Considerations concerning yield criteria insensitive to hydrostatic pressure
Keywords:
plasticity, yield criteria, pressure insensitive, biaxial state of stress, invariantsAbstract
For distinguishing between pressure insensitive and pressure sensitive criteria, the form of yield surface with invariants is preferred. It is known that when this function can be formulated only in terms of the stress deviator invariants, it describes a pressure-insensitive material behaviour. But expression of criteria in terms of invariants may be a difficult goal in some particular cases. In the present paper is mathematically demonstrated that all criteria developed for standard plastic materials, in other words homogeneous, isotropic, ductile (without so-called strength differential or SD effect) materials, loaded in plane state of stress (2D space), are insensitive to hydrostatic pressure.
References
YU, M.H., Advances in strength theories for materials under complex stress state in the 20th Century, Appl. Mech. Rev., 55, 3, pp. 169–218, 2002.
HU, L.W., MARKOWITZ, J., BARTUSH, T.A., A triaxial-stress experiment on yield condition in plasticity, Experimental Mechanics, 6, 1, pp. 58–64, 1966.
PAE, K.D., The macroscopic yielding behaviour of polymers in multiaxial stress fields, Journal of Materials Science, 12, pp. 1209–1214, 1977.
YU, M.-H., MA, G.-W., QIANG, H.-F., ZHANG, Y.-Q., Generalized Plasticity, Springer-Verlag, 2006.
CHRISTENSEN, R., The theory of materials failure, Oxford University Press, 2013.
KOLUPAEV, V.A., YU, M.-H., ALTENBACH, H., Fitting of the strength hypotheses, Acta Mech., 227, 6, pp. 1533–1556, 2016.
ALTENBACH, H., ÖCHSNER, A. (Editors), Plasticity of pressure-sensitive materials, SpringerVerlag, 2014.
DONATO, G.H.B., BIANCHI, M., Pressure dependent yield criteria applied for improving design practices and integrity assessments against yielding of engineering polymers, Journal of Materials Research and Technology, 1, 1, pp. 2–7, 2012.
HU, L.W., PAE, K.D., Inclusion of the hydrostatic stress component in formulation of the yield condition, Journal of The Franklin Institute, 275, 6, pp. 491–502, 1963.
DING, B., LI, X., An eccentric ellipse failure criterion for amorphous materials, Journal of Applied Mechanics, 84, pp. 1–7, 2017.
LUBLINER, J., Plasticity theory (revised edition), Pearson Education, Inc., 2006.
HOSFORD, W., Fundamentals of engineering plasticity, Cambridge University Press, 2013.
BÂRSANESCU, P.D., SANDOVICI, A., SERBAN, A., Mohr-Coulomb criterion with circular failure envelope, extended to materials with strength-differential effect, Materials and Design, 148, pp. 49–70, 2018.
REES, D.W.A., Basic engineering. Plasticity, Butterworth-Heinemann, 2006, p. 79.
PRAWOTO, Y., Integration of mechanics into materials science research, Lulu Entrerpises, Morrisville, USA, 2013.
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