13th International Conference on Fracture June 16–21, 2013, Beijing, China -3- value of (ai – a0) at the intersection of the test P-Δ curve and the numerical P-Δ curve computed from the FE model with a crack size of ai. Since the crack size of the FE model equals the current crack size in the experimental specimen, the energy release rate calculated from the multiple FE specimens, using the same approach as the conventional multiple-specimen experimental approach, represents the J-value in the experimental specimen with the corresponding crack size. The CMODs corresponding to the intersection points between the experimental curve and the numerical curves, i.e., Δ1 to Δn in Figure 1a, define the CMOD levels to compute the strain energy U for each crack depth. The evaluation of the strain energy U from the P-Δ curve becomes the primary step in applying the CMOD-based hybrid approach. Since the strain energy for the SE(B) specimen dissipates mainly through the rotation of the crack plane, the strain energy U equals the bending strain energy in the mode I SE(B) specimen. Based on the J-integral calculation proposed by Tohgo and Ishii [9], the bending strain energy for SE(B) specimen follows, IU Md θ =∫ . (1) Equation (1) also represents the mode I strain energy in mixed-mode I and II specimens. In such mixed-mode specimens, the shear strain energy follows, II V V U F d δ =∫ , (2) where, FV is the shear force on the crack plane, and δV corresponds to the relative shear displacement between two crack planes. For the SE(B) specimens, the shear force remains zero and the bending moment M derives from equilibrium principles. The rotation of the crack plane, θ, depends on the current crack length, 1 1 CMOD ( ) i i p i a r W a θ − − = + − , (3) where rp represents the plastic rotation factor and equals 0.44 as suggested in ASTM E1820 [1] for SE(B) specimens, ai–1 corresponds to the crack depth determined at the previous intersection point between the experimental P-Δ curve and that obtained from the FE analysis, as demonstrated in Figure 1a. Figure 1b illustrates the schematic variation of the strain energy with respect to the crack depth, calculated from multiple FE models. To facilitate the calculation of the energy release rate from the FE models, the hybrid approach utilizes a regression analysis to derive approximate polynomial functions in terms of the crack size, a, to describe the strain energy variations shown in Figure 1b. The solid circles in Figure 1b indicate the displacement level where the energy release rate calculated from multiple FE models equals (theoretically) the energy release rate in the experimental fracture specimen with a growing crack. The J-values at these solid circles are computed from Eq. (4), 1 dU J= B da − . (4) Figure 1c sketches the J-values calculated at these solid circles with respect to the corresponding crack extensions. Tohgo and Ishii [9] separated the J-value for mixed-mode I and II specimens as, T I II J J J = + , (5) where, JI and JII correspond to the energy release rate contributed by the bending and shear deformation of the crack plane, respectively. 3. Validation on SE(B) Specimen This section presents the validation of the proposed CMOD-based hybrid approach based on the
RkJQdWJsaXNoZXIy MjM0NDE=