Issue 35

S. Boljanović et alii, Frattura ed Integrità Strutturale, 35 (2016) 313-321; DOI: 10.3221/IGF-ESIS.35.36 314 stress ratio can be taken into account by the effective stress intensity factor range instead of the stress intensity range and developed the crack closure model. Based on observations related to the crack propagation under cyclic loading, Walker [13] proposed his stress-ratio dependence crack growth model. Kujawski [14] found that the crack growth propagation under cyclic loading can be simulated if the maximum stress intensity factor is involved, and introduced the two- parameter driving force model. Noroozi et al [15] took into account the combination of the maximum stress intensity factor and the stress intensity factor range together with the elastic-plastic crack tip stress-strain field and proposed a unified two-parameter crack growth model. In the present paper, computational models are formulated for the strength estimation of the damaged lug. The propagation of semi-elliptical crack emanating from the lug hole is investigated through the following issues: the stress analysis, the fatigue life evaluation and the crack path simulation. The two-parameter driving force crack growth model is applied for the failure analysis of lug under cyclic loading. The stress intensity factor is calculated by applying the finite element method and/or analytical approach. The predictive capability of proposed models is verified through the comparison between the calculations and experimental data. F ATIGUE LIFE ESTIMATION uring exploitation of cyclically loaded structural components, complex fatigue process could often lead to the unexpected failure. The crack propagation can be theoretically investigated through the cyclic rate of crack growth either in one direction (through-the-thickness crack) or in two directions (surface crack). In the present paper, the two-parameter driving force model proposed by Kujawski [14] is employed in order to simulate the propagation process under cyclic loading. Since the semi-elliptical crack is considered, the variation of crack shape can be evaluated from the crack growth rates at two positions on the crack front: the crack growth rate da/dN at the deepest point A (crack depth), and crack growth rate db/dN at point B on the lug surface (crack length), as follows:   * A m A A da C K dN   ;   0.5 * max A IA A K K K     (1a)   * B m B B db C K dN   ;   0.5 * max B IB B K K K     (1b) where: A IA K K    and B IB K K    for 0 R  , and if 0 R  , max A IA K K    and max B IB K K    . Then, the number of loading cycles up to failure for both directions can be calculated if above relationships related to the crack growth rate are integrated i.e.:   0 * f A a m a A A da dN C K    (2a)   0 * f B b m b B B db dN C K    (2b) where C A , C B , m A and m B are material constants experimentally obtained, N denotes the number of loading cycles up to failure, R is the stress ration,  K IA ,  K IB , and  K IA max ,  K IB max represent the stress intensity factor ranges and maximum stress intensity factor under mode I loading conditions for depth and surface directions, respectively, a 0 , b 0 , and a f , b f denote initial and final crack length in depth and surface directions, respectively. Since awkward functions exist in Eqs. (2a) and (2b), the residual life for appropriate incremental crack lengths in depth and surface direction can be estimated if the numerical integration is employed, and for that purpose the present authors developed the software programme based on Euler’s algorithm. D