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Development of a theoretical equation for steady-state dislocation creep and comparison with data
Vo!.
8, No.
3
ABSTRACTS
OF ARTICLES
TO APPEAR
**Dept. Materials Science Engineering, Stanford University, Stanford, California
IN ACTA MET
University of Southern California Los Angeles, California 90007 Received November
Received November 13, 1973 Revised January 22, 1974 The replacement partition function is formulated for crystals and it is concluded that: (i) The replacement partition function is a welldefined fundamental quantity of the bulk crystal. (ii) It is due to the translational and the rotational motions of the "clusters" in the bulk crystal for which all the atoms are fixed at the local lattice sites defined for each "cluster", which is in agreement with the assertion by Lothe and Pound. 7.
DEVELOPMENT OF A THEORETICAL EQUATION FOR STEADY-STATE DISLOCATION CREEP AND COMPARISON WITH DATA J. H. Gittus United Kingdom Atomic Energy Authority, Springfields, Salwick, Preston, Lancashire England Received November 7, 1973 Revised December 26, 1973
For nineteen materials, including silver, tantalum and gamma iron, Ashby found that an empirical equation E =A(D ~ub/kT) (o/u) n gives a reasonable ~fit to steady-state creep data where A and n are materials constants. It is now shown that if the materials obey the Bailey-Orowan equation, Taylor's work-hardening model and Friedel's network-climb recoveryequation then an identical creep 3 equation is predicted with A = 8~ c. and n = 3. Here c = jogc~ncentration. In th~ cases of nickel, cadmium, beta thallium and stoichiometric UO~ the predicted and actual strengths differ by less than a factor two. 8.
THE TRANSITION FROM DISLOCATION CLIMB TO VISCOUS GLIDE IN CREEP OF SOLID SOLUTION ALLOYS Farghalli A. Mohamed & Terence G. Langdon Department of Materials
Science
xiii
26, 1973
T h e r e a r e two d i s t i n c t and separate classes of creep behavior in metallic solid solution alloys. The mechanism of creep in Class I alloys a p p e a r s t o be some form o f d i s l o c a t i o n climb process, whereas the mechanism i n C l a s s I I a l l o y s a p p e a r s t o be a viscous glide process. By m a k i n g assumptions concerning the nature of t h e c l i m b and g l i d e p r o c e s s e s , and using existing experimental results f o r an A1-3% Mg a l l o y , i t i s shown t h a t , to a f i r s t approximation, the criterion f o r d e f o r m a t i o n by v i s c o u s g l i d e is g i v e n by B~2
(Y)
k 2 (i-v)
~
3
T2 >
e2cb 6
where B ~8 x 1012 , o is the applied stress, k is Boltzmann's constant, v is Poisson's ratio, y is the stacking fault energy, G is the shear modulus, b is the Burgers vector, T is the absolute t e m p e r a t u r e , e is the solute-solvent size difference, and c is the concentration of solute atoms. The creep behavior of twenty-eight different solid solution alloys is analyzed, and it is shown that all alloys except one {Au-10% Ni) give results which are consistent with this criterion for viscous glide. 9.
KINETICS OF GROWTH OF PLATELIKE PRECIPITATES R. S a n k a r a n & C. L a i r d Dept. of Metallurgy & Materials Science, University of Pennsylvania, Philadelphia, Pa. Received November 26, 1973 Revised January 23, 1974
In order to resolve existing difficulties in the interpretation of the lengthening and thickening kinetics of platelike precipitates, these kinetics have been measured on @' and n plates in AI-4% Cu alloy and AI-0.2% Au alloy respectively, in conjunction with extensive observations of the ledge and misfit dislocation structures at the broad faces of the plates. Thickening has been found, in agreement with a well established theory of morphology, to occur bv a ledge mechanism, where the migration rates of the ledges were
8, No.
3
ABSTRACTS
OF ARTICLES
TO APPEAR
**Dept. Materials Science Engineering, Stanford University, Stanford, California
IN ACTA MET
University of Southern California Los Angeles, California 90007 Received November
Received November 13, 1973 Revised January 22, 1974 The replacement partition function is formulated for crystals and it is concluded that: (i) The replacement partition function is a welldefined fundamental quantity of the bulk crystal. (ii) It is due to the translational and the rotational motions of the "clusters" in the bulk crystal for which all the atoms are fixed at the local lattice sites defined for each "cluster", which is in agreement with the assertion by Lothe and Pound. 7.
DEVELOPMENT OF A THEORETICAL EQUATION FOR STEADY-STATE DISLOCATION CREEP AND COMPARISON WITH DATA J. H. Gittus United Kingdom Atomic Energy Authority, Springfields, Salwick, Preston, Lancashire England Received November 7, 1973 Revised December 26, 1973
For nineteen materials, including silver, tantalum and gamma iron, Ashby found that an empirical equation E =A(D ~ub/kT) (o/u) n gives a reasonable ~fit to steady-state creep data where A and n are materials constants. It is now shown that if the materials obey the Bailey-Orowan equation, Taylor's work-hardening model and Friedel's network-climb recoveryequation then an identical creep 3 equation is predicted with A = 8~ c. and n = 3. Here c = jogc~ncentration. In th~ cases of nickel, cadmium, beta thallium and stoichiometric UO~ the predicted and actual strengths differ by less than a factor two. 8.
THE TRANSITION FROM DISLOCATION CLIMB TO VISCOUS GLIDE IN CREEP OF SOLID SOLUTION ALLOYS Farghalli A. Mohamed & Terence G. Langdon Department of Materials
Science
xiii
26, 1973
T h e r e a r e two d i s t i n c t and separate classes of creep behavior in metallic solid solution alloys. The mechanism of creep in Class I alloys a p p e a r s t o be some form o f d i s l o c a t i o n climb process, whereas the mechanism i n C l a s s I I a l l o y s a p p e a r s t o be a viscous glide process. By m a k i n g assumptions concerning the nature of t h e c l i m b and g l i d e p r o c e s s e s , and using existing experimental results f o r an A1-3% Mg a l l o y , i t i s shown t h a t , to a f i r s t approximation, the criterion f o r d e f o r m a t i o n by v i s c o u s g l i d e is g i v e n by B~2
(Y)
k 2 (i-v)
~
3
T2 >
e2cb 6
where B ~8 x 1012 , o is the applied stress, k is Boltzmann's constant, v is Poisson's ratio, y is the stacking fault energy, G is the shear modulus, b is the Burgers vector, T is the absolute t e m p e r a t u r e , e is the solute-solvent size difference, and c is the concentration of solute atoms. The creep behavior of twenty-eight different solid solution alloys is analyzed, and it is shown that all alloys except one {Au-10% Ni) give results which are consistent with this criterion for viscous glide. 9.
KINETICS OF GROWTH OF PLATELIKE PRECIPITATES R. S a n k a r a n & C. L a i r d Dept. of Metallurgy & Materials Science, University of Pennsylvania, Philadelphia, Pa. Received November 26, 1973 Revised January 23, 1974
In order to resolve existing difficulties in the interpretation of the lengthening and thickening kinetics of platelike precipitates, these kinetics have been measured on @' and n plates in AI-4% Cu alloy and AI-0.2% Au alloy respectively, in conjunction with extensive observations of the ledge and misfit dislocation structures at the broad faces of the plates. Thickening has been found, in agreement with a well established theory of morphology, to occur bv a ledge mechanism, where the migration rates of the ledges were