XXIV ICTAM, 21-26 August 2016, Montreal, Canada

YIELD SURFACE EFFECTS ON STABLITY AND FAILURE

William M. Scherzinger * Solid Mechanics, Sandia National Laboratories, Albuquerque, New Mexico, USA

Summary This work looks at the effects of yield surface description on the stability and failure of metal structures. We consider a number of different yield surface descriptions, both isotropic and anisotropic, that are available for modeling material behavior. These yield descriptions can all reproduce the same nominal stress-strain response for a limited set of load paths. However, for more general load paths the models can give significantly different results that can have a large effect on stability and failure. Results are shown for the internal pressurization of a cylinder and the differences in the predictions are quantified.

INTRODUCTION

Stability and failure in structures is an important field of study that provides solutions to many practical problems in solid mechanics. The boundary value problems require careful consideration of the geometry, the boundary conditions, and the material description. In metal structures the material is usually described with an elastic-plastic constitutive model, which can account for many effects observed in plastic deformation. Crystal plasticity models can account for many microstructural effects, but these models are often too fine scaled for production modeling and simulation. In this work we limit the study to rate independent continuum plasticity models. When using a continuum plasticity model, the hardening behavior is important and much attention is focused on it. Equally important, but less well understood, is the effect of the yield surface description. For classical continuum metal plasticity models that assume associated flow the yield surface provides a definition for the elastic region of stress space along with the direction of plastic flow when the stress state is on the yield surface. Often the direction of plastic flow is overlooked even though it can have the greatest effect on the results of a simulation. For comparisons we consider a number of models that employ different yield surface descriptions that describe isotropic and anisotropic material behavior. We consider the yield surfaces due to Tresca, von Mises, Hosford [1], Hill [2], Barlat, et. al. [3], and Karafillis and Boyce [4]. As an example boundary value problem we examine the internal pressurization of an aluminum cylinder. The analysis results show significant sensitivity to the form of the yield surface and insight into how assumptions in the constitutive model affect the behavior.

Figure 1: Boundary value problem for the internal pressurization of a cylinder in plane strain.

BOUNDARY VALUE PROBLEM

We consider the internal pressurization of an aluminum cylinder as shown in Figure 1. The problem is modeled using continuum finite elements. We enforce plane strain in the axial direction; with �/ℎ = 100 the state of stress is nearly plane stress. The material is 2090-T3 Al which has been parameterized for the Yld2004-18p model by Barlat et. al. [3]. The parameterization is used to fit the Tresca, von Mises, and Hosford yield surfaces in such a way that the yield stress is matched in uniaxial tension. The Hill yield surface is also fit so that the yield stresses are the same in uniaxial tension and shear relative to the principal material directions. The material models are implemented in Sandia National Laboratories’ Sierra Solid Mechanics code [5], which is used to solve the boundary value problem. The finite element model is loaded through a prescribed radial displacement on the inner surface of the cylinder and the internal pressure is calculated from the reaction forces and the current geometry. This is necessary so that a solution can be found through the maximum load.

* Corresponding author. Email: [email protected].

MODELING RESULTS

The internal pressure is plotted in Figure 2 as a function of the radial displacement for models using the Barlat, Hill, and von Mises yield surfaces. The Barlat and Hill yield surfaces are two choices one can choose for an anisotropic model, but they give significantly different results; the results using the Hill model have a maximum pressure that is approximately 15% higher than that calculated with the Barlat model. This shows a significant difference in behavior for two models that, to the extent that they can, model the same material behavior.

Figure 2: The pressure vs. radial displacement curve for the internally pressurized cylinder showing significantly different results for 2090-T3 Al.

We analyze the results to understand the influence of the yield surface on the structural loads. The stress paths are plotted in plane stress space in Figure 3. For this load path the effect of the yield surface is obvious. While the yield stress in the circumferential direction is the same for all three models, and the yield stress in the axial direction is the same for the two orthotropic models, the results are very different, even for the orthotropic models. The shape of the yield surface between the two material directions along with the different plastic flow directions leads to significant differences in the results.

Figure 3: The pressure vs. radial displacement curve for the internally pressurized cylinder showing significantly different results for 2090-T3 Al.

We have many choices for plasticity models, and many aspects of a plasticity model - including the hardening model, temperature dependence, and rate dependence - are important. The yield surface, however, is often overlooked. As shown in this work, significantly different results can be obtained for models that ostensibly capture the same behavior.

References

[1] Hosford W. F.: A generalized isotropic yield criteria. J. Applied Mech 39(2):607-609, 1972. [2] Hill R.: A theory of the yielding and plastic flow of anisotropic metals. Proc. Roy. Soc. London A 193:281-297,1948. [3] Barlat F., Aretz H., Yoon J. W., Karabin M. E., Brem, J. C., Dick R. E.: Linear transformation-based anisotropic yield functions. Int. J. Plasticity, 21:1009- 1039, 2005. [4] Karafillis A. P., Boyce M. C.: A general anisotropic yield criterion using bounds and a transformation weighting tensor. J. Mech. Phys. Solids, 41(12):1859- 1886, 1993. [5] Sierra/SM Development Team: Sierra/SM 4.36 User’s Guide. SAND2015-2199, Sandia National Laboratories, 2015.