2021 年 62 巻 11 号 p. 1673-1676
Tomographic images with absolute units have been reconstructed successfully from Small Angle X-ray Scattering (SAXS) intensities of an interdiffusion layer of a precipitation strengthened model alloy cut from a multilayered Al/Al–Zn/Al sample after heat treatment. Cross sectional images of specimen with Zn concentration distribution was obtained from the absolute X-ray mass attenuation coefficient; the volume fraction of precipitates from the absolute SAXS integrated intensity in each voxel. Mechanical property of the same cross-section was estimated from the nanostructure and composition obtained for each voxel determined by the reconstructed images.
Composite materials with the combination of multiple component materials have already being widely used to fulfil the growing demands of multi-functional properties such as superior electrical, environmental, mechanical properties in vehicles, aerospace industry etc. In these composite materials, the property in the bonding area, e.g., the welded joint, is known to be deviated from the adjacent similar/dissimilar bulk materials.1–4) For this reason, it is important to assess the property within the bonding area when designing the whole composite. In the metallic composite, especially the clad composites which composed of metallic alloy layers, compositional modulation is often observed in a mesoscopic scale as a result of interdiffusion during production or artificial heat treatments. In such interdiffusion layers, local nanostructures, precipitation for example, changes with the modulating local composition, and this nanostructure distribution determines the local mechanical property.5) Small-Angle X-ray Scattering (SAXS) method is a well-established approach to evaluate nanostructure distribution in a specimen over a macroscopic area illuminated with incident X-ray nondestructively.6–11) So in the previous study,6) we demonstrated the visualization of composition and the integrated intensity from SAXS measurements using relative units, with the focus on a model material of interdiffused 3-layered Al/Al–Zn/Al composite.
Unlike conventional computed tomography study for medical use, we are focusing on interpreting the mechanical property inside the specimen by the assessment of nanostructure distribution. Hence, a quantitative and nondestructive analysis on nanostructure distribution in a 2D cross-section of the specimen is presented in the present work. In this study, we have successfully reconstructed a layer of absolute absorption coefficient (scalar) tomography without using any standard specimen, and the absolute profiles of scattering intensity, also the following total integrated intensity following a standard procedure of quantitative SAXS measurements.12,13) Reconstruction was performed using the method of Convolution Back-Projection (CBP) method.14)
Specimen used in the present work is a pillar with a rectangular cross section approximately 400 µm × 800 µm cut from 3-layered Al/Al–Zn/Al composite sheet, perpendicular to the interdiffusion direction, as shown in Fig. 1(a).
(a) Illustration of 3-layered composite and the cutting process of pillared specimen. (b) SEM image of a cross-section of specimen. (c) 2D EDX result of Zn concentration. (d) Zn concentration profile from tomography and EDX.
The three-layered sandwich composite with pure Al and an Al–Zn alloy has been studied in the previous study15) by 1D scanning. As shown in Fig. 1(a), as well as the previous study,15) the top and bottom layer corresponds to pure Al, and the middle layer corresponds to Al–14.07 wt% Zn alloy. All layers have a uniform thickness. The production process and detailed chemical compositions of these layers has been fully described in the previous study.15)
Before cut into this rectangular pillar, the 3-layered sample underwent a series of heat treatments: the composite has been dipped into salt bath at 773 K for 4 h to control the thickness of interdiffusion layer, and quenched into iced water. After this heat treatment, the specimen was cut along the cross-section with a 1 mm thickness and solution treated at 623 K for 5 min, followed by an artificial aging at 313 K for 4 h. Figure 1(b) and (c) give the cross-sectional Scanning Electron Microscope (SEM) image and Energy dispersive X-ray spectroscopy (EDX) map of Zn at 1 mm above the position where tomography measurement was applied.
Average solute distribution curve was obtained by taking the average of Zn composition over the position in the direction normal to the interdiffusion direction, between y = 320 µm and 470 µm and shown with black dots, Fig. 1(c).
2.2 MethodsSynchrotron-radiation measurements were performed at BL10C in Photo Factory (PF), Tsukuba, Japan for a preliminary evaluation and at BL40XU and BL03XU, SPring-8, Hyogo, Japan for the scattering tomography. Figure 2(a) shows a photograph of a specimen placed in a schematic illustration of the measurement. The experimental details in BL40XU were described in the previous 1D scanning and tomography measurement.6,15) High-flux X-ray beam collimated with a definition pinhole of 20 µm in diameter was used with a camera length of about 2 m, and photon energy of 15 keV at BL40XU and a camera length of 1.7 m with photon energy of 18 keV at BL03XU. Tomography measurement was performed with a camera length of 1.7 m, and operated for a sample rotation with 3° step for 0 ≦ θ ≦ 180°, and a sample translation for approximately 1 mm at a step of 20 µm. The pillar specimen was positioned along the rotation axis as shown in Fig. 2(a), indicating that the measured area is the round sliced cross section of the pillared specimen. The scattered X-ray intensity with a small angle was detected using a Pilatus 100 K.
(a) A photographic image of the specimen and illustration of Small Angle X-ray Scattering (SAXS) tomography of the present experiments. (b) Measured 2D SAXS intensity profile and (c) the 1D profile after averaged in the azimuthal direction.
Same as the Filtered Back-Projection method in the previous study,6) the parameter used for reconstruction in CBP method has to be a linear character. For example, for a voxel (i, j), attenuation constant μt for a pixel size of t in the rotation angle θ and position u satisfies the relationship of
| \begin{equation} -\ln [\text{T}(\text{u},\theta)] = \int_{\text{u},\theta} \mu \text{t} (\text{i},\text{j})\text{dr} \sim \sum\nolimits_{\text{u},\theta} \mu \text{t} (\text{i},\text{j}) \end{equation} | (1) |
By a similar procedure, reconstruction of the integrated intensity of SAXS intensity was performed. The integrated intensity Q also satisfies a linear relationship of
| \begin{equation} \text{Q}(\text{u},\theta) = \frac{1}{\text{T}(\text{u},\theta)} \int_{\text{u},\theta} 4\pi\boldsymbol{q}^{2}\mathbf{I}_{\text{i},\text{j}}(q)d\boldsymbol{q} = \sum\nolimits_{\text{u},\theta} \text{Q}(\text{i},\text{j}) \end{equation} | (2) |
Figure 3(a) shows the reconstructed 2D image for absolute absorption coefficient distribution with a pixel size of 20 µm × 20 µm. This quantitative map ranges between 23 cm−1 and 53 cm−1, and was converted into a map of Zn distribution in Al–Zn alloy shown in Fig. 3(b), by using the relationship of
| \begin{equation} \frac{\mu_{\text{Alloy}}}{\rho_{\text{Alloy}}} = \sum\nolimits_{\alpha}\omega_{\alpha} \cdot \frac{\mu_{\alpha}}{\rho_{\alpha}} \end{equation} | (3) |
Reconstructed tomography of (a) absolute absorption coefficient (b) Zn density calculated from absorption coefficient (c) total absolute integrated intensity (d) volume fraction of GP zones. (e) calculated UTS distribution from volume fraction tomography and 1D averaged Rg result.
Figure 3(b) was compared with the previous EDX result in Fig. 1(c) to confirm the validity. By taking an average in the y direction inside the specimen and converted into 1D profile (gray dots in Fig. 1(c)), an excellent agreement was confirmed between the black & gray two plots, except for which in the edge position of the pillar. Present result indicates that the Zn composition in the sample ranges from 0 to 13.8% in mass.
3.2 Tomography of G.P. Zone volume fractionA typical 2D profile and an averaged 1D profile in the azimuthal direction, which used for tomography reconstruction are shown in Fig. 2(b) and (c). Then the integrated intensity in absolute unit was calculated from each corrected SAXS intensities with calibration using the scattering intensity of glassy carbon.16,17) Figure 3(c) shows the result of reconstructed distribution of the absolute integrated intensity. This figure indicates that precipitation of Guinier-Preston Zone (G.P. Zone)18–20) was observed when the composition of Zn exceeds 5.3% in mass inside the interdiffusion layer, and this agrees with the previous result about 1D scanning case of 5.2% Zn in mass.15) In this reconstruction, since no standard specimen is known for integrated intensity, the reconstruction of absolute scalar tomography without standard specimen mentioned above is a mandatory.
When the SAXS intensity was reconstructed in an absolute unit, the volume fraction Vf of the precipitates for each voxel can be evaluated by:12,13)
| \begin{equation} \text{Q} = 2\pi^{2}\Delta \rho^{2}\text{V}_{\text{f}} \end{equation} | (4) |
Guinier radius12,13) which is identical to radius of gyration, is an averaged parameter describes the dimension of precipitates illuminated by incident X-ray. Hence, it is nonlinear and can be used as a mean parameter where X-ray pass through in each SAXS measurement. If recall the discussion in the previous study of 1D scanning,15) a local hardness value was discussed with the measured local nanostructure, which was taken the averaged value along the direction which Zn component a constant. Thus, while discussing the relationship of local nanostructure and its corresponding local hardness, it is reasonable to use the same Guinier radius at the same thickness direction in the previous 1D study.15)
The Guinier radius in the SAXS measurement performed along y direction in the present tomography image was evaluated, which ranged from 2.16 nm to 3.56 nm. Hence, with the evaluated volume fraction in Fig. 3(c), the hardness of each voxel of the tomographic measurements was estimated from these nanostructure parameters, using the underaged relationship28,29) obtained for the underaging conditions.15) For the solid solution region, the hardness was evaluated as the function of concentration using the relationship of Zn concentration and the hardness in 1D result.15) These results were summarized as Fig. 3(e). For convenience, the hardness was shown in UTS using an empirical relationship28,29) of
| \begin{equation} \sigma(UTS) = 0.32\times \varDelta \mathrm{HV} \end{equation} | (5) |
Critical resolved shear stress (CRSS) Δτ0 was also estimated in this underaged structure with the work of V. Gerold and H. Haberkorn:30)
| \begin{equation} \Delta \tau_{0}\approx 3\mu |\varepsilon|^{1.5} \left(\frac{\mathrm{RV}_{\text{f}}}{\text{b}} \right)^{0.5} \end{equation} | (6) |
Therefore, a 2D local ultimate tensile strength tomography in the whole cross-section, and a distribution of yield stress in the precipitated strengthened area in the cross-section of a metallic composite pillar was calculated nondestructively, with a resolution of 20 µm × 20 µm. The resolution may be easily extended to better resolution, depending on that required from the materials microstructures.
Quantitative tomographic analysis has been made for an interdiffusion layer of a model composite Al/Al–Zn/Al, where the composition gradient by interdiffusion was observed. Microstructural distributions in the reconstructed images of the cross-section were consistent with the preceding works made with uniform samples. Present results demonstrated the quantitative evaluation of distribution of local solute density in a square pillar nondestructively without any standard specimen. The absolute integrated intensity and the consequent volume fraction of precipitates were reconstructed for the first time. A 2D distribution of ultimate tensile strength of the same cross-section and its yield stress with precipitates was estimated by using the absolute tomography of nanostructure for the first time. These results indicate that performing tomography measurement with absolute SAXS method is a useful tool for investigating precipitation hardened composite materials having a complex shape and solute distribution, and is useful for the 3-dimensional designing in composite material.
The present work has been supported by grant-in-aid from Japan Aluminium Association, grant numbers R2-12, and grant in aid for scientific research from JSPS, grant numbers 18K18944 and 18H05476. Measurements have been performed under proposal number 2018B1043 and 2020A7224 of Spring-8, and 2016G060 and 2020G637 of PF. The authors acknowledge technical support by Mr. K. Aoyama of JASRI during the measurements at BL40XU, Spring8. Acknowledgments should be made at the end of the manuscript, leaving an interval of one line after the body of the text. Financial assistance, the use of apparatus and the receipt of research funding and so on, should all be acknowledged in this section.
