### A New Scheme for Crack Growth Modeling by Coupling Modified Quarter Point Crack-Tip Element and the Level Set Method

Y Abdelaziz

#### Abstract

In this paper, an efficient, numerical procedure is presented to track crack growth modeling without remeshing. The method's key feature is the coupling of a modified quarter-point crack tip element (MQPE) with the level set method (LSM) for crack growth problems. The LSM was used to represent the crack location, including the location of crack tips. The MQPE was used to compute the stress and displacement fields necessary for determining the rate of crack growth. Numerical test cases including various geometrical exceptions (the center-crack plate specimen, the single edge-crack plate specimen, and the double-edge crack plate) demonstrate the accuracy, robustness, and efficiency of the MQPE/LSM coupling. The extrapolation technique was used to estimate numerically the calibration factor for various specimens. This work confirms the feasibility of the MQPE/LSM to model accurately the singularity existing in the vicinity of the cracks. It allows an economic and adequate calculation of the stress intensity factors, which can be introduced into the various criteria of fracture or laws of propagation of the crack. The new method reduces the need for remeshing, and results agree well with reference data.

#### Keywords

Fracture, Crack, Singularity, SIFs, MQPE, Level set method, Calibration factors

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#### References

Abdelaziz Y, Benkeira S, Rikioui T, Mekkaoui A (2010), A double degenerated finite element for modeling the crack tip singularity. Applied Mathematical Modeling 34:4031-39.

Alashoaibi A, Arifin K (2006), Finite element simulation of stress intensity factors in elastic-plastic crack growth. J Zhejiang Univ Sci. A:1336-42.

Anderson TL (2005), Fracture mechanics: Fundamentals and Applications. Boca Raton, Florida, USA, CRC Press.

Barsoum RS (1974), Application of quadratic isoparametric finite elements in linear fracture mechanics. Int J Fract. 10:603-5.

Belytschko T, Black T (1999), Elastic crack growth in finite elements with minimal remeshing. Int J Numer Meth Eng. 45:601-20.

Chen Y, Hasebe N (1995), New integration scheme for the branch crack problem. Eng Fract Mech. 52:791-801.

Cruse TA (1988), Boundary element analysis in computational fracture mechanics. Norwell, Massachusetts, Kluwer Academic Publishing.

Fleming M, Chu Y, Moran B, Belytschko T (1997), Enriched element-free Galerkin methods for crack tip fields. Int J Numer Methods Eng. 40:1483- 1504.

Gifford J, Hilton P (1978), Stress intensity factors by enriched finite elements. Eng Fract Mech. 10:485- 96.

Gray L, Phan A, Paulino H, Kaplana T (2003), Improved quarter point crack tip element. Eng Fract Mech. 70:269-83.

Long Y, Cen S, Long Z (2009), Advanced finite element method in structural engineering.

Nestor P (2004), Fracture Mechanics. Dordrecht, The Netherlands, Kluwer Academic Publishers.

Newman J (1971), An improved method of collocation for the stress analysis of cracked plates with various shaped boundaries. Technical Report TN D-6376 NASA.

Nisitani H (1985), Body force method for determination of the stress intensity factors. J Aeronautical Soc India (Special Issue on Fracture Mechanics) 37:21-41.

Osher S, Sethian JA (1988), Fronts propagating with curvature-dependent speed : Algorithms based on Hamilton-Jacobi formulations. J Comput. Phys 79:12-49.

Oliver J (1995), Continuum modeling of strong discontinuities in solid mechanics using damage models. Comput Mech. 17:49-61.

Oñate E (2009), Structural analysis with the finite element method. Linear Statics: Vol. 1, Basis and Solids. Wiesbaden, Germany, Springer Science + Business Media.

Rashid M (1998), The arbitrary local mesh refinement method: an alternative to remeshing for crack propagation analysis. Comput Meth Appl Mech Eng. 154:133-50.

Sneddon I (1973), Integral transform methods, in: Methods of Analysis and Solutions of Crack Problems. Leyden, The Netherlands, Nordhoff International.

Souiyah M, Muchtar A, Alshoaibi A, Ariffin AK (2009), Finite element analysis of the crack propagation for solid materials. J App Sci 6:1396- 1402.

Tada H, Paris P (2000), The stress analysis of cracks handbook. New York, USA, ASME Press.

DOI: http://dx.doi.org/10.24200/tjer.vol10iss2pp46-51

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