Constraints on the applicability range of pressure-sensitive yield/failure criteria: strong orthotropy or transverse isotropy

摘要

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, 2003; 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 (BurzyA"ski in study on strength hypotheses (in Polish). Akad Nauk Tech Lww, 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 38:2083-2088, 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, 2014). 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.