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Termination of Elastic Range of Pressure Sensitive Materials—Isotropic and Anisotropic Initial Yield/Failure Criteria

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Book cover Mechanics of Anisotropic Materials

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

Abstract

Yield/failure initiation criteria discussed in this chapter account for the three following effects: the hydrostatic pressure dependence, tension/compression asymmetry, and isotropic or anisotropic material response. For isotropic materials, the criteria accounting for pressure/compression asymmetry (strength differential effect) must include all three stress invariants (Iyer, Gao, Yoon, Coulomb–Mohr criteria). In a narrower case, when only pressure sensitivity is accounted for, rotationally symmetric surfaces independent of the third invariant are considered and broadly discussed (Burzyński, Drucker–Prager criteria). For anisotropic materials, the explicit formulation based on either all three common invariants (Goldenblat–Kopnov, Kowalsky) or the first and second common invariants (von Mises–Tsai–Wu) is addressed, especially in case of transverse isotropy when the difference between tetragonal and hexagonal symmetries is highlighted. A mixed way to formulate pressure sensitive tension/compression asymmetric initial failure criteria capable of describing fully distorted limit surfaces, which are based on all stress invariants and also the second common invariant (Khan, Liu) alone, are received and particularly addressed to orthotropic materials where fourth-order linear transformation tensors are used to achieve extension of the isotropic criterion.

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Authors and Affiliations

  1. Solid Mechanics Division, Institute of Applied Mechanics, Cracow University of Technology, al. Jana Pawła II 37, 31-864, Kraków, Poland

    Jacek J. Skrzypek & Artur W. Ganczarski

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  1. Jacek J. Skrzypek
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  2. Artur W. Ganczarski
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Correspondence to Jacek J. Skrzypek .

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Editors and Affiliations

  1. Solid Mechanics Division, Institute of Applied Mechanics, Cracow University of Technology, Al. Jana Pawła II 37, 31-864, Krakow, Poland

    Jacek J. Skrzypek

  2. Solid Mechanics Division, Institute of Applied Mechanics, Cracow University of Technology, Al. Jana Pawła II 37, 31-864, Krakow, Poland

    Artur W. Ganczarski

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Skrzypek, J.J., Ganczarski, A.W. (2015). Termination of Elastic Range of Pressure Sensitive Materials—Isotropic and Anisotropic Initial Yield/Failure Criteria. In: Skrzypek, J., Ganczarski, A. (eds) Mechanics of Anisotropic Materials. Engineering Materials. Springer, Cham. https://doi.org/10.1007/978-3-319-17160-9_6

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