Abstract
The singular stresses at the tip of a sharp angular notch are analysed for the most general case of elastic anisotropy. The problem is stated in relation with the kinked crack and is modelled by means of continuous distributions of dislocations which are assumed to be singular at the notch vertex, the kind of the main singularity λ being unknown and weaker than at the crack tip. The Mellin transform is applied to obtain a system of simultaneous functional equations that enables one to find the parameter λ. The reciprocal theorem is used to compute the generalised stress intensity factor which characterises the singular stresses in a neighbourhood of the notch tip.
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References
Atkinson, C. (1979). Stress singularities and fracture mechanics. Applied Mechanics Reviews 32, 123–135.
Atkinson, C., Bastero, J.M. and Martinez-Esnaola, J.M. (1988). Stress analysis in sharp angular notches using auxiliary fields. Engineering Fracture Mechanics 31, 637–646.
Bastero, J.M., Atkinson, C. and Martinez-Esnaola, J.M. (1989). Use of path-independent integral A for mixed-mode fast crack propagation in uncoupled thermoelastic media. Engineering Fracture Mechanics 34, 325–335.
Blanco, C. (1997). Modelos de dislocaciones para grietas en recubrimientos y para grietas acodadas en el caso general de anisotropia elkstica, Tesis Doctoral, Escuela Superior de Ingenieros de San Sebastian, Universidad de Navarra.
Bogy, D.B. (1972). The plane solution for anisotropie elastic wedges under normal and shear loading. Journal of Applied Mechanics 39, 1103–1109.
Busch, M., Heinzelmann, M. and Maschke, H.G. (1994). A cohesive zone model for the failure assessment of V-notches in micromechanical components. International Journal of Fracture 69, R15 - R21.
Cherepanov, G.P. (1979). Mechanics of Brittle Fracture, McGraw-Hill, New-York.
Eshelby, J.D., Read, W.T. and Shockley, W. (1953). Anisotropie elasticity with applications to dislocations theory. Acta Metallurgica 1, 251–259.
Heinzelmann, M., Kuna, M. and Busch, M. (1994). FEM and BEM analyses of notch stress intensity factors in anisotropic materials, ECF 10–Structural Integrity: Experiments, Models and Applications, Vol. 1 ( Edited by K-H. Schwalbe and C. Berger), EMAS, Warley (UK), 329–334.
Huntington, H.B. (1958). Solid State Physics, Vol. 7 (Edited by F. Seitz and Turubull), Academic Press, New York, 214–351.
Muskhelishvili, N.I. (1977). Some Basic Problems of the Mathematical Theory of Elasticity, Noordhoff Int. Pub., Leyden, The Netherlands.
Sih, G.C. and Ho, J.W. (1991). Sharp notch fracture strength characterised by critical energy density. Theoretical and Applied Fracture Mechanics 16, 179–214.
Stern, M., Becker, E.B. and Dunham, R.S. (1976). A contour integral computation of mixed-mode stress intensity factors. International Journal of Fracture 12, 359–368.
Stroh, A.N. (1958). Dislocations and cracks in anisotropic elasticity, Philosophical Magazine 3, 625–646.
Williams, M.L. (1952). Stress singularities resulting from various boundary conditions in angular corners of plates in extension. Journal of Applied Mechanics 19, 526–528.
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Blanco, C., Martínez-Esnaola, J.M., Atkinson, C. (1998). Analysis of sharp angular notches in anisotropic materials. In: Knauss, W.G., Schapery, R.A. (eds) Recent Advances in Fracture Mechanics. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-2854-6_19
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DOI: https://doi.org/10.1007/978-94-017-2854-6_19
Publisher Name: Springer, Dordrecht
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