Crystal plasticity analysis of texture development in magnesium alloy during extrusion

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Abstract

The texture development mechanism during the extrusion of magnesium alloy is investigated by experimental observation and numerical analysis. First, we perform a finite element analysis of a full extrusion process using a phenomenological constitutive equation, and it is confirmed that the loading condition of the extrusion process near the central axis of the billet is approximated by an equi-biaxial compression mode. Then, the equi-biaxial compression problem is adopted as a simplified boundary value problem to be solved using a crystal plasticity model to clarify the detailed texture development mechanism during the extrusion process. The crystal plasticity analysis of equi-biaxial compression successfully reproduces the texture development from an initial random texture to the final experimentally observed texture. The effects of the deformation modes (i.e. slip and twinning systems) implemented in the calculation and the reference stress ratio of basal to nonbasal slip systems on texture development are studied in detail. Finally, the mechanism of texture development during the extrusion process is discussed in terms of the lattice rotation caused by the activated slip systems.

Introduction

The application of lightweight materials with high strength and formability to mechanical components is expected to contribute to the abatement of global warming and the reduced use of fossil fuels, because the energy consumed in their manufacture and operation is less than that of conventional heavier structural materials such as steels. Therefore, considerable attention has been focused on magnesium, the lightest structural metal.

Extensive research on magnesium alloys indicates that their strength and ductility can be simultaneously improved by severe plastic deformation (Chen et al., 2008a, Chen et al., 2008b, Ma et al., 2009). The grain size, which is refined through forming processes, has a significant effect on material properties, especially in magnesium alloys. The slope of the Hall–Petch relation for magnesium alloys that have the hexagonal close-packed (HCP) crystal structure is larger than those for other metallic materials with cubic crystal structures (Mabuchi and Higashi, 1996). Thus, the mechanical properties of magnesium alloys can be significantly improved through severe forming processes. Meanwhile, processes such as rolling and extrusion generally induce strong textures in magnesium alloys (e.g., Wang and Huang, 2007, Liang et al., 2008, Al-Samman and Gottstein, 2008a, Al-Samman and Gottstein, 2008b). Magnesium alloys with strong texture exhibit significant anisotropy including tension–compression asymmetry (e.g., Lee et al., 2009, Chino et al., 2008a, Chino et al., 2008b). Both the strong texture and the significant anisotropy of magnesium originate from the HCP crystal structure with low symmetry. That is, nonequivalent deformation modes realized by different types of slip systems and frequently activated twinning are considered to be essential causes of the development of the strong texture and anisotropy in magnesium. Since each deformation mode has different value of the critical resolved shear stress (CRSS) (e.g., Yoshinaga and Horiuchi, 1963a), the active deformation mode cannot be specified only from the Schmid factors for each deformation mode. In addition, deformation twinning has a loading direction dependence (polarity of twinning), which is the main cause of the tension–compression asymmetry (Chino et al., 2008a, Chino et al., 2008b, Mayama et al., 2009). These complicated deformation mechanisms make it difficult to determine the anisotropy and texture development mechanism in magnesium.

Recently, a number of studies on HCP metals have been carried out using crystal-plasticity-based simulations (Staroselsky and Anand, 2003, Graff et al., 2007, Mayeur and McDowell, 2007, Beausir et al., 2007, Capolungo et al., 2009, Tadano, 2010). Because the crystal plasticity model explicitly considers deformation mechanisms at the scale of the crystal structure, the activation of nonequivalent deformation modes is systematically calculated. Therefore, crystal-plasticity-based simulations are a powerful tool for determining the complicated deformation mechanism in magnesium alloys (e.g., Agnew et al., 2003, Mayama et al., 2009, Neil and Agnew, 2009, Proust et al., 2009, Choi et al., 2010, Hama and Takuda, 2011). Although several investigations of texture development in magnesium alloys in terms of plane strain compression, rolling and equal-channel angular extrusion processes have been reported (e.g., Agnew et al., 2001, Agnew et al., 2005, Styczynski et al., 2004; Bohlen et al., 2007, Beausir et al., 2008, Li et al., 2008, Biswas et al., 2010), the number of computational studies on texture development in a conventional extrusion process using the crystal plasticity model has been limited.

In the present study, to determine the mechanisms of texture development during the extrusion of a magnesium alloy, we conduct experiments and crystal-plasticity-based analyses on commercial magnesium alloy AZ31. The microstructural evolution and texture development are observed using a scanning electron microscope (SEM) with electron back scattering diffraction (EBSD) equipment. Since crystal plasticity simulations of the full extrusion process are rather time-consuming, we first perform a finite element analysis of a full extrusion process using a phenomenological constitutive equation. It is confirmed that the loading condition of the extrusion process near the central axis of the billet can be approximated by an equi-biaxial compression mode. Thus, in simulations to clarify the texture development in detail we adopt a simplified boundary value problem of equi-biaxial compression, which is analyzed using the crystal plasticity model. Using this simplified problem formulation, the effects of the deformation modes implemented in the analysis and the reference stress ratio of the basal slip system to the nonbasal slip system on texture development are investigated. Finally, the texture development mechanism is discussed in terms of lattice rotation caused by the activation of slips.

Section snippets

Material and experimental method

The texture development of the extruded magnesium alloy AZ31 was experimentally observed. The observations were conducted by using a SEM with EBSD equipment. The chemical compositions of the AZ31 ingot used in this study are 3.0 wt.% Al, 0.9 wt.% Zn, 0.3 wt.% Mn and balance Mg. From the ingot, as-cast AZ31 alloy were prepared by high-frequency induction melting in an Ar atmosphere. From the as-cast alloy, an extrusion billet with a diameter De of 29 mm was machined. The billet without

Finite element analysis of the extrusion process

In the present study, we aim to capture the texture development in the extrusion process using a crystal plasticity finite element method. However, direct simulation of the full extrusion process using this method may be time-consuming owing to a huge computational load. Thus, a finite element analysis of the full extrusion process is first carried out using a phenomenological constitutive equation to obtain a simplified boundary condition for crystal plasticity simulations.

The explicit finite

Effect of implemented deformation modes

In this section, to evaluate the effect of the implemented deformation modes, calculations with four sets of reference stress values for each deformation mode, as shown in Table 4 are considered. Calculations using the sets of reference stress values are denoted as ALL, No-PRI, No-PY1 and No-TW. Here, ALL consider basal, prismatic, pyramidal-1 and pyramidal-2 slip system as well as twinning system while No-PRI, No-PY1 and No-TW does not consider prismatic slip, pyramidal-1 slip or twinning

Conclusions

In this study, texture development during extrusion in the magnesium alloy AZ31 was investigated by experimental observation and numerical analysis. To clarify the texture development mechanism in the magnesium alloy during extrusion the effects of each deformation mode and the reference stress ratio of the basal slip system to the nonbasal slip systems on texture development were studied by crystal plasticity analysis. Consequently, the following conclusions were obtained.

  • 1.

    The crystal

Acknowledgements

The work of T.M. was partially supported by a Grant-in-Aid for Scientific Research from the Ministry of Education, Culture, Sports, Science and Technology of Japan (KAKENHI: No. 21760082) and the Kumamoto Prefecture Collaboration of Regional Entities for the Advancement of Technological Excellence from Japan Science and Technology Agency.

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