Experimental determination of coefficients of a multiparameter decomposition of field of crack tip stresses: photoelasticity method

L. V. Stepanova   ; V. S. Dolgikh

Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ, no. 1 (2017), pp. 59-68

Résumé

The purpose of this study is multiparameter asymptotic analysis of the stress field in the immediate vicinity of the crack tip in a linearly elastic material and construction of complete asymptotic expansion of M. Williams stress field in the vicinity of the crack tip. Multiparametric analysis of the stress field is based on the polarization-optical methods of mechanics of a deformable solid (the method of photoelasticity). Digital processing of the results of optoelectronic measurements performed on a series of samples with cracks and notches is carried out. Different classes of samples from optically sensitive materials, in particular a sample with two collinear cracks under conditions of normal detachment, were considered. A set of programs has been prepared that makes it possible to determine the scale (amplitude) multipliers of complete asymptotic expansion of M. Villiams for the stress field at the crack tip. Using the basic law of photoelasticity, first five coefficients of complete asymptotic expansion of M. Williams are calculated. The results of the experiments are compared with the available analytical solution. It is shown that the results of processing optoelectronic measurements are in good agreement with the analytical solution obtained for an infinite plate with two collinear cracks.

Détail

Keywords: M. Williams asymptotic expansion, stress field in the vicinity of the crack tip, two collinear cracks, plate stretching, multiparametric description of the stress field, polarization-optical methods of mechanics of deformable solids.

Bibliographie

[1] Broek D., Foundations of fracture mechanics, Vysshaia shkola, M., 1980, 368 pp. (in Russian)

[2] Stepanova L. V., Mathematical methdos of fracture mechanics, Fizmatlit, M., 2009, 336 pp. (in Russian)

[3] Voyiadjis G. Z., Handbook of Damage Mechanics: Nano to Macro Scale for Materials and Structures, Springer, Berlin, 2015, 1577 pp. (in English)

[4] Williams M. L., “On the stress distribution at the base of a stationary crack”, Journal of Applied Mechanics, 24 (1957), 109–114 (in English) | MR | Zbl

[5] Igonin S. A., Stepanova L. V., “Asymptotics of stress and continuity fields at the tip of a fatigue crack in a damaged medium in conditions of plane stress state”, Vestnik of Samara State University, 2013, no. 9-2(110), 97–108 (in Russian)

[6] Kukushkin E. V., Menovshchikov V. A., Eresko T. T., “Analysis of modern views and approaches in the study of fatigue fractures of needle bearings”, Reshetnev Readings, 2013, no. 17, 287–288 (in Russian)

[7] Stepanova L. V., Roslyakov P. S., “Complete asymptotic expansion of M. Williams at the tips of two collinear cracks of finite length in an infinite plate”, Bulletin PNRPU. Mechanics, 2015, no. 4, 188–225 (in Russian) | Zbl

[8] Ramesh K., Gupta S., Kelkar A. A., “Evaluation of stress field parameters in fracture mechanics by photoelastisity-revisited”, Engineering Fracture Mechanics, 56 (1997), 25 pp. (in English) | MR | Zbl

[9] Stepanova L. V., Roslyakov P. S., “Multi-parameter description of the crack-tip stress field: analytic determination of coefficients of crack-tip stress expansions in the vicinity of the crack tips of two finite cracks in an infinite plane medium”, International Journal of Solids and Structures, 100–101 (2016), 11–28 (in English) | DOI

[10] Stepanova L. V., Roslyakov P. S., “Complete Williams asymptotic expansion of the stress field near the crack tip: Analytical solutions, interference-optic methods and numerical experiments”, AIP Conference Proceedings, 1785, 2016, 030029 (in English) | DOI

[11] Stepanova L. V., Roslyakov P. S., Gerasimova T., “Complete Williams Asymptotic expansion near the crack tips of collinear cracks of equal lengths in an infinite plane”, Solid State Phenomena, 258 (2017), 209–212 (in English) | DOI

[12] Gupta M., Alderliesten R. C., Benedictus R., “A review of T-stress and it's effectsin fracture”, Engineering Fracture Mechanics, 134 (2015), 218–241 (in English) | DOI

[13] Botvina L. R., Destruction, Nauka, M., 2008, 334 pp. (in Russian)

[14] Skaletskaya I. E., Skaletsky E. K., Prokopenko V. T., Nikushchenko E. M., Polarization and optical methods of investigation, Tutorial, Universitet ITMO, SPb., 2015, 142 pp. (in Russian)

[15] Troshchenko V. T., Pokrovsky V. V., Prokopenko A. V., Crack resistance of metals at cyclic loading, Naukova dumka, Kiev, 1987, 256 pp. (in Russian)

[16] Berto F., Lazzarin P., “On higher order terms in the crack tip stress field”, International Journal of Fracture, 161 (2010), 221–226 (in English) | DOI | Zbl

[17] Alsiya S., Jeya Leksmi C., Jishna Priya B. P., Mehta R. C., “Image Processing Algorithm for Fringe Analysis in Phototelasticity”, Scholars Journa of Engineering and Technology, 4:7 (2016), 325–328 (in English) | DOI

[18] Surendra K. V. N., Simha K. R. Y., “Digital Image Analysis around isotropic points for photoelastic pattern recognition”, Optic Engineering, 54:8 (2015) (in English) | DOI

[19] Williams M. L., “Stress singularities resulting from various boundary conditions in angular corners of plates in tension”, Journal of Applied Mechanics, 19 (1952), 109–114 (in English)