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Phenomenological Yield and Failure Criteria

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Plasticity of Pressure-Sensitive Materials

Part of the book series: Engineering Materials ((ENG.MAT.))

Abstract

Models for isotropic materials based on the equivalent stress concept are discussed. At first, so-called classical models which are useful in the case of absolutely brittle or ideal ductile materials are presented. Tests for basic stress states are suggested. At second, standard models describing the intermediate range between the absolutely brittle and ideal-ductile behavior are introduced. Any criterion is expressed by various mathematical equations formulated, for example, in terms of invariants. At the same time the criteria can be visualized which simplifies the application. At third, in the main part pressure-insensitive, pressure-sensitive and combined models are separated. Fitting methods based on mathematical, physical and geometrical criteria are necessary. Finally, three examples (gray cast iron, poly(oxymethylene) (POM) and poly(vinyl chloride) (PVC) hard foam) demonstrates the application of different approaches in modeling certain limit behavior. Two appendices are necessary for a better understanding of this chapter: in Chap. 2 applied invariants are briefly introduced and a table of discussed in this chapter criteria with references is given.

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Notes

  1. 1.

    This criterion was also formulated 1865 in a letter of Maxwell to Lord Kelvin [204].

  2. 2.

    Note that in material testing another definition of basic tests is given [32].

  3. 3.

    Here the substitution \(I_3'= \frac{2\,\sqrt{3}}{3^2}\,(I_2')^{3/2}\) is used, which corresponds to the meridian with the angle \(\theta =0\) (Sect. 8.2). The point \(Z\) (tension) belongs to this meridian (Table 1).

  4. 4.

    This hypothesis is analyzed in [38, 65, 94, 220, 221]. It does not reflect the experimental results [22, 50, 78, 157, 213] and is used in combinations of various hypotheses (Sect. 11).

  5. 5.

    In the original papers the following definition of the stress angle is used

    $$\begin{aligned} \sin 3\varphi = - \frac{3\sqrt{3}}{2}\frac{I_3'(\pmb s)}{I'_2(\pmb s)^{3/2}}, \qquad |\varphi |\le \frac{\pi }{6}. \end{aligned}$$
  6. 6.

    This model is dedicated to Jurij Antonovič Radcig (1900–1976), who was a professor at the Kazan State University of Technology (KAI), Kazan, Russia.

  7. 7.

    Theory of elasticity with different Young’s moduli \(E_+\ne E_-\) and elastic Posisson’s ratios \(\nu _+^{\mathrm {el}}\ne \nu _-^{\mathrm {el}}\) at tension and compression [9, 212]

  8. 8.

    3.08 % total C, 2.04 % Si, 0.56 % Mn, 0.112 % S, 0.33 % P

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  1. Lehrstuhl für Technische Mechanik, Institut für Mechanik, Fakultät für Maschinenbau, Otto-von-Guericke-Universtät Magdeburg, Universitätsplatz 2, 39106, Magdeburg, Germany

    Holm Altenbach

  2. Abteilung Werkstoffe und Bauteile, Fraunhofer-Institut für Betriebsfestigkeit und Systemzuverlässigkeit LBF, Bartningstr. 47, 64289, Darmstadt, Germany

    Alexandre Bolchoun

  3. Deutsches Kunststoff-Institut (DKI), Schloßgartenstr. 6, 64289, Darmstadt, Germany

    Vladimir A. Kolupaev

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Altenbach, H., Bolchoun, A., Kolupaev, V.A. (2014). Phenomenological Yield and Failure Criteria. In: Altenbach, H., Öchsner, A. (eds) Plasticity of Pressure-Sensitive Materials. Engineering Materials. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-40945-5_2

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