## 2 Materials and Methods
### Tensile Tests at Elevated Temperatures  
The yield stress of individual phases are essential in modeling the residual stresses as described in Section 1.1. The tensile tests were carried out in a quenching and deformation dilatometer, Dil805 A/D/T from Baehr Thermoanalyse (TA Instruments). The flat specimens used for the tensile tests had a geometry as shown in Figure 3. The temperatures at which the phases were tested were chosen according to the temperatures the individual phases experience during the Tempcore(tm) process. As shown in Figure 1, the martensite that is generated during the initial quenching step sustains from 200 \({}^{\circ}\)C up to 600 \({}^{\circ}\)C in the following tempering step. The austenite in the core experiences slow cooling and would start transforming at A\({}_{\text{c3}}\); hence, it was tested in the temperature regime above and slightly below A\({}_{\text{c3}}\)[2; 19; 23].  
The reason for using the dilatometer instead of a conventional tensile testing machine is the fast inductive heating in the dilatometer, which allows the specimens to be heated quickly to the testing temperature. This is important because the specimens have to be  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline
**C** & **Si** & **Mn** & **Cu** & **Ni** & **Cr** & **P** & **S** \\ \hline
0.17 & 0.25 & 0.79 & 0.37 & 0.12 & 0.07 & 0.01 & 0.04 \\
0.19 & 0.28 & 0.80 & 0.37 & 0.13 & 0.08 & 0.03 & 0.05 \\
0.19 & 0.23 & 0.84 & 0.25 & 0.12 & 0.09 & 0.01 & 0.03 \\
0.23 & 0.29 & 0.88 & 0.24 & 0.11 & 0.10 & 0.00 & 0.04 \\ \hline
0.19 & 0.26 & 0.83 & 0.31 & 0.12 & 0.09 & 0.02 & 0.04 \\ \hline \end{tabular}
\end{table}
Table 1: Chemical composition of four rebar samples and the mean value (wt%). The balance is Fe.  
tested at some temperatures where the phases are unstable and will start transforming. In the conventional tensile testing machine with an oven, the specimen has to be held at the testing temperature for approx. 30 min to reach a homogeneous temperature distribution. This would lead to substantial tempering of the martensite [24]. In the dilatometer the specimens were inductively heated at ca. 10 K s\({}^{-1}\) to the testing temperature, and the strain rate was 0.02 s\({}^{-1}\). This allowed the specimens to be tested within two minutes.  
In order to obtain the stress-strain curve of austenite, a thermocouple was tack welded in the middle of the specimens, where the temperature reaches its maximum. After mounting the specimens in the dilatometer, they were heated above A\({}_{\text{c3}}\) to 850 \({}^{\circ}\)C for 60 s to ensure homogeneous austenitization. Thereafter they were quickly cooled with a cooling rate of ca. 100 K s\({}^{-1}\) to the testing temperature and tested.  
To investigate the martensitic phase, specimens were first austenitized by soaking in a heat treatment oven at 850 \({}^{\circ}\)C for 30 min and afterwards water-quenched, since the quenching rate in the dilatometer was insufficient for in situ transformation to a fully martensitic state. The Vickers hardness of these quenched specimens exceeded 500 HV30, which corresponds to a fully martensitic structure [25]. Thereafter, isothermal tensile tests were conducted at various temperatures reached with a heating rate of 10 K s\({}^{-1}\). The tests lasted ca. 2 min, including heating the specimen from room temperature to the testing temperature. In practice, the tempering time is directly proportional to the mass of the workpiece [26]. Since the specimens are thin sheets of metal, they are likely to be tempered to some extent even within the duration of testing [27; 28]. Tempering, however, also occurs during the Tempcore(tm) process when the martensite in the surface region is heated up; therefore, the results of the experiments are still relevant to the process.