## 2 Materials and Methods
### Thermography  
Non-destructive testing (NDT) includes several methods--for example, eddy current, ultrasonic testing, or thermography. The latter is a well-known method for CFRP testing. One main advantage of this method is contactless testing of large areas in a really short amount of time. For the problems arising with this hybrid specimen, thermography as NDT method is most suitable. First, this is because the specimen is installed in the tensile testing machine and not easily accessible for mechanical contact, thus contactless testing comes in handy. Second, large areas can be tested in a short period of time. Third, the resulting temperature difference especially for CFRP is high (see Equation (1) [30]):  
\[\Delta T_{\mathit{diss}}(\mathrm{t})=\frac{\mathrm{Q}_{\mathit{diss}}(t)}{ \rho\,c_{p}} \tag{1}\]  
where \(\Delta T_{\mathit{diss}}\) is the temperature difference induced by the dissipated heat quantity \(\mathrm{Q}_{\mathit{diss}}\), density \(\rho\), and the specific heat capacity \(\ c_{p}\). CFRP exhibits a relatively low density and \begin{table}
\begin{tabular}{c c c c} \hline  & **Young’s Modulus** & **Tensile Strength** & **Elongation at Break** \\  & **[GPa]** & **[MPa]** & **[\%]** \\ \hline PPA-GF30 & 11 & 160 & 1.7 \\ \hline Carbon fiber & 230 & 3530 & 1.5 \\ \hline aluminium & 67 & 310 & 10 \\ \hline \end{tabular}
\end{table} 
Table 1: Mechanical data of the materials extracted from their data sheets [24; 26; 27]. Figure 2: **Left**: dog bone PPA-GF30 specimen; **middle**: flat tensile CFRP specimen; **right**: assembled hybrid specimen. a medium specific heat capacity, which increases \(\Delta T\), considering the largest and most important area of the hybrid specimen consists of CFRP. Thermography relies on infrared (IR) irradiation, which is emitted by objects above zero Kelvin according to Planck's Law:  
\[L_{\lambda,h}=\frac{2 hc_{0}^{2}}{\lambda^{5}\left[\exp\left(\frac{hc}{\lambda kT }\right)-1\right]} \tag{2}\]  
Planck's Law describes the emittance of the spectral radiance \(L\) by a blackbody dependent on wavelength \(\lambda\) and temperature \(T\). The spectral radiance \(L\) is a parameter measured by the thermography camera, which is then converted to a temperature. Therefore, the emissivity \(\varepsilon\) also plays an important role when a temperature value is assigned to a value of \(L\). Equation (2) only applies to black objects, but under real circumstances spectral radiance also depends on the solid angle \(\omega\), radiant power \(\phi\), the angle between centre line of the radiation cone, and the sphere normal \(\theta\) as well as the surface increment dA from which the electromagnetic waves are emitted:  
\[(\lambda,\theta,\phi)=\frac{d^{3}\phi}{dA\ cos\theta\ d\omega\ d\lambda} \tag{3}\]  
Emissivity \(\varepsilon\) now relates the spectral radiance \(L_{\lambda}\) of a specimen to the spectral radiance of a blackbody \(L_{\lambda,b}\)[31; 32]:  
\[\varepsilon(\lambda,\ T,\theta,\Phi)=\frac{L_{\lambda}(\lambda,\ T,\theta, \Phi)}{L_{\lambda,b}(\lambda,\ T)} \tag{4}\]  
In consequence to that, \(\varepsilon\) is also dependent on all of these parameters which makes it very difficult to measure. For a precise quantitative measurement of the temperature, the emissivity must be known. The contrast in thermography images comes from different temperature, surface properties, emissivity, or material type besides the temperature distribution of the surface. Additionally, porosities can be the origin of an inhomogeneous distribution or an apparent higher temperature. Furthermore, mechanical loading can alter the temperature of a specimen. Under tensile loading a specimen will expand and thus lower its temperature vice-versa for compression. Sometimes it is more beneficial for thermographic measurements to build temperature differences. In most cases, emissivity can then be neglected [31]. For thermography, there are 2 typical wavelength segments. The first one is called mid-wavelength infrared (MWIR).