Hardening evolution of AZ31B Mg sheet

Abstract

The monotonic and cyclic mechanical behavior of O-temper AZ31B Mg sheet was measured in large-strain tension/compression and simple shear. Metallography, acoustic emission (AE), and texture measurements revealed twinning during in-plane compression and untwinning upon subsequent tension, producing asymmetric yield and hardening evolution. A working model of deformation mechanisms consistent with the results and with the literature was constructed on the basis of predominantly basal slip for initial tension, twinning for initial compression, and untwinning for tension following compression. The activation stress for twinning is larger than that for untwinning, presumably because of the need for nucleation. Increased accumulated hardening increases the twin nucleation stress, but has little effect on the untwinning stress. Multiple-cycle deformation tends to saturate, with larger strain cycles saturating more slowly. A novel analysis based on saturated cycling was used to estimate the relative magnitude of hardening effects related to twinning. For a 4% strain range, the obstacle strength of twins to slip is 3 MPa, approximately 1/3 the magnitude of textural hardening caused by twin formation (10 MPa). The difference in activation stress of twinning versus untwinning (11 MPa) is of the same magnitude as textural hardening.

Introduction

With increasing demand for the application of light materials in the transportation industry, the plastic deformation behavior of magnesium alloys has been of recent interest. Compared with casting counterparts, wrought magnesium alloys have better mechanical properties, including tensile properties (Roberts, 1960, Bettles and Gibson, 2005) and fatigue resistance (Duygulu and Agnew, 2003). However, because of poor formability at room temperature, the large-scale utilization of sheet-formed magnesium alloys, for example AZ31B magnesium alloy sheet, has not developed.

The low formability at room temperature mainly arises from the limited number of slip systems in the hexagonal close packed (HCP) Mg alloys. The dominant slip system of magnesium AZ31B alloy at room temperature is slip in the close packed direction $〈11\overline{2}0〉$ or 〈a〉 on the basal (0 0 0 1) plane (Roberts, 1960). The critical resolved shear stress (CRSS) of basal slip in pure magnesium is about 0.5 MPa (Burke and Hibbard, 1952, Kelly and Hosford, 1968, Kleiner and Uggowitzer, 2004). Other slip systems, such as non-basal slip of 〈a〉 on prismatic $\{10\overline{1}0\}$ planes (Ward Flynn et al., 1961), 〈a〉 on pyramidal $\{10\overline{1}1\}$ planes and 〈c + a〉 on pyramidal $\{11\overline{2}2\}$ planes (Obara et al., 1973, Agnew et al., 2001) were also observed in magnesium, although their critical resolved shear stresses are two orders higher than basal slip (Kelly and Hosford, 1968, Kleiner and Uggowitzer, 2004). According to the Von Mises criterion (Von Mises, 1928, Taylor, 1938), five independent slip systems are needed to accommodate the arbitrary homogeneous deformation of polycrystalline materials. (Fewer deformation systems can accommodate certain special strain paths.) Basal 〈a〉 slip, prismatic 〈a〉 slip and pyramidal 〈a〉 slip provide only four independent slip systems. Pyramidal 〈c + a〉 slip, which in principle provides the additional independent slip systems, is difficult to activate at room temperature because of its high CRSS (Agnew et al., 2001, Yoo et al., 2002). At elevated temperature, the activation of pyramidal 〈c + a〉 slip and other non-basal slip occurs at lower CRSS, reducing flow stress and increasing formability (Agnew and Duygulu, 2003, Agnew and Duygulu, 2005). At room temperature, twinning can provide an independent deformation mechanism (in addition to basal and non-basal 〈a〉 slip systems) to satisfy the Von Mises criterion (Kocks and Westlake, 1967).

In HCP crystals, the twinning systems are strongly correlated with c/a ratio (Partridge, 1967, Yoo, 1981). The c/a ratio for pure magnesium is 1.624 (Roberts, 1960), which is close to, but less than, the ideal hard-sphere value of 1.633. Two common twin modes, $\{10\overline{1}2\}〈10\overline{1}\overline{1}〉$ and $\{10\overline{1}1\}〈10\overline{1}\overline{2}〉$, are observed in magnesium (Yoo, 1981), with $\{10\overline{1}2\}〈10\overline{1}\overline{1}〉$ being the most common and easily activated twin in magnesium and many other HCP metals (Roberts, 1960, Partridge, 1967, Kelly and Hosford, 1968). A CRSS for twinning, while low (Koike, 2005), is not well established because twin nucleation is inhomogeneous and depends on microstructure features (Partridge, 1967, Reed-Hill and Abbaschian, 1994). A fresh twin has a higher nucleation stress than the stress to propagate an existing twin (Partridge, 1965, Reed-Hill and Abbaschian, 1994).

Because of crystal symmetry, the shear direction for $\{10\overline{1}2\}$ twin reverses at $c/a=\sqrt{3}$. Since the c/a ratio of magnesium is smaller than $\sqrt{3}$, the $\{10\overline{1}2\}$ twin is a ‘tension’ twin, that is, its activation is associated with extension parallel to the c-axis in the HCP crystal structure (Yoo, 1981), and with contraction in a direction lying normal to 〈c〉. Because of the polar nature of twinning, the shear can occur only in one direction rather than opposite directions (Kocks and Westlake, 1967, Agnew and Duygulu, 2005). Therefore, a contraction along the c-axis cannot be accommodated by a $\{10\overline{1}2\}$ twin. In magnesium, a theoretical maximum extension of 6.4% along c-axis can be accommodated by complete reorientation of $\{10\overline{1}2\}〈10\overline{1}\overline{1}〉$ twins (Kocks and Westlake, 1967). After twinning, the c-axis will reorient to lie approximately in the original basal plane (Nave and Barnett, 2004).

Rolled AZ31B magnesium sheet alloy usually has very strong basal texture generated by rolling (Roberts, 1960, Agnew et al., 2001, Yukutake et al., 2003, Styczynski et al., 2004), where the c-axis of HCP lattice is predominantly aligned parallel to the sheet normal (McDonald, 1937, Yukutake et al., 2003). A state of stress which causes an extension in the sheet normal direction will activate twinning at low stress, while a state of stress that causes contraction normal to the sheet plane does not activate twinning (Kocks and Westlake, 1967, Reed-Hill, 1973, Gharghouri et al., 1999, Agnew et al., 2001, Nobre et al., 2002, Staroselsky and Anand, 2003, Styczynski et al., 2004). Conversely, an in-plane compression activates twinning but in-plane extension does not (Reed-Hill and Abbaschian, 1994). Of course, local inhomogeneities from grain-to-grain interactions can activate limited twinning, particularly in view of the limited number of independent slip systems, as can orientations of some grains that do not lie in the predominant basal texture.

Table 1 summarizes CRSS values reported for Mg and its alloys containing aluminum and zinc solutes. The upper section represents single-crystal data for Mg and dilute Mg–Zn. Clearly, basal slip has the lowest CRSS, ranging from 0.45 to 0.81 MPa. Twinning has a CRSS two-to-four times larger, and prismatic slip has a CRSS much larger, 48–87 times.

There is apparently no single-crystal data for AZ31B (second section of Table 1). Instead, CRSS values are fit by polycrystal texture calculations in order to match the macroscopic response, or CRSS values are obtained using in situ neutron diffraction to track lattice strain and peak intensity variation (Gharghouri et al., 1999, Brown et al., 2005). The texture calculations include unknown errors and effects of stress concentration, grain size, and incompatibility. The scatter is quite large. The neutron diffraction results in yield activation stresses only for twinning. Nonetheless, some generalizations may be drawn. It appears that the addition of aluminum and zinc solutes raises the CRSS for all deformation mechanisms, as expected, and compresses the ratios among them. For example, the basal slip CRSS is in the range of 10–45 MPa while the CRSS range for twinning is 15–35 MPa. Thus, basal slip and twinning have roughly equal CRSS’s, as compared with twinning having a CRSS twice that of basal slip in pure Mg. Prismatic slip in AZ31B has even more scattered results, with CRSS varying from 1-to-5 times that of basal slip, as compared with 48–87 times in pure Mg.

Sheet materials are typically formed by combinations of bending and stretching, both of which are dominated by in-plane loading, with much smaller through-thickness stresses. Therefore, the in-plane plastic deformation properties are of interest for sheet forming application. The yield stress for in-plane compression of Mg sheet is typically one half of that for in-plane tension (Ball and Prangnell, 1994, Nobre et al., 2002). After yield, the compressive hardening curve exhibits an inflected stress–strain curve with initially low strain hardening rate, distinct from the tensile behavior of AZ31B Mg alloy (Klimanek and Potzsch, 2002, Nobre et al., 2002, Yukutake et al., 2003, Barnett et al., 2004, Nave and Barnett, 2004). At larger compressive strain, when twinning is exhausted, or nearly so, and slip dominates, the compressive hardening curve takes on the appearance of the tensile one (Yukutake et al., 2003). At high temperatures, as twinning is suppressed by lower slip system CRSS’s, the inflection hardening curve disappears (Yukutake et al., 2003).

In addition to dislocation slip and twinning, untwinning (or detwinning) may occur in a twinned material. It is responsible for the shape memory effect in shape memory alloys (Liu et al., 1999, Liu and Xie, 2003, Sehitoglu et al., 2003), where untwinning is the growth of one variant in martensite at the expense of another (Liu and Xie, 2003, Sehitoglu et al., 2003). Microscopically, untwinning can be characterized by the disappearance of existing twin bands. Deformed magnesium alloy, which has a high density of twins, can undergo untwinning (Caceres et al., 2003, Keshavarz and Barnett, 2005). Twins can disappear or become narrower under reverse loading or unloading, and can reappear under reloading. The crystal deformation process of untwinning is similar to twinning, although nucleation is not required or occurs more readily. Therefore, untwinning can also result in an inflected and concave strain hardening behavior (Kleiner and Uggowitzer, 2004). The strain caused by twinning in compression can be reversed by untwinning in subsequent tension. Untwinning is a contraction of twinned regions, a process that does not require nucleation (Partridge, 1965). The stress required for untwinning is less than that for twinning nucleation, but greater than that for twinning growth (Partridge, 1965). In cyclic loading, twinning and untwinning appear alternately (Gharghouri et al., 1999).

Understanding the large strain plastic behavior of sheet alloys along non-proportional strain paths is an important requirement for sheet metal forming application. The Bauschinger Effect (Bauschinger, 1886), which refers to a lower yield stress developed with strain upon reverse loading following an initial strain/stress path, has been related to various mechanisms: residual stresses generated in forward deformation (Abel, 1987), Orowan loops around strong precipitates (Atkinson et al., 1974, Brown, 1977), internal stress from dislocation interactions (Hasegawa et al., 1986), and dislocation pileups at grain boundaries (Margolin et al., 1978). Regardless of mechanism, the macroscopic interpretation involves development of a “back stress” during loading that assists reverse loading.

The foregoing interpretations of the Bauschinger Effect rely on material hardening characteristics of dislocation slip. In materials that twin significantly, twinning and its interaction with slip can provide alternate Bauschinger Effect mechanisms. The twin boundaries operate as hard but deformable obstacles, with dislocation pileups developing at the twin boundaries which generate a long-range back stress field and large Bauschinger Effect (Karaman et al., 2001). In magnesium alloys at room temperature, where deformation in some stress states depends intimately on twinning, large asymmetry of cyclic deformation has been noted (Attari et al., 1990), but not studied in detail, particularly at large strain. Noster and Scholtes (2003) reported a pronounced Bauschinger Effect for small strain reversal. Consistent with the role of twins as obstacles for slip, pre-compression followed by tension was reported to produce a larger Bauschinger Effect than the opposite path, pre-tension followed by compression.

In contrast to extensive studies of magnesium bulk alloys, there is little data for large-strain in-plane compression of magnesium sheet alloys. Such measurements are limited by buckling. The large-strain cyclic deformation behavior of magnesium alloy, important to sheet metal forming behavior and simulation, has not been reported. Knowledge of the Bauschinger Effect, and more generally of the evolution of yield and hardening under non-proportional loading paths, is required to enable development of novel forming methods to take advantage of the unusual plastic properties of wrought Mg sheet.

In the current work, the constitutive behavior of O-tempered AZ31B Mg sheet alloy was investigated at room temperature. Monotonic and continuous reverse-path tests were conducted in uniaxial tension/compression and simple shear. Novel test designs were utilized to obtain large-strain deformation (Gsell et al., 1983, Rauch and Schmitt, 1989, Rauch, 1998, Balakrishnan, 1999, Lopes et al., 2003, Boger et al., 2005). In order to understand the origins of the mechanical response, optical metallography, texture analysis and acoustic emission measurements were conducted in parallel with the mechanical tests.