Propagation of Crack in Linear Elastic Materials with Considering Crack Path Correction Factor

Document Type : Persian


1 Assistant Professor, Mechanical Engineering Department, Isfahan University of Technology

2 M.Sc., Mechanical Engineering Department, Isfahan University of Technology


Modeling of crack propagation by a finite element method under mixed mode conditions is of prime importance in the fracture mechanics. This article describes an application of finite element method to the analysis of mixed mode crack growth in linear elastic fracture mechanics. Crack - growth process is simulated by an incremental crack-extension analysis based on the maximum principal stress criterion which is expressed in terms of the stress intensity factor. In this paper a procedure is employed to correct direction of crack propagation to ensure that a unique final crack path is achieved for different analysis of a problem by using different increments of crack. For each increment of crack extension, finite element method is applied to perform a single - region stress analysis of the cracked structure. Results of this incremental crack – extension analysis are presented for several geometries.


[1] Aliabadi M. H., Boundary element method, Queen mary, UK, 2002.
[2] Tracy D. M., Finite elements for determination of crack tip elastic stress intensity factors, Engineering Fracture Mechanics, Vol. 3, 1971, pp. 255-265.
[3] Fehl B. D., Truman K. Z., An evaluation of fracture mechanics quarter – point displacement techniques used for computing stress intensity factors, Engineering Structures, Vol. 21, 1999, pp. 406-415.
[4] Mahajan R. V., Ravi–Chandar K., An experimental investigation of mixed – mode fracture, International Journal of fracture, Vol. 41, 1989, pp.235-252.
[5] Rethore J., Gravouil A., Combescure A., A stable numerical scheme for the finite element simulation of dynamic crack propagation with remeshing, Comput. Methods Appl. Mech. Engg., Vol. 193, 2004, pp. 4493-4510,.
[6] Kaufman J. G., Moore R. L., Schilling P. E., Fracture toughness of structural aluminum alloys, Engineering Fracture Mechanics, Vol. 2, 1970, pp. 197-210,.
[7] Grigoriu M., Saif M. T. A., Borgi S., Ingraffea A. R., mixed mode fracture initiation and
trajectory prediction under random stresses, International Journal of fracture, Vol.45, 1990, pp. 19-34.
[8] Aliabadi M. H., Young A., Wen P.H., Crack growth analysis for malti – layerd airframe structures by boundary element method, Engineering Fracture Mechanics, Vol. 71, 2004, pp. 619-631.
[9] عباسی، ع، تحلیل مسائل ترک در محدوده الاستیک خطی به روش اجزا محدود با کمک نرم‎افزارANSYS، پایان‎نامه کارشناسی ارشد، دانشکده مهندسی مکانیک، دانشگاه صنعتی اصفهان، 1380.
[10] Reddy J. N., An introduction to the finite element method, Second Edition, McGraw–Hill, Inc., New York, 1993.
[11] Gdoutos E. E., problems of mixed mode crack propagation, Martinus Nijhoff, Netherlands, 1984.
[12] Gomez L. H. H., Meza I. S., Calderon, G. U., Balankin, A. S., Susarrey, O., Evaluation of crack initiation angle under mixed mode loading at diverse strain rates, Theoretical and Applied Fracture Mechanics, Vol. 42, 2004, pp. 53-61.
[13] Parton, V. Z., Morozov, E. M., Elastic – plastic fracture mechanics, Mir Publishers, 1978.
[14] Rashid M. M., The arbitrary local mesh replacement method: An alternative to remeshing for crack propagation analysis, Comput. Methods Appl. Mech. Eng., Vol.154, 1998, pp.133-150,.
[15] Bouchard P. O., Bay F., Chastel Y., Tovena I., Crack propagation modeling using an advanced remeshing technique, Comput. Methods Appl. Mech. Engg. Vol. 189, 2000, pp.732-742.
[16] Portela A., Aliabadi M. H., Rooke, D. P., Dual boundary element incremental analysis of crack propagation, Computers and structures, Vol. 46. No. 2, 1993, PP.237-247.