13th International Conference on Fracture June 16–21, 2013, Beijing, China -2- 2. Proposed J-Measurement for Surface Cracks The proposed approach to measure the energy release rate, quantified by the J-integrals, predicates the fundamental principle prescribing the variation of the strain energy with respect to the crack extension, 1 dU J B da =− , (1) where B refers to thickness of the conventional planar fracture specimen with a through-thickness straight crack. The definition of the J value in Eq. (1) requires that the parameter B characterizes the length of the crack front, as the physical interpretation of the J refers to the energy released per extended crack area. Replacing B by the crack-front length for a curved surface crack, Eq. (1) becomes, avg crack U J A ∂ =− ∂ , (2) where Acrack denotes the crack area. The J-value determined from Eq. (2) thus represents the energy release rate averaged over the entire curved crack front in the surface crack specimens. To facilitate the experimental measurement of the energy release rate, previous researchers [3, 5] have developed an η-approach for different fracture specimens with a through-thickness crack, U J Bb η = , (3) where η remains as a dimensionless parameter dependent on the specimen geometry, and equals 2.0 for SE(B) specimens [3]. The parameter b in Eq. (3) denotes the length of the remaining ligament in a fracture specimen with a through-thickness crack. The η parameter needs to be re-calculated for surface cracked specimens. Equation (3) provides a convenient calculation of the energy release rate based on some simple geometric parameters and the strain energy U, which often derives from the area under the load versus the load-line displacement. The denominator in Eq. (3) quantifies the remaining net area of the cracked cross section in the fracture specimen. When applied to specimens with a surface crack, Eq. (3) becomes, avg net U J A η = , (4) where Anet refers to the net intact area of the cracked cross section, or, net total crack A A A = − , (5) where Atotal denotes the gross cross-sectional area of the specimen. Equation (4) allows the determination of a single characteristic energy release rate for a surface crack in the experimental procedure. In contrast, the numerical domain integral approach often computes the varying energy release rates along the curved front for a surface crack. The energy release rate, averaged over the entire crack front, thus derives from the individual J-values along the crack front, n i i i avg total BJ J B = ∑ . (6) In calculating the average energy release rate along the crack front, Eq. (6) divides the curved crack front into multiple segments, each with a length Bi and a corresponding energy release rate Ji. Btotal
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