In Situ Investigation of Deformation Mechanisms and Stress Evolution in Mg-3Al-1Zn (AZ31) Alloy Using Synchrotron X-Ray Microdiffraction

Abstract

This study employs synchrotron polychromatic X-ray microdiffraction (micro-XRD) to resolve the dynamic interplay between deformation mechanisms and stress redistribution in a commercial Mg-3Al-1Zn (AZ31) alloy under uniaxial tension. Submicron-resolution mapping across 13 incremental load steps (12–73 MPa) reveals sequential activation of deformation modes: basal slip initiates at 46 MPa, followed by tensile twinning at 64 MPa, and non-basal slip accommodation during twin propagation at 68 MPa. Key findings include accelerated parent grain rotation (up to 0.275° basal plane tilt) between 43–46 MPa, stress relaxation in parent grains coinciding with twin nucleation, and a ~35 MPa stress reversal within twins. The critical resolved shear stress (CRSS) ratio of twinning to basal slip is experimentally determined as 1.8, with orientation-dependent variations attributed to parent grain crystallography. These results provide unprecedented insights into microscale deformation pathways, critical for optimizing magnesium alloy formability and performance in lightweight applications.

1. Introduction

Magnesium alloys, with their hexagonal-close-packed (HCP) structure, are pivotal for lightweight structural applications in aerospace and automotive industries due to their exceptional strength-to-weight ratio [1]. However, limited ductility arising from restricted slip systems at room temperature remains a persistent challenge [2]. Recent advancements in alloy design, such as rare-earth (RE) element additions [3] and thermo-mechanical processing [4], aim to enhance ductility by promoting non-basal slip and deformation twinning. Twin-mediated plasticity, in particular, plays a dual role: it accommodates strain but also induces stress concentrations that influence macroscopic failure [5].

Many studies have reported that the macro-scale deformation behaviors of magnesium alloys were clarified by neutron diffraction and crystal plasticity finite element models. Kot et al. [6] proposed a novel original method of determining stress and critical resolved shear stresses (CRSSs) using neutron diffraction. It can directly determine the stresses for groups of grains that have similar orientations. Cheng et al. [7] found that the crystal plasticity finite element models demonstrated good alignment with the stress–strain curves and lattice strain results in the RD tension cases. However, real-time microscale stress evolution during twin nucleation and growth remains inadequately understood. Synchrotron-based techniques, such as polychromatic X-ray microdiffraction (micro-XRD), now enable submicron-resolution tracking of grain-scale dynamics. For instance, Lynch et al. [8] quantified slip-twin interactions in embedded Mg grains, and the shear stresses were resolved with an accuracy of ±8 MP. Moreover, Kada et al. [9] investigated the correlation between twin back stresses and precipitate–dislocation interactions in AZ91 alloys, and quantified CRSS for basal slip and twinning modes based on X-ray diffraction methodologies. Despite these advances, discrepancies in reported CRSS ratios for twinning versus basal slip (ranging from 1.3 to 7 [10,11,12]) highlight unresolved orientation-dependent stress partitioning mechanisms.

This study addresses these gaps by integrating high-resolution micro-XRD with advanced indexing protocols to map stress evolution and deformation sequences in the AZ31 Mg alloy. Specific objectives include correlating orientation fluctuation to lattice dislocation activities during elastic–plastic transition, quantifying CRSS ratios for basal slip and tensile twinning across different crystallographic orientations and addressing the redistribution of stress between parent grains and their twins throughout the process of incremental loading.

2. Materials and Methods

2.1. Material Preparation and Characterization

The raw material is a commercial AZ31 Mg alloy strip (Mg-3Al-1Zn, extruded rod), which was annealed at 300 °C for 1 h after extrusion. It was machined into dog-bone tensile specimens (gauge dimensions: 10 mm × 3 mm × 1.5 mm). Initial texture analysis conducted using electron backscatter diffraction (EBSD, JEOL JSM-7800F, Tokyo, Japan) confirmed a strong basal fiber texture, with most grains oriented such that their c-axes were perpendicular to the sheet normal direction. Electrochemical polishing with a Struers LectroPol-5 (Ballerup, Denmark) ensured a strain-free surface for micro-XRD measurements.

2.2. In Situ Synchrotron X-Ray Microdiffraction

Uniaxial tensile tests were performed at Beamline 12.3.2 (located at the Advanced Light Source, Lawrence Berkeley National Laboratory, Berkeley, CA, USA) with the aid of a custom-designed deformation stage (in Figure 1). To perform in situ uniaxial tensile loading experiments, a deformation stage, previously used for micro-XRD studies [13], was utilized. The loading system provides accurate control and feedback of the loading parameters necessary to recreate the macroscopic stress–strain curve. The tensile experiment was carried out under displacement control at a rate of 0.016 mm/s. To ensure the exact same positions on the specimen throughout the loading, the polycrystalline AZ31 sample was electrochemically polished and a series of fiducial markers in the form of micro-scale indents were introduced on the surface to define the region of interest.

The polychromatic X-rays, spanning an energy spectrum of 5–25 keV, were concentrated into a 0.8 µm × 0.8 µm area using Kirkpatrick–Baez mirrors, resulting in a penetration depth of around 500 µm. Laue diffraction patterns were acquired at 12 µm (X) × 20 µm (Y) step intervals across a 300 µm × 300 µm region of interest. Fiducial markers (micro-indents) enabled precise spatial registration across load steps.

2.3. Simulation of Elastic Strain/Stress Tensor

Grain and twin orientations were indexed using XMAS software (@2003) [14], prioritizing sharp, non-overlapping Laue reflections. Elastic strain tensors (ε) were derived from lattice parameter shifts using Hooke’s law:

$${\epsilon }_{ij}=C_{ijkl}\times {\delta }_{kl}$$

(1)

C_ijkl denotes the anisotropic stiffness tensor transformed into the sample coordinate system [15]. Mosaic spread analysis identified active slip systems by matching experimental Laue streaking to kinematic simulations for 8 deformation modes (

Table 1. Summary of dislocation slipping modes for Laue spot streaking simulation.

(VI) six {$11\overline{2}3$}<$2\overline{1}\overline{1}2$> $\overrightarrow{c}$ slips
(V) six {$\overline{1}\overline{1}21$}<$2\overline{1}\overline{1}3$> $\overrightarrow{c}$ slips
(IV) six {$\overline{1}011$}<$2\overline{1}\overline{1}3$> $\overrightarrow{c}$ slips
(III) six {$\overline{1}011$}<$\overline{1}2\overline{1}0$> $\overrightarrow{a}$ slips
(I) three basal slips	(II) three prismatic $\overrightarrow{a}$ slips

).

3. Results

3.1. Parents and Twins Indexation

Figure 2 shows indexed Laue patterns from the target grain. In Figure 2a, over 50 reflections are indexed. Diffraction spots were observed at 12 MPa. As load increased to 64 MPa in Figure 2b, spots showed mosaic spread due to dislocation activity, resulting in orientation fluctuation.

Figure 3 shows the morphologies of three grains with typical orientations representing different twinning tendencies. Researchers mapped the three grains utilizing the integrated intensities of the ($4\overline{4}03$), ($2\overline{4}22$) and ($\overline{5}32\overline{1}$) reflections. The criteria for selecting these reflections centered around their roundness, sharpness, and absence of overlap. Three hexagonal lattices in the X_SY_SZ_S frame for the selected grain exhibited different twinning tendencies based on the projections of the c-axis in the X_S direction. Grain A was free of twins, while Grain C was expected to readily produce twins. The active twin plane is marked in cyan.

It is well known that twin nucleation is initiated by dislocation slip, and twinning itself is often regarded as dislocation glide for most purposes. The maximum Schmid factor (SF) values for various deformation modes in the parent and twin grains have been determined and tabulated in

Table 2. SFs for eight deformation modes across Grains A–C.

Deformation Mode	{${\displaystyle 10\overline{1}2}$} Twin	Basal $\overrightarrow{\mathit{a}}$ Slips	{${\displaystyle 10\overline{1}0}$} $\overrightarrow{\mathit{a}}$ Slips	{${\displaystyle 10\overline{1}1}$} $\overrightarrow{\mathit{a}}$ Slips	{${\displaystyle 10\overline{1}1}$} $\overrightarrow{\mathit{c}}$ Slips	{${\displaystyle 11\overline{2}1}$} $\overrightarrow{\mathit{c}}$ Slips	{${\displaystyle 11\overline{2}2}$} $\overrightarrow{\mathit{c}}$ Slips	{${\displaystyle 11\overline{2}3}$} $\overrightarrow{\mathit{c}}$ Slips	{${\displaystyle 10\overline{1}2}$} Twin
Grain A	−0.033	0.033	0.499	0.452	0.336	0.366	0.430	0.466	−0.033
Grain B	0.096	0.405	0.388	0.478	0.446	0.378	0.409	0.285	0.096
Grain C	0.456	0.276	0.045	0.151	0.466	0.431	0.493	0.456	0.456

. A total of eight types of deformation modes, including tensile twinning, were evaluated. For instance, tensile twinning includes six variants, with the maximum SF value for the parent being 0.456.

3.2. Orientation Fluctuation of Grains and Twins

The new “single-shot” technique [8] enabled observation of the evolution of crystal orientation in the area of interest under applied load. Figure 4 displays the changes in rotation angle maps for three grains as the load increased from 12 to 46 MPa. Each spot’s orientation is characterized by a rotation angle/axis pair. As the load rose, the orientation distribution diverged from its initial state, notably at grain boundaries. Figure 5 reveals the statistical distribution of rotation angles across the three grains. With increasing load, rotation angles tended towards diffused values. While plastic anisotropy often prevails, the elastic anisotropy of the surrounding polycrystal is mirrored in these orientation fluctuations. Notably, grain rotation intensified between 38 MPa and 46 MPa. The rotation events imply the occurrence of plasticity burst [16]. The shifts of rotation density peak fall between 0.16° and 0.18°, basically consistent with the results of previous work [16]. This load range corresponds to elastic–plastic transition.

Figure 6 depicts the evolution of morphologies and misorientation maps for three twins between 64–73 MPa. The misorientation angle is the difference between the measured orientations and the calculated ones via the activated twin variant ([$\overline{1}2\overline{1}0$]/86.4°) from the parent orientation at 64 MPa. As the load increased, the morphologies of the twins evolved through widthwise and lengthwise growth, indicating relaxation. Local orientation changes reveal the material’s plastic behavior. As depicted in Figure 6, the range of misorientation angles expanded from 0.35° at 64 MPa to 0.60° at 68 MPa, and subsequently to 1.0° at 73 MPa. This indicates that the rate of misorientation amplitude escalated with each incremental load. Notably, the misorientation at the twin boundaries was pronounced, indicating substantial plastic deformation. However, at 73 MPa, the maximum and minimum angles were not at the twin tips, indicating that at high load levels, plastic relaxation may occur anywhere within the twin domains.

3.3. Mosaic Spread and Deformation Modes

In addition to twin morphology analysis, the technique revealed dislocation activity through mosaic spread. Considering that different slip systems result in distinct Laue pattern (LP) streaking [17], simulations of LP streaking were conducted based on given crystal orientations and potential slip systems for the HCP crystal, as listed in Table 1. Given that basal slip in magnesium is easy to initiate, the measured grain rotation was likely dominated by the slip mode. The measured LPs for parent and twin grains and their simulated ones for mosaicity streaking based on basal slip are presented in Figure 7. For clarity, Figure 8 illustrates the simulated streak behavior and the corresponding five experimental reflections obtained from a single LP at 64 MPa. The simulated pattern in Figure 7b, based on the (0002) [$\overline{2}110$] slip system, aligns well with the parent pattern in Figure 7a. This was also supported by the local stress data and the maximum SF value among the three basal slip modes. However, pyramidal slips {$11\overline{2}3$} <$2\overline{1}\overline{1}2$> also exhibited similar streaking patterns, so this mode cannot be excluded. For the twins’ measured pattern in Figure 7c, the simulated pattern in Figure 7d, based on the (0002) [$1\overline{2}10$] slip system, matched well. However, the active basal slipping within the twins adopted the lowest SF value (0.042) among the three basal slips, instead of the maximum value of 0.140.

At the higher load level of 68 MPa, non-basal slip was identified in the parent grain’s mosaic spread, as shown in Figure 9. Upon comparing the measured LPs with the simulated ones based on various slip modes, the simulated LPs were arranged in the order of slip modes listed in Table 1. The measured patterns matched well with the simulated ones based on the {$\overline{1}011$}<$\overline{1}2\overline{1}0$> and {$\overline{1}\overline{1}21$}<$2\overline{1}\overline{1}3$> slip modes, marked by yellow squares.

3.4. Stress and Strain Evolution

To assess the reliability of strain measurements from the synchrotron, 12 LPs from the same position were indexed from 12 MPa to 64 MPa to observe deviatoric strain evolution. Figure 10 depicts the evolution of elastic deviatoric strain components with applied load. Initially, strains followed elastic behavior. Deviations from the elastic line in normal components were noted at 46 MPa due to changes in grain orientation stress state, indicating relaxation onset. Shear strains, especially ε_xz’, deviated more significantly due to measurement noise and limited pole coverage [18]. Micro-yielding was identified by sharp variations in the gradient, confirming the accuracy of the measurements.

Figure 11 presents numerical values of specific stress components for the parent grain as a function of applied load from 19 MPa to 64 MPa. Due to significant error at 64 MPa, only the mean value is plotted, attributed to heterogeneous deformation at the subgrain level [19]. Experimental results aligned with simulated elastic lines for Mg single crystals during the elastic stage. In Figure 11a, σ_x denotes stress along the tension axis (Xs). Notably, σ_x was lower than applied stress from 19 to 54 MPa, indicating plastic “softness” consistent with its SF value of 0.276 for basal slip (Table 2). Consequently, more plastic deformation was observed in this grain compared to others at this loading level.

Figure 11b depicts resolved shear stress evolution on basal slip directions for parent and twin grains with increasing load from 12 MPa to 64 MPa. The flat σ_n between 46 and 54 MPa signifies parent grain relaxation and onset of basal slip, with CRSS identified as ~−15 MPa. Shear stress for basal slip in twins dropped ~40 MPa with sign reversal. Figure 11c shows τ_rs, resolved shear stress on the twin plane for the parent grain. Furthermore, τ_rs by V3 agreed with the predicted elastic line but departed between 54 and 58 MPa, indicating parent grain relaxation. Prior to twin reflections (at 64 MPa), the twinning system accumulated stresses rapidly. Upon twin reflection observation, the mean stresses relaxed ~18 MPa. Average stresses on the active twinning system in twins were ~35 MPa less than in the parent, with sign reversal. This implies a large residual strain gradient at parent–twin boundaries.

4. Discussion

Our study found plasticity began with basal slip, evident by accelerated grain rotation at 46 MPa. Local misorientation increased due to geometrically necessary dislocations [20]. The magnitude of rotations varies between 0.16° and 0.18° (0.0028 and 0.0031 radians in Δθ). This corresponds to an increase in geometrically necessary dislocation density of the order of 1011 m/m³ (calculated by Δθ/db where d is the grain size and b the Burgers vector magnitude). The avalanche of lattice dislocations occurs at applied stresses between 46 and 51 MPa, as indicated by the plateau region in Figure 11c. Basal slip alone does not meet the Taylor criterion, but twinning may relax this. Additional slip modes, like non-basal slip, were observed mosaic streaking directions at 64–68 MPa in the parent’s LP.

Twinning was detected at 64 MPa. Inspection of twin diffraction peaks also showed basal slip. The SF criterion for basal slip mode selection was invalid, as shown in Figure 7c,d, implying that stress distribution within the twin domain was complex beyond the criterion. Researchers have directly observed that twins are formed under backward stresses relative to the remainder of the aggregate (see Figure 11). This discovery aligns with previous studies indicating that twinning alleviates local stresses, accompanied by a significant reversal in stress direction [21,22]. It can be deduced that huge stress gradients exist on parent–twin boundaries. Thus, twin dislocations move under the stress to accommodate twinning shear during twin propagation. Plasticity was concentrated at twin tips (see Figure 6), indicating their inhomogeneous distribution.

The corresponding resolved shear stress acting on the deformation system amounted to 15 MPa, with fluctuations within the elastic range yielding this value with a margin of error of ±4 MPa (see Figure 11b). For twin formation, occurring at applied loads between 54 and 58 MPa, the corresponding value ranged from 24 to 30 MPa, determined as 27 ± 3 MPa (in Figure 11c). This finding agreed with previous research [23], which reported values between 22 and 42 MPa for the initiation of twinning.

The ratio of the CRSS for twinning to that for basal slip is approximately 1.8, which is lower than previously reported by Muránsky and Barnett [24]. They provided values in the range of 2–7 based on crystal plasticity simulations, focusing on grains that are most favorably oriented for twinning. In other words, these grains exhibit high SFs for twinning but low SFs for basal slip. As illustrated in Table 2, the parent grain in the current study has an SF of 0.456 for twinning and 0.276 for basal slip. Additionally, another study by Lynch, using the same methodology, reported a ratio of approximately 1.3 in a parent grain with an SF of 0.33 for twinning and 0.46 for basal slip. It is plausible that prior basal slip activity facilitates twin nucleation, resulting in a lower ratio for twin growth. Thus, the ratio can be affected by the crystal orientation of the parent grain in which twins are formed.

5. Conclusions

The analysis of 13 load steps confirmed the sequence of deformation behaviors as follows: the onset of basal slip, the onset of tensile twinning, the accommodation of non-basal slip, and the propagation of twins.

Prior to twinning, the intensive magnitude of grain rotations signifies the burst of lattice dislocations, corresponding to an increase in geometrically necessary dislocation density.

Upon the occurrence of twin reflections, the variation in misorientation angle increases. The misorientation amplitude increases with respect to load steps, especially for twin tips.

In the twin propagation activated by stress concentration, twin dislocations move under the huge stress gradients on the parent–twin boundaries.

The CRSS for basal slip and tensile twinning were directly identified as 15 ± 4 MPa and 27 ± 3 MPa, respectively. Once the twins become detectable, the resolved shear stresses shift significantly, reversing their signs. The ratio of the CRSS for twinning to that of basal slip is influenced by the crystal orientation of the parent grain in which the twins form.