Oana Cazacu

Generalization of Drucker's Yield Criterion to Orthotropy:

Within the framework of the theory of representation, generalizations to anisotropic conditions of the invariants of the deviatoric stress are proposed. Using these generalized invariants, any isotropic yield criterion can be extended such as to describe any type of material symmetry. In this paper, we apply this method to extend to orthotropy Druckers isotropic criterion. Comparison with data on aluminum alloys show that this new criterion describes with improved accuracy the anisotropy of the plastic response.

Application of the theory of representation to describe yielding of anisotropic aluminum alloys

Abstract In this paper a rigorous method to extend any isotropic yield criterion such as to describe any type of material symmetry is developed. Using this approach, extensions of Drucker’s [J. Appl. Mech. 16 (1949) 349] isotropic yield criterion to transverse isotropy, cubic symmetries, and orthotropy are presented. Comparison with representative sets of data show that the present theory can successfully describe anisotropy of both the plastic strain ratio and yield of aluminum thin sheets as well as the yield anisotropy of extruded bars.

On the Combined Effect of Pressure and Third Invariant on Yielding of Porous Solids With von Mises Matrix

In this paper, a new plastic potential for porous solids with von Mises perfectly-plastic matrix containing spherical cavities is derived using a rigorous limit analysis approach. For stress-triaxialities different from 0 and ±∞, the dilatational response depends on the signs of the mean stress and the third invariant of the stress deviator. The classic Gurson potential is an upper-bound of the new criterion. A full-field dilatational viscoplastic Fast Fourier Transform (FFT)-based approach is also used to generate numerical gauge surfaces for the porous material. The numerical calculations confirm the new features of the dilatational response, namely: a very specific dependence with the signs of the mean stress and the third invariant that results in a lack of symmetry of the yield surface.

A new anisotropic failure criterion for transversely isotropic solids

A coordinate-free formulation of a failure criterion for transversely isotropic solids is proposed. In the three-dimensional stress space the criterion is represented by an elliptic paraboloid. The anisotropic form of the proposed criterion is based on generalization of the second invariant of the deviatoric stress and of the mean stress obtained through the introduction of a unique fourth-order tensor. For isotropic conditions, the criterion reduces to the Mises–Schleicher failure condition. It is shown that the criterion satisfactorily predicts the strength anisotropy of transversely isotropic rocks subjected to an axisymmetric stress state. The procedure for the identification of the parameters of the criterion from a few simple laboratory tests is outlined.

Anisotropy and Formability

The chapter presents synthetically the most recent models of the anisotropic plastic behavior. The first section gives an overview of the classical models, In the next step, the discussion is focused on the anisotropic formulations developed on the basis of the theories of linear transformations and tensor representations, respectively. Those models are applied to different types of materials: body centered, faced centered and hexagonal-close packed metals. A brief review of the experimental methods used for observing and modeling the anisotropic plastic behavior of metallic sheets and tubes under biaxial loading is presented together with the models and methods developed for predicting and establishing the limit strains. The capabilities of some commercial programs specially designed for the computation of forming limit curves (FLC) are also analyzed.

A paraboloid failure surface for transversely isotropic materials

Abstract An invariant 3-D failure criterion for transversely isotropic solids is presented. For isotropic conditions, this criterion reduces to Mises–Schleicher failure criterion. It is shown that the anisotropic Mises–Schleicher (AMS) criterion can accurately describe the observed failure characteristics of transversely isotropic rocks under both compressive and tensile stresses. This criterion predicts that the application of multiaxial tensile stresses on rock reduces the value of the failure strength, i.e., the predicted value of the hydrostatic tensile strength as well as of the biaxial tensile strength is less than the uniaxial tensile strength in any direction. The intersections of the AMS failure surfaces with the octahedral plane demonstrates the ability of the criterion to describe the directional character of the strength of transversely isotropic materials under general loading conditions. The application of this criterion to conventional triaxial compression, reduced triaxial extension, and biaxial conditions, shows that this criterion captures the influence of the magnitude of the intermediate principal stress on strength. Representative sets of data from tests on rock have been analyzed and comparison between the theoretical predictions and the data appears to be quite good with the accuracies generally within the natural scatter of test data. In this paper, the AMS criterion is applied to rock materials; however, it can be used to describe the strength anisotropy of any material exhibiting transverse isotropy.

New three-dimensional strain-rate potentials for isotropic porous metals: Role of the plastic flow of the matrix

Abstract At present, modeling of the plastic response of porous solids is done using stress-based plastic potentials. To gain understanding of the combined effects of all invariants for general three-dimensional loadings, a strain-rate based approach appears more appropriate. In this paper, for the first time strain rate-based potentials for porous solids with Tresca and von Mises, matrices are obtained. The dilatational response is investigated for general 3-D conditions for both compressive and tensile states using rigorous upscaling methods. It is demonstrated that the presence of voids induces dependence on all invariants, the noteworthy result being the key role played by the plastic flow of the matrix on the dilatational response. If the matrix obeys the von Mises criterion, the shape of the cross-sections of the porous solid with the octahedral plane deviates slightly from a circle, and changes very little as the absolute value of the mean strain rate increases. However, if the matrix behavior is described by Tresca’s criterion, the shape of the cross-sections evolves from a regular hexagon to a smooth triangle with rounded corners. Furthermore, it is revealed that the couplings between invariants are very specific and depend strongly on the particularities of the plastic flow of the matrix.

Importance of the coupling between the sign of the mean stress and the third invariant on the rate of void growth and collapse in porous solids with a von Mises matrix

Recently, Cazacu et al (2013a J. Appl. Mech. 80 64501) demonstrated that the plastic potential of porous solids with a von Mises matrix containing randomly distributed spherical cavities should involve a very specific coupling between the mean stress and , the third invariant of the stress deviator. In this paper, the effects of this coupling on void evolution are investigated. It is shown that the new analytical model predicts that for axisymmetric stress states, void growth is faster for loading histories corresponding to than for those corresponding to . However, void collapse occurs faster for loadings where than for those characterized by . Finite-element (FE) results also confirm these trends. Furthermore, comparisons between FE results and corresponding predictions of yielding and void evolution show the improvements provided by the new model with respect to Gursons. Irrespective of the loading history, the predicted rate of void growth is much faster than that according to Gursons criterion.

Applications of a Recently Proposed Anisotropic Yield Function to Sheet Forming

In this paper the predictive capabilities of a recently proposed yield criterion, CB2001, are assessed. Also, a numerical scheme for identifying the material coefficients is presented. It is shown that although convexity is not a default property of the criterion, it can be achieved numerically. Applications to two sheet forming operations are presented. Using the commercial FE code ABAQUS, simulations of the deep-drawing of a cylindrical cup and springback analysis for unconstrained bending are performed. Two aluminum alloys were considered and modelled with Hill’48 (ABAQUS) and CB2001 (UMAT). The results are also compared with another popular criterion, Yld’96. We conclude that for sheet forming operations were large plastic deformations are involved, accurate fit of the initial plastic anisotropy is a basic condition for successful FE simulations.

Unusual plastic deformation and damage features in titanium: Experimental tests and constitutive modeling

Abstract In this paper, we present an experimental study on plastic deformation and damage of polycrystalline pure HCP Ti, as well as modeling of the observed behavior. Mechanical characterization data were conducted, which indicate that the material is orthotropic and displays tension-compression asymmetry. The ex-situ and in-situ X-ray tomography measurements conducted reveal that damage distribution and evolution in this HCP Ti material is markedly different than in a typical FCC material such as copper. Stewart and Cazacu (2011) anisotropic elastic/plastic damage model is used to describe the behavior. All the parameters involved in this model have a clear physical significance, being related to plastic properties, and are determined from very few simple mechanical tests. It is shown that this model predicts correctly the anisotropy in plastic deformation, and its strong influence on damage distribution and damage accumulation. Specifically, for a smooth axisymmetric specimen subject to uniaxial tension, damage initiates at the center of the specimen, and is diffuse; the level of damage close to failure being very low. On the other hand, for a notched specimen subject to the same loading the model predicts that damage initiates at the outer surface of the specimen, and further grows from the outer surface to the center of the specimen, which corroborates with the in-situ tomography data.