\chapter{Validation Data}\label{cha:validation_data}

Significant effort was put into gathering local property distributions that were directly influenced by the heat treatment process.
These would act as validation data for the models-upon-models of the process simulation, where errors could accumulate over the multiple simulation stages.
%Sanity checks on resulting data were paramount.

The main repositories of published data accumulated during the span of this thesis are J\'aszfi's Paper on rod materials\autocite{jaszfi2022residual} and publication~\ref{apx:pub3} on the crankshafts bearings.

\section{Hardness}
Hardness is one of the easiest properties to measure, with standardized methods being well established\autocite{astme18, iso6507-1, astme92}.
It is often one of the target properties that processes want to control, and thus an important metric of a simulated heat treatment process is whether it arrives at a plausible hardness.
It is, however, also a property that is resultant of a long chain of processes and can only indicate a discrepancy through a unexpected value, giving litte indication of its cause.


\subsection*{Sample Preparation and Testing}
Hardened samples of the rods and crankshafts were cut and embedded in resin as shown in figure~\ref{fig:hardness-samples}.
Lengthwise sections of the rods were extracted from two samples (the upper and lower half of the zone had to be separated to fit into the embedding machine), while a crankshaft bearing was cut lengthwise into wedges at \ang{45} intervals, resulting in eight samples.
Publication~\ref{apx:pub3} shows all 8 samples, which were all etched to show the local hardening depth.

\begin{figure}[htbp]
    \centering
    \begin{tabular}{cc}
       \subfloat[Cut rod\label{fig:hardness-samples-cut-rod}]{\includegraphics[height=4.5cm]{Abbildungen/13723-48107_Gehaertet_nach_Trennen.JPG}}
         & \quad
        \subfloat[Embedded rod sample \textbf{2g} with overlayed hardness map\label{fig:hardness-samples-embedded-rod}]{\includegraphics[height=4.5cm]{Abbildungen/NOG_makro_2G_.png}}\\
        \subfloat[Prepared bearing with cut marks]{\includegraphics[height=4.5cm]{Abbildungen/KW1_HV_Schnittebenen.png}}
         & \quad
        \subfloat[Embedded sample at \ang{0} with measurelent lines marked in]{\includegraphics[width=6.75cm]{Abbildungen/KW_5_HV_0.png}}
    \end{tabular}
    \caption{Hardness samples}\label{fig:hardness-samples}
\end{figure}



\subsection*{Results}

Since the rods were through-hardened, linear hardness measurements would yield little information, so a surface scan of hardness tests was conducted and stitched together over both samples \textbf{2g} and \textbf{3g}, yielding the distribution shown in figure~\ref{fig:hardness-results-rod}.
From this distribution (and the kerf from figure~\ref{fig:hardness-samples-cut-rod}) the heated zone can be measured to be \qty{42}{mm} at the surface and \qty{38}{mm} in the rod's center.
Further the steep hardness gradient at the edges indicates a similarly steep temperature gradient.

\begin{figure}[htbp]
    \centering
    \includegraphics[height=4cm]{Abbildungen/NOG_hardness_wide.png}
    \caption{Hardness distribution across rod. The figue has been oriented to align with the orientation of figure~\ref{fig:hardness-samples-embedded-rod}.}\label{fig:hardness-results-rod}
\end{figure}

The since the crankshaft's hardening profile was more complex and varied around the circumference, a single bisection would not yield all data of interest.
The as-hardened bearing was hterefore cut into eight slices at \ang{45} angles, and to keep measurement effort reasonable, three points of interest were defined: One at the centers of the bearing journal surface and the two fillets that transition into the bearing webs.
Measurement lines starting at \qty{0.2}{\mm} depth with test points every \qty{0.4}{\mm} ran until a hardness plateau under \qty{400}{HV1} was reached, which signified the untreated base material (figunre~\ref{fig:hardness_lf}).
With this cut-off point, the resulting hardness lines could yield information about the case hardening depth around the circumference.
Figure~\ref{fig:hardness_depth} shows the case hardening depth at the bearing center to be somewhat constant (between \qtyrange{3.7}{5.2}{\mm}) while the dteph at the notches shows more extreme variation of \qtyrange{3.2}{6.1}{\mm}, with it's maximum at the center's minimum position at \ang{180}.
This interaction can easily be explained by thebearing web's effect on the heated zone:
The webs guide the magnetic flux and thus the heat generation up somewhat leaving a radius for the notches to show ``true'' hardening depth while the diagonal measurements cut through a rather strainght segment at the \ang{180} position.

Figures to how the etched micrographs of the \ang{0} and \ang{180} positions to show the hardened zones ? reference to publication~\ref{apx:pub2}??
 
\begin{figure}

    \centering
    % \begin{tabular}
    % \subfloat[]{\includegraphics[]{Abbildungen/hardness_P1_LF.png}}
    % \end{tabular}
    \includegraphics[width=9cm]{Abbildungen/hardness_P1_LF.png}
    \caption{Hardness measurements at bearing surface center of hardened crankshaft. The hardening threshold of \qty{400}{HV1} is shown as a dashed line, with all lines showing a clear drop to an unhardened level of \qty{\sim300}{HV1}.  }\label{fig:hardness_lf}
\end{figure}

\begin{figure}
    \centering
    \includegraphics[width=9cm]{Abbildungen/hardness_HD_P1.png}
    \caption{Hardened depth of three points of interest on hardened Crankshaft. The red line shows the measurements from the flange facing notch, the greeen line those of the pin facing notch, and the blue line the bearing center measurements.}\label{fig:hardness_depth}
\end{figure}

\section{Temperature and Phase Distributions}

Temperature data is the most direct way of verifying the correct simulation of the inductive heat generation, but unlike hardness, it generally requires in situ measurement. 
For surface Temperatures this may be achieved at a distance through pyrometers, but may lack precision.
For best results, a sample must be  instrumented with thermocoulpes (on it's surface or at depth) and heat treated.
Tihs does require a mchine and process that allows for the thermocouples' cables to run out to a measurement station or computer.
Measurements of the 50CrMo4 rods were collected through instrumented samples in the in-house test rig, with thermal probes placed at the level of the induction coil through axial holes that were drilled centrally and \qty{0.5}{\mm} under the surface. 

Since the crankshaft’s heat treatment requires rotation and is not accessible within the large furnace, a temperature curve was extrapolated as detailed in publication~\ref{apx:pub2}.

Phase distribution data is useful for validating the material transformation models, but is resource intensive to generate as grid data. 
Manual microstructural examinations were performed on a hardened crankshaft bearing surface centrally at the \ang{0} position and documented in publication~\ref{apx:pub2}.
Some microscope analysis was also done on sample plates cut from rod samples, but the most expansive data set describes the residual austenite disribution and was derived from the \acrshort{hexrd} analysis also used to gather stress data.

?? WHAT ABOUT THE ROD SAMPLES ??

\subsection*{Sample Preparation}
\subsection*{Results}

\section{Residual Stresses and Austenite}

As explained in section~\ref{sec:sota_residual_stress}, measuring internal residual stresses of three-dimensional parts is always full of compromise. 
For this thesis, a high spatial resolution of data points was accomplished by machining sample plates from the heat treated parts that could be examined through \acrshort{hexrd} at the particle accelerator at DESY, Hamburg.
The trade-off was accepting a relaxation of tangential residual stresses, that would have to be compensated during the validation of the simulation results.
\subsection*{Sample Preparation}

\begin{figure}[htbp]
    \centering
    \subfloat{\includegraphics[width=0.5\linewidth]{Abbildungen/KW_sample_cut-1.png}} \\
    \subfloat{\includegraphics[width=0.5\linewidth]{Abbildungen/KW_sample_cut-2.png}} \\
    \subfloat{\includegraphics[width=0.5\linewidth]{Abbildungen/KW_sample_cut-3.png}} \\
    \caption{Steps of sample extraction for the synchrotron experiments. Cuts going from \textbf{(b)} to \textbf{(c)} were done by electrical discharge machining to a thickness of \qty{3}{\mm}?? and then carefully ground to eliminiate surface stresses from the \acrshort{edm} process, resulting in a final thickness of \qty{2.43}{\mm}.}\label{fig:hexrd-sample-prep}
\end{figure}


\begin{figure}[htbp]
    \centering
    \includegraphics[width=0.75\linewidth]{Abbildungen/KW_samples.png}
    \caption{Side by side of the three sample plates cut from crank shafts at differetn processing stages: \textbf{2}---hardened, \textbf{4}---annealed, \textbf{6}---ground. The geometric difference of plate \textbf{6} to the others is evidence of a misalignment during sample cutting.}\label{fig:hexrd-samples-photo}
\end{figure}

\begin{figure}[htbp]
    \centering
    \includegraphics[width=0.5\linewidth]{Abbildungen/KW_sample_actual.png}
    \caption{Actual sample positions in crankshaft. The dashed black line indicates the intended position, the solid double line shows the path of the oil channel used for alignment.}\label{fig:hexrd-sample-pos}
\end{figure}

\begin{table}[htbp]
    \centering
    \caption{Deviation of actual sample positions for plate samples}\label{tab:hexrd-sample-pos}
    \begin{tabular}{ccrrr}\toprule
         Sample ID & processing state & \makecell{Rotation along \\ bearing axis} & \makecell{Distance from \\ bearing axis} & {Thickness} \\ \midrule
         2 & hardened & \qty{8.706}{\degree} & \qty{-0.657}{\mm} & \qty{2.43}{\mm} \\
         4 & tempered & \qty{8.373}{\degree} & \qty{-0.525}{\mm} & \qty{2.43}{\mm} \\
         6 & ground & \qty{-23.163}{\degree} & \qty{-2.911}{\mm} & \qty{2.43}{\mm} \\
         \bottomrule
    \end{tabular}
\end{table}

\begin{figure}[htbp]
    \centering
    \includegraphics[width=0.5\linewidth]{Abbildungen/KW_hexrd_paths.png}
    \caption{Measurement paths and paths of \acrshort{hexrd} Measurements. 3 areas were defined so as to cover to \qty{10.5}{\mm} depth.}\label{fig:hexrd-paths}
\end{figure}


\begin{figure}[htbp]
    \centering
    \begin{tabular}{cc}
        \subfloat[Location in bearing]{\includegraphics[width=0.45\linewidth]{Abbildungen/kw_sample_discs_1.png}} & 
        \subfloat[Lineup of both discs showing differentiating features]{\includegraphics[width=0.45\linewidth]{Abbildungen/kw_sample_discs_2.png}}\\
        \subfloat[Disk 1 - bearing edge]{\includegraphics[width=0.45\linewidth]{Abbildungen/kw_sample_discs_3.png}} & 
        \subfloat[Disk 2 - bearing center]{\includegraphics[width=0.45\linewidth]{Abbildungen/kw_sample_discs_4.png}}
    \end{tabular}
    \caption{Summary of sample extraction of disks.}\label{fig:hexrd-disk-pos}
\end{figure}

\begin{figure}[htbp]
    \centering
    \includegraphics[width=0.45\linewidth]{Abbildungen/Disc_Lines.png}
    \caption{Line paths for disk samples.}\label{fig:hexrd-paths-disk}
\end{figure}




\begin{table}[htbp]
    \centering
    \caption{HEXRD parameters of the subpaths making up each masurement line}\label{tab:hexrd-disk-subpaths}
    \begin{tabular}{cccc}\toprule
         Depth & Step & Aperture & Exposure \\\midrule
         \qtyrange[range-units = single]{-0.10}{1.00}{\mm}&\qty{0.05}{\mm}&\qtyproduct[product-units=power]{0.05 x 0.05}{\mm} & \qty{8}{\s} \\
         \qtyrange[range-units = single]{1.10}{5.00}{\mm}&\qty{0.10}{\mm}&\qtyproduct[product-units=power]{0.10 x 0.10}{\mm} & \qty{2}{\s} \\
         \qtyrange[range-units = single]{5.25}{15.00}{\mm}&\qty{0.25}{\mm}&\qtyproduct[product-units=power]{0.10 x 0.10}{\mm} & \qty{1}{\s} \\
         \bottomrule
    \end{tabular}
\end{table}

\subsection*{Results}



\begin{figure}[htbp]
    \centering
    \includegraphics[width=0.45\linewidth]{Abbildungen/DiskStress_Cart_hardening.png}
    \caption{Comparison of hardening and stress transition depth for disks 1 and 2. For disk 1, the comparison is imperfect due to the hardness measurement path being at an angle in the web radius where the disk could only be cut straight down. It does however show the effect of the missing web on the hardened geometry reaching a maximum at \ang{180}.}\label{fig:hardnesses-disc}
\end{figure}
