## 2 Research Methodology  
### Material and Research Equipment  
Laboratory tests involving the deformation of samples to the point of fracture were performed with the use of a 5 MN hydraulic press, depicted in Figure 1. The samples were deformed with the assumed tool movement speed equal to 1 mm/s. The tests were performed at a temperature of 320 \({}^{\circ}\)C (measured on the work surface before putting the sample in the tools), whereas tool temperature (upper and lower die as indicated in Figure 1) during the experiments was 170 \({}^{\circ}\)C. In each case, the processes were carried out until the crack appeared. Using the DIC system, also presented in Figure 1, the distribution of the strain and their concentration level at the moment just before the fracture were analyzed. As the specifics of DIC analysis require special preparation of the sample surface, in the conducted tests, the surface of the tested samples was covered with a black, specialist varnish based on silicone resin, resistant to high temperatures. In specific, boron nitride (white) was sprayed onto the painted sample, which is used in industrial conditions as a protective coating for equipment operating at high temperatures or as a lubricant in some metal forming processes. The aim of such an operation was to achieve a high contrast between the background and the measurement points at which the deformation of the material was analyzed. Moreover, the stochastic pattern painted on the specimen surface was used to determine the displacement of the objects on the sample using the image correlation calculation. In the present study, the system with two high resolution CCD cameras was used to track the position of the same physical point on the reference and deformed image (Figure 2). If the cameras observe an object from different angles, the position of each point is focused on a specific pixel in the camera plane. Knowing the position of both cameras, relative to each other, the magnification of the lenses and all image parameters, it is possible to calculate the three-dimensional coordinates of any surface point. In the current work, the system of two cameras with the lens of 1.9/35 was used. The system was calibrated using the calibration target of 9 \(\times\) 9 black and white squares with total side length of 60 mm (Figure 2. In the correlation procedure, the face size was 17 px, the grid spacing was 15 px and the maximum value of accuracy was 0.1 px. In the DIC method, the subset size has a strong influence on the measurement accuracy [43]. In the case of a region with small displacement, the statistical error connected with noise or light fluctuation has a stronger impact than the systematic error connected with, e.g., the DIC algorithm. On the other hand, for a region with a large deformation, the smaller subset size is recommended because the systematic error is increasing. Summarizing, as the subset size increases, the spatial resolution decreases but the accuracy is increased. Figure 1: Experimental laboratory research: (**a**) the initial sample, (**b**) laboratory hydraulic press, (c) DIC system coupled with a laboratory press. Figure 2: The DIC Q400 system components and schematic diagram of measurement before and after deformation. In the calculation procedure, the basic work was carried out using Istra4D software. The average grayscale intensity in the subset was computed and the reference and the deformed image were compared. The correlation algorithm is based on the tracking the grey value pattern in small local neighborhoods. In the DIC method, the important components are the shape and correlation functions. The former is the component to relate the coordinates of the pixel of interest in the reference and deformed image, as well as the target variables to determine. The latter, i.e., the correlation function, is used to calculate a coefficient which represents the similarity between two sets of data. As already mentioned, the algorithm is based on the tracking of the grey value pattern in small local neighborhoods.