13th International Conference on Fracture June 16–21, 2013, Beijing, China -5- Direction of crack growth Figure 3. Two parts of the elongation of a single bar According to this idea, we should firstly determine the global strain of each single bar during the course of failure. As shown in Fig. 3, using FRASTA to reconstruct the process of fracture, considering that the crack has extended to the “present crack tip”, that is material behind the present crack tip (between the “initial crack tip” and the “present crack tip” in Fig. 3) has been fractured, thus forces acting on the bars composing this part had been released. While for material in front of the “present crack tip”, it still bears load before failure. Add the loads acting on these bars together, the applied load of the specimen can then be determined. As shown in Fig. 3 and introduced above, suppose the final elongation of the bar is ijδ and divide the elongation into two parts, ijδ′ and ijδ′′ , where ijδ′ represents the elongation of the bar when the crack extends to the “present crack tip” and ijδ′′ represents the residual elongation of the bar with the crack extending further from the “present crack tip” until final failure. As introduced above, it is easy to get ijδ, ijδ′ and ijδ′′ by reconstructing the process of crack extension using FRASTA. According to Eq. (11), the initial length of the bar can then be calculated and the global strain of the bar when the crack reaches to the “present crack tip” can be calculated as Eq. (13), ij ij ij l δ ε ′ = . (13) Furthermore, the relationship between true stress σ and true strain ε can be expressed as Eq. (14), n K σ ε = , (14) where K is a constant and n is work hardening exponent.
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