13th International Conference on Fracture June 16–21, 2013, Beijing, China -3- This paper defines 2 ( ) y y π ε ε = . (5) It is obvious that yε is a constant. According to elastic-plastic fracture mechanics, at the crack tip, when the strain component along y axis direction reaches some certain value, crack extends. This certain value is defined as fε in this paper. Fig. 1 displays a cross-sectional plot of a compact tension specimen. The hatched area is the overlap of the upper and lower fracture surfaces when driven to the initial position (state before test started) after being broken. It refers to the plastic deformation left on the specimen. In order to simplify the calculation, this paper supposes the plastic deformation is symmetry about the fracture surface as shown in Fig. 2. It means that the specimen fractures along x axis. Furthermore, this paper defines the area which is plastically deformed during the course of testing as plastic field. It is worth noting that plastic field is different from plastic deformation as shown in Fig. 2. In this paper, according to the simple bar hypothesis, the fracture surfaces are assumed to be composed of independent rectangular bars. The sizes of these bars in the X and Y directions (the directions of crack extension and specimen thickness, respectively) are determined by the resolution of the laser microscope for the X and Y axes (represented by p and q, respectively). In this paper, they are both 50 μm. Thus, along the direction of crack extension, the amount of plastic deformation which is gray-scaled in Fig. 2 can be considered as the elongation of the bar. This paper supposes the original half length of the bar is l and the half elongation is lΔ . l lΔ y x yε fε ( ) F y Initial crack tip aΔ Plastic deformation Plastic field Figure 2. Principle of determining plastic field left on specimen As introduced in [4], the strain distribution of a simple rectangular bar along the axis can be expressed as the curve shown in Fig. 2. The function of curve was supposed to can be written as Eq. (6), ( ) exp( ) F y a by = . (6)
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