13th International Conference on Fracture June 16–21, 2013, Beijing, China -7- max ( ) exp( )(1 0.001 ) / c n n F A B T u λ σ λ λ λ δ = − − = (5) Table 2 The constants in Eq.(12) Simulated temperature (K) σmax(GPa) A B C 300 8.61 3.75 2.73 0.37 0 2 4 6 8 10 0 0.2 0.4 0.6 0.8 1 σyy(GPa) non-dimension parameter(λ) T-λ smooth curve fitting curve Figure 10. T-λ relationship 5. Simulation of the T-S fracture test In order to model stable crack growth under static loading and analyze cohesive behavior derived from MD towards greater length scales, we perform a simulation of crack growth for a CT specimen subject to displacement loading via prescribed motion of loading pins. Fracture of a CT specimen can verify whether the cohesive law derived from MD simulations displays behavior consistent with linear elastic fracture mechanics. The geometry and mesh of our CT specimen is shown in Fig.11. The specimen is 384 nm wide by H = 369 nm tall, with an effective width (the distance between the pin holes and the uncracked edge) of W = 307 nm, an initial crack length of a = 155 nm (a/W ≈ 0.5), and pin holes of radius 38.4 nm. Cohesive elements are placed along the predefined crack path, and are 1Å wide. The displacement loadings are applied on reference points, i.e. PR-1 and PR-2. The parameterized T-S law given was implemented in ABAQUS to simulate the behavior of the CZM.
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