PSI - Issue 28

574 14

Stepan Major et al. / Procedia Structural Integrity 28 (2020) 561–576 Stepan Major/ Structural Integrity Procedia 00 (2019) 000–000

Due fish-eye small dimensions, we will use for reconstruction of the sub-surface crack network with square side length a 05 = 5 μm. This dense mesh makes it possible to capture the fundamental difference between the optically smooth part of the inside of the fish-eye crack (the area of crack growth in a vacuum) and the area, where the process of crack growth is influenced by presence of air. While the inclination to the axis of the sample indicates the overall loading conditions in the formation and growth of the crack. The difference between the area of crack growth without presence and under its action can be described by comparing the deviations of the angle α from its average, respectively mean values. This probably a very smooth surface will be characterized by very small dispersion from the mean value of inclination angle α . On the contrary, it can be assumed that in the area where the crack grew in the presence of gases the surface will be much rougher. We can therefore compare the mean value of the alpha angle with the individual angles for the squares with edge length a 05 = 5 μm. In this case, we will study the magnitude of the deviation of the angle α of the elementary surface S i from its mean value α m in the area of interest. We will mark the deviation of the angle from its mean value. We see this comparison in Fig. 11 (b). On the left part of this image we can see an SEM image of the fish-eye crack (this fish-eye crack is characterized almost circular shape) and on the right side, it compares the average values of inclination and variance of angles Δ α . This variation is defined as Δ α = α i - α m . Therefore, also the dispersion from mean value of inclination angle. It is clear from the figure that in the area in which air was present during the crack growth, the scattering of the angle values is much higher. Therefore, the assumption was confirmed. The scattering more than doubled after the transition to the area in which the crack grew in the presence of air. It should be noted that the exact site of inclusion was omitted from the analysis. Because it represents a fault.

Fig. 11. Analysis of spatial orientation of the surface elements in area of fish-eye formation at the microscopic level (used square network with elementary length of edge a 05 = 5 μm): (a) SEM image of fish-eye crack; (b) variance of deviation angles Δ α in the area inside fish-eye and outside fish-eye crack, i.e. crack growth in vacuum and with presence of air. Another quantity that was measured in this work was the angle β , which represents deviation angel between normal vector of elementary flat and primary crack growth direction. This angle could be (theoretically) used to create a crack growth map. We see the result of such an effort on Fig. 12. The basic problem here is the selection of suitable points. Resp optimal network, as it would probably be appropriate to use a different network A for each specific area and then compile the resulting map from partial maps. However, the presented crack growth map was implemented using a single a 99 = 99 μm network, which makes the result harder to read.