# Fracture Evolution and Mechanical Properties of Mortar Containing Different Inclusions
## 3 Test Results
### Failure Pattern  
The final failure patterns of samples containing different inclusions are presented in Table 3. Points A-D on each sample are measurement circles positioned on the paths of cracks. To avoid the potential error of the manual selection of fractures, the failure patterns are automatically recognized by self-documenting code based on MATLAB 2018b. In the failure pattern, the independent fractures in each sample are distinguished by different colors. It can be seen from Table 3 that the failure pattern of the samples is very similar to the corresponding DIC analysis of the strain contour. For sample S1-1, the final failure of the sample is caused by three major tensile cracks. The cracks on the left form an approximate \"Y\" shape along the inclusion's left boundary, and another crack is basically along the tangent of the boundary on the right side of the boundary. The inclusions are not penetrated through by these macro cracks due to the support of the inclusion with higher strength. For sample S3-1, the final failure of the sample is caused by an inverted \"Y\" shape crack on the left side of the sample. The inverted \"Y\" shape crack is initiated and propagated parallel to the loading direction at the beginning but deflects towards the inclusion when approaching the loading ends of the sample. An independent crack is observed in the inclusion but fails to reach the boundary. In sample S4-1, the crack's distribution is more complicated than in the other sample. Several cracks rapidly propagate along the loading direction and penetrate through the entire sample, including the inclusion. Figure 10: Fracture process of sample S5-1. Figure 13 shows the curves of the maximum principal strain over time for these measurement circles as well as the sudden change in the maximum principal strain contours during key stages. A notable observation is that a turning point on the strain curve typically signals the abrupt emergence of a concentrated strain area. For example, for sample S1-1, as the loading time reaches approximately 270 s, the strain curves on all four measurement circles begin to show a marked increase from a stable state. Comparing the strain contour maps between 269 s and 291 s, it becomes evident that a high-strain concentration zone suddenly emerges beneath the inclusion at this time, suggesting the potential formation of a crack in this area. Similar phenomena have been observed in other samples as well. Observing the strain curves of the four measurement circles for each of the three samples in Figure 13 reveals a trend in some of the circles that can be characterized as a sequence of calm to rapid rise to slow rise to rapid rise. This pattern is evident in measurement circles B and D of sample S1-1, B and C of sample S3-1, and B and D of sample S5-1. This trend reflects the complete process of a crack evolution: the initial rapid increase from a calm state indicates the onset of a strain concentration in the area of the measurement circle. This is followed by a relatively slow and stable increase, suggesting that the concentrated strain area is gradually forming a crack and extending stably. The subsequent rapid increase indicates that the crack in the sample has entered a late, unstable expansion phase in that region, and the material in the area has lost its load-bearing capacity. Overall, these curves comprehensively depict the complete process of a crack evolution, from initial appearance through stable development to unstable progression. It should be noted that not all measurement circles' strain curves exhibit this complete trend. For some circles, such as measurement circle C in sample S1-1, circle A in S3-1, and circle C in S5-1, the strain curves do not clearly show the unstable phase of crack development by the end of the tests, which is when the samples as a whole have already been broken. This could be due to the emergence of major macroscopic cracks in other regions of the sample.