A mode-III crack with variable surface effects

• Autorzy: Wang X. , Schiavone P.

Identyfikatory

DOI

10.15632/jtam-pl.54.4.1319

• Języki publikacji: EN

Abstrakty

EN

We study the contribution of variable surface effects to the antiplane deformation of a linearly elastic material with a mode-III crack. The surface elasticity is incorporated using a modified version of the continuum based surface/interface model of Gurtin and Murdoch. In our discussion, the surface moduli are not constant but vary along the crack surfaces. Using Green’s function method, the problem is reduced to a single first-order Cauchy singular integro-differential equation, which is solved numerically using Chebyshev polynomials and a collocation method. Our results indicate that the gradient of the surface shear modulus exerts a significant influence on the crack opening displacement and on the singular stress field at the crack tips.

Słowa kluczowe

EN

surface elasticity; variable surface moduli; mode-III crack; Cauchy singular integro-differential equation

• Wydawca: Polskie Towarzystwo Mechaniki Teoretycznej i Stosowanej
• Czasopismo: Journal of Theoretical and Applied Mechanics
• Rocznik: 2016
• Tom: Vol. 54 nr 4
• Strony: 1319--1327
• Opis fizyczny: Bibliogr. 16 poz., rys.

Twórcy

autor

Wang X.

• School of Mechanical and Power Engineering, East China University of Science and Technology, Shanghai, China

autor

Schiavone P.

• University of Alberta, Department of Mechanical Engineering, Edmonton, Canada

Bibliografia

• 1. Antipov Y.A., Schiavone P., 2011, Integro-differential equation for a finite crack in a strip with surface effects, Quarterly Journal of Mechanics and Applied Mathematics, 64, 87-106
• 2. Chen T., Dvorak G.J., Yu C.C., 2007, Size-dependent elastic properties of unidirectional nano- -composites with interface stresses, Acta Mechanica, 188, 39-54
• 3. Gurtin M.E., Murdoch A., 1975, A continuum theory of elastic material surfaces, Archive for Rational Mechanics and Analysis, 57, 291-323
• 4. Gurtin M.E., Weissmuller J., Larche F., 1998, A general theory of curved deformable interface in solids at equilibrium, Philosophical Magazine, A78, 1093-1109
• 5. Kim C.I., Ru C.Q., Schiavone P., 2013, A clarification of the role of crack-tip conditions in linear elasticity with surface effects, Mathematics and Mechanics of Solids, 18, 59-66
• 6. Kim C.I., Schiavone P., Ru C.Q., 2010, The effects of surface elasticity on an elastic solid with mode-III crack: complete solution, ASME Journal of Applied Mechanics, 77, 021011-1–021011-7
• 7. Kim C.I., Schiavone P., Ru C.Q., 2011a, Analysis of plane-strain crack problems (mode I and mode II) in the presence of surface elasticity, Journal of Elasticity, 104, 397-420
• 8. Kim C.I., Schiavone P., Ru C.Q., 2011b, Effect of surface elasticity on an interface crack in plane deformations, Proceedings of the Royal Society of London. Series A, 467, 3530-3549
• 9. Markenscoff X., Dundurs J., 2014, Annular inhomogeneities with eigenstrain and interphase modeling, Journal of the Mechanics and Physics of Solids, 64, 468-482
• 10. Ru C.Q., 2010, Simple geometrical explanation of Gurtin-Murdoch model of surface elasticity with clarification of its related versions, Science China, 53, 536-544
• 11. Sharma P., Ganti S., 2004, Size-dependent Eshelby’s tensor for embedded nano-inclusions incorporating surface/interface energies, ASME Journal of Applied Mechanics, 71, 663-671
• 12. Steigmann D.J., Ogden R.W., 1997, Plane deformations of elastic solids with intrinsic boundary elasticity, Proceedings of the Royal Society of London. Series A, 453, 853-877
• 13. Walton J.R., 2012, A note on fracture models incorporating surface elasticity, Journal of Elasticity, 109, 95-102
• 14. Wang X., 2015, A mode III arc shaped crack with surface elasticity, Zeitschrift f¨ur Angewandte Mathematik und Physik, 66, 1987-2000
• 15. Wang X., Schiavone P., 2015, A mode III interface crack with surface strain gradient elasticity, Journal of Integral Equations and Applications, 28, 123-148
• 16. Wang X., Schiavone P., 2016, Bridged cracks of mode III with surface elasticity, Mechanics of Materials, 95, 125-135

Uwagi

PL

Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniajacą naukę.