Estimation of Stress Intensity Factors from Near Crack Tip Field
All current experimental methods for determination of
stress intensity factors are based on the assumption that the state of
stress near the crack tip is plane stress. Therefore, these methods rely
on strain and displacement measurements made outside the near
crack tip region affected by the three-dimensional effects or by
process zone. In this paper, we develop and validate an experimental
procedure for the evaluation of stress intensity factors from the
measurements of the out-of-plane displacements in the surface area
controlled by 3D effects. The evaluation of stress intensity factors is
possible when the process zone is sufficiently small, and the
displacement field generated by the 3D effects is fully encapsulated
by K-dominance region.
[1] Y. Murakami, Stress intensity factors handbook. Pergamon Press, New
York, 1987.
[2] D. P. Rooke, D. J. Cartwright, Compendium of stress intensity factors.
Her Majesty’s Stationery Office, London, 1976.
[3] H. Tada, P.C. Paris, G.R. Irwin, The stress analysis of cracks handbook.
Second ed. Paris Productions, St. Louis, Mo, 1985.
[4] S. Courtin, C. Gardin, G. Bezine, H.B.H. Hamouda, “Advantages of the
J-integral approach for calculating stress intensity factors when using the
commercial finite element software ABAQUS,” Eng. Fract. Mech., vol.
72, pp. 2174-2185, 2005.
[5] I. Lim, I.W. Johnston, S.K. Choi, “On stress intensity factor computation
from the quarter-point element displacements,” Appl. Numer. Math., vol.
8, pp. 291-300, 1992.
[6] Y. E. Pak, S. Kim, “On the use of Path-independent integrals in
calculating mixed-mode stress intensity factors for elastic and
thermoelastic cases,” J. Therm. Stresses, vol. 33, pp. 661-673, 2010.
[7] W. X. Zhu, D. J. Smith, “On the use of displacement extrapolation to
obtain crack tip singular stresses and stress intensity factors,” Eng.
Fract. Mech., vol. 51, pp. 391-400, 1995.
[8] P. S. Theocaris, “Experimental methods for determining stress intensity
factors,” Int. J. Fract.Mech., vol. 1, pp. 707-728, 1984.
[9] J. R. Berger, J. W. Dally, “An overdeterministic approach for measuring
K_I using strain gages,” Exp. Mech., vol. 28, pp. 142-145, 1988.
[10] A. Dorogoy, D. Rittel, “Optimum location of a three strain gauge rosette
for measuring mixed mode stress intensity factors,” Eng. Fract. Mech.,
vol. 75, pp. 4127-4139, 2008.
[11] J. Wei, J. H. Zhao, “A two-strain-gage technique for determining mode I
stress-intensity factor,” Theor. Appl. Fract. Mech., vol. 28, pp. 135-140,
1997.
[12] L. Humbert, V. Valle, M. Cottron, “Experimental determination and
empirical representation of out-of-plane displacements in a cracked
elastic plate loaded in mode I,” Int. J. Solids Struct., vol. 37, pp. 5493-
5504, 2000.
[13] R. D. Pfaff, P. D. Washabaugh, W. G. Knauss, “An interpretation of
Twyman-Green interferograms from static and dynamic fracture
experiments,” Int. J. Solids Struct., vol. 32, pp. 939-955, 1995.
[14] K. Ravi-Chandar, “Fracture mechanics,” in: Springer handbook of
experimental solid mechanics. Springer Science + Business Media, New
York, pp. 125-158, 2008.
[15] M.C. Baik, S.H. Choi, J.S. Hawong, J.D. Kwon, “Determination of
stress-intensity factors by the method of caustics in anisotropic
materials,” Experimental Mechanics, vol. 35, pp. 137-143, 1995.
[16] P. S. Theocaris, E. Gdoutos, “An optical method for determining
opening-mode and edge sliding-mode stress-intensity factors,” J. Appl.
Mech., vol. 7, pp. 39-91, 1972. [17] A. Yazdanmehr, N. Soltani, “Evaluation of stress intensity factors of
rounded V and U notches under mixed mode loading, using the
experimental method of caustics,” Theor. Appl. Fract. Mech., vol. 74,
pp. 79-85, 2014.
[18] M. R. Ayatollahi, M. Nejati, “Experimental evaluation of stress field
around the sharp notches using photoelasticity,” Mater. Des., vol. 32, pp.
561-569, 2011.
[19] G. R. Irwin, “The dynamic stress distribution surrounding a running
crack – A photoelastic analysis,” Proc. SESA, vol. 16, pp. 93-96, 1958.
[20] T. Brynk, A. Laptiev, O. Tolochyn, Z. Pakiela, “The method of fracture
toughness measurements of high speed camera and DIC,”
Computational Materials Science, vol. 64, pp. 221-224, 2012.
[21] N. McCormick, J. Lord, “Digital image correlation,” Mater. Today, vol.
13, pp. 52-54, 2010.
[22] S. R. McNeill, W. H. Peters, M. A. Sutton, “Estimation of stress
intensity factor by digital image correlation,” Eng. Fract. Mech., vol. 28,
pp. 101-112, 1987.
[23] S. Yoneyama, Y. Morimoto, M. Takashi, “Automatic Evaluation of
mixed-mode stress intensity factors utilizing digital image correlation,”
Strain, vol. 42, pp. 21-29, 2006.
[24] R. Zhang, L. He, “Measurement of mixed-mode stress intensity factors
using digital image correlation method,” Opt. Lasers Eng., vol. 50, pp.
1001-1007, 2012.
[25] T. Nakamura, D. M. Parks, “Three-dimensional stress field near the
crack front of a thin elastic plate,” J. Appl. Mech., vol. 55, pp. 805-813,
1988.
[26] C. She, W. Guo, “The out-of-plane constraint of mixed-mode cracks in
thin elastic plates,” Int. J. Solids Struct., vol. 44, pp. 3021-3034, 2007.
[27] W. Yang, L. B. Freund, “Transverse shear effects for through-cracks in
an elastic plate,” Int. J. Solids Struct., vol. 9, pp. 977-994, 1985.
[28] F. Berto, P. Lazzarin, A. Kotousov, “On presence of the out-of-plane
singular mode induced by plane loading with KII = KI = 0,” Int. J.
Fract., vol. 167, pp. 119-126, 2011.
[29] S. Harding, A. Kotousov, P. Lazzarin, F. Berto, “Transverse singular
effects in V-shaped notches stressed in mode II,” Int. J. Fract., vol. 164,
pp. 1-14, 2010.
[30] A. Kotousov, “Effect of plate thickness on stress state at sharp notches
and the strength paradox of thick plates,” Int. J. Solids Struct., vol. 47,
pp. 1916-1923, 2010.
[31] A. Kotousov, “Fracture in plates of finite thickness,” Int. J. Solids
Struct., vol. 44, pp. 8259-8273, 2007.
[32] C. K. Desai, S. Basu, V. Parameswaran, “Determination of complex
stress intensity factor for a crack in a bimaterial interface using digital
image correlation,” Opt. Lasers Eng., vol. 50, pp. 1423-1430, 2012.
[33] M. R. Y. Dehnavi, I. Eshraghi, N. Soltani, “Investigation of fracture
parameters of edge V-notches in a polymer material using digital image
correlation,” Polymer Testing, vol. 32, pp. 78-784, 2013.
[34] A. Kotousov, P. Lazzarin, F. Berto, S. Harding, “Effect of the thickness
on elastic deformation and quasi-brittle fracture of plate components,”
Eng. Fract. Mech., vol. 77, pp. 1665-1681, 2010.
[35] A. Kotousov, P.J. Tan, “Effect of the plate thickness on the out-of-plane
displacement field of a cracked elastic plate loaded in mode I,” Int. J.
Fract., vol. 127, pp. 97-103, 2004.
[36] A. Kotousov, F. Berto, P. Lazzarin, F. Pegorin, “Three dimensional
finite element mixed fracture mode under anti-plane loading of a crack,”
Theor. Appl. Fract. Mech., vol. 62, pp. 26-33, 2012.
[37] F. Berto, A. Kotousov, P. Lazzarin, F. Pegorin, “On a coupled mode at
sharp notches subjected to anti-plane loading,” Eur. J. Mech. A. Solids,
vol. 38, pp. 70-78, 2013.
[38] A. Kotousov, P. Lazzarin, F. Berto, L.P. Pook, “Three-dimensional
stress states at crack tip induced by shear and anti-plane loading,” Eng.
Fract. Mech., vol. 108, pp. 65-74, 2013.
[39] Z. He, A. Kotousov, A. Fanciulli, F. Berto, G. Nguyen, “On the
evaluation of stress intensity factor from displacement field controlled
by 3D corner singularity,” Int. J. Solids Struct., submitted for
publication.
[40] Z. He, A. Kotousov, A. Fanciulli, F. Berto, “A new experimental method
for the evaluation of stress intensity factors from near crack tip field,”
Int. J. Fract., submitted for publication.
[41] L.P. Pook, “Crack profiles and corner point singularities,” Fatigue
Fract. Eng. Mater. Struct., vol. 23, pp. 141-150, 2000.
[42] M.L. Williams, “Stress singularities resulting from various boundary
conditions,” J. Appl. Mech., vol. 19, pp. 526-528, 1952.
[43] M.R. Ayatollahi, M.R.M. Aliha, H. Saghafi, “An improved semi-circular
bend specimen for investigating mixed mode brittle fracture,” Eng.
Fract. Mech., vol. 78, pp. 110-123, 2011.
[44] A. Sutton, J. J. Orteu, H. W. Schreier, Image correlation for shape
motion and deformation measurements. Springer, 2009.
[1] Y. Murakami, Stress intensity factors handbook. Pergamon Press, New
York, 1987.
[2] D. P. Rooke, D. J. Cartwright, Compendium of stress intensity factors.
Her Majesty’s Stationery Office, London, 1976.
[3] H. Tada, P.C. Paris, G.R. Irwin, The stress analysis of cracks handbook.
Second ed. Paris Productions, St. Louis, Mo, 1985.
[4] S. Courtin, C. Gardin, G. Bezine, H.B.H. Hamouda, “Advantages of the
J-integral approach for calculating stress intensity factors when using the
commercial finite element software ABAQUS,” Eng. Fract. Mech., vol.
72, pp. 2174-2185, 2005.
[5] I. Lim, I.W. Johnston, S.K. Choi, “On stress intensity factor computation
from the quarter-point element displacements,” Appl. Numer. Math., vol.
8, pp. 291-300, 1992.
[6] Y. E. Pak, S. Kim, “On the use of Path-independent integrals in
calculating mixed-mode stress intensity factors for elastic and
thermoelastic cases,” J. Therm. Stresses, vol. 33, pp. 661-673, 2010.
[7] W. X. Zhu, D. J. Smith, “On the use of displacement extrapolation to
obtain crack tip singular stresses and stress intensity factors,” Eng.
Fract. Mech., vol. 51, pp. 391-400, 1995.
[8] P. S. Theocaris, “Experimental methods for determining stress intensity
factors,” Int. J. Fract.Mech., vol. 1, pp. 707-728, 1984.
[9] J. R. Berger, J. W. Dally, “An overdeterministic approach for measuring
K_I using strain gages,” Exp. Mech., vol. 28, pp. 142-145, 1988.
[10] A. Dorogoy, D. Rittel, “Optimum location of a three strain gauge rosette
for measuring mixed mode stress intensity factors,” Eng. Fract. Mech.,
vol. 75, pp. 4127-4139, 2008.
[11] J. Wei, J. H. Zhao, “A two-strain-gage technique for determining mode I
stress-intensity factor,” Theor. Appl. Fract. Mech., vol. 28, pp. 135-140,
1997.
[12] L. Humbert, V. Valle, M. Cottron, “Experimental determination and
empirical representation of out-of-plane displacements in a cracked
elastic plate loaded in mode I,” Int. J. Solids Struct., vol. 37, pp. 5493-
5504, 2000.
[13] R. D. Pfaff, P. D. Washabaugh, W. G. Knauss, “An interpretation of
Twyman-Green interferograms from static and dynamic fracture
experiments,” Int. J. Solids Struct., vol. 32, pp. 939-955, 1995.
[14] K. Ravi-Chandar, “Fracture mechanics,” in: Springer handbook of
experimental solid mechanics. Springer Science + Business Media, New
York, pp. 125-158, 2008.
[15] M.C. Baik, S.H. Choi, J.S. Hawong, J.D. Kwon, “Determination of
stress-intensity factors by the method of caustics in anisotropic
materials,” Experimental Mechanics, vol. 35, pp. 137-143, 1995.
[16] P. S. Theocaris, E. Gdoutos, “An optical method for determining
opening-mode and edge sliding-mode stress-intensity factors,” J. Appl.
Mech., vol. 7, pp. 39-91, 1972. [17] A. Yazdanmehr, N. Soltani, “Evaluation of stress intensity factors of
rounded V and U notches under mixed mode loading, using the
experimental method of caustics,” Theor. Appl. Fract. Mech., vol. 74,
pp. 79-85, 2014.
[18] M. R. Ayatollahi, M. Nejati, “Experimental evaluation of stress field
around the sharp notches using photoelasticity,” Mater. Des., vol. 32, pp.
561-569, 2011.
[19] G. R. Irwin, “The dynamic stress distribution surrounding a running
crack – A photoelastic analysis,” Proc. SESA, vol. 16, pp. 93-96, 1958.
[20] T. Brynk, A. Laptiev, O. Tolochyn, Z. Pakiela, “The method of fracture
toughness measurements of high speed camera and DIC,”
Computational Materials Science, vol. 64, pp. 221-224, 2012.
[21] N. McCormick, J. Lord, “Digital image correlation,” Mater. Today, vol.
13, pp. 52-54, 2010.
[22] S. R. McNeill, W. H. Peters, M. A. Sutton, “Estimation of stress
intensity factor by digital image correlation,” Eng. Fract. Mech., vol. 28,
pp. 101-112, 1987.
[23] S. Yoneyama, Y. Morimoto, M. Takashi, “Automatic Evaluation of
mixed-mode stress intensity factors utilizing digital image correlation,”
Strain, vol. 42, pp. 21-29, 2006.
[24] R. Zhang, L. He, “Measurement of mixed-mode stress intensity factors
using digital image correlation method,” Opt. Lasers Eng., vol. 50, pp.
1001-1007, 2012.
[25] T. Nakamura, D. M. Parks, “Three-dimensional stress field near the
crack front of a thin elastic plate,” J. Appl. Mech., vol. 55, pp. 805-813,
1988.
[26] C. She, W. Guo, “The out-of-plane constraint of mixed-mode cracks in
thin elastic plates,” Int. J. Solids Struct., vol. 44, pp. 3021-3034, 2007.
[27] W. Yang, L. B. Freund, “Transverse shear effects for through-cracks in
an elastic plate,” Int. J. Solids Struct., vol. 9, pp. 977-994, 1985.
[28] F. Berto, P. Lazzarin, A. Kotousov, “On presence of the out-of-plane
singular mode induced by plane loading with KII = KI = 0,” Int. J.
Fract., vol. 167, pp. 119-126, 2011.
[29] S. Harding, A. Kotousov, P. Lazzarin, F. Berto, “Transverse singular
effects in V-shaped notches stressed in mode II,” Int. J. Fract., vol. 164,
pp. 1-14, 2010.
[30] A. Kotousov, “Effect of plate thickness on stress state at sharp notches
and the strength paradox of thick plates,” Int. J. Solids Struct., vol. 47,
pp. 1916-1923, 2010.
[31] A. Kotousov, “Fracture in plates of finite thickness,” Int. J. Solids
Struct., vol. 44, pp. 8259-8273, 2007.
[32] C. K. Desai, S. Basu, V. Parameswaran, “Determination of complex
stress intensity factor for a crack in a bimaterial interface using digital
image correlation,” Opt. Lasers Eng., vol. 50, pp. 1423-1430, 2012.
[33] M. R. Y. Dehnavi, I. Eshraghi, N. Soltani, “Investigation of fracture
parameters of edge V-notches in a polymer material using digital image
correlation,” Polymer Testing, vol. 32, pp. 78-784, 2013.
[34] A. Kotousov, P. Lazzarin, F. Berto, S. Harding, “Effect of the thickness
on elastic deformation and quasi-brittle fracture of plate components,”
Eng. Fract. Mech., vol. 77, pp. 1665-1681, 2010.
[35] A. Kotousov, P.J. Tan, “Effect of the plate thickness on the out-of-plane
displacement field of a cracked elastic plate loaded in mode I,” Int. J.
Fract., vol. 127, pp. 97-103, 2004.
[36] A. Kotousov, F. Berto, P. Lazzarin, F. Pegorin, “Three dimensional
finite element mixed fracture mode under anti-plane loading of a crack,”
Theor. Appl. Fract. Mech., vol. 62, pp. 26-33, 2012.
[37] F. Berto, A. Kotousov, P. Lazzarin, F. Pegorin, “On a coupled mode at
sharp notches subjected to anti-plane loading,” Eur. J. Mech. A. Solids,
vol. 38, pp. 70-78, 2013.
[38] A. Kotousov, P. Lazzarin, F. Berto, L.P. Pook, “Three-dimensional
stress states at crack tip induced by shear and anti-plane loading,” Eng.
Fract. Mech., vol. 108, pp. 65-74, 2013.
[39] Z. He, A. Kotousov, A. Fanciulli, F. Berto, G. Nguyen, “On the
evaluation of stress intensity factor from displacement field controlled
by 3D corner singularity,” Int. J. Solids Struct., submitted for
publication.
[40] Z. He, A. Kotousov, A. Fanciulli, F. Berto, “A new experimental method
for the evaluation of stress intensity factors from near crack tip field,”
Int. J. Fract., submitted for publication.
[41] L.P. Pook, “Crack profiles and corner point singularities,” Fatigue
Fract. Eng. Mater. Struct., vol. 23, pp. 141-150, 2000.
[42] M.L. Williams, “Stress singularities resulting from various boundary
conditions,” J. Appl. Mech., vol. 19, pp. 526-528, 1952.
[43] M.R. Ayatollahi, M.R.M. Aliha, H. Saghafi, “An improved semi-circular
bend specimen for investigating mixed mode brittle fracture,” Eng.
Fract. Mech., vol. 78, pp. 110-123, 2011.
[44] A. Sutton, J. J. Orteu, H. W. Schreier, Image correlation for shape
motion and deformation measurements. Springer, 2009.
@article{"International Journal of Mechanical, Industrial and Aerospace Sciences:70012", author = "Zhuang He and Andrei Kotousov", title = "Estimation of Stress Intensity Factors from Near Crack Tip Field", abstract = "All current experimental methods for determination of
stress intensity factors are based on the assumption that the state of
stress near the crack tip is plane stress. Therefore, these methods rely
on strain and displacement measurements made outside the near
crack tip region affected by the three-dimensional effects or by
process zone. In this paper, we develop and validate an experimental
procedure for the evaluation of stress intensity factors from the
measurements of the out-of-plane displacements in the surface area
controlled by 3D effects. The evaluation of stress intensity factors is
possible when the process zone is sufficiently small, and the
displacement field generated by the 3D effects is fully encapsulated
by K-dominance region.", keywords = "Digital image correlation, stress intensity factors,
three-dimensional effects, transverse displacement.", volume = "9", number = "7", pages = "1176-5", }
