On the plastic anisotropy of an aluminium alloy and its influence on constrained multiaxial flow

Abstract

The influence of plastic anisotropy on the mechanical behaviour of a rolled aluminium plate under quasi-static loading conditions is studied experimentally and numerically. Material tests in different directions with respect to the rolling direction of the plate were carried out on various specimen shapes providing a wide range of stress states. The Yld2004-18p anisotropic yield function was identified through uniaxial tensile tests, shear tests and upsetting tests. This yield function was found to provide an adequate description of the significant anisotropic behaviour of a high-strength AA7075-T651 plate. Numerical simulations of all the material tests were then performed with an elasto-plastic material model using both the anisotropic and an isotropic version of the yield function. The numerical predictions of the mechanical response for notched tensile tests obtained with the isotropic version of the material model clearly over-estimated the experimental results. Similar results have been reported in the literature on other materials using isotropic constitutive relations. This over-estimation was significantly reduced when using the anisotropic version of the material model, and the reason why plastic anisotropy is so important for an accurate prediction of the notch-strengthening effect is explained. It was also established that the exponent of the yield function Yld2004-18p has a strong influence on the results for the notched tensile tests. When the exponent of the yield surface was assigned a sufficiently high value, an almost perfect fit between the numerical predictions and the experimental results was obtained.

Introduction

Structural components in various aluminium alloys are widely used by the automotive and aircraft industries. A variety of different extrusion techniques, rolling processes and forming operations is used to manufacture these components. Because of the extreme deformations taking place during processing, such components may have highly anisotropic properties. This anisotropy is an important material factor determining the magnitude of local deformations and may have significant effects on the final shape of the component and local strain instabilities during operation. Thus, the anisotropic behaviour during deformation must be taken into account if one wants to correctly predict the mechanical behaviour of an aluminium component.

The plastic behaviour of a metallic material is usually described through a yield surface in stress space, the associated plastic flow rule and an isotropic hardening law. The modelling of plastic anisotropy is still a difficult task for macroscopic models and particularly for complex multiaxial paths. The use of crystal plasticity theories can help in this direction, but their use is restricted by computational limitations and the observation that they do not predict the flow stresses and the plastic flow simultaneously, as shown for instance in Darrieulat and Montheillet, 2003, Lopes et al., 2003. Since the pioneering work of Hill (1948), a tremendous effort has been made during the last two decades to improve the modelling of anisotropy in macroscopic models (Hill, 1987, Hill, 1990, Van Houtte et al., 1989, Arminjon and Bacroix, 1991, Barlat and Chung, 1993, Karafillis and Boyce, 1993, Arminjon et al., 1994, Barlat et al., 2003, Bron and Besson, 2004, Van Houtte and Van Bael, 2004, Choi et al., 2006, Leacock, 2006, Aretz et al., 2007, Hu, 2007, Kim et al., 2007, Monchiet et al., 2008, Soare and Barlat, 2010).

Most theories of plasticity assume that the hydrostatic pressure has no or very limited effect on the strain hardening of metals and metallic alloys. Another common assumption in these theories is plastic incompressibility. Since the beginning of the 1980s, Richmond and Spitzig, 1980, Brownrigg et al., 1983, Spitzig and Richmond, 1984, Brünig, 1999 reported pressure dependence of the flow stress for metals such as steel and aluminium. The effect of this observation is an increase in flow stress of metals with hydrostatic pressure. In these studies (despite the claimed dependence of the flow stress on the hydrostatic pressure), the plastic dilatancy is negligible and not related to the normality rule. Even though the effect of hydrostatic pressure was not directly studied, Freed and Sandor (1985) observed plastic volume change in uniaxial tension on the aluminium alloy AA7075-T651. They found elastic and plastic volume changes of similar magnitude and suggested plastic anisotropy to be the prime cause of this plastic compressibility. More recently, Bai and Wierzbicki (2008) proposed a new model of metal plasticity and fracture with pressure and lode dependence.

The ductility of aluminium alloys is also found anisotropic (e.g. Chen et al., 2009), which reveals the influence of the microstructure on the damage process. It is well established that fracture in ductile materials is due to the nucleation, growth and coalescence of voids (see e.g. Thomason, 1990, Anderson, 1991). Under such circumstances, the stress triaxiality and the strain intensity are considered as the most important factors that control the initiation of fracture. Therefore, the deformation and loading history is important to correctly predict failure. In that context, using an appropriate anisotropic model for aluminium alloys is an essential step to enable a proper description of the damage leading to fracture. For instance, a numerical representation of the microstructure coupled with damage models enabled Steglich et al. (2008) to represent the complexity of the fracture mode with anisotropy. Although fracture is the final goal of this work, the current paper is limited to the plastic behaviour only.

Rolled plates of AA7075 aluminium alloy in temper T651 are studied in this paper. This alloy belongs to the AlZnMg series and contains precipitates which increase the mechanical properties such as the yield limit and the tensile strength. Due to the rolling, the grains are flat and elongated along the rolling and transverse directions, the alloying particles are organized in the plane of the plate, and a strong crystallographic texture is engendered. The anisotropy caused by this complex microstructure is observable on the yield limit and the ductility through tensile tests in different directions regarding the rolling direction of the plate (see Børvik et al., 2010, Pedersen et al., 2011). However, by constraining the deformation (e.g. by varying the initial stress triaxiality in the specimens), the properties are affected differently by anisotropy.

The objective of this study is to analyse in detail the effects of anisotropy on the mechanical behaviour and constrained plastic flow of the AA7075-T651 plate. Here, the anisotropy is only considered to affect the yielding behaviour of the alloy. Though some works (see e.g. Stoughton and Yoon, 2009, Rousselier et al., 2010) have studied the effect of anisotropy on the strain hardening of aluminium alloys, the elastic behaviour and the strain hardening are in our study assumed isotropic. The yield surface is represented by the linear transformation-based yield function Yld2004-18p proposed by Barlat et al. (2005), and a corotational formulation (Belytschko et al., 2000) was adopted to simplify the formulation of plastic anisotropy. The stress measure is defined with respect to the un-rotated configuration and expressed in the rectangular Cartesian coordinate system given by the principal axes of anisotropy of the material. These axes are assumed to remain orthogonal during deformation. This formulation was successfully used by Grytten et al. (2008) to model the plastic behaviour of the aluminium alloy AA5083-H116. The used yield function together with the associated flow rule presumes pressure insensitivity. The yield criterion is identified through tension tests on smooth tensile specimens with longitudinal axes aligned at different directions with respect to the rolling direction of the plate and upsetting test in the thickness direction of the plate. Both measured directional yield stresses and the ratios of transverse to thickness plastic strain increments are used to identify the coefficients of the yield function. The hardening parameters are identified from tensile tests in the rolling direction of the plate. In addition, shear and upsetting tests were used to identify the coefficients of the yield function. The model is then applied in non-linear finite element simulations to reproduce the plastic behaviour of different type of specimens (notched axisymmetric specimens, butterfly shear specimens and cylindrical specimens for upsetting tests) cut from different material directions. It will be shown that the effects of anisotropy must be taken into account for a good representation of the mechanical behaviour of the alloy at various stress states.

Section 2 describes the aluminium alloy, the experimental procedures and the test programme applied in this investigation. Section 3 presents the constitutive model used for the modelling of the anisotropic behaviour of the material and the procedures allowing the identification of the different parameters. In Section 4, the numerical procedures are presented which allow the simulation of the plastic behaviour of the different specimens. Sections 5 Discussion, 6 Conclusions contain discussions of the main results and concluding remarks, respectively.