## 2 Methods and Materials
### Data Processing
#### 2.4.1 Tensile Data Processing
As soon as the neck sets in, the 1D extensometer data are not accurate any more. An alternative way of estimating the stress tensor is to use the measured local strains in Equation (14) averaged over the cross-section of interest. As long as the deformation is uniform, the results are the same as those estimated from the extensometer. However, measuring local strains yields significantly better stress estimates when strain localisation occurs. Other than longitudinal components in the stress tensor can be estimated from flow rules [99] or from other correction schemes reviewed by [PERSON] et al. [100], if necessary. Once the stress and the deformation rate are known, the mechanical power can be calculated by Equation (5). Calculations based on infrared thermography data are dependent on the temperature development over both time and space. Since large deformations can be encountered in a tensile test, it might be challenging to track a point on the specimen surface precisely. The sufficiently accurate tracking, however, can be achieved with DIC. To be able to use DIC to track IRT data, the transformation matrix was found between the DIC and IRT images obtained from specific cameras. The transformation matrix maps coordinates from one image to the other. Assuming the deformation pattern is equal on the both opposite surfaces, the displacement field can be transformed to fit IRT data and vice versa. To find the transformation matrix, calibration points, which simply refer to specific chosen locations in an IRT image and a corresponding DIC image, are needed. If there are 3 points, the software finds an affine transformation, and if there are more, the transformation type is _projective_. The transformation was found using the Matlab embedded function [101]. This procedure and the result are illustrated in Figure 4, where the rightmost image shows a superposition of two images based on the difference between them. Figure 4: Graphical software used to find the transformation matrix; the coloured points are the operator–chosen reference points. Once the transformation matrix is found, the ROI can be mapped from the DIC optical domain to the IRT temperature domain. The challenge, which the practitioners usually face with the heat Equation (10), is related to the second-order spatial derivatives. The temperature field measured by the camera is affected by the quality/ or roughness of the surface [102], the texture of the paint, the emissivity of the paint (which is lower than unity, inhomogeneous, and can possibly change during the test, particularly at large strains when the deformed surface gets rough), sensors, internal noise, etc. The inevitable fluctuations in the temperature distribution make the estimation of the second-order spatial derivative a formidable task. The grey-body emissivity correction method using Equation (7) can be employed to reduce the impact of reflections from surroundings. The method is easy to implement as the emissivity is considered to be constant in the narrow spectral band (3-5 um due to the lens used). Two main assumptions, however, stand behind this method: (i) the grey-body approximation is valid, and (ii) the reflected radiance is represented by the Planck's function. If the emissivity change appreciably during the test, it must also be accounted for. The error of a black body assumption can be calculated using Equation (6). When the emissivity is high, and the temperature of the specimen is close to the temperature of the reflected surroundings, and the error will be negligible. Once the temperature field is corrected, noise filtering or noise cancelling procedures are required, although they can introduce some artefacts specific for the filters used. To overcome this problem, the local regression procedure was implemented in the present work. A small circular region close to the point of interest is selected, and a second-order polynomial surface is fitted to it.