2.1 Process principle

Staggered extrusion is a bending profile forming process in which the cross-section of the traditional convex mold extrusion direction is changed from a rectangle to a stepped structure. During the loading process, due to the force of the biased load on the billet, the billet exhibits flow diversion behavior. A part of the billet flows towards the gap and fills the space between the convex mold and the sleeve, while another part fills the core mold cavity. The billet as a whole flows downward and is extruded from the core mold cavity to form the desired shape. Staggered extrusion causes deformation of the billet and leads to biased stress distribution within the billet. There is a flow inconsistency at the core mold cavity, resulting in a gradient difference in flow velocity distribution and a linear change in velocity distribution. The extruded profile exhibits certain bending characteristics, which is the principle of staggered extrusion forming. Figure 1 shows the complete process of staggered extrusion. The device includes the convex mold (the height difference between the vertical directions of the left and right convex molds is referred to as the mismatch value h, and the horizontal difference is referred to as the eccentricity value e), billet, split core mold, sleeve, base, etc. The split core mold is adopted for easy removal of the bent profile after extrusion. To prevent the core mold from breaking during extrusion due to excessive pressure, an appropriate sizing belt is set on the core mold to reduce the pressure during extrusion. Then, the core mold, billet, and convex mold are aligned and placed into the sleeve, and heated to the specified temperature. For convenience, in this study the eccentricity value of e=10 mm is defined as SEE1, e=20 mm as SEE2, and e=30 mm as SEE3.

Figure 1全屏查看

Diagram of stagger extrusion process (Unit: mm)

2.2 Experimental plan

The experimental material used was commercially available extruded AZ31 magnesium alloy with the chemical composition shown in Table 1. The billets used in the study were cylindrical with a diameter of 40 mm and a height of 50 mm. The extrusion ratio was calculated to be 11.01, and the extrusion speed was set at 1 mm/s. For easy specimen retrieval, a split-core mold was used, with water-based graphite as a lubricant. First, the sleeve was evenly divided into four sections and labeled accordingly. The boundary of the split-core mold was marked at the top of the staggered stem. Graphite was applied to the surface of the core mold, aligning the boundary of the core mold with the horizontal marks on the sleeve. Next, the billet and staggered stem were placed inside the extrusion cylinder. The top of the staggered stem was marked corresponding with the direction of the core mold. A caution line was marked on the punch to prevent collision with the core mold and ensure safety. The extrusion direction was also marked on the sleeve. The assembly is then placed in a resistance furnace and heated to 350 ℃ for 30 min for preheating. Afterward, the assembly was taken out for the staggered extrusion forming process. To preserve the microstructure, the extruded curved samples were cut and water-quenched after the experiment.

2.3 Microstructure testing

In order to investigate the influence of shear behavior of the staggered stem on the microstructure and structural changes of the bent profiles, samples were cut from typical sections of the extruded profiles for observation and analysis. The size of the cut samples was 3 mm×3 mm× 2.5 mm. The preparation of the samples involved grinding with silicon carbide sandpaper (80#, 400#, 1000#, 2000#, 3000#, 5000#). The surfaces were then polished using 1 µm diamond polishing suspension and water-based lubricant. After polishing, the surface was etched using a mixed solution of 1 mL acetic acid, 1 mL nitric acid, 1 g oxalic acid, and 150 mL water for 3 s. The microstructure was observed using a metallographic microscope. Electrolytic polishing using phosphoric acid (60 mL) and alcohol (100 mL) was performed on the samples. Electron backscatter diffraction (EBSD) testing is conducted on the TD-ED direction of the profiles, using a working voltage of 20 kV and an electrolysis time of 120 s.

2.4 Mechanical properties testing

To test the strength and ductility of the magnesium alloy, mechanical properties were generally tested along the direction of extrusion, which was the flow direction of the extruded profiles. In this study, due to the bent shape of the profiles, samples were taken along the reverse direction of the bending tangent as much as possible, to account for shape limitations. To ensure the accuracy of the experimental data, each test was performed 5 times. Tensile tests were conducted at room temperature, with a test speed of 1 mm/min. Before testing, the sample surfaces were polished with sandpaper to remove surface oxides and defects, ensuring a smooth surface. The tensile strength, yield strength, and elongation at fracture of the samples were obtained. The fracture morphology of the tensile samples at room temperature is observed using a Quanta 200F Field Emission Scanning Electron Microscope to determine the fracture type and clarify the fracture mechanism.

3.1 Curvature feature

The clearance between the convex mold and the deformity of the billet are the two primary factors that determine the curvature of the bent component. Therefore, the curvature of the bent component obtained under different conditions is measured and calculated. The two endpoints of the bent component obtained under different conditions are placed on the same horizontal line. By connecting these two endpoints to form a straight line, equidistant points are selected on the line. Assuming that the bending height of both endpoints is 0 mm, the curvature radius of each point is measured. Taking 13 equidistant points as an example, as shown in Figure 2(a), the curvature radius of each point is calculated, as shown in Figure 2(b). Three bent components with equal horizontal lengths are chosen for curvature measurement. The maximum bending heights of the bent components are (18.1±0.5) mm, (17.2±0.5) mm, and (8±0.5) mm, respectively. As the eccentricity increases, the bending height of the bent component also increases. The greater the eccentricity, the more pronounced the change in the bending height.

Figure 2全屏查看

Curvature measurement: (a) Principle of bending radius method; (b) Bending height distribution of bending members

3.2 Mechanical properties

Figure 3 presents the engineering stress-strain curves for the initial billet and extruded profiles obtained from room temperature tensile tests conducted parallel to the axial direction. After the SE process, compared to the billet, the elongation (EL) increased to 10.5%, 12.1%, 15.9%, respectively, and the tensile strength improved to 250, 270 and 235 MPa. As mentioned earlier, DRX occurred during misalignment extrusion, resulting in grain refinement. The significant increase in tensile strength and elongation compared to the billet indicates the strengthening effect of grain refinement on the properties of material. In SEE1, both the yield strength and elongation are lower than those in SEE2. This can be attributed to changes in grain size at different parameters. The larger grain size corresponds to lower yield strength and tensile strength, which is consistent with the Hall-Petch formula. The changes of grain size and microstructure on mechanical properties need to be further analyzed.

Figure 3全屏查看

Engineering stress-strain curve of initial billet and extruded profiles

3.3 Fracture analysis

Figure 4 shows the fracture morphology and SEM characterization results, along with local magnified images, for the original billet and different eccentricities under staggered extrusion. In Figure 4(a), the original billet sample exhibits numerous intergranular fractures (indicated by yellow arrows) and intergranular steps. Additionally, transgranular fractures can be observed in the dimple area. Intergranular fractures and intergranular steps are characteristic of brittle fracture. Their occurrence is attributed to the increase in internal dislocations within the coarse grains during tension, where the internal slip bands have undergone a decrease in their strength and ductility, leading to crack propagation and transgranular fracture. On the other hand, misalignment extrusion achieves the goal of grain refinement through dynamic recrystallization. Furthermore, through the local magnified images in Figures 4(e) and (f)), it can be observed that there are a significant number of dimples (indicated by red arrows) within the fracture surface. Therefore, the alloy exhibits transgranular fracture during failure, indicating that misalignment extrusion promotes ductile fracture. The plastic deformation of the billet during extrusion enhances the strength and ductility of the magnesium alloy.

Figure 4全屏查看

Fracture SEM analysis of (a) billet, (b) SEE1, (c) SEE2, and (d) SEE3; Local amplification (e) SEE1, (f) SEE2, and (g) SEE3

3.4 Grain misorientation angles of boundary and grain size

To study the relationship between grain orientation and grain boundaries, Figure 5 shows the inverse pole figure (IPF) and the percentage of grain misorientation angles of boundary. The colors in the figure correspond to different grain orientations: red represents grains with (0001)//ED orientation, green represents grains with orientation, and blue represents grains with orientation. Grain misorientation angles of boundary of 2°-15° are generally classified as low-angle boundaries and represented in white, while grain misorientation angles of boundary greater than 15° are classified as high-angle boundaries and represented in black [20-23]. In the figure, most of the grains are red, indicating that the grains are predominantly oriented parallel to the (0001) direction due to the triaxial compressive stress during the extrusion process. In Figures 5(d)-(f), the percentages of low-angle boundaries are 12.3%, 21.4% and 13.6%, respectively. This is because the shear deformation caused by the die in the extrusion process induces less non-uniform deformation in the billet under the SEE1 process, resulting in fewer low-angle boundaries (LABs). As the eccentricity increases to SEE2, the non-uniform deformation of the billet increases, providing sufficient energy for lattice distortion and leading to an increase in dislocations, which in turn generate a large number of LABs through slip. However, as the eccentricity further increases to SEE3, the LABs decrease. This is because more severe reverse flow occurs during the die extrusion process, resulting in the generation of significant frictional and deformational heat in the billet, providing energy for the growth of recrystallized grains. At the same time, grain growth relies on grain boundary migration. The driving force for grain boundary migration is directly proportional to the grain boundary energy. As the misorientation between grain boundaries increases and the degree of grain distortion increases, the interfacial energy also increases, making grains with high-angle boundaries (HABs) more likely to grow. In Figures 5(g)-(i), the grain sizes are 15.98, 12.28 and 20.32 µm, respectively.

Figure 5全屏查看

IPF maps of (a) SEE1, (b) SEE2, and (c) SEE3; Grain boundary diagrams of (d) SEE1, (e) SEE2, and (f) SEE3; Grain size diagrams of (g) SEE1, (h) SEE2, and (i) SEE3

3.5 Twinning analysis

In order to illustrate the influence of twinning on crystal orientation, the red color in Figure 6(a) represents the twinned crystal. Different morphologies of twin grains were selected from Figure 4 for analysis. Based on the specific misorientation and rotation axis between the twin and its parent crystal (<1210> axis 86.3°±5°), the twin variants and their relationship with the parent crystal can be clearly identified, as shown in Figures 6(b) and (f). In G₁, the twin variants actively interact with and intersect the surrounding grains, depleting the parent grains P significantly (Figure 6(b)). The corresponding (0001) pole figure (Figure 6(b)) and inverse pole figure (Figure 4(c)) reveal that the T₁ grain, which undergoes a lattice rotation of 86°±5°, features a fiber texture. The grain orientation is finally confirmed to be 86.3° through point tracking in Figure 6(d). T₁ penetrates almost across the entire grain P (Figure 6(i)). T₁ exhibits a slightly deviated fiber orientation at around 30°. In Figure 6(e), T₁, T₂, T₃ and T₄ still maintain their typical elongated shape, with T₁ showing a preferential growth (Figure 6(e)). T₁ belongs to the fiber orientation, with a slight deviation of 12° from // ED, while T₂, T₃ and T₄ deviate significantly from the fiber orientation (Figures 6(c) and (g)). Based on these observations, it can be inferred that twin is responsible for the reorientation of the initial grains, promoting the formation of the fiber texture during the early stages of extrusion. Further elucidation is provided on the twinning behavior of and its impact on grain orientation, as well as the selection mechanism of twin variants.

Figure 6全屏查看

Twin analysis ((b-e), (f-i) are partial enlarged detail in (a))

3.6 Recrystallization mechanism

Through the analysis above, it is found that the microstructure of I-beam curved profiles changes during the forming process due to the different eccentricities of the misalignment extrusion die. Figures 7(a)-(c) show the volume fractions of recrystallized grains, subgrains, and deformed grains for three different parameters of misalignment extrusion. The blue color represents recrystallized grains, the yellow color represents subgrains, and the red color represents deformed grains. From Figure 7(d), it can be seen that at SEE1, the proportion of deformed grains is the highest at 61%, at SEE2 the recrystallized grains gradually increase to 28%, and at SEE3 the highest proportion of recrystallized grains is 58%. This indicates that as the eccentricity e increases during the misalignment extrusion process, the uneven deformation of the billet increases, leading to the generation of a large number of dislocation accumulations and the formation of subgrains. With the increase in the amount of deformation provided, the subgrains gradually transform into dynamically recrystallized grains. To further investigate dynamic recrystallization, the grains were further analyzed. From Figure 7(a), it can be observed that the deformed grain boundaries exhibit a “serrated” shape [24-26]. It is found that the deformed grains have a bow-out shape, and subgrains and recrystallization are found near them. which is a typical feature of DDRX mechanism. In Figure 7(b) under the SEE2 process, when the proportion of deformed grains decreases to 31%, it is found that recrystallization and subgrains occur near the deformed grains with a bulging shape, and the transformation from LABS to HABS dominates. This is the main characteristic of CDRX, indicating that the recrystallization process involves both CCRX and DDRX. As shown in Figure 7(c), a large number of twins are found, resulting in the misalignment of twin boundaries and the occurrence of twin-induced recrystallization (TDRX) process, leading to a significant increase in recrystallized grains.

Figure 7全屏查看

Recrystallization: (a) SEE1; (b) SEE2; (c) SEE3; (d) Recrystallization volume ratio

3.7 Kernel average misorientation

In order to investigate the relationship between heterogeneous deformation and dislocations during plastic deformation, KAM is called kernel average misorientation, which is a method to characterize the local mismatch angle in EBSD data analysis, as shown in Figures 8(a)-(c), where a higher KAM value is represented by a greater amount of green color, while lower values are represented by blue color. In Figure 8(a), the highest amount of green color indicates a higher KAM value, suggesting larger strains within the grains. The average misorientation angles were calculated to be 1.131, 0.729, and 0.379 for each case, respectively. At the same time, in SEE1, most of the grains were deformed grains, and the local deformation inhomogeneity caused severe dislocation accumulation and strain gradient. Figure 8(a) shows different grain colors indicating significant misorientation, leading to the accumulation of dislocations at grain boundaries, ultimately resulting in an increase in θ_KAM. In SEE2, the uneven deformation of the billet provided sufficient energy for the occurrence of continuous dynamic recrystallization. Additionally, the shear deformation of the billet consumed a large number of dislocations and reduced local strain concentration. As shown in Figure 8(c), in SEE3, most of the grains exhibit a blue color. This is because the peculiar structure of the die results in the longest reverse extrusion time, and the billet may undergo static recovery while providing energy through shear deformation. The opposite-sign dislocations within the grains offset each other, reducing local strain and decreasing the misorientation angles at grain boundaries, simultaneously reducing θ_KAM and increasing the alloy’s ductility. As shown in Eq. (1), GND represents the density of geometrically necessary dislocations (GND density), θ_KAM represents the average local misorientation within the EBSD scanning area, μ is the scanning step size, and in this chapter, a step size of 1 μm was used. b represents the Burgers vector, which in this chapter has a value of 0.286 nm. It can be observed that the distribution of GND follows a linear relationship with KAM values. The calculated values of GND were 7.91×10¹⁴/m², 5.10×10¹⁴/m² and 2.65×10¹⁴/m², which correspond to the values of KAM.

Figure 8全屏查看

Crystal grain orientation graphs and kernel average misorientation KAM: (a) SEE1; (b) SEE2; (c) SEE3; : (d) SEE1; (e) SEE2; (f) SEE3

(1)

3.8 Schmid factor

The influences of internal material anisotropy can be more comprehensively explained by considering basal <a> slip, prismatic <a> slip, pyramidal <a> slip, and pyramidal <c+a> slip. Figure 9 illustrates the difficulty level of activation for different slip systems in various regions. From the observation of the figure, it can be seen that in SEE1, the Schmid factors for basal <a> slip, prismatic <a> slip, and pyramidal <c+a> slip are 0.281, 0.153 and 0.399, respectively. In SEE2, the Schmid factors for basal <a> slip, prismatic <a> slip, and pyramidal <c+a> slip are 0.299, 0.118 and 0.403, respectively. In SEE3, the Schmid factors for basal <a> slip, prismatic <a> slip, and pyramidal <c+a> slip are 0.243, 0.141 and 0.411, respectively. It is well known that the larger the SF value, the easier the slip is to open.

Figure 9全屏查看

Schmid factor of AZ31 alloy extruded at different eccentricity: (a-c) SEE1; (d-f) SEE2; (g-i) SEE3

From Figures 9(c), (f), (i), it can be observed that misalignment extrusion activates mainly basal <a> slip and pyramidal <c+a> slip, as HAN et al [27, 28] discovered that shear strain can promote the activation ofpyramidal <c+a> slip, thus altering the texture type of magnesium alloys. Decreased Schmid factors for basal slip were observed in the same alloy under misalignment extrusion, which is beneficial for improving the plasticity and strength enhancement of the extruded alloy. Additionally, the activation of pyramidal <c+a> slip contributes to the enhancement of plasticity. The presence of twins [29] in SEE3 indicates that twins can promote basal <a> slip and prismatic <a> slip, further confirming that twins can improve the performance of the alloy.

3.9 Pole figures and inverse pole figures

Figure 10 shows the pole figures and inverse pole figures for different eccentricities under misalignment extrusion. In Figure 10(a), for the SEE1 region, the pole figure exhibits a bimodal structure, with the c* axis of the grains parallel to the ED direction and a pole density of 10.98. XU et al [30-32] proposed that the introduction of shear strain during the extrusion process of magnesium alloys causes a deviation in the basal texture and suggested that this is due to the activation of pyramidal <c+a> slip, leading to texture type alterations. In Figure 10(b), the c* axis of the grains is parallel to the ED direction, with a maximum pole density of 12.68. The inverse pole figure also reveals a strong presence of the basal orientation, confirming the activation of basal slip as indicated by the Schmid factor. Additionally, due to lower shear strain values, some grains may undergo dynamic recrystallization. As for SEE3, it experiences the least shear stress, resulting in the highest degree of deformation for the grains. The newly formed grains maintain their original orientation, as shown in Figure 10(c), with a pole density of 23.34. Additionally, this region exhibits the highest texture strength, indicating that misalignment extrusion leads to heterogeneous deformation of the billet, resulting in an increase in pole density in the pole figures.

Figure 10全屏查看

Polar and inverse polar graphs of different eccentricity: (a, d) SEE1; (b, e) SEE3, SEE2; (c, f) SEE3