4.2 Thermal data processing
Thermal sequences provided by the IR camera, were processed according to the procedure presented in [40].
A signal reconstruction algorithm based on the least squares method was performed in order to extract pixel by pixel from the generic thermal signal S , Eq.7, its components:
\(S\left(\frac{N}{f}\right)=S_{\text{mean}}(\frac{N}{f})+S1\sin\left(\omega\frac{N}{f}+\varphi\right)+S2\cos\left(2\omega\frac{N}{f}+\varphi_{d}\right)\)(7)
where the Smean is the term describing the mean temperature while S1 and S2 \(\ \)are respectively the first and second amplitude harmonics, \(\varphi\) and \(\varphi_{d}\)are phase shift of first and second harmonics respectively and the system pulsation is \(\omega=2\pi f\).
In this research, the first amplitude harmonic signal representative of the thermoelastic signal and the related map were considered for the analysis according to the procedure of Fig.4. The first consideration on matrixes in Fig. 4, obtained by frequency domain analysis, is thatSmean does not provide local information [40] while S1allows for assessing more local information[39-40]. The algorithm involves the following steps according to Fig. 4:
- the size reduction to the gage length of mapsS1N, in order to refer thermoelastic signal to the area controlled by extensometer, the output map is(S1_red)N. The subscript N represents the number of cycles at which thermal sequence was recorded. - a 2D median filtering of (S1_red)N maps. Each output pixel represents the median value in a 3-by-3 neighbourhood around the corresponding pixel of the input image,(S1_filt)N. - the extraction of the mean value, 98th and 2nd percentiles,(S1_mean)N, (S1_98prc)N and (S1_2prc)N respectively, to make a preliminary analysis of the behaviour of thermoelastic signal. - the normalization of each (S1_filt)N map by initial value (number of cyclesN0),(S1_filt)N/(S1_filt)N0. - the extraction of the mean value, 98th and 2nd percentiles,(S1_mean)N/(S1_mean)N0, (S1_98prc)N/(S1_98prc)N0and (S1_2prc)N/(S1_2prc)N0respectively. These latter represent the thermal metrics used for evaluating the damage. The use of percentile instead of maximum/minimum values allows to avoid outliers in the analysis.
In Fig. 5, the evolution of percentiles and mean values of thermoelastic signal (S1_mean)N , (S1_98prc)N and (S1_2prc)N are reported. Each test was named as sample/50-60-65-70/% UTS. The index (S1_98prc)N , Fig. 5a, presents a variable trend (increasing/decreasing) demonstrating the complexity of damage mechanisms and their effects on composites. Fig. 5b reports the mean values (S1_mean)N which seem more affected by the influence of maximum signal. The signal (S1_2prc)N in Fig. 5c exhibits a decreasing behaviour through the cycles that is reproducible for each test. This latter parameter seems to be more robust to follow the stiffness degradation than others as confirmed by the analysis of[37].
Results