Some observations on work hardening of polycrystalline iron and nickel containing non-deformable particles
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Some Observations on Work Hardening of Polycrystalline Iron and Nickel Containing Non-Deformable Particles
l a r to those of F e - T a 4 except deviation f r o m a p a r a bolic r e l a t i o n s h i p o c c u r r e d at a s q u a r e root s t r a i n value of 0.3 in the Nt-ThO2 a l l o y s as c o m p a r e d to 0.2 to 0.22 for the F e - T h O 2 and 0.15 to 0.20 for the F e - T a a l l o y s . It was o b s e r v e d 4 that the l i m i t of p a r t i c l e r e lated work hardening coincided with this deviation from p a r a b o l i c hardening in the F e - T a a l l o y s ; however, in the Fe-ThOz and Ni-ThO2 a l l o y s the p a r t i c l e r e l a t e d work hardening did not s e e m to s a t u r a t e as in the F e Ta a l l o y s . I n a c c u r a c i e s in data taken f r o m a published graph do not allow a f i r m conclusion about t h e i r behavior. The slopes of the l i n e a r portion of F i g s . 1 and 2 have been d e t e r m i n e d and f r o m these s l o p e s the values of
Table I, Work Hardening Coefficient, C, for Iron and Nickel Containing Nondeformable Particles
RUSSELL H. JONES In his work hardening model for single c r y s t a l s containing hard, n o n - d e f o r m a b l e p a r t i c l e s , Ashby I p r o posed that g e o m e t r i c a l l y n e c e s s a r y s e c o n d a r y d i s l o c a tions a r e generated about a p a r t i c l e as p l a s t i c flow p r o c e e d s . The flow s t r e s s was p r o p o s e d to be dependent on the square r o o t of the s h e a r s t r a i n . Support for this model was given by Ebeling and Ashby e for copper single c r y s t a l s containing SiO2 p a r t i c l e s . The followIng r e l a t i o n s h i p was p r e s e n t e d : 7" = r y + CG ( b f y / D ) 112
f o r m e r l y w i t h Westinghouse Research Laboran o w Senior Research Scientist w i t h Battelle R i c h l a n d , Wash. 9 9 3 5 2 . O c t o b e r 11, 1973.
9 7 0 - V O L U M E 5, APRIL 1974
Fe-Ta
Value of C
Ref.
0+51 0.52 0.46 0.43 0.44 0.35 0.36 0.80 0.62 0.63 0.58 0.57
4 4 4 4 4 5 5 6 6 6 6 6
0.73 1.44 3.08 4.14 5.32 0.90 1.7 1.0 1.5 2.0 2.5 3.0
Fe-ThO2 Ni-ThO2
[1]
where 7- is the flow s t r e s s , Ty the yield s t r e s s of the two phase alloy, G the m a t r i x s h e a r modulus, C a constant, b the m a t r i x B u r g e r s v e c t o r , f the p a r t i c l e volume fraction, y the s h e a r s t r a i n a n d / ~ the mean p a r t i c l e diam. Ashby and Ebeling mobtained a value of 0.24 • 0.04 for the constant C while Ashby z p r e d i c t e d a value of 0.24. This t h e o r e t i c a l value was obtained by taking the p r o b a b i l i t y of one s e c o n d a r y loop i n t e r s e c t i n g a p r i m a r y slip plane as I / d - 2 t i m e s the a v e r a g e loop d i a m e t e r and the r e s u l t s of Kroupa a for the a v e r a g e f o r c e e x e r t e d by one loop opposing a s t r a i g h t d i s l o c a tion in its slip plane. This model, adapted for p o l y c r y s t a l s , has been used by Jones 4 to calculate the s t r e s s - s t r a i n behavior of p o l y c r y
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