Engineering Materials and Their Applications
Investigation of the Cause of Serration Generation in Al-Mg Alloy Using In-situ XRD/DIC Simultaneous Measurement
2025 Volume 66 Issue 1 Pages 117-122
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2025 Volume 66 Issue 1 Pages 117-122
Type-B serrations were observed during room-temperature tensile deformation of Al-2.17 mass%Mg alloy with an average grain size of 12 µm. Digital image correlation was used to visualize Portevin-Le Chatelier (PLC) bands, and microstructural changes in these bands were observed by in-situ X-ray diffraction measurements using synchrotron radiation at SPring-8. The results indicated that the overall density of dislocations, including both mobile and pinned dislocations inside the PLC bands, increased substantially as the bands formed. This suggests that serration occurs due to an increase in the mobile dislocation density resulting from the formation of new dislocations from sources inside the PLC bands.
This Paper was Originally Published in Japanese in J. JILM 73 (2023) 628–632.
Fig. 8 Change in stress (black line), lattice strain (dash line) and dislocation density (gray line) from 333.83 to 345.22 s.
When tensile deformation is applied to Al-Mg alloys, serrated stress oscillations called serrations are sometimes observed on the stress-strain curve, which is called the Portevin-Le Chatelier (PLC) effect [1–12]. Various shapes of serrations have been reported, including Type A with relatively large load fluctuations and long onset period and Type B with relatively small load fluctuations and short onset period, which are affected by microstructures such as alloy composition, grain size, temperature, strain rate, and deformation conditions [1–6, 9, 11, 12]. In addition, the occurrence of serration causes a localized band-like deformation pattern (Portevin-Le Chatelier band: PLC band) to appear on the specimen surface, which is considered to be a problem because it spoils the appearance of the product.
As a cause of serration in Al-Mg alloys, the mechanism that dislocations adhered by Mg atoms are simultaneously released from the adherence due to increased stress and the number of mobile dislocations increases has been reported in many cases [1, 2, 6, 13]. On the other hand, another mechanism, although less common, is thought to be caused by an increase in mobile dislocations from dislocation sources such as grain boundaries [3, 6, 14]. Although both mechanisms agree that serration is caused by an increase in mobile dislocations due to increased stress, it is not clear which theory is correct because the factors that increase mobile dislocations are different and there are no examples of direct observation of the inside of the generated PLC bands. However, it is not clear which theory is correct so far.
The authors have investigated microstructural changes in various Al alloys, such as dislocation density and dislocation microstructure, by performing in-situ XRD measurements during tensile deformation using synchrotron radiation [15–19]. In this study, we used the Digital Image Correlation (DIC) method [12, 13, 18, 20, 21] to observe the occurrence behavior of PLC bands on the surface of tensile specimens, while performing in-situ XRD measurements with high temporal resolution to determine the PLC bands at the X-ray irradiated position before and after the moment of PLC band formation. The microstructural changes before and after the moment of the PLC band formation at the X-ray irradiation position were investigated by using the DIC method. The cause of serration in Al-Mg alloys was examined.
In this study, rolled Al-2.17 mass% Mg alloy sheet with 1 mm thickness provided by UACJ, Inc. was used. Table 1 shows the chemical composition. The plate was annealed in an air furnace under the conditions of 448 K 1.8 ks+643 K 1.8 ks to remove the strain introduced by rolling. The cross section (RD-ND plane) of the annealed material was polished using emery paper, alumina, and colloidal silica, and electron backscatter diffraction (EBSD) measurements were made using a TSL OIM mounted on a JEOL JSM-6500F field emission scanning electron microscope to observe grain structure. Tensile specimens were cut from the annealed material using an electric discharge machine so that the parallel sections were parallel to the rolling direction (Fig. 1).
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Dimensions of tensile test piece in mm.
The tensile specimens with a random-pattern painted on the surface were mounted on a small tensile testing machine installed on a goniometer at BL46XU, SPring-8, and X-rays were injected from the direction normal to the parallel part of the specimen. A schematic diagram of the measurement system is shown in Fig. 2. The incident position of the X-rays was always fixed. The X-ray energy was 30 keV, and the cross-sectional shape of the X-ray beam was 0.5 mm in the specimen width direction and 0.2 mm in the tensile direction. A wide-range one-dimensional detector consisting of six DECTRIS-MYTHEN one-dimensional detectors was installed at 18.5° above the transmission direction, and a slit of 4 mm width was placed just before the detection plane. The distance from the specimen to the detector is 711.07 mm, and a diffraction angle range of 2θ = 2.8 to 34.2° can be measured simultaneously. The camera for DIC measurement was placed 16° to the right in the horizontal direction from the transmission direction, and the illumination was placed on the opposite side 16° to the left.
Schematic illustration of in-situ XRD/DIC simultaneous measurement system.
Changes in diffraction peaks from the (111), (200), (220), (311), (222), and (331) planes were measured at a time resolution of 0.2 s at room temperature while tensile deformation was performed at an initial strain rate of 3.3 × 10−4 s−1 until the specimen fractured. From the obtained diffraction peaks, the diffraction angle θ and the width at half maximum Δ2θ were obtained, and the inhomogeneous strain η was calculated using the following Williamson-Hall formula. The diffraction peak of CeO2 powder was used as the instrumental function.
| \begin{equation} \frac{\varDelta 2\theta \cos \theta}{\lambda} = \frac{0.9}{D} + 2\eta \frac{\sin \theta}{\lambda} \end{equation} | (1) |
where D is the crystallite size and λ is the wavelength [22, 23]. The obtained η was substituted into the (2) equation to obtain the dislocation density ρ [23].
| \begin{equation} \rho = 16.1 \times \left(\frac{\eta}{b} \right)^{2} \end{equation} | (2) |
where b is the magnitude of the Burgers vector [23], b = 0.286 nm.
The crystal plane spacing d was calculated from the diffraction angle using the following equation.
| \begin{equation} \lambda = 2d\sin \theta \end{equation} | (3) |
The lattice strain e was further obtained by substituting d into eq. (4), where d0 is the unloaded crystal plane spacing. The obtained lattice strain is the average elastic strain in the direction normal to the diffraction plane.
| \begin{equation} e = \frac{d - d_{0}}{d_{0}} \end{equation} | (4) |
Local strain changes and strain rate changes on the specimen surface were obtained from the coordinate changes of random patterns on the specimen surface as the tensile deformation progresses. Correlation Solutions VIC-2D was used for the analysis.
We visualized the PLC bands from DIC measurements and investigated the dislocation density change and lattice strain change when PLC bands are formed by chance at fixed X-ray irradiation positions.
The reverse pole figure orientation map of the RD-ND cross section of the 448 K 1.8 ks+643 K 1.8 ks annealed material is shown in Fig. 3. Equiaxed grains with a grain size of 12 µm were observed, which are considered to be recrystallized structure.
TD IPF map of ND-RD plane in Al-2.17 mass% Mg alloy subjected to cold-rolling and subsequently annealed at 448 K for 1.8 ks + at 643 K for 1.8 ks and the color key. (online color)
The stress-stroke change (upper axis: tensile time) curve obtained during simultaneous in-situ XRD/DIC measurement during tensile deformation is shown in Fig. 4(a). The stroke change was calculated by dividing the stroke length change by the initial stroke length. In this study, since a small tensile testing machine of our own design was used, the rigidity of the testing machine was low, and the stroke change is considered to include the amount of deformation of the testing machine. After the yield point drop was observed, Luders deformation was observed, followed by the onset of serration, and Fig. 4(b) shows a magnified view from 333.49 s to 345.54 s. One stress oscillation consisted of a gradual stress increase and a sudden stress decrease, with an average stress oscillation width of about 6 MPa, and the average period was 0.8 s. The short period can be classified as Type B serration. The time resolution of the in-situ XRD measurements in this study was 0.2 s, which was sufficiently smaller than this serration period. The slope of the serration at increasing stress was almost the same for all serrations, averaging 16.9 GPa, which is consistent with the slope of 16.9 GPa in the elastic deformation region before yielding, suggesting that the entire specimen is deformed by elastic deformation at increasing stress. The fact that the slope in the elastic deformation region and serration stress increase is smaller than Young’s modulus of aluminum and the strain rate of the specimen during elastic deformation is smaller than the initial strain rate is due to the low rigidity of the small tensile testing machine used in this study as mentioned above.
(a) Nominal stress-Stoke change and test time curve of Al-2.17 mass% Mg alloy and (b) enlarged curve from 333.49 to 345.54 s.
Figure 5 shows the variation of local strain rate in the tensile direction on the specimen surface obtained by DIC measurement. Figure 6 shows the variation of local strain in the tensile direction during the measurement time range corresponding to Fig. 5. Between 333.83 s and 336.59 s, the PLC bands formed and disappeared repeatedly and did not propagate continuously, since new PLC bands were formed adjacent to the previously formed one. At 335.46 s, the PLC band formed at the X-ray irradiated position suggesting that X-rays irradiated the edges of the formed PLC band at 334.08 and 336.46 s.
Time change of local strain rate in tensile direction from 333.83 to 345.22 s on the specimen surface and color bar indicate the amount of strain rate. The black arrow indicates the X-ray irradiation position (x = 0). (online color)
Time change of local strain in tensile direction from 333.83 to 345.22 s at the width center of specimen and horizontal axis, x corresponds to the position in Fig. 5.
At 337.84 s, PLC bands were formed at the shoulders of the specimen parallels, and then at 340.22 s, new PLC bands were formed at a distance from the PLC bands formed between 333.84 s and 336.59 s. At this time, X-rays were irradiated to areas where no PLC bands were formed. At first glance, the PLC bands appear to form at random locations, but Fig. 6 shows that they preferentially form at locations where the strain is locally small. The formation of these PLC bands coincides with the time of stress drop shown in Fig. 4(b).
Figure 7 shows the XRD pattern measured at 0.2 s time resolution. Only aluminum diffraction peaks were observed, confirming that the alloy is in solid solution. The diffraction peak from the (220) plane, which has the lowest diffraction intensity, has a count of about 1000, which is sufficient for the following analysis. Figure 8 shows the nominal stress and the changes of the lattice strain and dislocation density at the position of X-ray irradiation from 333.83 s to 345.22 s. The changes in stress and lattice strain correspond very well. This is because the lattice strain represents the average amount of elastic deformation and the stress is proportional to the amount of elastic deformation even during plastic deformation. This can be understood from the fact that in Fig. 8, the nominal stress divided by the lattice strain is 61.5 GPa, a value close to Young’s modulus of aluminum [24].
XRD pattern from specimen with an exposure time of 0.2 s before tensile deformation.
Change in stress (black line), lattice strain (dash line) and dislocation density (gray line) from 333.83 to 345.22 s.
As shown in Fig. 5, the PLC band formed and disappeared at the X-ray irradiation position around 335 s. At this instant, a rapid increase in dislocation density of about 5 × 1013 m−2 was observed. From 338.44 s to 345.10 s, when the PLC band was formed outside the X-ray irradiated region, only fluctuations within the measurement error were observed in the dislocation density in the X-ray irradiated region and the increase in dislocation density around 335 s can be attributed to the increase in dislocation density associated with the formation of the PLC band.
Figure 9 shows the relationship between the amount of increase in dislocation density Δρ and the amount of stress drop Δσ when the PLC band forms and disappears in the X-ray irradiated region from the start of tension to rupture. There is a correlation between the amount of increase in dislocation density and the amount of stress drop, suggesting that the increase in dislocation density is the cause of the stress drop.
Relationship between increase in dislocation density and amount of stress reduction accompanied by PLC band formation.
Here, we discuss the dislocation density obtained by XRD. As is clear from eqs. (1) and (2), the dislocation density is obtained from the amount of heterogeneous strain formed around the dislocations, so the dislocation density obtained from XRD measurement this time does not distinguish between mobile dislocations and locked dislocations, and is the total dislocation density in the X-ray irradiation region. In other words, the dislocation density obtained by XRD does not change if dislocations locked to Mg atoms are detached from the Cottrell atmosphere and become mobile dislocations due to increased stress, and the increase in dislocation density observed by XRD suggests that new mobile dislocations are generated from the dislocation source during the formation of the PLC band. The increase in dislocation density observed by XRD suggests that new mobile dislocations were generated from the dislocation source when the PLC band formed.
Strain rate in tensile deformation $\dot{\varepsilon }$ is the strain rate produced by elastic deformation $\dot{\varepsilon }_{el}$ and the strain rate produced by plastic deformation $\dot{\varepsilon }_{pl}$. The strain rate in tensile deformation can be expressed as the sum of
| \begin{equation} \dot{\varepsilon} = \dot{\varepsilon}_{el} + \dot{\varepsilon}_{pl} \end{equation} | (5) |
Also, the $\dot{\varepsilon }_{pl}$ can be expressed by the density of mobile dislocations ρm and the average velocity of dislocations v, $\dot{\varepsilon }$ can be expressed as,
| \begin{equation} \dot{\varepsilon} = \dot{\varepsilon}_{el} + 2\rho_{m}bv \end{equation} | (6) |
In the region of increased stress in serration ρm ≅ 0. Therefore, eq. (6) becomes $\dot{\varepsilon } \cong \dot{\varepsilon }_{el}$ i.e., the whole deformation is almost solely elastic, and the stress increases due to the increase in elastic strain.
If the dislocation source is activated in a certain region due to increased stress and ρm rapidly increased, $\dot{\varepsilon } \cong \dot{\varepsilon }_{pl} = 2\rho_{m}bv$ and plastic deformation causes localized deformation (PLC bands formation). Then, since the flow stress of the mobile dislocation is lower than the stress increased by the increase in elastic deformation, the stress drops rapidly with the formation of the PLC band. In plastic deformation, the flow stress σ can be expressed as follows [25, 26].
| \begin{equation} v = \left(\frac{\sigma}{D}\right)^{n} \end{equation} | (7) |
where D and n are constants that vary with material and microstructure. Also, from eq. (6)
| \begin{equation} \sigma = D\left(\frac{\dot{\varepsilon}_{el}}{2\rho_{m}b}\right)^{1/\text{n}} \end{equation} | (8) |
Therefore, it can be assumed that the more mobile the dislocation density ρm is larger, i.e., the larger the increase in dislocation density Δρ determined by XRD, the smaller the flow stress and the larger the stress drop at serration, which could explain the experimental results in Fig. 9.
However, it is not clear whether the local deformation of the PLC band is caused only by the mobile dislocations generated by the dislocation source. This is because it is possible that an increase in the number of dislocations generated by the dislocation source triggers a kind of dislocation avalanche, in which the surrounding dislocations that had been locked are detached from their Mg atoms [14]. However, as shown in Fig. 8, there is a correlation between the amount of increase in dislocation density generated from the dislocation source and the amount of stress drop, so it is expected that either there is a correlation between the amount of dislocations generated from the dislocation source, or that the amount of dislocations detached from the locking point is small.
The changes in lattice strain and dislocation density associated with the formation and annihilation of PLC bands were investigated by simultaneous in-situ XRD/DIC measurements during tensile deformation of an Al-2.17 mass% Mg alloy with a grain size of 12 µm using synchrotron radiation at SPring-8. The results were as follows,
The authors are grateful to UACJ Inc. for providing the samples used in this study. The synchrotron radiation experiments were performed at BL46XU of SPring-8 with the approval of Japan Synchrotron Radiation Research Institute (JASRI) (Proposal No. 2019A1809 and 2021A1673).
