Summary
Axially symmetric stress distribution in the neighbourhood of a penny-shaped crack stituated in an infinite isotropic elastic solid under general surface loadings and general surface temperature is considered. Surface loadings and surface temperature applied on the crack surfaces are axisymmetric but they are unsymmetrical about the crack planez=0. The equations of equilibrium of an elastic solid conducting heat have been solved using Hankel transforms and Abel integral operator of the second kind. The stresses, displacements, temperature and flux functions at a general point in the solid are derived in terms of stress, displacement, temperature and heat flux discontinuities at the plane of the crack. Using the boundary conditions and the continuity conditions problem is reduced to that of solving Abel integral equations of the first and the second kind. Explicit expressions are obtained for stress components, crack opening displacement and stress intensity factors in terms of the prescribed surface temperature functions. For some special cases of thermal loading these quantities are compared with those available in the literature. Stress at a general point of the medium is obtained in the special case, when the one face of the crack is subjected to constant temperature while the other face is kept at the reference temperature.
Übersicht
Eine axialsymmetrische Spannungsverteilung in der Umgebung eines münzförmigen Risses im unbegrenzten isotropen elastischen Raum wird für allgemeine Randbedingungen bezüglich der Last- und Temperaturverteilung untersucht. Die Randwerte sind axialsymmetrisch verteilt, aber nicht-symmetrisch gegenüber der Rißebenez=0. Die Gleichgewichtsgleichungen werden unter Einbeziehung der Hankelschen Transformationen und des Abelschen Integralope-rators zweiter Art gelöst. Es werden die Feldvariablen der Spannungen, Verschiebungen, der Temperatur und der Wärmeströme als Funktionen ihrer Sprünge in der Rißebene hergeleitet. Die Stetigkeits- und Randbedingungen reduzieren die Aufgabe auf die Lösung der Abelschen Integralgleichungen erster und zweiter Art. In einigen Spezialfällen der Wärmebeanspruchung werden die Lösungen mit den in der Literatur veröffentlichten Angaben verglichen.
Similar content being viewed by others
References
Olesiak, Z.;Sneddon, I. N.: The distribution of thermal stress in an infinite elastic solid containing a penny-shaped crack. Arch. Rat. Mech. Anal. 4 (1959) 238–254
Shail, R.: Some thermoelastic stress distribution in an infinite solid and a thick plate containing penny-shaped cracks. Mathematika 11 (1964) 102–118
Florence, A. L.;Goodier, J. N.: The linear thermoelastic problem of uniform heat flow distributed by a penny-shaped insulated crack. Int. J. Engng. Sci. 1 (1963) 533–540
Sneddon, I. N.: Fourier transforms. New York: McGraw-Hill 1951
Sneddon, I. N.;Lowengrub, M.: Crack problems in the classical theory of elasticity. New York: Wiley 1969
Kassir, M. K.;Sih, G. C.: Three dimensional crack problems. In: Sih, G. C. (ed) Mechanics of Fracture, Vol. 2. Leyden: Noordhoff 1975
Parihar, K. S.;Krishna Rao, J. V. S.: Axially symmetric stress distribution in the neighbourhood of a penny-shaped crack under general surface loadings Engng. Fract. Mech. 39 (1991) 1067–1095
Parihar, K. S.;Krishna Rao, J. V. S.: On axially symmetric problem of a penny-shaped crack under general surface lodings. Int. J. Engng. Sci. 31 (1993) 953–966
Sneddon, I. N.;Berry, D. S.: The classical theory of elasticity. In: Handbuch der Physik, Band b. Berlin: Springer 1958
Sneddon, I. N.: Use of integral transforms New York: McGraw-Hill 1972
Sneddon, I. N.: The distribution of stress in the neighbourhood of a crack in an elastic solid. Proc. Roy. Soc. London Ser. A 187 (1946) 229–260
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Krishna Rao, J.V.S., Hasebe, N. Axially symmetric thermal stress of a penny-shaped crack subjected to general surface temperature. Arch. Appl. Mech. 64, 481–496 (1994). https://doi.org/10.1007/BF00788881
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF00788881