A two dimensional Simulation of crack propagation using Adaptive Finite Element Analysis

Document Type : Research Paper


Department of Mechanical Engineering, Jazan University, P. O. Box 706, Jazan 45142, Kingdom of Saudi Arabia


Finite element method (FEM) is one of the most famous methods which has many applications in varies studies such as the study of crack propagation in engineering structures. However, unless extremely fine meshes are employed, problem arises in accurately modelling the singular stress field in the singular element area around the crack tip. In the present study, the crack growth simulation has been numerically simulated by using the dens mesh finite element source code program using Visual FORTRAN language. This code includes the mesh generator based on the advancing front method as well as all the pre and post process for the crack growth simulation under linear elastic fracture mechanics theory. The stress state at a crack tip has been described by the stress intensity factor which is related to the rate of crack growth. The displacement extrapolation technique is employed to obtain crack tip singular stresses and the stress intensity factors values. The crack direction is predicted using the maximum circumferential theory.
Verification of the predicted stress intensity factors and crack path direction are validated with relevant experimental data and numerical results obtained by other researchers with good agreements.


Main Subjects

[1]     J. A. George, Computer implementation of the finite element method, Ph.D Thesis, Computer Science Stanford University, USA, 1971.
[2]     S. Lo, A new mesh generation scheme for arbitrary planar domains, International Journal for Numerical Methods in Engineering, Vol. 21, No. 8, pp. 1403-1426, 1985.
[3]     J. Peraire, M. Vahdati, K. Morgan, O. C. Zienkiewicz, Adaptive remeshing for compressible flow computations, Journal of computational physics, Vol. 72, No. 2, pp. 449-466, 1987.
[4]     S. Lo, Dynamic grid for mesh generation by the advancing front method, Computers & Structures, Vol. 123, pp. 15-27, 2013.
[5]     M. Malekan, L. L. Silva, F. B. Barros, R. L. Pitangueira, S. S. Penna, Two-dimensional fracture modeling with the generalized/extended finite element method: An object-oriented programming approach, Advances in Engineering Software, Vol. 115, pp. 168-193, 2018.
[6]     Y. Liu, G. Glass, Choose the Best Element Size to Yield Accurate FEA Results While Reduce FE Models’s Complixity, British Journal of Engineering and Technology, Vols, Vol. 1, pp. 13-28, 2013.
[7]     N. Benamara, A. Boulenouar, M. Aminallah, N. Benseddiq, On the mixed-mode crack propagation in FGMs plates: Comparison of different criteria, Structural Engineering and Mechanics, Vol. 615, No. 3, pp. 371-379, 2017.
[8]     S. Soman, K. Murthy, P. Robi, A simple technique for estimation of mixed mode (I/II) stress intensity factors, Journal of Mechanics of Materials and Structures, Vol. 13, No. 2, pp. 141-154, 2018.
[9]     M. Yaylaci, The investigation crack problem through numerical analysis, Structural Engineering and Mechanics, Vol. 57, No. 6, pp. 1143-1156, 2016.
[10]   S. P. Jena, D. R. Parhi, D. Mishra, Comparative study on cracked beam with different types of cracks carrying moving mass, Structural Engineering and Mechanics, Vol. 56, No. 5, pp. 797-811, 2015.
[11]   S. T. More, R. Bindu, Effect of mesh size on finite element analysis of plate structure, Int. J. Eng. Sci. Innovative Technol, Vol. 4, No. 3, pp. 181-185, 2015.
[12]   A. M. Alshoaibi, Finite element procedures for the numerical simulation of fatigue crack propagation under mixed mode loading, Structural Engineering and Mechanics, Vol. 35, No. 3, pp. 283-299, 2010.
[13]   A. M. Alshoaibi, An Adaptive Finite Element Framework for Fatigue Crack Propagation under Constant Amplitude Loading, International Journal of Applied Science and Engineering, Vol. 13, No. 3, pp. 261-270, 2015.
[14]   R. S. Barsoum, Application of quadratic isoparametric finite elements in linear fracture mechanics, International Journal of Fracture, Vol. 10, No. 4, pp. 603-605, 1974.
[15]   R. Henshell, K. Shaw, Crack tip finite elements are unnecessary, International journal for numerical methods in engineering, Vol. 9, No. 3, pp. 495-507, 1975.
[16]   G. V. Guinea, J. Planas, M. Elices, KI evaluation by the displacement extrapolation technique, Engineering fracture mechanics, Vol. 66, No. 3, pp. 243-255, 2000.
[17]   F. Erdogan, G. Sih, On the crack extension in plates under plane loading and transverse shear, Journal of basic engineering, Vol. 85, No. 4, pp. 519-525, 1963.
[18]   J. E. Srawley, Wide range stress intensity factor expressions for ASTM E 399 standard fracture toughness specimens, International Journal of Fracture, Vol. 12, No. 3, pp. 475-476, 1976.
[19]   L. Parnas, Ö. G. Bilir, E. Tezcan, Strain gage methods for measurement of opening mode stress intensity factor, Engineering fracture mechanics, Vol. 55, No. 3, pp. 485-492, 1996.
[20]   A. Mourad, M. Alghafri, O. A. Zeid, S. Maiti, Experimental investigation on ductile stable crack growth emanating from wire-cut notch in AISI 4340 steel, Nuclear engineering and design, Vol. 235, No. 6, pp. 637-647, 2005. 
Volume 49, Issue 2
December 2018
Pages 335-341
  • Receive Date: 30 August 2018
  • Revise Date: 06 October 2018
  • Accept Date: 17 October 2018