Two-dimensional Numerical Estimation of Stress Intensity Factors and Crack Propagation in Linear Elastic Analysis

A. Boulenouar, N. Benseddiq, M. Mazari


When the loading or the geometry of a structure is not symmetrical about the crack axis, rupture occurs in mixed mode loading and the crack does not propagate in a straight line. It is then necessary to use kinking criteria to determine the new direction of crack propagation. The aim of this work is to present a numerical modeling of crack propagation under mixed mode loading conditions. This work is based on the implementation of the displacement extrapolation method in a FE code and the strain energy density theory in a finite element code. At each crack increment length, the kinking angle is evaluated as a function of stress intensity factors. In this paper, we analyzed the mechanical behavior of inclined cracks by evaluating the stress intensity factors. Then, we presented the examples of crack propagation in structures containing inclusions and cavities.


stress intensity factor; crack propagation; mixed mode; inclusion

Full Text:



T. Denyse De Araújo, T. N. Bittencourt, D. Roehl, L. F. Martha, “Numerical Estimation of Fracture Parameters in Elastic and Elastic-plastic Analysis”, ECCOMAS 2000, European Congress on Computational Methods in Applied Sciences and Engineering, Barcelona, September, 2000.

A. B. de Morais, “Calculation of stress intensity factors by the force method”, Engineering Fracture Mechanics, Vol. 74, No. 5, pp. 739-750, 2007

J. Chang, J. Xu, Y. Mutoh, “A general mixed-mode brittle fracture criterion for cracked materials”, Engineering Fracture Mechanics, Vol. 73, No. 9, pp. 1249-1263, 2006

G. Anlas, M. H. Santare, J. Lambros, “Numerical calculation of stress intensity factors in functionally graded materials”, International Journal of Fracture, Vol. 104, No. 2, pp. 131-143, 2000

S. K. Chan, I. S. Tuba, W. K. Wilson, “On the finite element method in linear fracture mechanics”, Engineering Fracture Mechanic, Vol. 2, No. 1, pp.1-17, 1970

D. M. Parks, “A stiffness derivative finite element technique for determination of crack tip stress intensity factors”, International Journal of Fracture, Vol. 10, No. 4, pp. 487-502, 1974

B. Moran, C. F. Shih, “A general treatment of crack tip contour integrals”, International Journal of Fracture, Vol. 35, No. 4, pp. 295-310, 1987

S. Phongthanapanich, P. Dechaumphai, “Adaptive Delaunay triangulation with object-oriented programming for crack propagation analysis”, Finite Element in Analysis and Design, Vol. 40, No. 13-14, pp.1753-1771, 2004

A. M. Alshoaibi, A. K. Ariffin, “Finite element simulation of stress intensity factors in elastic-plastic crack growth”, Journal of Zhejiang University SCIENCE A, Vol. 7, No. 8, pp. 1336-1342, 2006

P. O. Bouchard, F. Bay, Y. Chastel, I. Tovena,, “Crack propagation modelling using an advanced remeshing technique”, Computer Methods in Applied Mechanics and Engineering, Vol. 189, No. 3, pp. 723–742, 2000

M. Souiyah, A. Alshoaibi, A. Muchtar, A. K. Ariffin, “Finite element model for linear-elastic mixed mode loading using adaptive mesh strategy”, Journal of Zhejiang University SCIENCE A, Vol. 9, No. 1, pp. 32-37, 2008

T. N. Bittencourt, P. A. Wawrzynek, A. R.Ingraffea, J. L. Sousa, “Quasi-automatic simulation of crack propagation for 2D LEFM problems”, Engineering Fracture Mechanics, Vol. 55, No. 2, pp. 321-334, 1996

M. M. Rashid, “The arbitrary local mesh replacement method: an alternative to remeshing for crack propagation analysis”, Computer Methods in Applied Mechanics and Engineering, Vol. 154, No. 1-2, pp. 133-150, 1998

D. Azócar, M. Elgueta, M. C. Rivara, “Automatic LEFM crack propagation method based on local Lepp–Delaunay mesh refinement”, Advances in Engineering Software, Vol. 41, No. 2, pp. 111–119, 2010

P. O. Bouchard, F. Bay, Y. Chastel, “Numerical modelling of crack propagation: automatic remeshing and comparison of different criteria”, Computer Methods in Applied Mechanics and Engineering, Vol. 192, No. 35-36, pp. 3887–3908, 2003

eISSN: 1792-8036     pISSN: 2241-4487