13th International Conference on Fracture June 16–21, 2013, Beijing, China -4- 13 2 3 2 3 (0, , ) 0 ( ,0 / 2) 0 x x x W x t δσ = ≤ ≤ ≤ ≤ (5) 1 2 3 0 2 3 ( / 2, , ) (0 ,0 / 2) u L x x u x W x t δ = ≤ ≤ ≤ ≤ (6) 12 2 3 2 3 ( / 2, , ) 0 (0 ,0 / 2) L x x x W x t δσ = ≤ ≤ ≤ ≤ (7) 13 2 3 2 3 ( / 2, , ) 0 ( ,0 / 2) 0 L x x x W x t δσ = ≤ ≤ ≤ ≤ (8) 3 1 2 1 2 ( , ,0) 0 (0 / 2,0 ) u x x x L x W δ = ≤ ≤ ≤ ≤ (9) 23 1 2 1 2 ( , ,0) 0 (0 / 2,0 ) x x x L x W δσ = ≤ ≤ ≤ ≤ (10) 13 1 2 1 2 ( , ,0) 0 (0 / 2,0 ) x x x L x W δσ = ≤ ≤ ≤ ≤ (11) ( , , ) f m c δ= where 0u is the prescribed displacement in the direction of the loading axis. In addition to the symmetry conditions, one node was fixed in the 2x -direction to prevent rigid body motion. Figure 3 Finite element model of the SENT specimen Under incrementally applied loading, stress analyses were carried out to identify the damage location according to a failure criterion. The von Mises criterion was selected as the criterion for microcracking of the matrix and the coating layer [5]. 2 2 2 22 33 33 11 11 22 ( ) ( ) ( ) δ δ δ δ δ δ σ σ σ σ σ σ − + − + − 2 2 2 2 23 31 12 6{( ) () ()}2()( , ) T m c δ δ δ δ σ σ σ σ δ + + + ≥ = (12) where T δσ is the tensile strength. The maximum stress criterion was also used to evaluate breaking of the fiber strand. 11 f f T σ σ ≥ (13) where f Tσ is the tensile strength of fiber strand. Once the failure criterion is satisfied, all of the stiffness terms are reduced to 4 1 10− × of the original value. The epoxy matrix and coating layer are assumed to be elastic and isotropic. For the epoxy matrix, the Young’s modulus and Poisson’s ratio are taken to be 3.48GPa [6] and 0.35 [7], respectively, and the measured tensile strength is 70MPa. In previous work on this self-healing system [1], an investigation of tensile properties of epoxy specimens with the microcapsule and catalyst revealed that the Young’s modulus and tensile strength of the specimen decreased with increasing the microcapsule concentration. Thus, the Young’s modulus, Poisson’s ratio and tensile strength of the coating layer are assumed to be 1.74GPa, 0.35 and 35MPa, respectively. The carbon fiber strand is modeled as an elastic and transversely isotropic composite (unidirectional carbon/epoxy composite) with properties as shown in Table 1 [8]. ( 1E , 2E , 3E ) are the Young’s moduli, ( 12 G , 23 G , 31 G ) are the shear moduli and ( 12ν , 23ν , 13ν ) are the Poisson’s ratios, and the Poisson’s ratio 12ν ( 23ν , 13ν ) x2 x1 o a0 W L/2 t/2 Coating layer Matrix Initial notch Fiber strand x3
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