Estimation of Stress Intensity Factors from Near Crack Tip Field

Authors: Zhuang He, Andrei Kotousov

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.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1106459

References:

[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.