Abstract
Curved thermal cracks are considered running along special principal stress trajectories of thermal stress fields originated in different shaped glassy two-phase solids by a steady cooling process. The resulting boundary-value problems of the stationary plane thermoelasticity are solved by means of the method of complex analysis as well as of the finite element method. Moreover, using appropriate directional criteria established for crack path prediction, the further extension of a thermal crack starting at the external surface of a glassy two-phase compound with a circular cross section has been determined. Furthermore, the corresponding fracture mechanical data like crack edge displacements, strain energy release rates and stress intensity factors, respectively, have been calculated by additional consideration of the influence of inner stress concentrators onto the paths of quasistatic extending thermal cracks. Finally, the theoretical investigations are compared with calculations concerning the quasistatic growth of interface cracks in thermally loaded glassy multiphase solids as well as with the results of cooling experiments. Thereby the latter concentrate on the determination of experimental principal stress trajectories in stable uncracked bimaterial specimens as well as on the evaluation of fracture mechanical data governing the propagation behaviour of curved thermal cracks by means of the shadow optical method of caustics.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
England, A., ‘An arc crack around a circular elastic inclusion’, J. Appl. Mech. 33 (1966), 637–640.
Toya, M., ‘A crack along the interface of a circular inclusion embedded in an infinite solid’, J. Mech. Phys. Solids 22 (1974), 325–348.
Herrmann, K., ‘Curved thermal crack growth in the interfaces of a unidirectional Carbon-Aluminum composite’, Mechanics of Composite Materials, Recent Advances (Eds. Z. Hashin and C. T. Herakovich), Pergamon Press, New York (1983), 383–397.
Cotterell, B. and Rice, J.R., ‘Slightly curved or kinked cracks’, Intl.J. of Fracture 16 (1980), 155–169.
Bergkvist, H. and Guex, L., ‘Curved crack propagation’, Intl. J. of Fracture 15 (1979), 429–441.
Nemat-Nasser, S., ‘On stability of the growth of interacting cracks, and crack kinking and curving in brittle solids’, Numerical Methods in Fracture Mechanics (Eds. D. R. J. Owen and A. R. Luxmoore), Pineridge Press, Swansea (1980), 687–706.
Palaniswamy, K. and Knauss, W. G., ‘On the problem of crack extension in brittle solids under general loading‘, Mechanics Today 4 (Ed. S. Nemat-Nasser), Pergamon Press, New York (1978), 87–148.
Kerkhof, F., Bruchvorgange in Glasern, Verlag der Deutschen Glas- technischen Gesellschaft Frankfurt (Main) (1970).
Hieke, M., ‘Die RiBentstehung in Glasscheiben unter Eigenspannun- gen’, Z. Naturforsch. 15a (1960), 543–546.
Hieke, M. and Loges, F., ‘Das ZerreiBen von Glasern unter dem Ein- fluB definierter Eigenspannungsquellen’, Z. Angew. Phys. 22 (1966), 14–19.
Blauel, H., Ph. D. Dissertation, Freiburg University (1970).
Karihaloo, B. L. and Nemat-Nasser, S., ‘Thermally induced crack curving in brittle solids’, Analytical and Experimental Fracture Mechanics (Eds. G. C. Sih and M. Mirabile), Sijthoff & Noordhoff, Alphen,aan den Rijn (1981), 265–272.
Grebner, H. and Hermann, K., ‘Quasistatische Ausbreitung eines ge- krummten Warmespannungsrisses in einem Zweikomponentenmaterial’. DVM-Berichte, 12. Sitzung des AK Bruchvorgange, Freiburg (1980), 207–214.
Grebner, H., Ph. D. Dissertation, Paderborn University (1983).
Herrmann, K. and Grebner, H., ‘Curved thermal crack growth in a bounded brittle two-phase solid’, Intl. J. of Fracture 19 (1982), R 69 – R 74.
Herrmann, K. P. and Grebner, H., ‘Curved thermal crack growth in nonhomogeneous materials with different shaped external boundaries’, I. Theoretical results, Theoretical and Applied Fracture Mechanics 2 (1984), 133–146.
Herrmann, K. P. and Grebner, H., ‘Curved thermal crack growth in nonhomogeneous materials with different shaped external boundaries’, II. Experimental results, Theoretical and Applied Fracture Mechanics 2 (1984), 147–155.
Herrmann, K. P. and Grebner, H., ‘Slow thermal crack growth in thermally loaded two-phase composite structures containing inner stress concentrators’, Life Assessment of Dynamically Loaded Materials and Structures (Ed. L. Faria) 2, Laboratorio Nacional de Engenharia e Tecnologia Industrial, Lissabon (1984), 691–700.
Herrmann, K. P. and Grebner, H., ‘Quasistatic thermal crack extension in the interfaces of bounded self-stressed multiphase compounds’, Theoretical and Applied Fracture Mechanics 4 (1985), 127–135.
Hieke, M. and Herrmann, K., ‘Ober ein ebenes inhomogenes Problem der Thermoelastizitat’, Acta Mechanica 6 (1968), 42–55.
Muskhelishvili, N. I., Einige Grundaufgaben zur mathematischen Elastizitatstheorie, Fachbuchverlag Leipzig (1971).
Herrmann, K. and Grebner, E., ’Uber ein Randwertproblem der Thermo- viskoelastizitatstheorie‘, ZAMM 60 (1980), T 120–T 122.
Rybicki, E. F. and Kanninen, M. F., ‘A finite element calculation of stress intensity factors by a modified crack closure integral’, Eng. Fracture Mechanics 9 (1979), 931–938.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1987 ECSC, EEC, EAEC, Brussels and Luxembourg
About this chapter
Cite this chapter
Herrmann, K.P. (1987). Thermal Crack Growth in Self-Stressed Glassy Compounds. In: Herrmann, K.P., Larsson, L.H. (eds) Fracture of Non-Metallic Materials. Ispra Courses. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-4784-9_10
Download citation
DOI: https://doi.org/10.1007/978-94-009-4784-9_10
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-8621-9
Online ISBN: 978-94-009-4784-9
eBook Packages: Springer Book Archive