Three-Dimensional SGBEM-FEM Alternating Method for Analyzing Fatigue-Crack Growth in and the Life of Attachment Lugs
Publication: Journal of Engineering Mechanics
Volume 141, Issue 4
Abstract
In the present paper, stress intensity factor (SIF) analyses and fatigue-crack-growth simulations of corner cracks emanating from loaded pinholes of attachment lugs in structural assemblies are carried out for different load cases. A three-dimensional (3D) symmetric Galerkin boundary-element method (SGBEM) and FEM alternating method is developed to analyze the nonplanar growth of these surface cracks under general fatigue. The 3D SGBEM-FEM alternating method involves two very simple and coarse meshes that are independent of each other: (1) a very coarse FEM mesh to analyze the uncracked lug, and (2) a very coarse SGBEM mesh to model only the growing crack surface. By using the SGBEM-FEM alternating method, the nonplanar growth of cracks in 3D (surfaces of discontinuity) up to the failure of structures are efficiently simulated, and accurate estimations of fatigue lives are made. The accuracy and reliability of the SGBEM-FEM alternating method are verified by comparing them to other FEM solutions, as well as experimental data for fatigue-crack growth available in the open literature. The SIF calculations, crack surface evolutions, and fatigue-life estimations are all in good agreement with other detailed FEM solutions and experimental observations. It is noted that for fracture and fatigue analyses of complex 3D structures such as attachment lugs, a pure FEM requires several hundreds of thousands or even millions of elements, whereas the present 3D SGBEM-FEM alternating method requires only up to 1,000 FEM elements and SGBEM elements. It thus demonstrates that the present SGBEM-FEM alternating method, among the many Schwartz-Neumann-type alternating methods developed in the past 20–30 years are suitable for analyzing fracture and fatigue-crack propagation in complex 3D structures in a very computationally efficient manner, as well as with very low human labor costs.
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgments
The first author gratefully acknowledges the financial support of the China Scholarship Council (grant 201306260034), the National Basic Research Program of China (973 Program, grant 2011CB013800), and the New Century Excellent Talents Project in China (grant NCET-12-0415).
References
Atluri, S. N. (1986). Computational methods in the mechanics of fracture, North Holland, Amsterdam, Netherlands.
Atluri, S. N. (1997). Structural integrity and durability, Tech Science Press, Forsyth, GA.
Atluri, S. N., and Kathiresan, K. (1978). “Stress analysis of typical flaws in aerospace structural components using three-dimensional hybrid displacement finite element methods.” Proc., AIAA/ASME 19th Space and Missile Defense (SMD) Conf., American Institute of Aeronautics and Astronautics (AIAA), Reston, VA, 340–350.
Atluri, S. N., Kobayashi, A. S., and Nakagaki, M. (1975). “An assumed displacement hybrid finite element model for linear fracture mechanics.” Int. J. Fract., 11(2), 257–271.
Barsoum, R. S. (1976). “Application of triangular quarter-point elements as crack tip elements of power law hardening material.” Int. J. Fract., 12(3), 463–466.
Boljanović, S. (2012). “Fatigue strength analysis of semi-elliptical surface crack.” Sci. Tech. Rev., 62(1), 10–16.
Boljanović, S., and Maksimović, S. (2011). “Analysis of the crack growth propagation process under mixed-mode loading.” Eng. Fract. Mech., 78(8), 1565–1576.
Boljanović, S., and Maksimović, S. (2014). “Fatigue crack growth modeling of attachment lugs.” Int. J. Fatigue, 58(Jan), 66–74.
Bonnet, M., Maier, G., and Polizzotto, C. (1998). “Symmetric Galerkin boundary element methods.” Appl. Mech. Rev., 51(11), 669–704.
Bowie, O. L. (1956). “Analysis of an infinite plate containing radial cracks originating at the boundary of an internal circular hole.” J. Math. Phys., 35(1), 60–71.
Carpinteri, A. (1993). “Shape change of surface cracks in round bars under cyclic axial loading.” Int. J. Fatigue, 15(1), 21–26.
Carpinteri, A. (1994). “Propagation of surface cracks under cyclic loading.” Handbook of fatigue crack propagation in metallic structures, Elsevier, Amsterdam, Netherlands, 653–705.
Carpinteri, A., Brighenti, R., and Vantadori, S. (2006). “Notched shells with surface cracks under complex loading.” Int. J. Mech. Sci., 48(6), 638–649.
Carpinteri, A., and Vantadori, S. (2009a). “Sickle-shaped cracks in metallic round bars under cyclic eccentric axial loading.” Int. J. Fatigue, 31(4), 759–765.
Carpinteri, A., and Vantadori, S. (2009b). “Sickle-shaped surface crack in a notched round bar under cyclic tension and bending.” Fatigue Fract. Eng. Mater. Struct., 32(3), 223–232.
Dong, L., and Atluri, S. N. (2012). “SGBEM (using non-hyper-singular traction BIE), and super elements, for non-collinear fatigue-growth analyses of cracks in stiffened panels with composite-patch repairs.” Comput. Model. Eng. Sci., 89(5), 417–458.
Dong, L., and Atluri, S. N. (2013a). “Fracture & fatigue analyses: SGBEM-FEM or XFEM? Part 1: 2D structures.” Comput. Model. Eng. Sci., 90(2), 91–146.
Dong, L., and Atluri, S. N. (2013b). “Fracture & fatigue analyses: SGBEM-FEM or XFEM? Part 2: 3D solids.” Comput. Model. Eng. Sci., 90(5), 379–413.
Dong, L., and Atluri, S. N. (2013c). “SGBEM Voronoi cells (SVCs), with embedded arbitrary-shaped inclusions, voids, and/or cracks, for micromechanical modeling of heterogeneous materials.” Comput. Mater. Continua, 33(2), 111–154.
Elber, W. (1971). “The significance of fatigue crack closure.” Damage tolerance in aircraft structure (ASTM STR 486), ASTM, West Conshohocken, PA, 230–242.
Erdogan, F., and Roberts, R. (1965). “A comparative study of crack propagation in plates under extension and bending.” Proc., 1st Int. Conf. on Fracture, Vol. 1, Japanese Society for Strength and Fracture of Materials, Sendai, Japan, 341–362.
Eshelby, J. D. (1951). “The force on an elastic singularity.” Philos. Trans. R. Soc. London, Ser. A, 244(877), 87–112.
Frangi, A., and Novati, G. (1996). “Symmetric BE method in two-dimensional elasticity: Evaluation of double integrals for curved elements.” Comput. Mech., 19(2), 58–68.
Frangi, A., Novati, G., Springhetti, R., and Rovizzi, M. (2002). “3D fracture analysis by the symmetric Galerkin BEM.” Comput. Mech., 28(3–4), 220–232.
Han, Z. D., and Atluri, S. N. (2002). “SGBEM (for cracked local subdomain)—FEM (for uncracked global structure) alternating method for analyzing 3D surface cracks and their fatigue-growth.” Comput. Model. Eng. Sci., 3(6), 699–716.
Han, Z. D., and Atluri, S. N. (2003). “On simple formulations of weakly-singular traction & displacement BIE, and their solutions through Petrov-Galerkin approaches.” Comput. Model. Eng. Sci., 4(1), 5–20.
Han, Z. D., and Atluri, S. N. (2007). “A systematic approach for the development of weakly-singular BIEs.” Comput. Model. Eng. Sci., 21(1), 41–52.
Heliot, J., Labbens, R., and Pellissier-Tanon, A. (1980). “Application of the boundary integral equation method to three-dimensional crack problems.” Proc., Century 2 Pressure Vessels and Piping Conference (CTPVP) Conf., ASME, New York, 1980-80-CZ/PVP-119.
Henshell, R. D., and Shaw, K. G. (1975). “Crack tip finite elements are unnecessary.” Int. J. Numer. Methods Eng., 9(3), 495–507.
Hong, H.-K., and Chen, J.-T. (1988). “Derivations of integral equations of elasticity.” J. Eng. Mech., 1028–1044.
Kathiresan, K., and Brussat, T. R. (1984). “Advanced life analysis methods: Tabulated test data for attachment lugs.” Rep. No. AFWAL-TR-84-3080, U.S. Air Force Wright Aeronautical Laboratories, Wright-Patterson AFB, OH.
Kujawski, D. (2001). “A new driving force parameter for crack growth in aluminum alloys.” Int. J. Fatigue, 23(8), 733–740.
Levén, M., and Rickert, D. (2012). “Stationary 3D crack analysis with Abaqus XFEM for integrity assessment of subsea equipment.” M.S. thesis, Chalmers Univ. of Technology, Göteborg, Sweden.
Li, S., Mear, M. E., and Xiao, L. (1998). “Symmetric weak-form integral equation method for three-dimensional fracture analysis.” Comput. Meth. Appl. Mech. Eng., 151(3–4), 435–459.
Maksimovic, S., Posavljak, S., Maksimovic, K., Nikolic, V., and Djurkovic, V. (2011). “Total fatigue life estimation of notched structural components using low-cycle fatigue properties.” Strain, 47(S2), 341–349.
Moon, J. E. (1980). “Improvements in the fatigue performance of pin-loaded lugs.” RAE Technical Rep. No. 80148, Royal Aircraft Establishment, Farnborough, U.K.
Newman, J. C., Jr. (1973). “Fracture analysis of surface- and through-cracked sheets and plates.” Eng. Fract. Mech., 5(3), 667–689.
Nikishkov, G. P., Park, J. H., and Atluri, S. N. (2001). “SGBEM-FEM alternating method for analyzing 3D non-planar cracks and their growth in structural components.” Comput. Model. Eng. Sci., 2(3), 401–422.
Nishioka, T., and Atluri, S. N. (1983). “Path-independent integrals, energy release rates, and general solutions of near-tip fields in mixed-mode dynamic fracture mechanics.” Eng. Fract. Mech., 18(1), 1–22.
Okada, H., Rajiyah, H., and Atluri, S. N. (1988). “A novel displacement gradient boundary element method for elastic stress analysis with high accuracy.” J. Appl. Mech., 55(4), 786–794.
Okada, H., Rajiyah, H., and Atluri, S. N. (1989). “Non-hyper-singular integral-representations for velocity (displacement) gradients in elastic/plastic solids (small or finite deformations).” Comput. Mech., 4(3), 165–175.
Paris, P. C., and Erdogan, F. A. (1963). “A critical analysis of crack propagation laws.” J. Fluids Eng., 85(4), 528–533.
Qian, J., and Fatemi, A. (1996). “Mixed mode fatigue crack growth: A literature survey.” Eng. Fract. Mech., 55(6), 969–990.
Raju, I. S., and Newman, J. C., Jr. (1979). “Stress intensity factors for two symmetric corner cracks.” Fracture mechanics, ASTM, West Conshohocken, PA, 411–430.
Rizzo, F. J. (1967). “An integral equation approach to boundary value problems of classical elastostatics.” Q. Appl. Math., 25(1), 83–95.
Rozumek, D. (2009). “Influence of the slot inclination angle in FeP04 steel on fatigue crack growth under tension.” Mater. Des., 30(6), 1859–1865.
Schijve, J. (1985). “Comparison between empirical and calculated stress intensity factors of hole edge cracks.” Eng. Fract. Mech., 22(1), 49–58.
Schijve, J., and Hoeymakers, A. H. W. (1979). “Fatigue crack growth in lugs.” Fatigue Fract. Eng. Mater. Struct., 1(2), 185–201.
Shah, R. C., and Kobayashi, A. S. (1972). “On the surface flaw problem.” The surface crack: Physical problems and computational solutions, ASME, New York, 79–124.
Sih, G. C., and Li, C. T. (1990). “Initiation and growth characterization of corner cracks near circular hole.” Theor. Appl. Fract. Mech., 13(1), 69–80.
Smith, C. W., Jolles, M., and Peters, W. H. (1977). “Stress intensities for cracks emanating from pin-loaded holes.” Flaw growth and fracture (ASTM STP 631), ASTM, West Conshohocken, PA, 190–201.
Tada, H., Paris, P. C., and Irwin, G. R. (2000). The stress analysis of cracks handbook, 3rd Ed., ASME, New York.
Tong, P., Pian, T. H. H., and Lasry, S. J. (1973). “A hybrid-element approach to crack problems in plane elasticity.” Int. J. Numer. Methods Eng., 7(3), 297–308.
Vijayakumar, K., and Atluri, S. N. (1981). “An embedded elliptical crack, in an infinite solid, subject to arbitrary crack-face tractions.” J. Appl. Mech., 48(1), 88–96.
Walker, E. K. (1970). “The effect of stress ratio during crack propagation and fatigue for 2024-T3 and 7076-T6 aluminum.” Effect of environment and complex load history on fatigue life (ASTM STP 462), ASTM, West Conshohocken, PA, 1–4.
Information & Authors
Information
Published In
Copyright
© 2014 American Society of Civil Engineers.
History
Received: Jun 3, 2014
Accepted: Aug 18, 2014
Published online: Sep 10, 2014
Published in print: Apr 1, 2015
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.