Summary
A nonhomogeneous elastic layer is weakened by an infinite, rectilinear crack separating two layers of different elastic materials. The boundary surfaces of the layer are rigidly clamped and the crack surfaces loaded by arbitrary forces satisfying the conditions of antiplane state of strain. Considered are two cases, the crack and its load propagating at a constant velocity along the horizontal axis, and the load being a harmonic function of time, respectively. In the both cases exact values of the stress intensity factor for arbitrary loading (arbitrary load amplitude) of the crack are given. In the limiting cases, solutions of static problems are obtained. The results are illustrated by particular solutions concerning the cases when the crack edge load (or its amplitude) is constant on its entire length.
Zusammenfassung
Eine aus zwei verschieden elastischen Schichten zusammengesetzte Schicht wird durch einen streifenförmigen Riß zwischen den Schichten geschwächt. Die Oberflächen der Schicht sind eingespannt und die Rißoberfläche durch beliebige, die Bedingungen des antiebenen Verzerrungszustandes genügenden Kräften belastet. Betrachtet werden die zwei Fälle, daß sich der Riß und seine Belastung mit konstanter Geschwindigkeit horizontal bewegen und daß die Last eine harmonische Funktion der Zeit ist. In beiden Fällen werden die exakten Werte des Spannungserhöhungsfaktors für beliebige Lasten (beliebige Lastamplituden) angegeben. In den Grenzfällen werden die Werte des statischen Problems erhalten. Die Resultate werden an Hand des Spezialfalles einer über die gesamte Länge konstanten Last (oder Amplitude) erläutert.
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On leave from the Institute of Fundamental Technological Research (Polish Academy of Sciences), Warsaw. The paper has been prepared during author's research visit at the Institute A for Mechanics, Munich Technical University, sponsored by the Alexander von Humboldt Foundation.
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Matczyński, M. Quasistatic problem of a non-homogeneous elastic layer containing a crack. Acta Mechanica 19, 153–168 (1974). https://doi.org/10.1007/BF01176483
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DOI: https://doi.org/10.1007/BF01176483