S. Boljanović et alii, Frattura ed Integrità Strutturale, 35 (2016) 313-321; DOI: 10.3221/IGF-ESIS.35.36 320 Fig.4b, respectively. The evaluated number of loading cycles for the pin-loaded lug is compared with experimental results [23]. Figs. 4a and 4b show that the calculations related to the lug configuration with semi-elliptical crack emanating from a hole, are in a good agreement with experimental observations. Now, for the same lug the crack growth path is simulated employing, step-by-step, the computed stress intensity factor for different crack increments. It should be noted that in every step, the crack length in surface direction is calculated thanks to the crack length in dept direction and the stress intensity factors from the preceding step. For the calculation of the stress intensity factor as well as crack lengths in surface direction, Eqs. (3)-(13) and (1a) and (1b) are used. The modeled crack growth paths for different crack lengths in depth direction are presented in Fig.4a and Fig.4b, respectively. Note that direction of x and y axels correlate with surface of the lug and the lug hole, respectively. C ONCLUSIONS computational model for crack growth analysis of the pin-loaded lug under cyclic loading is developed. The crack propagation process of either semi-elliptical crack or through-the-thickness crack emanating from a hole of the lug is investigated through the stress analysis and the residual life estimation. Further, the crack path is simulated for semi-elliptical crack configuration. For the stress analysis analytical and/or numerical approaches are employed. The stress field of the lug with semi-elliptical crack is evaluated by applying quarter-point (Q-P) singular finite element. Then, the two-parameter driving force crack growth model is employed in order to calculate the strength of lug. The comparison between the calculations and experimental results point out that developed mathematical model can be applied for reliable residual life estimation of the lug with semi-elliptical crack and through-the-thickness crack. A CKNOWLEDGEMENTS he authors would like to thank the Mathematical Institute of the Serbian Academy of Sciences and Arts and the Ministry of Science and Technological Development, Serbia for providing financial support of this research under Grant No. OI 174001. R EFERENCES [1] Shah, R.C., Stress intensity factors for through and part-through originating at fastener holes, In: Mechanics of crack growth, ASTM STP 590 (1976) 429-459. [2] Schijve, J., Hoeymakers, S.H.M., Fatigue crack growth in lugs, Fatigue Eng. Mater. Struct., 1 (1979) 185-201. [3] Impellizeri, L.F., Rich, D.L., Spectrum fatigue crack growth in lugs. In: Fatigue crack growth under spectrum loads, ASTM STP 595 (1976) 320-336. [4] Vainshok, V.A., Varfolomeyev, I.V., Stress intensity factor analysis for part-elliptical cracks in structures, Int. J. Fracture, 46 (1990) 1-24. [5] Sih, G.C., Chen, C., Non-self similar crack growth in elastic-plastic finite thickness plate, Theor. Appl. Fract. Mech., 3 (1985) 125-139. [6] Raju, I.S., Newman, Jr. J.C., Stress intensity factor for two symmetric corner cracks. In: Smith C.W., editor. Fracture mechanics, ASTM STR (1979) 411-430. [7] Smith, C.W., Jolls, M., Peters, W.H., Stress intensities for cracks emanating from pin-loaded holes. In: Flaw growth and fracture, ASTM STP 631 (1977) 190-201. [8] Grandt, Jr. A.F., Kullgren, T.E., Stress intensity factors for corner cracked holes under general loading conditions, J. Eng. Mater. Technol., 103 (1981) 171-176. [9] Paris, P.C., Erdogan, F.A., A critical analysis of crack propagation laws, J. Basic Eng. Trans. SME, Series D, 55 (1963) 528-534. [10] Forman, R.G., Study of fatigue crack initiation from flaws using fracture mechanic theory, Eng. Fract. Mech., 4 (1972) 333-345. [11] Weertman, J., Rate of growth of fatigue cracks calculated from the theory of indefinitesimal dislocations distributed on a plane, Int. J. Fract. Mech., 2 (1966) 460-467. A T

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