 | | Mechanics of Solids
A Journal of Russian Academy of Sciences | | Founded
in January 1966
Issued 6 times a year
Print ISSN 0025-6544
Online ISSN 1934-7936 |
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| A. A. Ostsemin and P. B. Utkin, "Theoretical and experimental studies in fracture mechanics of crack-like defects under biaxial loading," Mech. Solids. 44 (2), 277-287 (2009) |
| Year |
2009 |
Volume |
44 |
Number |
2 |
Pages |
277-287 |
| DOI |
10.3103/S0025654409020137 |
| Title |
Theoretical and experimental studies in fracture mechanics of crack-like defects under biaxial loading |
| Author(s) |
A. A. Ostsemin (Southern Ural Research and Production Center Ltd, Severo-Krymskaya 68-61, Chelyabinsk, 454106, Russia, ostsemin@math.susu.ac.ru)
P. B. Utkin (South Ural State University, pr-t Lenina 76, Chelyabinsk, 454080, Russia, neobart@inbox.ru) |
| Abstract |
It is a common point of view in fracture mechanics that, for any geometry of the body with a crack and any boundary conditions for the loading acting in the body plane, the stress and displacement components near the crack tip can be approximated in the framework of the theory of elasticity by a one-parameter or one-term representation, i.e., strictly in terms of the stress intensity coefficients KI and KII for an arbitrary failure crack [1, 2]. The authors of [2] specified the Westergaard function of the singular solution for a central crack under the biaxial loading of a plate. This approximate two-component solution has satisfactory accuracy.
It is clear from [2] that this method cannot be admitted as a general statement [1], although it has long been assumed to be correct. The cause is that one cannot reasonably justify neglecting the second term in the Williams representation of the stress components in the plane case in the form of eigenfunction series; the contribution of this term in the rectangular coordinate system x, y is independent of the distance from the crack tip. This method may result in a serious mistake, from both the qualitative and quantitative viewpoints, in the prediction of local stresses, displacements, and related variables that are of interest. Apparently, this can best be demonstrated by an example of biaxial loading of a plate with a crack [1]. The unfounded neglect of the second term (whose contribution is independent of the distance from the crack tip) in the series representing the stress components is the source of the above-mentioned difficulties. In this problem, the influence of the load applied in the direction parallel to the crack plane manifests itself only in the second term of the series [3]. Therefore, this term should be clearly determined and studied in detail in the case of technological welding defects (faulty fusions, incomplete fusions, undercuts, and slag inclusions) and crack-like defects (scratches and cuts) in the base metal. The influence of the stress σOX along the crack axis on the stress tensor σx, σy, τxy and on the displacements ux and uy is confirmed by experimental studies of cracks by the photoelasticity method [4]. |
| References |
| 1. | H. Liebowitz, J. Eftis, and D. Johns, "Several Recent Theoretical and Experimental Studies in Fracture Mechanics," in Fracture Mechanics. Construction Fracture, Ed. by R. V. Goldstein (Mir, Moscow, 1980), pp. 168–202 [in Russian]. |
| 2. | J. Eftis, N. Subramonian, and H. Liebowitz, "Crack Border Stress and Displacement Equations Revisited," Engng Fract. Mech. 9(1), 189–210 (1977). |
| 3. | A. Ya. Krasovskii, Metal Shortness at Low Temperatures (Naukova Dumka, Kiev, 1980) [in Russian]. |
| 4. | J. M. Etheridge and J. W. Dally, "A Critical Review of Methods for Determining Stress-Intensity Factors from Isochromatic Fringes," Experim. Mech. 17(7), 248–254 (1977). |
| 5. | N. I. Muskhelishvili, Some Fundamental Problems of Mathematical Elasticity Theory (Nauka, Moscow, 1966) [in Russian]. |
| 6. | G. C. Sih and H. Liebowitz, "Mathematical Theory of Brittle Failure," in Fracture, Vol. 2 (Mir, Moscow, 1975), pp. 83–203 [in Russian]. |
| 7. | J. Eftis and H. Liebowitz, "On the Modified Westergaard Equations for Certain Plane Crack Problems," Intern. J. Fract. Mech. 8(4), 383–392 (1972). |
| 8. | F. Paris and G. C. Sih, "Analysis of Stressed State near Cracks," in Applied Problems of Viscous Fracture (Mir, Moscow, 1968), pp. 64–142 [in Russian]. |
| 9. | S. P. Timoshenko and J. N. Goodyear, Theory of Elasticity (McGraw-Hill, New York, 1951; Nauka, Moscow, 1975). |
| 10. | A.A. Ostsemin, S. A. Deniskin, and L. L. Sitnikov, "Determination of the Stress Intensity Factor by Methods of Photoelastic Simulation." Probl. Prochn., No. 1, 33–37 (1990) [Strength of Materials (Engl. Transl.) 22 (11), 39–45 (1990)]. |
| 11. | A. Ya. Aleksandrov and M. Kh. Akhmetzyanov, Polarization-Optical Methods of Mechanics of Deformable Bodies (Nauka, Moscow, 1973) [in Russian]. |
| 12. | A. A. Ostsemin, S. A. Deniskin, L. L. Sitnikov, et al., "Determination of the Stress State of Bodies with Flaws by the Method of Holographic Photoelasticity," Probl. Prochn., No. 10, 77–81 (1982) [Strength of Materials (Engl. Transl.) 14 (10), 1375–1380 (1982)]. |
| 13. | L. L. Sitnikov, A. A. Ostsemin, S. A. Deniskin, and A. A. Zagrebalov, "Determining the Stress Intensity Coefficient K1 by the Method of Holographic Photoelasticity," Zavodskaya Laboratoriya. Diagnostika Materialov, No. 9, 81–83 (1982). |
| 14. | A. A. Kaminskii, Brittle Fracture near Holes (Izd-vo Kiev Inst. Mekh. AN Ukr. SSR, Kiev, 1982) [in Russian]. |
|
| Received |
27 March 2007 |
| Link to Fulltext |
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