Constraints on the applicability range of Hill’s criterion: strong orthotropy or transverse isotropy

摘要

Commonly used orthotropic Hill’s criterion of plastic flow initiation (Hill in Proc R Soc Lond A 193:281–297, 1948) suffers from some constraints and inconsistencies, which are of two different origins. Firstly, in case of high orthotropy degree, the quadratic form corresponding to Hill’s criterion may change type from convex and closed elliptic to concave and open hyperbolic in the deviatoric stress space (Ottosen and Ristinmaa in The Mechanics of Constitutive Modeling, Elsevier, Amsterdam, 2005). Secondly, application of classical Hill’s criterion to transversely isotropic materials shows a discrepancy between Hill’s limit curves in the transverse isotropy plane and the Huber-von Mises prediction for isotropic materials (Huber 1904; von Mises 1913). The basic result of the present paper is to propose the new transversely isotropic von Mises–Hu–Marin’s-type criterion of hexagonal symmetry that is free from both constraints. The new enhanced Hu–Marin’s-type limit surface represents an elliptic cylinder, the axis of which is proportional to stress/strength, in contrast to Hill’s-type limit surface possessing the hydrostatic axis. Hence, this condition does not exhibit the deviatoricity property, which is a price for coincidence with the Huber–von Mises condition in the transverse isotropy plane, but with cylindricity ensured for an arbitrarily high orthotropy degree. The hybrid-type transversely isotropic Hu–Marin’s criterion of mixed symmetry based on additional biaxial bulge test, capable of fitting experimental findings for some complex composites, is also proposed. Application of this criterion has been verified for a unidirectional SiC/Ti composite examined by Herakovich (Thermal stresses V, Lastran Corp. Publ. Division, pp 1–142, 1999).