Abstract
The computation of stress intensity factors (SIFs) for two- and three-dimensional cracks based on crack opening displacements (CODs) is presented in linear elastic fracture mechanics. For the evaluation, two different states are involved. An approximated state represents the computed displacements in the solid, which is obtained by an extended finite element method (XFEM) simulation based on a hybrid explicit-implicit crack description. On the other hand, a reference state is defined which represents the expected openings for a pure mode I, II and III. This reference state is aligned with the (curved) crack surface and extracted from the level-set functions, no matter whether the crack is planar or not. Furthermore, as only displacements are fitted, no additional considerations for pressurized crack surfaces are required. The proposed method offers an intuitive, robust and computationally cheap technique for the computation of SIFs where two- and three-dimensional crack configurations are treated in the same manner.
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References
Anderson, T.L.: Fracture mechanics: fundamentals and applications. CRC, Boca Raton (2005)
Belytschko, T., Black, T.: Elastic crack growth in finite elements with minimal remeshing. Int. J. Numer. Methods Eng. 45, 601–620 (1999)
Bourdin, B., Francfort, G., Marigo, J.: Numerical experiments in revisited brittle fracture. J. Mech. Phys. Solids 48, 797–826 (2000)
Cazes, F., Moës, N.: Comparison of a phase-field model and of a thick level set model for brittle and quasi-brittle fracture. Int. J. Numer. Methods Eng. 103, 114–143 (2015)
Chan, S.K., Tuba, I.S., Wilson, W.K.: On the finite element method in linear fracture mechanics. Eng. Fract. Mech. 2, 1–17 (1970)
Dolbow, J., Gosz, M.: On the computation of mixed-mode stress intensity factors in functionally graded materials. J. Solids Struct. 39, 2557–2574 (2002)
Duflot, M.: A study of the representation of cracks with level sets. Int. J. Numer. Methods Eng. 70, 1261–1302 (2007)
Fett, T.: Stress Intensity Factors and Weight Functions for Special Crack Problems, vol. 6025. FZKA, Karlsruhe (1998)
Fries, T.: A corrected XFEM approximation without problems in blending elements. Int. J. Numer. Methods Eng. 75, 503–532 (2008)
Fries, T., Baydoun, M.: Crack propagation with the extended finite element method and a hybrid explicit-implicit crack description. Int. J. Numer. Methods Eng. 89, 1527–1558 (2012)
Fries, T., Belytschko, T.: The extended/generalized finite element method: an overview of the method and its applications. Int. J. Numer. Methods Eng. 84, 253–304 (2010)
Gravouil, A., Moës, N., Belytschko, T.: Non-planar 3D crack growth by the extended finite element and level sets - Part II: level set update. Int. J. Numer. Methods Eng. 53, 2569–2586 (2002)
Gray, L., Phan, A., Paulino, G., Kaplan, T.: Improved quarter-point crack tip element. Eng. Fract. Mech. 70, 269–283 (2003)
Haboussa, D., Gregoire, D., Elguedj, T., Maigre, H., Combescure, A.: X-FEM analysis of the effects of holes or other cracks on dynamic crack propagations. Int. J. Numer. Methods Eng. 86, 618–636 (2011)
Miehe, C., Hofacker, M., Welschinger, F.: A phase field model for rate-independent crack propagation: robust algorithmic implementation based on operator splits. Comput. Methods Appl. Mech. Eng.. 199, 2765–2778 (2010)
Moës, N., Belytschko, T.: Extended finite element method for cohesive crack growth. Eng. Fract. Mech. 69, 813–833 (2002)
Moës, N., Dolbow, J., Belytschko, T.: A finite element method for crack growth without remeshing. Int. J. Numer. Methods Eng. 46, 131–150 (1999)
Moës, N., Gravouil, A., Belytschko, T.: Non-planar 3D crack growth by the extended finite element and level sets - Part I: mechanical model. Int. J. Numer. Methods Eng. 53, 2549–2568 (2002)
Moës, N., Stolz, C., Bernard, P.E., Chevaugeon, N.: A level set based model for damage growth: the thick level set approach. Int. J. Numer. Methods Eng. 86, 358–380 (2011)
Nejati, M., Paluszny, A., Zimmerman, R.: On the use of quarter-point tetrahedral finite elements in linear elastic fracture mechanics. Eng. Fract. Mech. 144, 194–221 (2015)
Nikishkov, G.P.: Accuracy of quarter-point element in modeling crack-tip fields. Comput. Model. Eng. Sci. 93, 335–361 (2013)
Peng, D., Merriman, B., Osher, S., Zhao, H., Kang, M.: A PDE-based fast local level set method. J. Comput. Phys. 155, 410–438 (1999)
Stolarska, M., Chopp, D., Moës, N., Belytschko, T.: Modelling crack growth by level sets in the extended finite element method. Int. J. Numer. Methods Eng. 51, 943–960 (2001)
Sukumar, N., Moës, N., Moran, B., Belytschko, T.: Extended finite element method for three-dimensional crack modelling. Int. J. Numer. Methods Eng. 48, 1549–1570 (2000)
Tada, H., Paris, P.C., Irwin, G.R.: The Analysis of Cracks Handbook. ASME Press, New York (2000)
Walters, M., Paulino, G., Dodds, R.: Interaction integral procedures for 3-D curved cracks including surface tractions. Eng. Fract. Mech. 72, 1635–1663 (2005)
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Schätzer, M., Fries, TP. (2016). Stress Intensity Factors Through Crack Opening Displacements in the XFEM. In: Ventura, G., Benvenuti, E. (eds) Advances in Discretization Methods. SEMA SIMAI Springer Series, vol 12. Springer, Cham. https://doi.org/10.1007/978-3-319-41246-7_7
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