A Numerical Approach for the Determination of Mode I Stress Intensity Factors in PMMA Materials


  • F. Khelil Laboratoire de Mécanique de Lille (LML), University of Lille1, France
  • M. Belhouari Department of Mechanical Engineering, University of Sidi Bel Abbes, Algeria
  • N. Benseddiq Laboratoire de Mécanique de Lille (LML), University of Lille1, France
  • A. Talha Haute Ecole d’Ingénieur, Lille, France


An evaluation technique of the KI stress intensity factors (SIF) by a numerical investigation using line strain method is presented in this paper. The main purpose of this research is to re-analyze experimental results of fracture loads from polymethyl-metacrylate (PMMA) specimens (fully finite plates). Stress intensity factor equation calculation is derived from the Williams stress asymptotic expansion. Possible error caused by strain gradients across the gage length is minimized by integrating the equation in the KI  calculation. Theoretical and computed values using finite element analysis of stress intensity factors are compared with experimental results. A good agreement is observed between the present approach and experimental values. It is shown that, in the case of a through-plate crack, the stress intensity factor can be calculated with adequate accuracy using the proposed method.


Finite elements, strain gage method, KI, PMMA edge crack


Download data is not yet available.


G. R. Irwin, “Analysis of stresses and strains near the end of a crack traversing a plate”, Journal of Applied Mechanics, Vol. 24, pp. 361-364, 1957

J. W. Dally, R. J. Sanford, “Strain gage methods for measuring the opening mode stress intensity factor KI”, Experimental Mechanics, Vol. 27, pp. 381-388, 1987 DOI: https://doi.org/10.1007/BF02330311

J. W. Dally, R. J. Sanford, “Measuring the stress intensity factor for propagating cracks with strain gages”, Journal of Testing and Evaluation, Vol. 18 No. 4, pp. 240–249, 1990 DOI: https://doi.org/10.1520/JTE12480J

J. W. Dally, W. F. Riley, Experimental stress analysis, McGraw-Hill, New York, 1965

J. R. Berger, J. W. Dally, “An overdeterministic approach for measuring KI using strain gages”, Experimental Mechanics, Vol. 28, No. 2, pp.142-145, 1988 DOI: https://doi.org/10.1007/BF02317564

Y. Z. Itoh, T. Murakami, H. Kashiwaya, “Experimental determination technique of stress intensity factor and its application”, Journal of Engineering Materials and Technology, Vol. 111, No. 1, pp. 81-86, 1988 DOI: https://doi.org/10.1115/1.3226437

R. J. Sanford, Principles of fracture mechanics, Prentice-Hall, Englewood Cliffs, NJ, 2002

R. J. Sanford, Principles of fracture mechanics, Prentice Hall, Upper Saddle River, NJ, 2003

R. J. Sanford, “A critical re-examination of the Westergaard method for solving opening-mode crack problems”, Mechanics Research Communications, Vol. 6, No. 5, pp. 289–294, 1979 DOI: https://doi.org/10.1016/0093-6413(79)90033-8

S. Swamy, M. V. Srikanth, K. S. R. K. Murthy, P. S. Robi, “Determination of mode I stress intensity factors of complex configurations using strain gages”, Journal of Mechanics of Materials and Structures., Vol. 3, No. 7, pp. 1239-1255, 2008 DOI: https://doi.org/10.2140/jomms.2008.3.1239

M. J. Maleski, M. S. Kirugulige, H. V. Tippur “A method for measuring mode I crack tip constraint under static and dynamic loading conditions”, Experimental Mechanics, Vol. 44, No. 5, pp. 522–532, 2004 DOI: https://doi.org/10.1007/BF02427964

A. Shukla, R. Chona, R. K. Agarwal, “Investigation of dynamic fracture using strain gage”. Proc. SEM Spring Conf. Houston, TX, USA 1987

N. Levy, P. V. Marcal, J. R. Rice, “Progress in three-dimensional elastic-plastic stress analysis for fracture mechanics”, Nuclear Engineering and Design, Vol. 17, No. 1, pp. 64-75, 1971 DOI: https://doi.org/10.1016/0029-5493(71)90040-9

T. Nakamura, D. M. Parks, “Three dimensional stress field near the crack front of a thin elastic plate”, Journal of Applied Mechanics, Vol. 55, No. 4, pp. 805-813, 1988 DOI: https://doi.org/10.1115/1.3173725

A. J. Rosakis, K. Ravi-Chandar, “On crack-tip stress state: an experimental evaluation of three-dimensional effects”, International Journal of Solids and Structures, Vol. 22, No. 2, pp.121-134, 1986 DOI: https://doi.org/10.1016/0020-7683(86)90002-8

J. Wei, J. H. Zhao, “A two-strain-gage technique for determining mode I stress-intensity factor”, Theoretical and Applied Fracture Mechanics, Vol. 28, No. 2, pp. 135–140, 1997 DOI: https://doi.org/10.1016/S0167-8442(97)00038-4

J. H. Kuang, L. S. Chen, “A single strain gage method for KI measurement”, Engineering Fracture Mechanics, Vol. 51, No. 5, pp. 871–878, 1995 DOI: https://doi.org/10.1016/0013-7944(94)00298-V

C. H. Chen, C. L. Wang, “Stress intensity factors and T-stresses for offset double edge-cracked plates under mixed-mode loadings”, International Journal of Fracture,Vol. 152, No. 2, pp. 149–162, 2008 DOI: https://doi.org/10.1007/s10704-008-9276-5

P. V. Jogdand, K. S. R. K. Murthy, “A finite element based interior collocation method for the computation of stress intensity factors and T-stresses” , Engineering Fracture Mechanics Vol. 77, No. 7, pp. 1116–1127, 2010 DOI: https://doi.org/10.1016/j.engfracmech.2010.03.002

M. L. Williams, “On the stress distribution at the base of a stationary crack”, Journal of Applied Mechanics, Vol. 24, pp. 109-114, 1957

R. Chona, G. R.Irwin, R. J. Sanford, “Influence of specimen size and shape on the singularity-dominated zone,” Fracture Mechanics 14th Symposium, Vol. 1: Theory and Analysis, ASTM-STP, Vol. 791, American Society for Testing and Materials, Philadelphia, PA, 492–502, 1983

P. V. Jogdand, “An investigation on overdeterministic approaches for determination of the mixed mode stress intensity factors and T-stresses, Masters Thesis, Indian Institute of Technology Guwahati, India, 2009

H. V. Tippur, S. Krishnaswamy, A. J. Rosakis, “Optical mapping of crack tip deformations using the methods of transmission and reflection coherent gradient sensing: a study of crack tip K-dominance”, International Journal of Fracture, Vol. 52, No. 2, pp. 91–117, 1991

L. Parnas, O. G. Bilir, “Strain gage methods for measurement of opening mode stress intensity factor”, Engineering Fracture Mechanics, Vol. 55, No. 3, pp. 485–492, 1996 DOI: https://doi.org/10.1016/0013-7944(95)00214-6

ABAQUS, Theory reference manual, Release 11. Swanson Analysis Systems, Inc, 2009

T. Fett, G. Rizzi, “Weight functions for stress intensity factors and T-stress for oblique cracks in a half-space”, International Journal of Fracture, Vol.132, No. 1, pp. L9–L16, 2005 DOI: https://doi.org/10.1007/s10704-005-0024-9

T. Fett, “Stress intensity factors and T-stress for internally cracked circular disks under various boundary conditions”, Engineering Fracture Mechanics , Vol. 68, No. 9, pp. 1119–1136, 2001 DOI: https://doi.org/10.1016/S0013-7944(01)00025-X

T. Fett, “T-stresses in rectangular plates and circular disks”, Engineering Fracture Mechanics, Vol. 60, No. 5-6, pp. 631–652, 1998 DOI: https://doi.org/10.1016/S0013-7944(98)00038-1

K. S. R. K. Murthy, M. Mukhopadhyay, “Unification of stress intensity factor (SIF) extraction methods with an h-adaptive finite element scheme”, Communications in Numerical Methods in Engineering, Vol. 17, No. 7, pp. 509–520, 2001 DOI: https://doi.org/10.1002/cnm.426

L. Banks-Sills, D. Sherman, “Comparison of methods for calculating stress intensity factors with quarter-point elements”, International Journal of Fracture, Vol. 32, No. 2, pp. 127–140, 1986 DOI: https://doi.org/10.1007/BF00019788

H. Tada, P. C. Paris, G. R. Irwin, The stress analysis of cracks handbook, New York, ASME, 2000 DOI: https://doi.org/10.1115/1.801535

M. Isida “Effect of width and length on stress intensity factors of internally cracked plates under various boundary conditions”. Engineering Fracture Mechanics, Vol . 7, No. 3, pp. 301–16, 1971 DOI: https://doi.org/10.1007/BF00184306


How to Cite

F. Khelil, M. Belhouari, N. Benseddiq, and A. Talha, “A Numerical Approach for the Determination of Mode I Stress Intensity Factors in PMMA Materials”, Eng. Technol. Appl. Sci. Res., vol. 4, no. 3, pp. 644–648, Jun. 2014.


Abstract Views: 853
PDF Downloads: 337

Metrics Information

Most read articles by the same author(s)