13th International Conference on Fracture June 16–21, 2013, Beijing, China -7- 4. Conclusions In summary, the proposed multiscale space-time formulation with harmonic enrichment function successfully simulates the practical fatigue loading histories. To capture the fatigue crack initiation and propagation, a two-scale damage model algorithm is implemented. Damage model algorithm is integrated with the multiscale space-time FEM formulation. Standard techniques of element deletion are used to predict the fatigue crack initiation and propagation. HCF simulations are performed on the notched plate without any ad hoc procedure to predict the total fatigue life. Based on the simulations, crack length verses number of cycles curve is generated. The trend of the results is similar to what is observed in the experiments. Mode I crack growth is successfully using XTFEM. Future plan is to verify the predictions by comparing with either literature data or analytical model (e.g., Paris law crack growth predictions). In addition, different fatigue-based material model can be integrated with the framework presented. Acknowledgements The authors gratefully acknowledge the financial support of the start-up fund from the University of Texas at Dallas and the ASEE Air Force Summer Faculty Fellowship. This work was also supported in part by an allocation of computing time from the Ohio Supercomputer Center. References [1] A. Griffith, "The Phenomena of Rupture and Flow in Solids," Philosophical Transactions of the Royal Society of London, vol. 221, pp. 163-198, 1920. [2] G. Irwin, "Analysis of stresses and strains near to the end of crack traversing a plate," ASME Journal of Applied Mechanics, vol. 24, pp. 361-364, 1957. [3] P. C. Paris and F. Erdogan, "A critical analysis of crack propagation laws," J basic Eng, vol. 85, pp. 209-219, 1963. [4] L. Molent, M. McDonald, S. Barter, and R. Jones, "Evaluation of spectrum fatigue crack growth using variable amplitude data," International Journal of Fatigue, vol. 30, pp. 119-137, 2008. [5] G. M. Hulbert and T. J. R. Hughes, "Space-Time Finite-Element Methods For 2nd-Order Hyperbolic-Equations," Computer Methods In Applied Mechanics And Engineering, vol. 84, pp. 327-348, Dec 1990. [6] S. U. Chirputkar and D. Qian, "Coupled atomistic/continuum simulation based on extended space-time finite element method," Cmes-Computer Modeling In Engineering & Sciences, vol. 24, pp. 185-202, Feb 2008. [7] J. Chessa and T. Belytschko, "Arbitrary discontinuities in space-time finite elements by level sets and X-FEM," International Journal for Numerical Methods in Engineering, vol. 61, pp. 2595-2614, 2004. [8] Y. Yang, S. Chirputkar, D. N. Alpert, T. Eason, S. Spottswood, and D. Qian, "Enriched space-time finite element method: a new paradigm for multiscaling from elastodynamics to molecular dynamics," International Journal for Numerical Methods in Engineering, vol. 92, pp. 115-140, Oct 12 2012. [9] J. Lemaitre, J. P. Sermage, and R. Desmorat, "A two scale damage concept applied to fatigue," International Journal of Fracture, vol. 97, pp. 67-81, 1999.
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