Summary
The J-integral technique is used to assess the risk of defects in a particular structure by explicit computation of the arising generalized forces. Three different situations are considered: stress concentrators in cycloidal specimens, the interaction of a dislocation with a circular inclusion, and the interaction between two dislocations. Special emphasis is given to an effective but analytical calculation of the corresponding path integrals.
Similar content being viewed by others
References
Kienzler, R.: Konzepte der Bruchmechanik: Integrale Bruchkriterien, Grundlagen und Fortschritte der Ingenieurwissenschaften. Braunschweig, Wiesbaden: Vieweg 1993.
Buggisch, H., Gross, D., Krüger, K.-H.: Einige Erhaltungssätze der Kontinuumsmechanik vom J-Integral-Typ. Ing. Arch.50, 103–111 (1981).
Kienzler, R., Kordisch, H.: Calculation of J1 and J2 using the L and M Integrals. Int. Fracture43, 213–225 (1990).
Gao, H., Müller, W. H., Kemmer, G.: Mixed mode fracture in epicycloid specimens I. Thermal inclusions. Int. J. Solids Struct. (in print).
Müller, W. H., Gao, H.: Mixed mode fracture in epicycloid specimens II. Point force loading. Int. J. Solids Struct.35, 205–217 (1998).
Bronstein, I. N., Semendjajew, K. A.: Taschenbuch der Mathematik, 16. Auflage. Zürich Frankfurt/Main Thun: Verlag Harri Deutsch 1976.
Muskhelishvili, N. I.: Some basic problems of the mathematical theory of elasticity, fourth, corrected and augmented edition. Groningen-Netherlands: P. Noordhoff 1963.
Rice, J. R.: A path independent integral and the approximate analysis of strain concentration by notches and cracks. J. Appl. Mech.35, 379–386 (1968).
Kienzler, R., Zhuping, D.: On the distribution of hoop stresses around circular holes in elastic sheets. J. Appl. Mech.54, 111–114 (1987).
Green, A. E., Zerna, W.: Theoretical elasticity, 2nd ed. New York: Dover Publications, Inc. 1992.
Dundurs, J., Mura, T.: Interaction between an edge dislocation and a circular inclusion. J. Mech. Phys. Sol.12, 177–189 (1964).
Dundurs, J.: On the interaction of a screw dislocation with inhomogeneities. In: Recent advances in engineering science (Eringen, A. C., ed.), pp. 223–233, New York: Gorden & Breach 1967.
Gong, S. X., Meguid, S. A.: A screw dislocation interacting with an elastic elliptical inhomogeneity. Int. J. Eng. Sci.32, 1221–1228 (1994).
Kanninen, M. F., Popelar, C. H.: Advanced fracture mechanics. Oxford Engineering Science Series 15. New York: Oxford University Press 1985.
Nabarro, F. R. N.: Theory of crystal dislocations. New York: Dover 1987.
Nabarro F. R. N.: Dislocations in solids, Vol. 1 and 4. Amsterdam: North-Holland 1979.
Rice, J. R.: Conserved integrals and energetic forces. In: Deformation and fracture, J. D. Eshelby Memorial Symposium, Sheffield 1984 (Bilby, B. A., ed.), pp. 33–56. Cambridge: Cambridge University Press, 1985.
Author information
Authors and Affiliations
Additional information
Dedicated to Professor Dr. rer. nat. Dr. h. c. Ingo Müller on the occasion of his 60th birthday
Rights and permissions
About this article
Cite this article
Müller, W.H., Kemmer, G. Applications of the concept of J-integrals for calculation of generalized forces. Acta Mechanica 129, 1–12 (1998). https://doi.org/10.1007/BF01379646
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01379646