Abstract
In fatigue crack growth analysis it is essential to know the stress distributions in the neighbourhood of stress raisers. If such distributions ahead of the uncracked notch are known, stress intensity factors may be obtained via the weight function or other methods. The procedure described in the present paper reconsiders the principal elastic stress expressions already reported by the authors for infinite plates with semi-infinite symmetric V-shaped notches and adapts them to some practical cases, in which the mutual influence of the notches as well as that of the plate finite size play an important role in stress distributions. The aim is therefore to give an approximate close-form solution for the longitudinal stress, valid for the entire ligament length, namely from notch tip to notch tip. Theoretical and numerical stress values are compared on this line, examining plates with semicircular, V and U-shaped notches subjected to remote uniaxial tension.
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References
Atzori, B., Lazzarin, P. and Tovo, R. (1997). Stress distributions for V–shaped notches under tensile and bending loading. Fatigue and Fracture of Engineering Materials and Structures 20, 1083–1092.
Carpenter, W.C. (1984). A collocation method for determining fracture mechanics parameters at a corner. International Journal of Fracture 24, 255–266.
Chen, C. and Pan, H. (1978). In: Collection of Papers on Fracture of Metals(Edited by C. Chen). Metallurgy Industry Press, Beijing, 197–219.
Creager, M. and Paris, P.C. (1967). Elastic field equations for blunt cracks with reference to stress corrosion cracking. International Journal of Fracture Mechanics 3, 247–252.
Glinka, G. (1985). Calculation of inelastic notch–tip strain–stress hystories under cyclic loading. EngineeringFracture Mechanics 22, 839–854.
Glinka, G. and Newport, A. (1987). Universal features of elastic notch–tip stress fields. International Journal ofFatigue 9, 143–150.
Howland, R.J. (1929–1930). On the stresses in the neighbourhood of a circular hole in a strip under tension. Philosophical Transactions of the Royal Society of London, Series A, 229, 49–86.
Inglis, C.E. (1913). Stresses in a plate due to the presence of cracks and sharp corners. Transactions Institution ofNaval Architecture 55, 219–230.
Irwin, G.R. (1957). Analysis of stresses and strain near the end of a crack transversing a plate. Journal of AppliedMechanics 24, 361–364.
Knight, R.C. (1935). Action of a rivet in a plate of finite breadth. Philosophical Magazine, Series 7, 19, 517–540.
Kujawski, D. (1991). Estimations of stress intensity factors for small cracks at notches. Fatigue and Fracture ofEngineering Materials and Structures 14, 953–965.
Kujawski, D. and Shin, C.S. (1997). On the elastic longitudinal stress estimation in the neighbourhood of notchers. Engineering Fracture Mechanics 56, 137–138.
Lazzarin, P. and Tovo, R. (1996). A unified approach to the evaluation of linear elastic fields in the neighbourhood of cracks and notches. International Journal of Fracture 78, 3–19.
Ling, C.B. (1947). Stresses in a notched strip under tension. Journal of Applied Mechanics 14, A–275–280.
Muskhelishvili, N.I. (1953). Some Basic Problems of the Mathematical Theory of Elasticity.Noordhof Leyden.
Neuber, H. (1958). Theory of Notch Stresses.Springer–Verlag, Berlin.
Shin, C.S. (1994b). Fatigue crack growth from stress concentrations and fatigue life predictions in notched components. In Handbook of Fatigue Crack Propagation in Metallic Structures(Edited by A. Carpinteri), Elsevier Science Publishers B.V., Amsterdam, 613–652.
Shin, C.S., Man, K.C. and Wang, C.M. (1994a). A practical method to estimate the stress concentration of notches. International Journal of Fatigue 16, 242–255.
Tada, H., Paris, P.C. and Irwin, G. (1973). In The Stress Analysis of Crack Handbook(Del Research Corporation), 2nd edition, Paris Productions, Inc., St. Louis (1985).
Westergaard, H.M. (1939). Bearing pressure and cracks. Journal of Applied Mechanics 6, A49–53.
Williams, M.L. (1952). Stress singularities resulting from various boundary conditions in angular corners of plates in tension. Journal of Applied Mechanics 19, 526–528.
Xu, R.X., Thompson, J.C. and Topper, T.H. (1995). Practical stress expressions for stress concentration regions. Fatigue and Fracture of Engineering Materials and Structures 18, 885–895.
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Lazzarin, P., Tovo, R. & Filippi, S. Elastic stress distributions in finite size plates with edge notches. International Journal of Fracture 91, 269–282 (1998). https://doi.org/10.1023/A:1007577629523
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DOI: https://doi.org/10.1023/A:1007577629523