Multiparametric analysis of the stress field near the crack tip

L. V. Stepanova   ; P. S. Roslyakov

Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ, no. 10 (2015), pp. 52-76

Résumé

The paper is devoted to analytical determination of coefficients of the Williams asymptotic expansion of the stress field in the neighborhood of two collinear crack tips in an infinite plate under mixed mode loading. On the basis of the Kolosof–Muskhelishvili approach the complete asymptotic expansion of the stress field in the vicinity of the crack tips of two collinear cracks of equal lengths under mixed mode loading is derived. The analysis of the higher order terms in the asymptotic expansion series is performed. It is clear that it is necessary to take into account the higher order terms.

Détail

Keywords: Williams asymptotic expansion, stress field in the neighborhood of crack tips, two collinear crack tips, mixed mode loading, higher order terms.

Bibliographie

[1] Hello G., Tahar M.-B., Roeland J.-M., “Analytical determination of coefficients in cracktip stress expansions for a finite crack in an infinite plane medium”, J. International Journal of Solids and Structures, 49 (2012), 556–566 (in English) | DOI

[2] Gerasimova T. E., Lomakov P. N., Stepanova L. V., “Digital photomechanics: numerical image processing of photoelasticity experiments and its application to the problems of fracture mechanics problems”, Vestnik of Samara State University, 2013, no. 9/2(110), 63–73 (in Russian)

[3] Pisarev V. S., Matvyenko Yu. G., Oditsev I. N., “Determination of fracture mechanics parameters at a small gain of length of a crack”, Industrial laboratory. Materials diagnostics, 78:4 (2012), 45–51 (in Russian)

[4] Matvyenko Yu. G., “Two approaches to the account of notsingular T-pressure in measure of a fracture mechanics of bodies with cuts”, Engineering and Automation Problems, 2011, no. 5, 104–110 (in Russian)

[5] Matvyenko Yu. G., “Nonsingular T-Stress in Problems of Two-Parameter Fracture Mechanics”, Industrial laboratory. Materials diagnostics, 78:2 (2014), 51–58 (in Russian)

[6] Matvyenko Yu. G., Pochinkov R. A., “Influence of not singular components of T-pressure on teh field of plastic strain at normal separation crack tip”, Deformatsiya i Razrushenie materialov, 2012, no. 3, 6–14 (in Russian)

[7] Stepanova L. V., Mathematical methods of fracture mechanics, Samarskii universitet, Samara, 2006, 231 pp. (in Russian)

[8] Stepanova L. V., “Eigenspectra and orders of stress singularity at a mode I crack tip for a power-low medium”, Comptes Rendus. Mechanique, 2008, no. 1–2, 232–237 (in English) | DOI | Zbl

[9] Z. Niu et al., “Evaluation of the stress singularities of plane V-notches in bonded dissimilar materials”, Applied Mathematical Modelling, 33 (2009), 1776–1792 (in English) | DOI | MR | Zbl

[10] Ding P., Wang X., “Solutions of the second elastic-plastic fracture mechanics parameter in test specimens”, Engn. Fracture Mechanics, 77 (2010), 3462–3480 (in English) | DOI

[11] Ayatollahi M. R., Dehgany M., Nejati M., “Fracture analysis of V-notched components — Effects of first non-singular stress term”, International Journal of Solids and Structures, 48 (2011), 332–341 (in English) | DOI

[12] Ayatollahi M. R., Nejati M., “Experimental evaluation of stress field around the sharp notches using photoelasticity”, Materials and Design, 32 (2011), 561–569 (in English) | DOI

[13] Ostsemin A. A., Utkin P. B., “Theoretical and experimental studies of fracture mechanics of crack like defects under biaxial loading”, Izvestiya RAN. Ser.: Solid Mechanics, 2009, no. 2, 130–142 (in Russian)

[14] Ostsemin A. A., Utkin P. B., “Stress-strain state and stress intensity coefficient in the vicinity of crack like defects under biaxial loading”, Journal of Applied Mechanics and Theoretical Physics, 55:6(328) (2014), 162–172 (in Russian) | MR

[15] Stepanova L. V., “Refined study of stress-strain state near the crack tip under cyclic loading in a damaged medium”, Vestnik of Samara State University, 2011, no. 2(83), 105–115 (in Russian)

[16] Adulina E. M., Stepanova L. V., “On development of multiscale fracture models”, Vestnik of Samara State University, 2012, no. 9(100), 70–83 (in Russian)

[17] Stepanova L. V., Phedina E. M., “Self-similar solution of antiplane shear crack problem in coupled (creep-damage) statement of the problem”, Journal of Applied Mechanics and Theoretical Physics, 43:5(255) (2002), 114–123 (in Russian) | MR

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

[19] Shih C. F., “Small-scale yielding analysis of mixed plane strain crack problem”, Fracture Analysis, ASTM STP, 560, 1974, 187–210 (in English)

[20] Kachanov M., Shafiro B., Tsukrov I., Handbook of elasticity solution, Springer-Science+Business Media, Berlin, 2003, 329 pp. (in English) | MR

[21] Mushelishvili N. I., Some basic problems of the mathematical theory of elasticity, Nauka, M., 1966, 707 pp. (in Russian)