and later Sayir [50], proposed a polynomial representation for Eq. (1) which controls initiation of anisotropic plastic flow or failure in a material by the tensorial-polynomial anisotropic criterion (π : σ ) α + (σ : : σ ) β + (σ : I¯I : σ : σ ) γ + · · · − 1 = 0.…”

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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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Section: Discussionmentioning

confidence: 99%

“…The authors are convinced of the conventional approach, which is based on rigorous application of common invariants formalism, see Goldenblat and Kopnov [21], Sayir [50], and others.…”

Section: Discussionmentioning

confidence: 99%

Section: C7mentioning

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%

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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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The limiting expansion ratio of real materials

Reissner

Weigl

1985

Steel Research

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The production of the precut hole was by drilling, turning and finishing. Subsequently, the edges of the hole were polished in order to prevent, as far as possible, any hardening of the edges and also to produce an idealised surface. This procedure is necessary since the effect of the surface quality of the hole edge on the expansion ratio is greater than that of the material itself. The present work shows a possibility of making available the improved results of modern measuring techniques in sheet metal forming for analytical processing as well. By means of numerical balancing calculations, the yield locus and stress‐strain curve are described with the help of polynomial representations and put into an energetic stability criterion. The limiting strains during plunging were calculated using a SWIFT material as an example.

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Vergleich einiger Ansätze zur Erfassung der Verformungsanisotropie und eine einfache Spannungs‐Verformungs‐Beziehung

Backhaus¹

1976

Z Angew Math Mech

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Ausgehend von einer allgemeinen anisotropen Fließbedingung [1] [2] werden die von Backhaus [3] [4], Baltov‐Sawczuk [5] und Danilov [6] verwendeten Tensoren des anisotropen Anteils der Fließbedingung miteinander verglichen. Es wird eine vereinfachte Spannungs‐Verformungs‐Beziehung angegeben, die eine isotrope Verfestigung, Bauschingereffekt und Quereffekt bei beliebiger Verformungsgeschichte erfaßt. Auf die Bestimmung des Quereffektes aus Messungen und auf Meßergebnisse wird kurz eingegangen.

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Zur Flie�bedingung der Plastizit�tstheorie

Cited by 53 publications

References 9 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

The limiting expansion ratio of real materials

Vergleich einiger Ansätze zur Erfassung der Verformungsanisotropie und eine einfache Spannungs‐Verformungs‐Beziehung

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