13th International Conference on Fracture June 16–21, 2013, Beijing, China -7- T cE e β α = (7) where α and β are two parameters need to be calibrated using experimental data. Two data points are needed to determine α and β. The tensile test provides one point. Figure 5(a) shows the 1/4 model for the tensile specimen and Figure 5(b) shows its experimental load-displacement curve. A sudden drop of the load-displacement curve suggests the onset of crack initiation. The stress and strain states for the critical element (at the geometry center of the specimen) at crack initiation are obtained through finite element analysis. The triaxiality T and strain εf are calculated as 0.45 and 0.5 respectively. Substitution of these values into Eq. (7) yields a relationship between α and β, 0.45= αe0.5 β. The next step of the calibration process seeks to match the model predicted load versus crack propagation curve with the experimental measurements for the C(T) specimen. This step entails several finite element crack growth analyses of the C(T) specimen using different values of β. Figure 4. Fracture specimens: (a) C(T) specimen, (b) M(T) specimen, (c) MSD specimen containing two cracks, (d) MSD specimen containing three cracks. The C(T) specimen has a width of 150 mm with a/W = 0.33, where a represents the initial crack length and W represents the specimen width. The quarter-symmetric finite element mesh has 27,400 eight-node, isoparametric solid elements (with reduced integration). The mesh near the crack front has six layers with varying thickness to capture the stress gradient in the thickness direction, where the thickest elements are at the symmetry plane. The elements directly ahead of the crack front have uniform in-plane dimensions (Le = 50 μm) and are governed by the GLD model. All other elements follow J2 flow plasticity. Loading of the C(T) specimen is controlled by prescribing a displacement a W L 2W 2a L 2W b a a L 2a2 L a1 a1 b b 2W (a) (b) (c) (d)
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