Abstract
The symmetric-Galerkin boundary element method (SGBEM) has previously been employed to model 2-D crack growth in particulate composites under quasi-static loading conditions. In this paper, an initial attempt is made in extending the simulation technique to analyze the interaction between a growing crack and clusters of perfectly bonded particles in a brittle matrix under cyclic loading conditions. To this end, linear elastic fracture mechanics and no hysteresis are assumed. Of particular interest is the role clusters of inclusions play on the fatigue life of particulate composites. The simulations employ a fatigue crack growth prediction tool based upon the SGBEM for multiregions, a modified quarter-point crack-tip element, the displacement correlation technique for evaluating stress intensity factors, a Paris law for fatigue crack growth rates, and the maximum principal stress criterion for crack-growth direction. The numerical results suggest that this fatigue crack growth prediction tool is as robust as the quasi-static crack growth prediction tool previously developed. The simulations also show a complex interplay between a propagating crack and an inclusion cluster of different densities when it comes to predicting the fatigue life of particulate composites with various volume fractions.
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References
Kitey R., Phan A.-V., Tippur H.V., Kaplan T.: Modeling of crack growth through particulate clusters in brittle matrix by symmetric-Galerkin boundary element method. Int. J. Fract. 141, 11–25 (2006)
Williams R.C., Phan A.-V., Tippur H.V., Kaplan T., Gray L.J.: SGBEM analysis of crack growth and particle(s) interactions due to elastic constants mismatch. Eng. Fract. Mech. 74, 314–331 (2007)
Hartmann F.: Introduction to Boundary Elements—Theory and Applications. Springer, Berlin (1989)
Bonnet M., Maier G., Polizzotto C.: On symmetric Galerkin boundary element method. ASME Appl. Mech. Rev. 51, 669–704 (1998)
Gray L.J.: Evaluation of hypersingular integrals in the boundary element method. Math. Comput. Model. 15, 165–174 (1991)
Martin P.A., Rizzo F.J.: Hypersingular integrals: how smooth must the density be? Int. J. Numer. Methods Eng. 39, 687–704 (1996)
Blackburn W.S., Hall W.S., Rooke D.P.: Numerical simulation of the initiation and growth of new fatigue cracks following crack intersections. Int. J. Fatigue 17, 437–446 (1995)
Prasad N.N.V., Aliabadi M.H., Rooke D.P.: Thermomechanical fatigue crack growth. Int. J. Fatigue 18, 349–361 (1996)
Cisilino A.P., Aliabadi M.H.: Three-dimensional BEM analysis for fatigue crack growth in welded components. Int. J. Pres. Ves. Piping 70, 135–144 (1997)
Blackburn W.S.: Three dimensional calculation of growth of cracks starting in parallel planes by boundary elements. Int. J. Fatigue 21, 933–939 (1999)
dell’Erba D.N., Aliabadi M.H.: Three-dimensional thermo-mechanical fatigue crack growth using BEM. Int. J. Fatigue 22, 261–273 (2000)
Yang B., Mall S., Ravi-Chandar K.: A cohesive zone model for fatigue crack growth in quasibrittle materials. Int. J. Solids Struct. 38, 3927–3944 (2001)
Dirgantara T., Aliabadi M.H.: Numerical simulation of fatigue crack growth in pressurized shells. Int. J. Fatigue 24, 725–738 (2002)
Cisilino A.P., Aliabadi M.H.: Dual boundary element assessment of three-dimensional fatigue crack growth. Eng. Anal. Boundary Elements 28, 1157–1173 (2004)
Yngvesson M., Nilsson F.: Fatigue crack growth of surface cracks under non-symmetric loading. Eng. Fract. Mech. 63, 375–393 (1999)
Spievak L.E., Wawrzynek P.A., Ingraffea A.R., Lewicki D.G.: Simulating fatigue crack growth in spiral bevel gears. Eng. Fract. Mech. 68, 53–76 (2001)
Barlow K.W., Chandra R.: Fatigue crack propagation simulation in an aircraft engine fan blade attachment. Int. J. Fatigue 27, 1661–1668 (2005)
Yan X.: Multiple crack fatigue growth modeling by displacement discontinuity method with crack-tip elements. Appl. Math. Model. 30, 489–508 (2006)
Yan X.: A boundary element modeling of fatigue crack growth in a plane elastic plate. Mech. Res. Commun. 33, 470–481 (2006)
Xiang Z., Lie S.T., Wang B., Cen Z.: A simulation of fatigue crack growth in a welded T-joint using 3D boundary element method. Int. J. Pres. Ves. Piping 80, 111–120 (2003)
Sekine H., Yan B., Yasuho T.: Numerical simulation study of fatigue crack growth behavior of cracked aluminum panels repaired with a FRP composite patch using combined BEM/FEM. Eng. Fract. Mech. 72, 2549–2563 (2005)
Henshell R.D., Shaw K.G.: Crack tip finite elements are unnecessary. Int. J. Numer. Methods Eng. 9, 495–507 (1975)
Barsoum R.S.: On the use of isoparametric finite elements in linear fracture mechanics. Int. J. Numer. Methods Eng. 10, 25–37 (1976)
Blandford G.E., Ingraffea A.R., Liggett J.A.: Two-dimensional stress intensity factor computations using the boundary element method. Int. J. Numer. Methods Eng. 17, 387–404 (1981)
Gray L.J., Paulino G.H.: Crack tip interpolation, revisited. SIAM J. Appl. Math. 58, 428–455 (1998)
Gray L.J., Phan A.-V., Paulino G.H., Kaplan T.: Improved quarter-point crack tip element. Eng. Fract. Mech. 70, 269–283 (2003)
Phan A.-V., Gray L.J., Kaplan T.: On some benchmarch results for the interaction of a crack with a circular inclusion. ASME J. Appl. Mech. 74, 1282–1284 (2007)
Erdogan F., Sih G.C.: On the crack extension in plates under plane loading and transverse shear. J. Basic Eng. 86, 519–527 (1963)
Rizzo F.J.: An integral equation approach to boundary value problems of classical elastostatics. Q. Appl. Math. 25, 83–95 (1967)
Maier G., Diligenti M., Carini A.: A variational approach to boundary element elastodynamic analysis and extension to multidomain problems. Comp. Methods Appl. Eng. 92, 193–213 (1991)
Hölzer S.M.: How to deal with hypersingular integrals in the symmetric BEM. Comm. Numer. Methods Eng. 9, 219–232 (1993)
Gray L.J., Paulino G.H.: Symmetric Galerkin boundary integral formulation for interface and multi-zone problems. Int. J. Numer. Methods Eng. 40, 3085–3101 (1997)
Williams M.L.: Stress singularities resulting from various boundary conditions in angular corners of plates in extension. ASME J. Appl. Mech. 19, 526–528 (1952)
Williams M.L.: On the stress distribution at the base of a stationary crack. ASME J. Appl. Mech. 24, 109–114 (1957)
Martin P.A.: End-point behavior of solutions to hypersingular equations. Proc. R. Soc. Lond. A 432, 301–320 (1991)
Sih G.C.: Strain energy density factor applied to mixed mode crack problems. Int. J. Fract. 10, 305–321 (1974)
Paris P.C., Erdogan F.A.: A critical analysis of crack propagation laws. Trans. ASME J. Basic Eng. 85, 528–534 (1963)
Portela A., Aliabadi M.H., Rooke D.P.: Dual boundary element incremental analysis of crack propagation. Comput. Struct. 46, 237–247 (1993)
Brown E.N., White S.R., Sottos N.R.: Retardation and repair of fatigue cracks in a microcapsule toughened epoxy composite—Part I: Manual infiltration. Compos. Sci. Technol. 65, 2466–2473 (2005)
Sih G.C., Barthelemy B.M.: Mixed mode fatigue crack growth predictions. Eng. Fract. Mech. 3, 439–451 (1980)
Frost N.E., Dugdale D.S.: The propagation of fatigue cracks in sheet specimens. J. Mech. Phys. Solids 6, 92–110 (1958)
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Roberts, D.J., Phan, AV., Tippur, H.V. et al. SGBEM modeling of fatigue crack growth in particulate composites. Arch Appl Mech 80, 307–322 (2010). https://doi.org/10.1007/s00419-009-0318-x
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DOI: https://doi.org/10.1007/s00419-009-0318-x