Phenomenological Yield Function Research Articles

An improved analytical description of orthotropy in metallic sheets

The correct description of initial plastic anisotropy of metallic sheets plays a key role in modelling of sheet forming processes since prediction of material flow, residual stresses and springback as well as wrinkling and limiting strains are significantly affected by the phenomenological yield function applied in the analysis. In the last decades considerable improvement of anisotropic yield criteria has been achieved. Among these, the yield criterion proposed by Paraianu et al. [An improvement of the BBC2000 yield criterion. In: Proceedings of the ESAFORM 2003 Conference] is one of most promising plane stress yield criteria available for orthotropic sheet materials. This work aims to improve this yield criterion with respect to flexibility. The capabilities of the modified yield function will be demonstrated by applications to an anisotropic aluminium alloy sheet material.

A yield function for anisotropic materials Application to aluminum alloys

A phenomenological yield function is proposed to represent the plastic anisotropy of aluminum sheets. It is an extension of the functions given by Barlat et al. [Int. J. Plasticity 7 (1991) 693] and Karafillis and Boyce [J. Mech. Phys. Solids 41 (1993) 1859]. The anisotropy is represented by 12 parameters in the form of two fourth order symmetric tensors. Four other parameters influence the shape of the yield surface uniformly. The role of each parameter is described in detail. The convexity of the yield surface is proved. The implementation of the proposed yield function is done in the 3D general case in an object-oriented finite element code. It is used to represent the anisotropy of a 2024 aluminum thin sheet and the adjustment is excellent. Other anisotropic materials from the literature are also well described by the proposed yield function.

Study on forming limit diagrams prediction using a phenomenological and a physical approach of plasticity theory

In the present work a study on the prediction of the Forming Limit Diagrams is developed, by using a phenomenological and a physical approach of the plasticity theory. Two advanced constitutive models of the plastic anisotropy are considered, namely the Yld'96 Barlat phenomenological yield function and a combined model of texture and strain-path-induced anisotropy. The studied material is a bake-hardened steel sheet. The experimental FLDs were determined for linear and complex strain paths. The necking phenomenon was modeled using the Marciniack-Kuczinsky theory. The YLD'96 predicted Lankford coefficients and normalized yield distributions were investigated and compared with experimental data. The effect of the hardening model on the FLDs is analyzed by using several hardening laws, namely Swift law, Voce law and the strain-path-induced anisotropy model. In proportional loading a successful correlation is observed between the experimental FLDs and the computed limit strains when the shape of yield locus is described by Yld'96 criterion and the hardening law represented either by Swift law or by using the combined model of texture and strain-path-induced anisotropy. As the strain-path induced anisotropy is more evident for the steels, the physical model can provide a better accuracy than the phenomenological one for the forming limits involving two-stage strain paths.

Prediction of yield surfaces of textured sheet metals

To predict the yield surfaces of textured sheet metals, two methods were conducted. The first method (crystallographic yield surface) is based on the Taylor-Bishop-Hill (TBH) polycrystal model, using the orientation distribution function (ODF) of the material as an input. The second method (phenomenological yield surface) makes use of phenomenological yield functions based on mechanical test data. Anisotropic properties for six texture components typical of aluminum alloy sheets were examined and the results based on crystal plasticity were compared with the results based on phenomenological yield functions. The experimental anisotropy measurements obtained for an AA6xxx sheet were also compared to crystallographic and phenomenological predictions.

Finite strain analysis of simple shear using recent anisotropic yield criteria

Abstract The finite strain response of a rectangular block subjected to constrained simple shearing deformations is considered in order to evaluate the predictive capability of some recently proposed anisotropic yield functions. It is shown that, in the presence of plane anisotropy, the prediction of realistic second order normal stresses cannot be expected since every different initial orientation of the material axes relative to the loading axes results in a different response due to the rotation of the material axes with shear. Parametric studies are performed in order to determine possible limits on the material constants so that the predicted normal stresses remain second order with respect to the shear stress itself. Our numerical results indicate that, in particular, the commonly employed range of one parameter associated with grain related anisotropy renders results which no longer imply predicting a proper second order effect but rather introduces errors of the first order. The results suggest that the modelling of anisotropy with such phenomenological anisotropic yield functions should be limited to near-quadratic yield surfaces for applications involving stress states outside the biaxial tensile stress range.

Experimental analysis of aluminum yield surface for binary AlMg alloy sheet samples

Abstract In this work, the yield surfaces of binary aluminum-magnesium alloy sheet samples were measured using biaxial compression tests. Sheet samples of a given material were stacked and bonded together with epoxy and cubic compression specimens were machined out of the laminate. The yielding behavior was assumed to be independent of the hydrostatic pressure. In the analysis of the biaxial compression tests, the effects of friction and of the elasticity of the die were accounted for. These effects were studied with the aid of finite element method (FEM) simulations of the test which proved to be useful in avoiding systematic errors. The yield surfaces of three binary alloy sheet samples containing 5 wt% Mg but with different crystallographic textures were analyzed. The different textures resulted from processing under different thermomechanical conditions. The experimental yield surfaces were compared to predictions made with the Taylor-Bishop and Hill (TBH) model and with a phenomenological yield function. The experimental and polycrystal yield surfaces were found to be in fair agreement. The yield function was found to be a suitable description of the plastic behavio for only two of the materials studied.

Yield function development for aluminum alloy sheets

In this work, yield surfaces were measured for binary aluminum-magnesium sheet samples which were fabricated by different processing paths to obtain different microstructures. The yielding behavior was measured using biaxial compression tests on cubic specimens made from laminated sheet samples. The yield surfaces were also predicted from a polycrystal model using crystallographic texture data as input and from a phenomenological yield function usually suitable for polycrystalline materials. The experimental yield surfaces were found to be in good agreement with the polycrystal predictions for all materials and with the phenomenological predictions for most materials. However, for samples processed with high cold rolling reduction prior to solution heat treatment, a significant difference was observed between the phenomenological and the experimental yield surfaces in the pure shear region. In this paper, a generalized phenomenological yield description is proposed to account for the behavior of the solute strengthened aluminum alloy sheets studied in this work. It is subsequently shown that this yield function is suitable for the description of the plastic behavior of any aluminum alloy sheet.

Phenomenological modeling of the mechanical anisotropy in AlZnMg extruded profiles

The mechanical anisotropy of two extruded AlZnMg alloys (AA7108 and AA7030) have been investigated by means of uniaxial tensile and simple shear tests. On the basis of these tests, two phenomenological yield functions, for use in finite element simulations, were applied to test their ability to describe the observations concerned with anisotropy. It was shown that the yield function proposed by Barlat et al. (1995) was the most suitable for the nonrecrystallized 7108 alloy. However, none of the two mentioned functions seemed to be able to describe the mechanical anisotropy of the recrystallized 7030 alloy.

Yielding description for solution strengthened aluminum alloys

In this work, yield surfaces were measured for binary aluminum-magnesium sheet samples which were fabricated by different processing paths to obtain different microstructures. The yielding behavior was measured using biaxial compression tests on cubic specimens made from laminated sheet samples. The yield surfaces were also predicted from a polycrystal model using crystallographic texture data as input and from a phenomenological yield function proposed previously. In general, experimental and predicted yield surfaces were found to be in relatively good agreement. However, for samples processed with high cold rolling reduction prior to solution heat treatment, a significant difference was observed between the phenomenological yield surface and the experimental/polycrystal yield surfaces in the pure shear region. In this paper, a refinement was proposed for the phenomenological yield description to account for the behavior of the solute strengthened aluminum alloy sheets studied in this work, and in general, for any sheet metal. This yield function was implemented into a finite element code and sample computations were carried out to assess the validity and the accuracy of this improved material description.

Observations and calculations on mechanical anisotropy and plastic flow of an AlZnMg extrusion

An extruded plate of the alloy AA7108 has been characterized using texture analysis and uniaxial tensile tests. The yield surface, directional yield stresses and plastic strain ratios are calculated from Taylor-Bishop-Hill analysis, employing the measured texture data in combination with either the full constraints model or a relaxed constraints model. Three phenomenological yield functions, capable of describing yield anisotropy, are compared by means of their ability to reproduce the shape of the crystallographic yield surface and to predict directional properties, i.e. R-values and yield stress. On the basis of experiments and calculations it has been found that the Taylor relaxed constraints model describes the present material more consistently with respect to experimental findings than the Taylor full constraints model.