INTRODUCHONTHE SHORT crack problem really encompasses three distinct areas:(i)the initiation and growth of cracks up to the order of the grain size (ii)the growth of cracks from notches (iii)the anomalous behaviour of cracks in plain material that, though "short" are none In this note the third of these is considered.The anomaly is that the growth rates associated with these "short" cracks are greater than those associated with long cracks having the same stress intensity factor range ( A K ) and that the threshold stress intensity factor range ( A K o ) also decreases as crack length decreases. Moreover what constitutes "short" is strongly material dependent.Clearly for these "short" cracks the characterisation of crack tip conditions by the stress intensity factor ( K ) is breaking down. In seeking an explanation for this, it seems sensible to review first the assumptions underlying the use of K . These are that(1) the material behaves as a continuum (2) the crack tip plastic zone is fully contained and constrained by surrounding elastic( 3 ) the stress distribution in the constraining elastic material adjacent to the plastic zone In support of (l), although variation of crack-growth rates from grain to grain and at different points within an individual grain would be anticipated, the number of grains cut by a through-thickness crack tip at any instant is sufficiently large to give an averaging effect, and this effect will be the same at all crack depths. Surface, semi-elliptical defects, other than microcracks, also usually sample an adequate number of grains for "average" material behaviour to be relevant.As a generalisation, assumption (2) is also valid; certainly this appears to be the case in a number of instances e.g. [l, 21 where the anomaly has been observed.Regarding assumption (3), crack tip stress fields can be described by equations of the form the less appreciably greater than the grain size. material is, to a close approximation, a function of K alone. and the use of K to characterize crack behaviour assumes that terms of higher order than r -t can be neglected. The process of elimination suggests therefore that if the problem is 343
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