## 3 Results and Discussion  
### FPZ Evolution and SIFs  
During a typical concrete fracture testing process, 13,089 images are captured by CCD in 872.6 s. A 55 \(\times\) 30 mm\({}^{2}\) interest area covering the crack extension trace is shown in Figure 5, the displacement contour map of the interest area is obtained by the DIC technique. The crack tip position and displacement data around the crack tip are used as the initial value of the solution to the iterative Equation (8), then the SIFs and real crack tip position are obtained. As shown in Figure 5, 230 data points are selected around the crack tip, the data point position is marked by black dots. Although the accurate positions of the pre-crack tip can hardly be precisely ascertained at the outset, it is well known that the failure must start from the upper edge of the notch. Therefore, the center point of the notch's upper edge is set as the crack tip's initial position for the first iterative procedure. Then the obtained value of crack tip position is set as a new crack tip position for the consequent iterative procedures. As it is mentioned above, a series crack tip position can be derived from the displacement field around the crack tip during the crack propagation process. These crack tip positions are in the crack extension trace. These crack tip positions are used to calculate crack extension length \(\delta_{a}\) during the FPZ evolution process. As shown in Figure 6, the crack extension length curve and loading curve are plotted together. Figure 4: Single-edge notched concrete specimen sprayed with a dot pattern. Figure 5: The speckle image captured by CCD and the displacement contour map of the interest area. As shown in Figure 6, the crack extension length gradually increases from \(t\) = 577.34 s, the crack extension speed increases sharply after \(t\) = 712.26 s, the crack extension speed slows down after \(t\) = 752.35 s. Therefore, the first stage is usually called crack stable growth stage or subcritical growth stage. In this stage, micro-cracks are nucleating in front of the pre-crack tip along the notch direction, the crack extension length can be set as FPZ length. As shown in Figure 6, the concrete subcritical growth stage can be identified quantitatively and easily from the crack extension curves, and the FPZ length is about 8.35 mm. The second stage is unstable crack growth stage, micro-cracks coalesce into meso- and macro cracks, the crack extension length increases sharply, and the FPZ length is about 20.5 mm. In the third stage, the crack extension speed is mainly controlled by the test machine displacement rate. So, the concrete FPZ length is obtained from crack extension length curve derived from displacement field by DIC technique proposed in this presentation. In Figure 7, the mode I SIF \(K_{\rm I}\) curve and loading curve are plotted together. The SIF \(K_{\rm I}\) is expected to be proportional to the applied load \(P\) and the square root of the length of preexisting crack \(a\), as per the theory of fracture mechanics, while the value of \(K_{\rm I}\) does not increase before \(t\) = 577.34 s. The SIF \(K_{\rm I}\) begins to increase from \(t\) = 577.34 s, and reaches a critical value \(K_{\rm I}\) = 3.332 MPa\(\cdot\)m\({}^{1/2}\) at \(t\) = 752.35 s. Then the curve of \(K_{\rm I}\) drops slightly and tends to a constant value. Hence, the critical value of \(K_{\rm I}\) = 3.332 MPa\(\cdot\)m\({}^{1/2}\) is defined as the mode I fracture toughness \(K_{\rm IC}\). As shown in Figure 8, the value of SIF \(K_{\rm II}\) are much less than the value of \(K_{\rm I}\). It means that the beam is mainly cracked by tension force. Based on the analysis above, the typical contour maps of horizontal displacement during the loading process are shown in Figure 9.  
Figure 6: The curves of loading and crack extension length. Figure 7: The curve of mode-I stress intensity factor \(K_{\rm I}\). The displacement contour maps are corresponded with four spots marked on loading curve in Figure 6, respectively.