Elastothermodynamic analysis of a Griffith crack
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When a homogeneous material is subjected to a nonuniform stress field, different regions undergo different temperature fluctuations due to the well-known thermoelastic effect. As a result irreversible heat conduction occurs, and entropy is produced which is manifested as a conversion of mechanical energy into heat. Moreover, the changes in temperature produce a thermal strain that is out of phase with the stress, thus converting mechanical energy into heat, i.e. work is lost. In this paper we present an approximate analysis of the entropy produced and work lost in the neighborhood of a Griffith crack subjected to a time-harmonic loading in modes I, II, and III. In all three modes the temperature at the crack tip remains bounded. In mode I the entropy produced (per unit volume per cycle) is finite at the crack tip, whereas the work lost (per unit volume per cycle) goes to infinity as 1/r. Conversely, in mode II the entropy produced goes to infinity as I/r as the crack tip is approached, whereas the work lost is finite. In mode III the thermoelastic effect disappears altogether and, therefore, both the entropy produced and the work lost are zero throughout the plate. Copyright 1996 Elsevier Science Ltd.
