Rectangular Strain-Rosette Method for Measuring the Mode I Stress-Intensity Factor KI and T-stress
Abstract
In this paper, a new experimental technique for measuring Stress Intensity Factor (SIF) and T-stress under mode I loading is developed. The expressions of the normal and tangential strains close to the crack tip are given using the first five terms of the generalized Westergaard formulation. In order to accurately determine the SIF and T-stress, the method exploits the optimal positioning of a rectangular strain gage rosette near a crack tip in mode I. Thus, errors due to the higher order terms of the asymptotic expansion are eliminated. Finally, a comparison of the analytical results with a finite element calculations, for different specimen dimensions, is carried out.
Keywords:
fracture toughness, stress intensity factor, t-stress, strain gage, finite element methodDownloads
References
M. L. Williams, “On the stress distribution at the base of a stationary crack”, Journal of Applied Mechanics, No. 24, pp. 109-114, 1957
D. E. Richardson, J. G. Goree, “Experimental Veri_cation of a New Two-parameter Fracture Mode”, Fracture mechanics: twenty-third Symposium, ASTM STP 1189, pp. 738-750, 1993 DOI: https://doi.org/10.1520/STP24299S
Y. J Chao, S. Liu, B. J. Broviak, “Brittle Fracture: Variation of Fracture Toughness with Constraint and Crack Curving Under Mode I Conditions”, Experimental Mechanics, Vol 41, No. 3, pp. 232-241, 2001 DOI: https://doi.org/10.1007/BF02323139
G. R. Irwin, “Discussion of the Dynamic Stress Distribution Surrounding a Running Crack – A Photoelastic Analysis”, Proceedings of the Society for Experimental Stress Analysis, Vol. 16, No. 1, pp. 93-96, 1958
N. Fleck, “Finite element analysis of plasticity-induced crack closure under plane strain conditions”, Engineering Fracture Mechanics, Vol. 25, No. 4, pp. 441-449, 1986 DOI: https://doi.org/10.1016/0013-7944(86)90258-4
B. Cotterell, J. R. Rice, “Slightly curved or kinked cracks”, International Journal of Fracture, Vol. 16, No. 2, pp. 155-169, 1980 DOI: https://doi.org/10.1007/BF00012619
N. A. Fleck, J. W. Hutchinson, Z. Suo, “Crack path selection in a brittle adhesive layer”, International Journal of Solids and Structures, Vol. 27, No. 13, pp. 1683-1703, 1991 DOI: https://doi.org/10.1016/0020-7683(91)90069-R
J.S. Langer, A.E. Lobkovsky, “Critical examination of cohesive-zone models in the theory of dynamic fracture”, Journal of the Mechanics and Physics of Solids, Vol. 46, No. 9, pp. 1521-1556, 1998 DOI: https://doi.org/10.1016/S0022-5096(98)00005-2
R. J. Sanford, Principles of Fracture Mechanics, Prentice Hall, New York, 2003.
R. M. Bonesteel, D. E. Piper, A.T. Davinroy, “Compliance and KI calibration of double cantilever beam (DCB) specimens”, Engineering Fracture Mechanics Vol. 10, No. 2, pp. 425-428, 1978 DOI: https://doi.org/10.1016/0013-7944(78)90022-X
J.C. Newman, “Stress-intensity factors and crack-opening displacements for round compact specimens”, International Journal of Fracture, Vol. 17, No. 6, pp. 567-578, 1981 DOI: https://doi.org/10.1007/BF00681557
E. E. Gdoutos, P. S. Theocaris, “A photoelastic determination of mixed-mode stress- intensity factors”, Engineering Fracture Mechanics, Vol. 18, No. 3, pp. 87-96, 1978 DOI: https://doi.org/10.1007/BF02325002
T. H. Hyde, N. A. Warrior, “An improved method for the determination of photoelastic stress intensity factors using the westergaard stress function”, International Journal of Mechanical Sciences, Vol. 32, No. 3, pp. 265-273, 1990 DOI: https://doi.org/10.1016/0020-7403(90)90022-B
M. Mahinfalah, L. Zackery, “Photoelastic determination of mixed mode stress intensity factors for sharp reentrant corners”, Engineering Fracture Mechanics, Vol. 52, No. 4, pp. 639-645, 1995 DOI: https://doi.org/10.1016/0013-7944(95)00041-S
P. S. Theocaris, “Local yielding around a crack tip in plexiglas”, Journal of Applied Mechanics, Vol. 37, No. 2, pp. 409-415, 1970 DOI: https://doi.org/10.1115/1.3408521
M. Konsta-Gdoutos, “Limitations in mixed-mode stress intensity factor evaluation by the method of caustics”, Engineering Fracture Mechanics, Vol. 55, No. 3, pp. 371-328, 1996 DOI: https://doi.org/10.1016/0013-7944(96)00029-X
J. W. Dally, R.J. Sanford, “Strain-gage methods for measuring the opening-mode stress intensity factor, KI”, Experimental Mechanics, Vol. 27, No. 4, pp. 381-388, 1987 DOI: https://doi.org/10.1007/BF02330311
S. Swamy, M.V. Srikanth, K.S.R.K. Murthy, P.S. Robi, “Determination of complex stress intensity factors of complex configurations using stra in 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
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
A. S. Kobayashi, Experimental techniques in fracture mechanics, SEM Monograph, Iowa State University Press, 1973
A. S. Kobayashi, iBocing Company, Document No. D2-23552, 1962
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
J. W. Dally, J.R. Berger, “A strain gage method for determining KI and KII in a mixed mode stress field”, The proceedings of the 1986 SEM spring conference on experimental mechanics. New Orleans, LA; , pp. 603-612, 1986
J. W. Dally, D.B. Barker, “Dynamic measurements of initiation toughness at high loading rates”, Experimental Mechanics Vol 28, No. 3, pp. 298-303, 1988 DOI: https://doi.org/10.1007/BF02329026
A. Shukla, B.D. Agarwal, B. Bhushan, “Determination of stress intensity factor in orthotropic composite materials using strain gages”, Engineering Fracture Mechanics, Vol. 32, No. 3, pp. 469-477, 1989 DOI: https://doi.org/10.1016/0013-7944(89)90318-4
S. K. K. Hanna, A. Shukla “Development of stress field equations and determination of stress intensity factor during dynamic fracture of orthotropic composite materials", Engineering Fracture Mechanics, Vol 47, No. 3, pp. 345-359, 1994 DOI: https://doi.org/10.1016/0013-7944(94)90092-2
S. K. K. Hanna, A. Shukla “On the use of strain gages in dynamic fracture mechanics”, Engineering Fracture Mechanics, Vol. 51, No. 6, pp. 933-948, 1995 DOI: https://doi.org/10.1016/0013-7944(94)00325-C
J. Wei, J. H. Zhao, “A two-strain-gage technique for determining mode I stressintensity 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. 871-908, 1995 DOI: https://doi.org/10.1016/0013-7944(94)00298-V
A. Dorogoy, D. Rittel, “Optimum location of a three strain gauge rosette for measuring mixed mode stress intensity factors”, Experimental Mechanics, Vol. 75, No. 14, pp. 4127-4139, 2008 DOI: https://doi.org/10.1016/j.engfracmech.2008.03.014
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
H. Sarangi, K. S. R. K. Murthy, D. Chakraborty, “Radial locations of strain gages for accurate measurement of mode I stress intensity factor”, Materials & Design, Vol. 31, No. 6, pp. 2840-2850, 2010 DOI: https://doi.org/10.1016/j.matdes.2009.12.043
H. Sarangi, K. S. R. K. Murthy, D. Chakraborty, “Optimum strain gage location for evaluating stress intensity factors in single and double ended cracked configurations”, Engineering Fracture Mechanics, Vol. 77, No. 16, pp. 3190-3203, 2010 DOI: https://doi.org/10.1016/j.engfracmech.2010.08.003
H. Sarangi, K. S. R. K. Murthy, D.Chakraborty, “Experimental verification of optimal strain gage locations for the accurate determination of mode I stress intensity factors”, Engineering Fracture Mechanics, Vol. 110, pp. 189-200, 2013 DOI: https://doi.org/10.1016/j.engfracmech.2013.07.014
J. R. Rice, “Limitations to the Small-scale Yielding Approximations for Crack Tip Plasticity”, Journal of the Mechanics and Physics of Solids, Vol. 22, No. 1, pp. 17-26, 1974 DOI: https://doi.org/10.1016/0022-5096(74)90010-6
S. G. Larsson, A. J. Carlsson, “Influence of Non-singular Stress Terms on Small Scale Yielding at Crack Tips in Elastic-plastic Materials”, Journal of the Mechanics and Physics of Solids, Vol. 21, No. 4, pp. 263-277, 1973 DOI: https://doi.org/10.1016/0022-5096(73)90024-0
G. E. Cardew, M. R. Goldthorpe, I. C. Howard, A. P. Kfouri, “On the elastic T-term”, In: Fundamentals of Deformation and Fracture: Eshelby Memorial Symposium, 1985
A. P. Kfouri, “Some evaluations of the elastic T-term using Eshelby's method”, International Journal of Fracture, Vol. 30, No. 4, pp. 301-315, 1986 DOI: https://doi.org/10.1007/BF00019710
T. Nakamura, D. M. Parks, “Determination of Elastic T-stress along Three-dimensional Crack Fronts Using Interaction Integral”, International Journal of Solids and Structures, Vol. 29, No. 1, pp. 1597-1611, 1992 DOI: https://doi.org/10.1016/0020-7683(92)90011-H
B. S. Henry, A. R. Luxmoore, “Three-dimensional evaluation of the T-stress in centre cracked plates”, International Journal of Fracture, Vol. 70, No. 1, pp. 35-50, 1995 DOI: https://doi.org/10.1007/BF00018134
J. Sladek, V. Sladek, P. Fedelinski, “Integral Formulation for Elastodynamic Tstresses”, International Journal of Fracture, Vol. 84, No. 2, pp. 103-116, 1997 DOI: https://doi.org/10.1023/A:1007376029969
B. Yang, K. Ravi-Chandar, “Evaluation of Elastic T-stress by Stress Di_erence Method”, Engineering Fracture Mechanics, Vol. 64, No. 5, pp. 589-605, 1999 DOI: https://doi.org/10.1016/S0013-7944(99)00082-X
M. R. Ayatolahi, M. J. Pavier, D. J. Smith, “Mode I cracks subjected to large T stress”, International Journal of Fracture, Vol. 117, No 2, pp. 159-174, 2002 DOI: https://doi.org/10.1023/A:1020973802643
F. A. Diaz, E. A. Patterson, R. A. Tomlinson, J.,R. Yates, “Measuring stress intensity factors during fatigue crack growth using thermoelasticity”, Fatigue & Fracture of Engineering Materials & Structures, Vol. 27, No. 7, pp. 571-583, 2004 DOI: https://doi.org/10.1111/j.1460-2695.2004.00782.x
J. R. Yates, M. Zanganeh, R. A. Tomlinson, M. W. Brown, F. A. D. Garrido, “Crack paths under mixed mode loading”, Engineering Fracture Mechanics, Vol. 75, No. 3-4, pp. 319-330, 2008 DOI: https://doi.org/10.1016/j.engfracmech.2007.05.014
M. Zanganeh, R. A. Tomlinson, J. R. Yates, “T-stress determination using thermoelastic stress analysis”, The Journal of Strain Analysis for Engineering Design, Vol 43, No. 6, pp. 529-537, 2008 DOI: https://doi.org/10.1243/03093247JSA349
M. Zanganeh, R. A. Tomlinson, J. R. Yates, “T-stress determination using digital image correlation”, Society for Experimental Mechanics- 11th International Congress and Exhibition on Experimental and Applied Mechanics, pp. 511-517, 2008
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 44, No. 5, pp. 522-532, 2004 DOI: https://doi.org/10.1007/BF02427964
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
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