Phenomenological Yield and Failure Criteria

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.

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

“…(7) can also be written as (6). The other stress invariant systems are broadly discussed by Haigh [22], Westergaard [59], Novoshilov [39],Życzkowski [61], and summarized by Altenbach et al [2] in a recent important monograph. In the last one monograph, the authors provide a complete review and comparison of a variety of phenomenological yield/failure pressure-insensitive versus pressure-sensitive isotropic criteria.…”

“…Tension/compression asymmetry, also called strength differential effect (see for instance Altenbach et al [2]), is included in a natural way in limit criteria for anisotropic materials. In the case of limit criteria for isotropic materials, this effect manifests itself by the presence of first stress invariant J 1σ and/or the third stress invariant J 3s , as shown in Fig.…”

“…Hill [24], Sayir [50], Betten [3],Życzkowski [62]), can be shown in a general fashion f = f (0) , (2) : σ , σ : (4) : σ , σ : (6) : σ : σ , . .…”

“…(1) uses unspecified representation of an unlimited number of common invariants. In such a case, initiation of plastic flow is governed by the structural tensors of plastic anisotropy of even-ranks: (0) = Π, (2) , (4) , (6) , . .…”

“…., etc., are arbitrary exponents of a polynomial representation. Assuming, further, α = 1, β = 1/2, γ = 1/3, and limiting an infinite form (2) to the equation that contains only three common invariants of the stress and structural anisotropy tensors of appropriate ranks, we arrive at the simpler form, which satisfies the homogeneity of three polynomial components, known as the Goldenblat and Kopnov criterion (cf. Goldenblat and Kopnov [21]) π : σ + (σ : : σ ) 1/2 + (σ : I¯I : σ : σ ) 1/3 − 1 = 0.…”