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Author's Reply GEORGE
F. H U R L E ' ~
T h e e x i s t e n c e o f p l a s t i c flow in a c r y s t a l u n d e r d e f i n e d c o n d i t i o n s m a y b e p r e d i c t e d by d e t e r m i n i n g if p l a s t i c flow can b e i n d u c e d u n d e r a n y c i r c u m s t a n c e s , by d e t e r m i n a t i o n of t h e flow s t r e s s u n d e r s u c h c o n d i t i o n s , a n d by e x t r a p o l a t i o n of t h i s flow s t r e s s to the d e f i n e d c o n d i t i o n s . T h e l a s t is of c r u c i a l i m p o r t a n c e s i n c e f a c tors such as strain rate, temperature, dislocation dens i t y , o r i e n t a t i o n (in s i n g l e c r y s t a l s ) o r g r a i n s i z e (in p o l y c r y s t a l s ) , and o t h e r f a c t o r s c a n a f f e c t the flow
stress. The brittle behavior of a solid crystalline material is usually a result of the action of flaws which can propagate at stresses lower than the theoretical cleavage stress. $imilarly~ the plastic behavior of a solid crystalline material is described by m e c h a n i s m s which operate as stresses lower than the theoretical shear strength. Thus, examination of the theoretical shear and cleavage stresses for perfect crystals at absolute zero cannot be used to show that dislocation motion canno! accompany fracture at elevated (relative to 0~K) temperature in imperfect crystals. For example, Kelly etrd. z7 have established a criterion to determine whether or not plastic flow can acc o m p a n y fracture in perfect single crystals. The criterion is that if the ratio of the m a x i m u m tensile stress to the m a x i m u m shear stress is greater than that of the theoretical cleavage stress to the theoretical shear stress, then the crystal can fail with no plastic work. A n example is given in Ref. 27 for sodium chloride. In this case it was demonstrated that the criterion as stated above was met and that it is possible to cleave sodium chloride with the work of fracture equal to the surface energy. However, this does not imply that sodium chloride is not capable of plastic flow. Indeed, it is possible to obtain plastic strains of greater than 7 pct in sodium chloride mechanical tests at r o o m temperature.aZ'a3 The implication that microindentation hardness testing in sapphire is accompanied by adiabatic heating sufficient to affect the nature of the observations r e q u i r e s c a r e f u l s c r u t i n y . W e e s t i m a t e d the i n c r e a s e of t e m p e r a t u r e w h i c h w o u l d a c c o m p a n y t h e c r e a t i o n of an i n d e n t a t i o n w i t h a 25 g m l o a d . W e did t h i s by c a l c u l a t ing t h e w o r k d o n e t h e n d i v i d i n g by t h e v o l u m e of m a terial affected. T h e w o r k d o n e by t h e i n d e n t e r ( ~ ) is g i v e n by t h e f o r c e t i m e s t h e d e p t h of t h e i n d e n t a t i o n (h). If the f o r c e is a f u n c t i o n of t h e d e p t h , t h e n : = ~ F(h)dh
S i n c e t h e i n d e n t e r is l o w e r e d to the s u r f a c e by m e a n s o f a n h y
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