13th International Conference on Fracture June 16–21, 2013, Beijing, China -5- Figure 4. Definition of the crack-plane rotation angle θ. 3.3. Evaluation of Energy Release Rate The calculation of the energy release rate in the plate specimens shown in Figures 1 and 3 depends on the evaluation of the strain energy U for the surface cracked specimens. The strain energy U, for the four-point bend specimens, follows, 0 2 U Md θ θ = ∫ , (7) in which the angle θ defines the rotation of one of the two crack planes and M refers to the bending moment applied on the cracked section. Assuming a center of rotation at a distance of r (W – a) away from the crack tip, the rotation of the crack plane thus derives from the measured crack-mouth opening displacement (CMOD), ( ) 2 CMOD a r W a h θ= ⎡⎣ + − + ⎤⎦ , (8) where h denotes the thickness of the knife-edge aluminum plate glued to the surface of the plate specimens in order to mount the crack-opening displacement (COD) gauge, as shown in Figure 5. Figure 5. Definition of the crack-plane rotation angle θ.
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