13th International Conference on Fracture June 16–21, 2013, Beijing, China -9- Through the examples above-presented, we can confirm that the proposed non-local crack growth models are highly accurate and efficient for the prediction of crack onset and crack propagation. Fracture in complicated microstructures can easily be simulated. Another notable advantage of the present method is its capacity to evaluate multiple crack growth as it doesn’t require the calculation of the energy release rate at each crack tip. The theoretical concept of the proposed non-local fracture criterion is clear and simple. The numerical model is robust, easy to apply to different engineering structures subjected to thermal shock. References [1] McClintock, F. A., 1958. Ductile Fracture Instability in Shear. J. Appl. Mech., 10, 582-588 [2] Irwin G, (1968), Linear fracture mechanics, fracture transition and fracture control, Eng. Fract. Mech., 1:241-257 [3] Ritchie, R., Knott, J., and Rice, J., 1973. On the Relation between Critical Tensile Stress and Fracture Toughness in Mild Steel. J. Mech. Phys. Solids, 21, 395-410 [4] Seweryn, A., Lukaszewicz, A., 2002. Verification of Brittle Fracture Criteria for Elements with V-shaped Notches. Eng. Fract. Mech., 69, 1487-1510 [5] Leguillon, D., 2002. Strength or Toughness? A Criterion for Crack Onset at a Notch, Eur. J. Mech. A/Solids, 21, 61-72 [6] Barenblatt, G., 1959. The Formation of Equilibrium Cracks During Brittle Fracture, J. Appl. Math. Mech., 23, 434-444. [7] Dugdale, D., 1960. Yielding of Steel Sheets Containing Slits. J. Mech. Phys. Solids, 8, 100–104. [8] Xu, X. P., and Needleman, A., 1994. Numerical Simulation of Fast Crack Growth in Brittle Solids. J. Mech. Phy. Solids, 42, pp. 1397-1434 [9] Camacho, G.T., and Ortiz M., 1996. Computational Modelling of Impact Damage in Brittle Materials, Int. J. Solids Struct., 33, 2899–938. [10] Mohammed, I., and Liechti, K.M., 2000. Cohesive Zone Modelling of Crack Nucleation at Bimaterial Corners. J. Mech. Phys. Solids, 48, 735–64. [11] Pijaudier-Cabot, G., Bazant, Z.P., 1987. Nonlocal damage theory. J. of Engng. Mechanics, ASCE, 113, 1512-1533. [12] Peerlings, R., de Borst, R., Brekelmans, W., De Vree, J., Spee, I., 1996. Some observations on localisation in non-local and gradient damage models. Eur. J. Mech. A/Solid, 15(6), 937-953 [13] Frémond, M., Nedjar, B., 1996. Damage, gradient of damage and principle of virtual power. Int. J. Solids Struct. 33, 1083-1103 [14] Francfort, G., Marigo, J-J., 1998. Revisiting brittle fracture as an energy minimization problem, J. Mech. Phys. Solids, 46, 1319-1342. [15] Bourdin, B., Francfort, G., Marigo, J-J., 2000. Numerical experiments in revisited brittle fracture, J. Mech. Phys. Solids, 48, 797-826. [16] Williams ML, (1961), The bending stress distribution at the base of a stationary crack. J. of Appl. Mech., 28:78–82 [17] Moulinec H, Suquet P (1998), A numerical method for computing the overall response of nonlinear composites with complex microstructure. Comput. Methods Appl. Mech. Engrg.; 157:69–94
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