This experiment was conducted out using AZ31B magnesium alloy as the base material, with its specific composition provided in Table 1. As shown in Fig. 1, two tensile specimens with dimensions of 90 mm × 10 mm × 5 mm were prepared by machining along the 0° and 90° directions, respectively. The tensile tests were performed along RD and TD at room temperature using the WDW-E100D electronic universal testing machine, with the strain rate set at ε=10−3s−1. An extensometer was used to measure strain during tensile testing, with all tests repeated at least three times. The initial texture and inverse pole figure (IPF) were characterized using EBSD. Sample preparation involved mechanical polishing down to approximately 60 μm with 1000# to 5000# sandpaper, followed by electrolytic polishing in a phosphate-alcohol solution (volume ratio 3:5) at a current of 0.1–0.4 A for 30–60 s. EBSD scanning was conducted with a step size of 1 μm. Data were processed using Aztec crystal: v2.1; MATLAB: R2024a software, and subsequent texture analysis was performed using magnetic texture (MTEX) toolbox in matrix laboratory (MATLAB). The orientation distribution function was discretized with the number of grains as the control variable, generating 2000 grain orientations as the initial input for the VPSC model.

The VPSC modeling framework considers each grain of the polycrystal as an ellipsoid embedded in an infinite homogeneous equivalent medium, and fully considers the interaction between the grains in the polycrystal.

In the VPSC model, the non-linear rate-sensitive constitutive model is used to represent the local viscosity [21,31], as follows: (1)εij(x¯)=∑mijsγ0(x¯)=γ0∑mijs{mklsσkl(x¯)τs}nwhere εij(x¯) is the strain deviatoric tensor, σkl(x¯) the stress, γ0 the normalized factorx, γ0(x¯) the critical shear rate, n = 0.05 the strain rate sensitivity index.

The Voce hardening formulation accurately captures the work hardening characteristics of deformation mechanism in magnesium alloy plasticity simulations. The extended equation [31,32] is: (2)τs=τ0s+(τ1s+θ1sΓ)(1−exp⁡(−Γ|θ0sτ1s|))where (τ0s+τ1s) is back-extrapolated CRSS value, τ0s indicates initial CRSS value, θ₁ and θ₀ are asymptotic and initial hardening rate, respectively. Г is the cumulative shear stress, as follows: (3)Γ=∑sΔγs

Tomé et al. [33] implemented the predominant twin reorientation scheme within the VPSC framework, enabling quantitative simulation of twin-induced texture evolution and twin volume fraction development. Meanwhile model assumes that the cumulative twin volume fraction for twin system in all grains of polycrystal is expressed as follows: (4)Vacc,mode=∑g∑tVt,gwhere Vt,g=γt,g/γ0 as the volume fraction of twin [21,33], Vth,mode is critical twin volume fraction: (5)Vth,mode=Ath1+Ath2Veff,modeVacc,modewhere Ath1 and Ath2 are material constants; Vacc,mode and Veff,mode refer to the effective twin fraction and accumulative twin fraction in a grain, respectively. If Vacc,mode value exceeds Vth,mode, the grain will reorient, the Vacc,mode and Veff,mode will be updated anew. If Vacc,mode is less than Vth,mode, the process will be repeated until Vacc,mode exceeds Vth,mode. The VPSC model has become a fundamental tool for numerically modeling and evaluating plastic deformation processes and texture development.

Initial texture file and initial pole figures were simulated using the Euler angle data of magnesium alloys tested by EBSD, and grain orientation data for 2000 grains were output to save computational time. Uniaxial tension along RD and TD were simulated by the following velocity gradients represented equation, respectively. (6)LRD=[1000−0.5000−0.5] (7)LTD=[−0.5000−0.50001]

To comprehensively analyze uniaxial tensile deformation behavior of AZ31B magnesium alloy, texture evolution is examined in detail. The EBSD sampling schematic is provided in Fig. 1a. In the corresponding VPSC simulation, the x-axis corresponds to the RD, y-axis to the normal direction (ND), z-axis to the TD. Fig. 2a illustrates the IPF of the AZ31B magnesium alloy. Fig. 2b shows the initial texture and the initial pole figure. A comparison between the experimental and VPSC-calculated pole figures reveals a remarkable similarity, which verifies the feasibility of the VPSC model in the selection of grains. The analysis shows that most grains have their c-axis parallel to ND, demonstrating strong basal texture. Fig. 2c shows the grain size distribution of the AZ31B magnesium alloy, from which the average grain size was determined to be 41.2 μm. Fig. 2d presents Intragranular Misorientation Axis (IGMA) distribution and Grain boundary misorientation angle histograms. Variations in grain orientation can result in differing mechanical characteristics of the material, and these differences are usually expressed in terms of grain boundary orientations. Classification of grain boundaries into low-angle (LAGB, θ < 15°) and high-angle (HAGB, θ > 15°) types are based on the magnitude of the grain boundary orientation difference. Through IGMA analysis, it is observed that the density points are primarily concentrated along <uvt0> axis, suggesting that basal <a> slip or pyramidal <c+a> slip as primary mechanisms during uniaxial tensile deformation of the original AZ31B magnesium alloy [34]. In most cases, basal <a> slip requires lower CRSS than pyramidal <c+a> slip activation [35]. Therefore, basal <a> slip dominates the initial plastic deformation, thus guiding the parameter settings in subsequent research.

Fig. 3 displays the distributions of the initial SFs along the RD and TD. During the early deformation stages of tensile testing along RD, the average SF were determined to be 0.39, 0.39, 0.45, and 0.42, respectively. Similarly, these values were 0.38, 0.42, 0.43, and 0.43 in the TD, respectively. And the main deformation modes considered were basal <a> slip, prismatic <a> slip, pyramidal <a> slip and pyramidal <c+a> slip, with corresponding CRSS of 41, 99, 200, and 180 MPa, respectively. The critical external stress necessary to activate the specific deformation mechanism in magnesium alloys as follows [36]:

(8)σ=τCRSSMwhere τCRSS indicates the CRSS of slip system, m denotes the Schmid factor along shear direction. M is the Schmid factor. From Eq. (8), it can be observed that for a specific deformation model, the higher SF or lower CRSS can effectively activate the deformation mechanism.

The Voce hardening parameters were optimized within the self-consistent scheme (neff = 10) to accurately replicate the experimental stress-strain response. As shown in Table 2, the VPSC model incorporated six deformation mechanisms to simulate mechanical response. The Voce hardening parameters were optimized through stress-strain curve fitting. The CRSS values determined for deformation mechanisms during tensile plastic deformation were 41, 70, 99, 180, 200, and 300 MPa, respectively. Notably, this order of presentation is consistent with numerous previous studies [37]. Previous studies report the following CRSS values: 0.45–0.81 MPa for basal <a> slip, 2–3 MPa for {10-12} twinning, 39.2 MPa for prismatic <a> slip, 45–81 MPa for pyramidal <c+a> slip and 76–153 MPa for {10-11} twinning [38]. Due to influencing factors such as grain size, morphology, and defects, the simulated values for these deformation mechanisms are relative. Through a methodology combining experimental and polycrystalline theoretical modeling to obtain the CRSS ratio of prismatic <a> slip to basal <a> slip between 2–2.5 [39]. In this study, the ratio was approximately 2.4, the result is the same as previous studies. Agnew et al. [39] identified dislocation activity in both basal and prismatic <a> slip systems, indicating that the applied shear stress was sufficient to activate both deformation mechanisms, as follows: (9)σ=τbasalMbasal=τprismMprism (10)τprismτbasal=MprismMbasal (11)M=τσ=cos⁡λcos⁡φwhere σ represents the true stress, λ indicating the angle between the loading direction and the slip direction, and φ denotes the angle subtended by the applied load and slip plane normal. Following Eq. (11), when fixed loading direction, the Schmid factor value determined predominantly on the orientation of grains. In conjunction with the SF, analysis suggests that prismatic and basal <a> slip dominate during the initial deformation.

Fig. 4 compares the experimental and simulated true stress-strain curves of rolled AZ31B magnesium alloy under uniaxial tension along the RD and TD. Results reveal the VPSC model accurately captures both the hardening response characteristics and mechanical anisotropy of the alloy. Uniaxial tensile tests demonstrate significant mechanical anisotropy, with the material exhibiting yield strengths of 179 and 109 MPa along RD and TD. And the ultimate tensile strength measurements demonstrate values of 295 and 309 MPa, respectively. The marked difference between the yield strengths along TD and RD, which is due to the inhomogeneity of the initial texture that leads to the activation of different deformation mechanisms when the material during deformation along different loading directions. Furthermore, Fig. 4b further reveals a marked difference in work-hardening rates between the tensile directions, with the TD exhibiting a significantly higher rate than the RD.

Fig. 5 compares the experimental and simulated (0001) pole figures of rolled AZ31B magnesium alloy under tension along RD and TD. A comparison of the experimental and simulated results verifies the VPSC model’s accuracy in predicting texture evolution. The textures after tensile testing exhibit significant anisotropy between RD and TD. During RD tension, the texture shows a tendency to spread toward the ND and TD with a maximum pole density of 9.7, whereas during TD tension, it exhibits a clear spreading trend toward the RD with a maximum pole density of 12. This anisotropy is preliminarily attributed to differences in deformation mechanisms activation.

This study modified the Voce hardening parameters while setting sufficiently high CRSS values to suppress specific slips and twinning. This approach enables facilitates a systematic study of tensile deformation and texture in AZ31B specimens. As the key parameter in crystal plasticity modeling, τ₀ in the Voce hardening formulation physically denotes the CRSS value for deformation, with its magnitude determining the onset stress of slip or twinning mechanisms. Controlling the activation of a specific slip mechanism by modifying τ₀ (i.e., modifying the CRSS value) to establish the correlation between specific slip system activities and resultant mechanical behavior and texture evolution.

Fig. 6 presents the simulated tensile behavior along RD, while Fig. 7 quantitatively analyzes the activities of other deformation mechanisms by suppressing specific deformation mechanisms. Fig. 6 reveals simulated stress-strain curves following selective suppression of specific deformation mechanisms, thereby systematically validating the impact of individual plastic deformation modes on macroscale mechanical performance. The relative activity levels in Fig. 7a indicate the initial dominance of basal <a> slip during RD tension, owing to its low CRSS, with activation of prismatic <a> slip under favorable SF conditions. Notably, given its lower CRSS relative to other non-basal <a> slip, prismatic <a> slip activates preferentially to coordinate the deformation in <a>-axis of grains during plastic deformation. As strain accumulates, prismatic <a> slip progressively becomes dominant, while the activity of basal <a> slip correspondingly decreases. This phenomenon is caused by grain rotation, more grains are gradually transformed into the basal <a> slip hard orientation, while the CRSS value gradually increases, leading to the activation of prismatic <a> slip. Due to their substantially higher CRSS values compared to basal and prismatic <a> slip, pyramidal <c+a> and pyramidal <a> slip exhibit limited activity initially. With progressing deformation, pyramidal <c+a> slip activate to accommodate strain requirements.

Fig. 7b illustrates the suppression of basal <a> slip, which leads to a notable increase in pyramidal <c+a> slip, while prismatic <a> slip only rises during initial deformation. Meanwhile, as corroborated by Fig. 6, the predicted curves demonstrate substantial modifications when the basal <a> slip is suppressed. Mechanical characterization demonstrates that basal <a> slip activation substantially affects the deformation behavior of AZ31B alloy, causing marked decreases in both yield and tensile strength along RD. Fig. 7c presents the predictions of deformation mechanism evolution with prismatic <a> slip suppressed. The simulation results reveal a significantly increased activation in both pyramidal <c+a> and pyramidal <a> slip systems. Fig. 7d illustrates the predicted deformation mechanism under suppression of pyramidal <a> slip, revealing that only prismatic <a> slip has most notable change. Fig. 7e depicts predicted deformation mechanisms with pyramidal <c+a> slip suppressed. Analysis indicates that the initial stages of deformation have a minimal impact on the other deformation mechanisms. However, both prismatic <a> and basal <a> slips become more active later in the deformation. Consequently, the suppression of pyramidal <a> slip leads to a marked late-stage hardening response in stress-strain curves in Figs. 6 and 7f illustrate the predicted deformation mechanisms with {10-12} ET twinning suppressed, showing a minimal effect on the overall plastic deformation.

Texture evolution in plastically deformed of AZ31B magnesium alloy is predominantly governed by the activity of slips and twinning deformation mechanisms. Fig. 8 presents the predicted texture under the suppression of specific slip systems and {10-12} extension twinning in rolled AZ31B magnesium alloy during RD tension at a strain of 0.2. Following basal <a> slip suppression, it can be observed that the pole density distribution spreads to 108° from 82° in Fig. 8a. This behavior results from the inability of some grains to deform effectively after basal <a> slip suppression, which restricts dislocation motion and hinders ND grain rotation. Consequently, when basal <a> slip is suppressed, the pole figure distribution is more dispersed and the maximum polar density decreases from 9.7 to 7.8. The results show that the activation of basal <a> slip produces in a more focused grain orientation, thereby increasing the maximum pole figure density. The suppression of prismatic <a> slip promotes increased activity of both pyramidal <c+a> slip and basal <a> slip, resulting in c-axis rotation toward the TD. However, overall trend remains relatively unchanged. Fig. 8d illustrates that suppression of the pyramidal <a> slip does not alter the pole figure significantly. The suppression of pyramidal <c+a> slip intensifies prismatic <a> and basal <a> slip activity, shifting pole density from TD to ND, and raising maximum pole density. Fig. 8f reveals a clear tendency for the texture to be deflected along the ND after suppressing the {10-12} ET, indicating that the activation of the {10-12} ET drives the texture deflection along the TD [40].

Fig. 9 presents simulated the TD tensile characteristics, while Fig. 10 quantifies the activities of other deformation mechanisms under suppressed specific deformation mechanisms. Fig. 9 reveals that the curve rises notably subsequent to basal <a> slip suppression. The analysis confirms that basal <a> slip activity promotes grain rotation and is the dominant mechanism responsible for the material’s reduced yield strength. Furthermore, prismatic <a> slip not only exhibits a synergistic effect on yield strength, but also dominates the work hardening during the initial plastic deformation. Following pyramidal <c+a> slip suppression, the curve displays only a limited rise in the subsequent stage, suggesting that its activation exerts relatively small influence on mechanical properties. Throughout the tensile deformation along TD, pyramidal <a> slip and {10-12} ET show negligible influence. Given their low CRSS values, prismatic <a> and basal <a> slip are easier activated.

As shown in Fig. 10a, basal and prismatic <a> slip are the dominant mechanisms throughout the deformation process. Fig. 10b demonstrates the activation of deformation mechanisms when basal <a> slip is suppressed. Analysis confirms increased activity of prismatic <a> and pyramidal <c+a> slip, with the plastic deformation previously accommodated by basal <a> slip now being redistributed through these two activated slip mechanisms. Fig. 10c illustrates the evolution of deformation mechanisms following prismatic <a> slip suppression. Due to the critical role of prismatic <a> slip in deformation coordination, its suppression induces substantial modifications in the deformation mechanisms. The analysis reveals enhanced the activation of basal <a> slip, while both pyramidal <c+a> and pyramidal <a> slip activate increases with accumulated strain. Additionally, {11-22} CT demonstrates only minor activity. As evidenced in Fig. 10d–f, pyramidal <a> slip, pyramidal <c+a> slip, and {10-12} ET have minimal influence on tensile deformation along the TD.

Fig. 11 presents the predicted texture in rolled AZ31B magnesium alloy during TD tension at strain of 0.24 under specific slip systems and {10-12} ET suppression. It is evident that a significant degree of texture spreading occurs toward the RD when prismatic <a> slip is suppressed, with the maximum pole density decreasing from 12 to 8.3. This phenomenon originates from the predominance of prismatic <a> slip during TD deformation. Fig. 11b demonstrates basal <a> slip suppression markedly increases pyramidal <c+a> slip activity, causing a significant redistribution of the pole density toward TD and a reduction in maximum pole density. (10-10) pole figure reveals that after suppression of basal <a> slip, some grains cannot be activated efficiently and the grain rotation is hindered leading to an obvious spreading of the pole figure from the ND toward the center. The results shown in Fig. 11c indicate a distinct redistribution of the pole figure into a toroidal shape following prismatic <a> slip suppression and (10-10) pole figure exhibits pronounced texture modifications. This phenomenon primarily results from the significant activation of pyramidal <a> and pyramidal <c+a> slip following prismatic <a> slip suppression. Furthermore, a small amount of {11-22} compression twinning activity contributes, deflecting the <a>-axis to accommodate strain. Fig. 11d–f reveals that pyramidal <a> slip and {10-12} ET exhibit negligible influence on the pole figure. Pyramidal slip has a relatively minor effect, increasing the maximum pole density from 12 to 13 while leaving the overall distribution trend largely unchanged.