Keywords: boundary element method, response surface method, fatigue crack growth, reliability analysis.

Fatigue crack propagation problems have been widely studied in the past years, because crack growth, coalescence and localisation phenomena can explain most of the structural failures. The accurate modelling of engineering structures, including complex geometry and boundary conditions, requires numerical techniques in order to take into account the boundary condition changes at each crack increment. The boundary element method (BEM) implies only the discretization of the boundary and crack surface. In the present work, the dual BEM which singular (displacement integral equation) and hyper-singular (traction integral equation) integral equations is adopted [1]. The displacement integral equations are used for collocation points along the crack surface, whereas the traction integral equations are used for collocation points along the opposite crack surface. This technique avoids singularities in the resulting algebraic system of equations. The fracture mechanics parameters are evaluated using the displacement correlation technique for the stress intensity factors and the maximum circumferential stress criterion to predict the direction of crack growth; Paris law is adopted to calculate the structural fatigue life.

As fatigue crack growth is highly affected by uncertainties, the deterministic methods fail to predict accurately the structural life [2]. The probabilistic models are therefore necessary to take into account the random parameters related to structural geometry, initial crack size, material properties and loading history.

The present work aims at coupling the reliability analysis with the BEM, for probabilistic mixed mode fatigue crack propagation [3]. The direct method and the response surface method have been applied to solve the reliability problem. The failure probability and the most likely failure point are correctly obtained by both methods. Although both methods can be applied to engineering structures, the numerical applications have shown that the direct method is more efficient than the response surface method. The proposed procedures have the capability of dealing with practically any engineering structure undergoing fatigue crack growth, including material heterogeneity and time-varying load cycles.

1

E.D. Leonel, W.S. Venturini, "Dual boundary element formulation applied to analysis of multi-fractured domains", Engineering Analysis with Boundary Elements, 34, 1092-1099, 2010. doi:10.1016/j.enganabound.2010.06.014

2

W.K. Liu, Y. Chen, T. Belytschko, Y.J. Lua, "Three Reliability methods for fatigue crack growth", Engineering Fracture Mechanics, 53, 733-752, 1996. doi:10.1016/0013-7944(95)00133-6

3

E.D. Leonel, A. Chateauneuf, W.S. Venturini, P. Bressolette, "Coupled reliability and boundary element model for probabilistic fatigue life assessment in mixed mode crack propagation", International Journal of Fatigue, 32, 1823-1834, 2010. doi:10.1016/j.ijfatigue.2010.05.001

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