In situ analysis of damage evolution in an Al/$\hbox {Al}_{2}\hbox {O}_{3}$ MMC under tensile load by synchrotron X-ray refraction imaging

Abstract

The in situ analysis of the damage evolution in a metal matrix composite (MMC) using synchrotron X-ray refraction radiography (SXRR) is presented. The investigated material is an Al alloy (6061)/10 vol$\%$ $\hbox {Al}_{2}\hbox {O}_{3}$ MMC after T6 heat treatment. In an interrupted tensile test the gauge section of dog bone-shaped specimens is imaged in different states of tensile loading. On the basis of the SXRR images, the relative change of the specific surface (proportional to the amount of damage) in the course of tensile loading was analyzed. It could be shown that the damage can be detected by SXRR already at a stage of tensile loading, in which no observation of damage is possible with radiographic absorption-based imaging methods. Moreover, the quantitative analysis of the SXRR images reveals that the amount of damage increases homogeneously by an average of 25% with respect to the initial state. To corroborate the experimental findings, the damage distribution was imaged in 3D after the final tensile loading by synchrotron X-ray refraction computed tomography (SXRCT) and absorption-based synchrotron X-ray computed tomography (SXCT). It could be evidenced that defects and damages cause pronounced indications in the SXRCT images.

Appendix: Derivation of equation (1)

The ratio of integrated experimental rocking curves yields the transmission, solely due to absorption:

$$\begin{aligned} \frac{\int I_{\text {R}}\left( \theta \right) \text { d}\theta }{\int I_{\text {R0}}\left( \theta \right) \text { d}\theta }=\frac{I_{\text {T}}}{I_{\text {T0}}} =\text {e}^{-\int \mu _{l}\text {d}r} \end{aligned}$$

(2)

Taking into account the additional reduction of intensity due to refraction, the ratio of the rocking curves’ peak intensity provides

$$\begin{aligned} \frac{I_{\text {R}}\left( \theta _{\text {B}}\right) }{I_{\text {R0}}\left( \theta _{\text {B}}\right) }= \text {e}^{-\int \left( \mu _{l}+C\right) \text {d}r}=\text {e}^{-\left( \int \mu _{l}\text {d}r+\int C\text {d}r\right) } \end{aligned}$$

(3)

where the refraction value $C$ is an additional attenuation coefficient due to scattering. By dividing Eqs. (3) by (2), we obtain the refraction value $C$ integrated along the ray path:

$$\begin{aligned} \text {e}^{-\int C\text {d}r}= & {} \frac{I_{\text {R}}\left( \theta _{\text {B}}\right) }{I_{\text {R0}}\left( \theta _{\text {B}}\right) }\frac{I_{\text {T0}}}{I_{\text {T}}},\,\text {or}\\ \int C\text {d}r= & {} -\ln \left( \frac{I_{\text {R}}\left( \theta _{\text {B}}\right) }{I_{\text {R0}}\left( \theta _{\text {B}}\right) } \frac{I_{\text {T0}}}{I_{\text {T}}}\right) \end{aligned}$$

Conventional series expansion of the logarithm yields a reasonable first-order approximation:

$$\begin{aligned} \int C\text {d}r\approx 1-\frac{I_{\text {R}}\left( \theta _{\text {B}}\right) }{I_{\text {R0}}\left( \theta _{\text {B}}\right) } \frac{I_{\text {T0}}}{I_{\text {T}}} \end{aligned}$$