Hardness and creep of Bi-Sb alloys under spherical indentation
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WE
define the h a r d n e s s H in the u s u a l way,
H =
2W 7zD (D - ~ - D - ~ )
[1]
where W is load, D indenter diam and d indentation diam. The temperature variation of hardness m a y be given by relations I'~
H = A exp ( - BT)
[2]
H = A' e x p ( 2 B ' / R T )
[3]
w h e r e T is a b s o l u t e t e m p e r a t u r e , B softening p a r a m e t e r , B' a p p a r e n t " a c t i v a t i o n e n e r g y " for indentation, A and A ' c o n s t a n t s . The Eqs. [2] and [3] a r e o b v i o u s l y i n c o m p a t i b l e , but the s c a t t e r p e r m i t s f i t t i n g the h a r d n e s s d a t a on both. The s t r e s s e s a c t i n g on the s u r f a c e d u r i n g s p h e r i c a l indentation a r e e s s e n t i a l l y c o m p r e s s i v e and t h e i r m e a n v a l u e given a s z P -
4W
[4]
~d 2
The t r u e s t r a i n d u r i n g i n d e n t a t i o n can be e x p r e s s e d a s z E = 0.2
d
[5]
The c r e e p under indentation m a y b e given b y the e q u a tion =
Kp ~ exp ( - Q c / R T )
[6]
w h e r e a is s t r e s s coeffigient, Qc t r u e a c t i v a t i o n e n e r g y and K a c o n s t a n t . The Eqs. [3] and [6] can be shown to be r e l a t e d 2
Vc = 2orB'
[7]
if (d/D) ~
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