\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.]{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 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 around crankshaft bearing surface.]{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.]{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.


\subsection*{Sample Preparation}

Samlpe preparation for crankshaft samples was identical to the hardness measurements above, in fact some of the samples were first used for micrography and then hardness testing.

\subsection*{Results}

FIGURE SHOWING TEMPERATURE CURVE OF ROD WITH MULTIPLE THERMOCOUPLES ??

\section{Residual Stresses and Austenite}\label{sec:residual_stresses}

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}

Crankshafts from three process stages were used as sources for \acrshort{hexrd} samples: one hardened by heating and quenching, one with the subsequent tempering treatment one with the final grinding to dimension.
These there marked as samples \textbf{2}, \textbf{4}, and \textbf{6} respectively.
From each crankshaft, the crank pin closest to the flange was separated at the centers of the adjacent main journals.
Then the sample plates were cut by \acrlong{edm} to a thickness of \qty{3}{\mm} along the \ang{0} plane, i.e. including the center axes of both the crank and main bearing journals.
After \acrshort{edm}, the plates were finally ground slowly and under constant cooling to reduce the high stresses that \acrshort{edm} can induce in the cut surfaces.
Figure~\ref{fig:hexrd-sample-prep} visualizes these stages of free-cutting, while figure~\ref{fig:hexrd-samples-photo} shows the finished samples next to one another.

\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 HEXRD.]{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 HEXRD sample plates.]{Side by side of the three sample plates cut from crank shafts at different 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}

An immediate difference in the hole position of sample plate \textbf{6} (ground to dimension) can be seen in this side-by-side comparison, which calls into question the locating precision of the \acrshort{edm} procedure. 
To determine the true position of the sample plate within the original crank geometry, the poitions, angles, and minor and major axes of the drill ellipses were determined, as well as the samples' distances of top and bottom bearing surface.
From these indicators the actual sample positions were calculated as presented in table~\ref{fig:hexrd-sample-pos} and figure~\ref{fig:hexrd-sample-pos}.
Due to the grave misalignment of sample \textbf{6}, it was excluded from further comparison with the other two in subsequent measurements.

\begin{figure}[htbp]
    \centering
    \includegraphics[width=0.5\linewidth]{Abbildungen/KW_sample_actual.png}
    \caption[Actual sample positions in crankshaft.]{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}

As detailed in publication~\ref{apx:pub3}, seven measurement paths and three area scans were run on each of the sample plates, shown in figure~\ref{fig:hexrd-paths}.

\begin{figure}[htbp]
    \centering
    \includegraphics[width=0.5\linewidth]{Abbildungen/KW_hexrd_paths.png}
    \caption[Measurement paths and paths of \acrshort{hexrd} Measurements.]{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}


The samples 50CrMo4 rods were manufactured in parallel with the same machining process.
Two treatment stages were chosen for \acrshort{hexrd} analysis: hardened and annealed. 
J\'aszfi~\cite{jaszfi2022residual} 

\begin{figure}
    \centering
    \includegraphics[width=0.3\linewidth]{example-image}
    \caption{ rod HEXRD sample?? }\label{fig:hexrd-rod}
\end{figure}

Later in the project it was determined that a sampling from an orthogonal plane as needed, so the above manufacturing procedure was repeated for two disks from a hardened flange-side crank-pin bearing, as shown in figure~\ref{fig:hexrd-disk-pos}.
Figure~\ref{fig:hexrd-paths-disk} shows the measurement paths on the disks' surfaces, akin to the paths of figure~\ref{fig:hexrd-paths}. 
As with the plate samples, the paths on the disk were split into three sections with more detail towards the surface region.
Differing from the plates, however, here the aperture sizes were always square (see table~\ref{tab:hexrd-disk-subpaths}) since lines were measured at varying angles, nullifying any alignment of the aperture with defined depths.

\begin{figure}[htbp]
    \centering
    \begin{tabular}{cc}
        \subfloat[Location in bearing, S1 at the edge and S2 at the center of the bearing journal]{\includegraphics[width=0.45\linewidth]{Abbildungen/kw_sample_discs_1.png}} & 
        \subfloat[Lineup of both discs showing differentiating features of bore position and S1's flared edge.]{\includegraphics[width=0.45\linewidth]{Abbildungen/kw_sample_discs_2.png}}\\
        \subfloat[Disk S1: bearing edge]{\includegraphics[width=0.45\linewidth]{Abbildungen/kw_sample_discs_3.png}} & 
        \subfloat[Disk S2: 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}

Publication~\ref{apx:pub3} is wholly devoted to illustrating and discussing the results of the \acrshort{hexrd} measurements of sample plates 2 and 4. 


\begin{figure}[htbp]
    \centering
    \includegraphics[width=0.45\linewidth]{Abbildungen/DiskStress_Cart_hardening.png}
    \caption[Comparison of hardening and stress transition depth for disks.]{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}
