# Carbon Fiber Traces in Cracked Surfaces of Mortar Prisms
## 4 Fiber Traces on the Cracked Surfaces  
The fiber traces on the cracked surfaces of prism samples with different fiber contents can provide essential clues to explain the reduction in flexural strength when fiber contents exceed a certain amount. For this purpose, the fiber traces on the cracked surface of each prism sample are scrutinized. Figure 6 presents both sides' cracked surfaces of CF 0.0-1 and 2. The surfaces of both samples reveal many air pockets of different sizes. The dark spots are mostly air pockets. Two-sided arrows designate the matching broken pieces of few air pockets. It is hard to identify the matching pieces of the broken air pockets because most of the breaking appears at the top edges of the air pockets. The ratio of the area occupied by the air pockets in the cracked surface to the total area of the cracked surface is expected to be the highest among the prism sample cross sections parallel to the force propagation direction. Figure 7 shows the top view of the cracked surfaces of both pieces of each fiber-added prism sample listed in Figure 3. To identify the matching fiber bunch in the left and right pieces, and the length of the cluster, a square grid pattern is drawn on each image. The pattern consists of seven lines with 6 mm distance between them and one more line added  
Figure 6: Cracked surfaces of both sides. The dark spots represent air pockets. with 4 mm distance in both the horizontal and vertical directions to cover the cracked surface of 40 mm \(\times\) 40 mm. The 6 mm corresponds to the length of each fiber strand. The cracked surfaces are just plane mortar with occasional dark spots. The dark spots in these images represent fiber clusters. For the case of CF 0.5-, these dark patterns are not very noticeable but become more noticeable and of bigger sizes as the fiber content increases, though the difference between CF 1.5- and CF 2.0- is hardly recognizable. The dominant traces for the prism samples of different fiber percentages for a selected area of each sample are shown in Figures 8-11. Each of these figures shows the magnified images of corresponding left and right sides for each of two same fiber percentage prism samples. Each image shows the fiber traces within a 12 mm \(\times\) 12 mm size area that corresponds to four squares in the grid pattern. The area is divided into regions by its surface relief. The solid lines in the image are boundary lines of the regions. The number of these regions indicates the roughness of the area. The size is good for showing details of the patterns in the area. However, the six bottom squares with the darkest patterns in the cracked surface are selected for CF 0.5-2 to compensate for the small number of traces in CF 0.5-1. This also shows the full shape of the patterns that are located across two adjacent squares in the grid. In addition, when counting the number of divides, the slope and slow varying areas at the edge of a sampled area are omitted from the counting because they  
Figure 7: Cracked surfaces of prism samples of different fiber contents: the dark squares and rectangles represent sampled areas. will be a part of hollows or humps in neighboring areas of the sampled area, and they are almost flat. In these images, the matching areas and the type of each trace are marked by dotted ellipses and a broken/solid both-sided arrow, respectively. The name of the trace is written above each arrow, as well as the features of the cracked surfaces. Roman numbers at the end of each trace name indicate the type. The areas selected to show the traces are specified in Figure 7 with thick lined squares and rectangles. Figure 8 shows the details of the fiber traces in the area specified in Figure 7 for CF 0.5-1 (Figure 8a) and CF 0.5-2 (Figure 8b). For CF 0.5-1, the entire area of the left image is just a low hump, and that of the right image is a shallow hollow. The entire areas reveal type I dividedness because no cemented fiber clusters or fiber-laden mortar are found in these areas.