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Analysis of the steady state hot deformation of aluminum Barclay, George Allan 1971

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ANALYSIS OF THE STEADY STATE HOT DEFORMATION OF ALUMINUM  by GEORGE ALLAN BARCLAY B.A.Sc., U n i v e r s i t y o f B r i t i s h Columbia, 1968.  A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCE  i n the Department of METALLURGY  We accept t h i s t h e s i s ' as conforming required standard  to the  THE UNIVERSITY OF BRITISH COLUMBIA F e b r u a r y , 1971  In  presenting  this  an a d v a n c e d  degree  the L i b r a r y  shall  I  f u r t h e r agree  for  scholarly  by h i s of  this  written  thesis at  the U n i v e r s i t y  make  that permission  representatives. thesis  for  It  by  financial gain shall  The U n i v e r s i t y o f B r i t i s h V a n c o u v e r 8, Canada  1971  Columbia  the  requirements  B r i t i s h Columbia, for  I agree  r e f e r e n c e and c o p y i n g of  this  that  not  copying  or  for  that  study. thesis  t h e Head o f my D e p a r t m e n t  is understood  Metallurgy  6,  of  for extensive  permission.  May  fulfilment of  it freely available  p u r p o s e s may be g r a n t e d  Department o f  Date  in p a r t i a l  or  publication  be a l l o w e d w i t h o u t my  i ACKNOWLEDGEMENT  The author i s g r a t e f u l f o r the advice and encouragement given by h i s research d i r e c t o r , Dr. J.A Lund.  Thanks are a l s o ex-  tended to f e l l o w graduate students and technicians f o r t h e i r h e l p f u l discussions and advice. F i n a n c i a l assistance was received i n the form of a s s i s t a n t ships from the Defence Research Board under grants 9535-41 and 7501-02. This f i n a n c i a l assistance i s g r a t e f u l l y acknowledged.  ABSTRACT  I t has been suggested by o t h e r s t h a t h o t working i s an e x t e n s i o n of h i g h temperature creep because of the s i m i l a r observed dependencies o f s t r e s s , s t r a i n r a t e , temperature and the s i m i l a r v a t i o n e n e r g i e s o f the two types o f d e f o r m a t i o n .  acti-  T h i s s u g g e s t i o n has  been e v a l u a t e d f o r commercial p u r i t y aluminum by o b t a i n i n g  stress, -4  s t r a i n r a t e and temperature data i n the s t r a i n r a t e range 10  to  10^/second.  tempera-  P u b l i s h e d hot compression, hot t o r s i o n , and h i g h  t u r e creep work of o t h e r s i s used t o p r o v i d e supplementary d a t a .  A  combination of the p u b l i s h e d work o f o t h e r s w i t h the p r e s e n t e x p e r i -  -7 mental work p r o v i d e s d a t a i n t h e s t r a i n r a t e range 10  +2 t o 10  /second.  From the p r e s e n t a n a l y s i s , c o n t r a d i c t i o n s a r i s e a g a i n s t t h e t h e o r y t h a t hot working i s an e x t e n s i o n of h i g h temperature creep.  F i r s t , the  method of e v a l u a t i o n of t h e m a t e r i a l c o n s t a n t a i n the h y p e r b o l i c n' —AH/RT s t r e s s - s t r a i n rate r e l a t i o n , e = A ' ' [ s i n h T  i n going from creep to h o t working.  (aa)]  e  , must change  Secondly, t h e a c t i v a t i o n energy  varies. Those t h a t have suggested t h a t hot working i s an e x t e n s i o n of h i g h temperature creep found t h a t a and t h e a c t i v a t i o n energy were independent o f s t r a i n r a t e .  T h e i r work i s compared t o t h e p r e s e n t  a n a l y s i s and many d i s c r e p a n c i e s were found. The work i n the l i t e r a t u r e l e f t a d a t a gap i n the s t r a i n  -3 r a t e range 10  0 to 10 /second.  Hot t e n s i l e t e s t s and h o t r o l l i n g  were used to p r o v i d e d a t a i n t h i s gap.  tests  iii TABLE OF CONTENTS Page INTRODUCTION  1  1.1 - E x p e r i m e n t a l Techniques  2  1.1.1 - Scaled-down I n d u s t r i a l P r o c e s s e s  ....  2  1.1.2 - T e n s i l e T e s t s  2  1.1.3 - Compression T e s t s  3  1.1.4 - Hot T o r s i o n  3  1.2 - Steady S t a t e Deformation  3  1.3 - E m p i r i c a l Flow S t r e s s R e l a t i o n s h i p s  5  1.3.1 - Power R e l a t i o n s h i p  5  1.3.2 - E x p o n e n t i a l  7  1.3.3 - H y p e r b o l i c  Relationship Sine R e l a t i o n s h i p  7  1.4 - Temperature Dependence  9  1.5 - Recovery Mechanisms  12  1.5.1 - Screw Model  13  1.5.2 - Climb Models  1.6 - Scope o f Present  ..  Investigation  EXPERIMENTAL 2.1 - M a t e r i a l P r e p a r a t i o n  1  15  1  ..  ..  4  7  17  iv Page  2.1.1..- R o l l i n g Procedure  18  2.1.2 - Load Measurement  18  2.1.3 - L u b r i c a t i o n  1  8  2  0  2.2 - T e n s i l e T e s t i n g 2.2.1 - M a t e r i a l  20  2.2.2 - Heating  21  2.2.3 - T e s t i n g  Procedures  RESULTS  21  ••  ••  23  3.1 - R o l l i n g  2  3  3.2 - T e n s i l e Data  2  4  3.2.1 - S t r e s s A n a l y s i s  24  3.2.2 - Power Law  31  3.2.3 - E x p o n e n t i a l Law  31  3.2.4 - H y p e r b o l i c S i n e R e l a t i o n s h i p  33  DISCUSSION  36  4.1 - Hot R o l l i n g  36  4.2 - T e n s i l e Deformation  37  4.2.1 - T r u e - S t r e s s - True S t r a i n Data  37  4.2.2 - S t r a i n Rate  39  4.2.3 - S t r e s s - S t r a i n Rate Dependence  39  V  Page 4.2.3.1 - Power Law Dependence  ....  ..  4.2.3.2 - E x p o n e n t i a l Law 4.2.3.3 - H y p e r b o l i c Sine R e l a t i o n s h i p 4.2.4 4.2.5  A c t i v a t i o n Energy - Zener-Hollomon Parameter  40 43  »'•  43 46 49  CONCLUSIONS  53  BIBLIOGRAPHY  55  VI  LIST OF TABLES  Table I  II  Page A c t i v a t i o n Energies AH (kcal/mole)  Published Hot Working Data f o r Similar Composition Aluminum  III  29  The Constants n, n', 6 and AH f o r Tensile, Compression and Creep Data of similar Purity Aluminum  IV  Wong and Jonas'  Values f o r the Constants  n, n', 8, a, A "  V  Evaluation of  and AH  4  2  the Stress Ranges where the  Hyperbolic Sine Relation i s more than 90% Accurate  47  vii LIST OF FIGURES  Figure 1  2  3  Page Comparison of s t r e s s v e r s u s s t r a i n curves der i v e d from d i f f e r e n t t e s t methods f o r : (a) lowcarbon s t e e l a t 1100°C and (b) Fe-25% Cr a l l o y at 1100°C. Reference (1)  ..  V a r i a t i o n of l o g minimum creep r a t e w i t h (a) l o g a, (b) a, and (c) l o g s i n h (ao) f o r aluminum. Reference (15).  4  6  Wong and Jonas's e x t r u s i o n d a t a p l o t t e d w i t h o t h e r s 'hot' compression, t o r s i o n , and creep data. The data i s p l o t t e d a c c o r d i n g to a hyperbolic sine r e l a t i o n s h i p . Reference (20).  ••  10  4  E x p e r i m e n t a l set-up f o r hot r o l l i n g . ••  ••  19  5  Typical  6a  E x p e r i m e n t a l set-up f o r hot t e n s i l e t e s t s  .•  •.  22  6b  T y p i c a l load  .•  ••  22  7  V a r i a t i o n of s t r a i n r a t e from the entrance p l a n e to the e x i t p l a n e f o r r o l l i n g a c c o r d i n g to the relation. The mean s t r a i n r a t e f o r r o l l i n g e, i s a l s o shown . ..  25  Hot r o l l i n g d a t a c o r r e l a t e d i n terms of the power s t r e s s - s t r a i n r a t e r e l a t i o n . A l d e r and P h i l l i p s (10) hot compression d a t a i s i n c l u d e d f o r comparison. ..  26  V a r i a t i o n of the f l o w s t r e s s w i t h temperature f o r t e s t s a t e = 0.0014 s e c . - l at 350°C and 450°C.  27  V a r i a t i o n of the f l o w s t r e s s w i t h s t r a i n r a t e f o r 450°C t e s t s at i = 0.13 s e c " ! and e = 0.0015 s e c .  28  Steady s t a t e s t r e s s - s t r a i n r a t e data c o r r e l a t e d a c c o r d i n g to the power s t r e s s - s t r a i n r a t e r e lations e = Aa e-^ / .  30  8  9a  9b  load  t r a c e f o r hot r o l l i n g .  ••  ••  19  #  t r a c e f o r hot t e n s i l e t e s t i n g  - 1  10  n  H  R T  viii  Figure 11  Page Steady s t a t e s t r e s s - s t r a i n r a t e d a t a c o r r e l a t e d a c c o r d i n g to the exponential stress-strain r a t e , £ = A " e ^ e " AH/RT_  32  Steady s t a t e s t r e s s - s t r a i n r a t e d a t a c o r r e l a t e d a c c o r d i n g to the h y p e r b o l i c s i n e r e l a t i o n , e = A " ' [ s i n h (ao) ] ' . a = 0.3 x 10"3 p s i - 1 .  34  13  Arrhenius plot for  35  14  Comparison of load-elongation and hot t o r s i o n (12).  12  n  -  A  H  /  R  T  e  15  16  17  tot  t e n s i l e deformation d a t a f o r hot  tension 3  C o r r e l a t i o n of s t r e s s - s t r a i n r a t e d a t a f o r hot d e f o r m a t i o n of commercial p u r i t y aluminum a c c o r d i n g to a power s t r e s s - s t r a i n r a t e dependence. Reference 17. C o r r e l a t i o n of hot working d a t a u s i n g the s t r u c t u r e c o r r e c t e d Zener-Hollomon parameter and the hyperb o l i c s i n e s t r e s s f u n c t i o n . Reference (1) Zener-Hollomon p l o t u s i n g v a t i o n energies  a c t u a l experimental  acti-  ..  8  41  51 52  1  INTRODUCTION  Hot w o r k i n g , i n p r a c t i c e , i n v o l v e s l a r g e r e d u c t i o n s , a t 3 h i g h r a t e s of s t r a i n approximately  (0.1 to 10 / s e c ) , and  one-half  at temperatures  the a b s o l u t e m e l t i n g temperature.  above I t i s used  e x t e n s i v e l y i n i n d u s t r y because these l a r g e r e d u c t i o n s can be accomp l i s h e d at low working s t r e s s e s without  intermediate anneals.  f a c t t h a t l a r g e s t r a i n s can be a c h i e v e d w i t h l i t t l e i n g suggests hardening ^  t h a t dynamic s o f t e n i n g p r o c e s s e s  The  or no s t r a i n harden-  are b a l a n c i n g the  strain  . For commercial p u r i t y aluminum as w e l l as f o r o t h e r pure  metals  and  simple a l l o y s , the f l o w s t r e s s at a p a r t i c u l a r  temperature  (2)  i n c r e a s e s as the r a t e of d e f o r m a t i o n i s i n c r e a s e d . Similarly, i f the s t r a i n r a t e i s kept c o n s t a n t , the f l o w s t r e s s decreases as the  (2) temperature i s i n c r e a s e d  .  T h e r e f o r e , to determine optimum hot work-  i n g c o n d i t i o n s the r e l a t i o n s h i p between s t r e s s , s t r a i n , s t r a i n r a t e and  temperature,must be known.  The  meters depends on the deformation  i n t e r r e l a t i o n between these  and  para-  r e c o v e r y mechanisms i n v o l v e d .  C o n s i d e r a b l e a t t e n t i o n has been p a i d to the development of (3-5) t e s t s f o r e v a l u a t i o n of the hot working parameters  .  In the  ideal  hot working experiment, the specimens are deformed u n i f o r m l y a t a constant rate  and  temperature w i t h a continuous measurement of l o a d or  stress.  I f s t r u c t u r a l o b s e r v a t i o n s are to be made, the specimen must be formed i n a s i n g l e o p e r a t i o n and changes d u r i n g c o o l i n g .  a d i a b a t i c h e a t i n g may  immediately  quenched to a v o i d  destructural  In the hot working range of s t r a i n r a t e s (3)  occur but  i t i s u s u a l l y neglected  used a r e scaled-down i n d u s t r i a l p r o c e s s e s , t e n s i l e t e s t s ,  .  The  tests  compression  (3—6) t e s t s , o r hot t o r s i o n 1.1  .  - E x p e r i m e n t a l Techniques 1.1.1  - Scaled-down I n d u s t r i a l P r o c e s s e s S c a l i n g down of i n d u s t r i a l p r o c e s s e s i s a u s e f u l  approach  because t h e mode of d e f o r m a t i o n i n the t e s t and t h e p r a c t i c a l working operation  a r e one and t h e same.  uniformity  of  But these p r o c e s s e s a l l i n v o l v e non-  d e f o r m a t i o n and r e q u i r e numerous assumptions i n the a n a l y s i s  /in to get t r u e s t r a i n r a t e , s t r a i n  and s t r e s s v a l u e s .  I n hot r o l l i n g  f o r example, t h e s t r a i n r a t e changes a l o n g the a r c of c o n t a c t . average s t r a i n r a t e must be a s s u m e d .  An  C a l c u l a t i o n of t h e deforming  s t r e s s i s based upon an assumption o f s t i c k i n g f r i c t i o n which may not (8) be  constant  .  The deforming s t r e s s cannot be c a l c u l a t e d as a f u n c t i o n  (8) of s t r a i n  .  In e x t r u s i o n ,  the s t r a i n r a t e i s s i m i l a r l y non-  (3-9) -, Tand e n s itlhee Ts e u n i f o r 1.1.2 m ts rt e s s cannot be p r e c i s e l y  calculated.  C o n v e n t i o n a l t e n s i l e t e s t i n g equipment does n o t p r o v i d e a s u i t a b l e s t r a i n r a t e range.  F o r a constant s t r a i n r a t e t e s t , t h e exda  :  tension  r a t e must be v a r i e d as (1/&) (~j^r) » where £ i s t h e gauge  length  of t h e specimen, t o permit a p r e c i s e a n a l y s i s of a, s t r e s s E, s t r a i n e, (5 6) s t r a i n r a t e and T, temperature ' ' .  When t e n s i l e t e s t i n g i s done aat t  temperatures above 0.51^, specimens neck t y p i c a l l y a t 10-30% s t r a i n Methods have  been d e v i s e d t o  a n a l y z e t h e necked r e g i o n  (5,6)  thus e n a b l i n g de-  f o r m a t i o n t o be c a r r i e d t o t r u e s t r a i n s of (2). However, t h e s e methods a r e very  complex.  1.1.3  - Compression T e s t s (3-5)  Compression t e s t s  , normally  to t r u e s t r a i n s of 2.3.  u n i a x i a l , can be used to  evaluate  s t r e s s up  T e s t machines t h a t g i v e a  constant  s t r a i n r a t e have been d e v i s e d , such as Orowan's Cam  (2 9) Plastometer' •  However, l u b r i c a n t s must be used to e l i m i n a t e f r i c t i o n between the  platens  A ^ • (3-5,10) and the specimen ,  1.1.A  - Hot Hot  constant up  Torsion  t o r s i o n t e s t s on t h i n - w a l l e d tubes g i v e f l o w curves  t r u e s t r a i n r a t e s i n the range 10  to 20 can be o b t a i n e d b e f o r e f r a c t u r e  specimens the s t r a i n and  s t r a i n r a t e vary  -3  3 t o 10 / s e c .  (3 11  '  12)  .  For  at  S t r a i n of solid torsion  from a maximum at the  surface  (9) to zero at the c e n t r e  .  S o l i d specimens are g e n e r a l l y used, and  the s u r f a c e s t r a i n r a t e and  s t r e s s e s examined.  T h i s i s done on  only  the  assumption that the o u t e r l a y e r makes the major s t r e s s c o n t r i b u t i o n because i t work hardens more.  T h i s assumption seems j u s t i f i e d when con-  s i d e r i n g F i g . 1 ( 1 ) , a f t e r Rossard and with  1.2-  t e n s i o n and  compression  B l a i n , which compares t o r s i o n data  data.  Steady S t a t e Deformation As  can be seen from F i g . l ,  t u r e t e n s i o n , compression  and  the f l o w curves  f o r high  t o r s i o n t e s t s e x h i b i t an i n i t i a l (2 10  i n g p o r t i o n up  to a t r u e s t r a i n of u s u a l l y 50-100%  f o l l o w e d by a r e g i o n of "steady independent of  strain.  The  '  12) '  .  This  l e v e l o f t h i s steady  s t a t e flow s t r e s s  Is  de-  strain  Such a dependence of flow s t r e s s i n d i c a t e s t h a t hot working i s a process.  harden-  s t a t e " where the s t r e s s i s e s s e n t i a l l y  creases w i t h i n c r e a s i n g temperature and w i t h d e c r e a s i n g  activated  tempera-  thermally  4  Fig.l  Comparison of s t r e s s v e r s u s curves d e r i v e d from d i f f e r e n t t e s t methods f o r : (a) low-carbon s t e e l a t 1100°C and (b) Fe- 25% Cr a l l o y at 1100°C. Reference (1) .  »  High temperature 10  /sec.  '  creep d e f o r m a t i o n i n the range o f 10  —8  to  i s an example of s i m i l a r steady s t a t e d e f o r m a t i o n .  c o n s t a n t s t r e s s c r e e p , a f t e r an i n i t i a l  For  t r a n s i e n t the s t r a i n i n c r e a s e s  l i n e a r l y w i t h time,  1.3  - E m p i r i c a l Flow S t r e s s R e l a t i o n s h i p s A number of mathematical  e x p r e s s i o n s have been proposed  to  d e s c r i b e the r e l a t i o n s h i p between s t r e s s and s t r a i n r a t e f o r h i g h temperature  steady s t a t e d e f o r m a t i o n .  1.3.1  - Power R e l a t i o n s h i p * • -, „ . • A n -AH/RT A simple power r e l a t i o n s h i p , e = A^a e , where AH  i s the apparent a c t i v a t i o n e n e r g y ^ a c t i v a t e d p r o c e s s , has  f o r the r a t e - c o n t r o l l i n g t h e r m a l l y  been found t o f i t a v a i l a b l e creep data f o r low  (13) stresses e =  ^ ^  . n  n  a  In an i n t e r m e d i a t e range of s t r e s s e s , the e q u a t i o n been found to f i t e x p e r i m e n t a l creep d a t a ^ " ^ ' ^ ^ f o r a  s  Q  f i x e d temperature. may  In t h i s case however, the s t r e s s exponent n may,or  not be, a f u n c t i o n of temperature,  depending  F o r low creep s t r e s s e s n i s c o n s t a n t ^ \  on the s t r e s s  level.  f o r h i g h s t r e s s e s n i s tempera-  (3) t u r e dependent F o r commercial 6.1  .  The f a c t o r A  q  may  a l s o be temperature (15)  p u r i t y aluminum G a r o f a l o  to 5 i n the temperature  range 0.51  reported that n v a r i e d to 0.575 T .  i l l u s t r a t e s a p l o t of l o g a v e r s u s l o g e illustrates  t h a t the  dependent.  Fig.2  (Ref.15)  f o r some creep d a t a .  power r e l a t i o n s h i p has o n l y l i m i t e d  from  It  applicability  because at a c r i t i c a l s t r e s s v a l u e , n f o r a p a r t i c u l a r temperature [1] I n t h i s paper the term a c t i v a t i o n energy r e f e r s to the apparent activation  energy.  6  Fig.2  V a r i a t i o n of l o g minimum creep r a t e w i t h (a) l o g a, (b) a, and (c) l o g s i n h (ao) f o r aluminum. R e f e r ence (15).  7 increases. In t h e p r e s e n t a t i o n o f h o t working  d a t a i t i s more .N  common t o a p p l y t h e e q u i v a l e n t power law a = a e  which i s an anomaly  Q  a c c o r d i n g to creep theory,.  I n t h i s case, b o t h o" and N a r e found o  to be a f u n c t i o n o f temperature  f o r steady s t a t e deformation.  e q u a t i o n has been used to c o r r e l a t e r e s u l t s from  The  compression^'"^'"*"^,  t o r s i o n ^ ' " ^ and e x t r u s i o n t e s t s . F o r commercial p u r i t y aluminum, N v a r i e s from 0.04 t o 0.2 i n the range 0.55 t o 0.9 T ( > » > > ) m 2  1 0  1 2  1 6  1 7  #  An e q u a t i o n i n which t h e c o n s t a n t s a r e a f u n c t i o n o f temperature  i s not  u s e f u l as an i n d i c a t o r of t h e d e f o r m a t i o n mechanism.  1.3.2  - Exponential Relationship A . i -a . . i 3a ,-AH/RT . An e x p o n e n t i a l law, e = A e e , applies n  f o r h i g h s t r e s s creep  '"'""'^ i n commercial  .. empirically  p u r i t y aluminum and f o r h o t  (1 2 6 18) working valid  data at high s t r e s s e s  ' > »  .  The r e l a t i o n s h i p becomes i n -  a t h i g h temperatures where t h e s t r e s s e s a r e low, however, and  t h i s p r e s e n t s d i f f i c u l t i e s i n t h e c a l c u l a t i o n of an a c t i v a t i o n  energy  In the case o f aluminum and i t s a l l o y s t h e parameter  A' has  (3)  (13) been found  t o be c o n s t a n t a t c o n s t a n t temperature. :  g has been found temperature  The v a l u e o f  (13) t o be r e l a t i v e l y independent  o f temperature  range 0.45 to 0.65 T^ b u t decreases w i t h i n c r e a s i n g  t u r e above the r a n g e ^ ^ ' " * " . 7  i n the tempera-  F i g . 2 ^ " ^ i l l u s t r a t e s how t h e exponent-  i a l law i s o n l y a p p l i c a b l e i n a l i m i t e d s t r e s s range and f a i l s a t low stresses. 1.3.3  - H y p e r b o l i c Sine R e l a t i o n s h i p Garofalo(13,15) ^  a  s  suggested an e q u a t i o n to cover t h e  dependence o f steady s t a t e creep r a t e on s t r e s s a t c o n s t a n t  temperature  f o r both h i g h and low s t r e s s e s . where A ' T  I t i s of the form e = A''  and a are constant and n = n',  a i n p s i ^ and a  in psi.  I f aa>  1.2  [sinh  (aa)]  n  The product aa i s u n i t l e s s ,  (high s t r e s s e s ) , the d i f f e r e n c e  . aa between s i n h (aa) and ^  i s l e s s than 10% and the h y p e r b o l i c s i n e  e = ^—7 e °. T h i s i s the same as 2 e = A' e^° where ^ — 7 - = A' and a = B/n. The e q u a t i o n e = A' e^° has 2 been shown to s a t i s f y the e x p e r i m e n t a l dependence of creep r a t e f o r h i g h e q u a t i o n i s approximated by  n  a  n  n  n' s t r e s s e s , so t h e r e f o r e , does e = A ' ' [ s i n h  (aa)]  .  F o r aa<  0.8  s t r e s s e s ) , the d i f f e r e n c e between s i n h (aa) and aa i s l e s s than and  e = A' [sinh 1  duces to e = Aa  11  (aa)]  n  can be approximated by e = A''a  f o r low s t r e s s e s and A''a  11  = A and n =  In G a r o f a l o ' s e m p i r i c a l e q u a t i o n n', and B, are f u n c t i o n s of temperature,  The  a  n  (low 10%  which r e -  n  n'.  to a s m a l l extent  r e l a t i o n a = B/n  defines  a.  T h e r e f o r e , i n G a r o f a l o ' s a n a l y s i s , creep data at both h i g h s t r e s s e s ( f o r d e t e r m i n a t i o n of B ) and a t low s t r e s s e s ( f o r d e t e r m i n a t i o n of n) must be a v a i l a b l e f o r the e v a l u a t i o n of a.  S i n c e n = n', n' i s a l s o tempera-  t u r e dependant. (19) S e l l a r s and Tegart  doubt G a r o f a l o ' s f i n d i n g s t h a t a  and n' are temperature dependent. G a r o f a l o were i n . a  They suggest  t h a t s i n c e the data of  narrow s t r e s s range on both s i d e s of the  v a l u e , h i s i n t e r p r e t a t i o n was  i n a d e q u a t e l y supported.  His  critical  interpretation  would p r e d i c t a temperature dependence of the a c t i v a t i o n energy f o r creep which i s  not observed  e x p e r i m e n t a l l y i n the c o n s i d e r e d s t r e s s range. —AH/RT n' They t h e r e f o r e propose the e q u a t i o n e = A''' e [ s i n h (aa)] and (18) a = B/n' where A''', a, and n', a r e independent of temperature. (1,3,12,17,20,21) , , _ ,. Others ' i n attempts to a n a l y s e hot working t e s t r e s u l t s , have adopted S e l l a r s and T e g a r t ' s v e r s i o n of the e m p i r i c a l relationship.  They have e v a l u a t e d the c o n s t a n t s a and n' by  plotting  log e versus  s i n h aa f o r v a r i o u s imposed v a l u e s of a.  The v a l u e o f a  t h a t gave a c o n s t a n t v a l u e of n' f o r t h e temperature range examined was taken as t h e c o r r e c t v a l u e of a. Wong^^  used t h i s approach to e v a l u a t e a f o r t h e hot ex-  t r u s i o n o f aluminum. The v a l u e of n  T  He used t h e r e l a t i o n  a = $/n' t o e v a l u a t e £.  used by Wong was based on r e s u l t s a t h i s h i g h e s t ex-  p e r i m e n t a l temperature. t r u s i o n were found the same m e t a l .  The v a l u e s o f n' and a thus o b t a i n e d f o r ex-  t o compare t o those f o r h i g h temperature creep i n Implying  t h a t t h e h o t working o f aluminum i s an ex-  t e n s i o n o f h i g h temperature c r e e p , W o n g ^ ^  used t h e h y p e r b o l i c s i n e  r e l a t i o n s h i p t o c o n s t r u c t p l o t s such as F i g . 3 . A  i  '"•  v  -  u  -  i •  A  Other p u b l i s h e d work  u  has  drawn a n a l o g i e s between h o t working and creep  1.4  - Temperature Dependence  (1,3,17,20,21)  A comparison o f the temperature dependence of h o t working and  creep  can a l s o be made through  the p r o c e s s e s .  I n steady  the apparent  s t a t e creep  a c t i v a t i o n energies of  t h e a c t i v a t i o n energy i s d e t e r -  mined i n t h e f o l l o w i n g way. From c o n v e n t i o n a l creep t e s t s t h e v a r i a t i o n o f l o g i w i t h T  a t constant  straight  s t r e s s i s found.  A p l o t of t h i s v a r i a t i o n g i v e s a  l i n e whose s l o p e y i e l d s a v a l u e o f AH, t h e e x p e r i m e n t a l  v a t i o n energy, i f one assumes f o r steady f a c t o r s which a r e o n l y s t r e s s dependent  ^ 2 f £  =  -  s t a t e creep  (13)  .  acti-  constant s t r u c t u r e  That i s :  AH/2.3R  9 T F o r h o t working i t i s more d i f f i c u l t constant  f l o w s t r e s s over l a r g e s t r a i n s .  t o conduct  a test at  To e v a l u a t e t h e a c t i v a t i o n  10  •I J  f  .'I  //./// // Ji ulljJi Ji iii / . m l  W  IK  it >'  EXTRUSION (IS 99 73%AI) • 320 °C present work • 376 °C « 445°C • 490°C . 555°C . 6I6°C COMPRESSION (2S 99 21' 250°C 993%AI) » 350°C « 450°C = 550°C TORSION (SP purity • 195 °C unspecified) T 280°C » 380°C A 450 C A 450°C a 480°C s 550 °C CREEP ISP 999945 7.AI) . 204 °C . 260°C ' 371 °C . 4 82°C . 593°C  I  10 Sinh (aa)  Fig.3  Wong and Jonas's e x t r u s i o n data p l o t t e d w i t h o t h e r s 'hot' compression, t o r s i o n and creep d a t a . The data i s p l o t t e d a c c o r d i n g to a h y p e r b o l i c s i n e r e l a t i o n ship. Reference (20).  11  energy a t c o n s t a n t s t r e s s thus r e q u i r e s can be seen from F i g . 3 . of Conrad  (22)  [sinh  (aa)]  An a l t e r n a t i v e approach based on the method  has been proposed  ^? e  A  H  d AH d l n sinh  (aa)  One s t a r t s w i t h e = A'''  where A''', a, n' a r e c o n s t a n t s independent of rate.  AH = RT [ l n A ' "  d l n sinh  (19 20 21) ' ' .  ^ j  temperature and s t r a i n  d  e x t e n s i v e e x t r a p o l a t i o n , as  + n' In s i n h  (aa) - l n e ]  = RT [ n' - ( • ^ r ^ ) V 9 l n s i n h (aa) ^  =  _  R T  (aa)  2  f, V  ( 9  l  n  o  sinh  g  (D  1 T  ^ (aa) J )  +  RTn'  (2)  RT  t  equate  RT  r [ n  ,  C? " ^9  -I _  lne l n sinh  (1) and (2)  (aa)^  R T  2  J - - RT  /3-1/T ^  l n sinh  "\ (aa) J  ,AlL V  , +  R  T  n  12  ATT  o OT>  f  log £  3  "\  /" 3 l o g [ s i n h  (aa)] ^  Each of the terms i n p a r e n t h e s i s i s a s l o p e which can determined to any  from e x p e r i m e n t a l  data.  The  above a n a l y s i s can be a p p l i e d  f u n c t i o n of s t r e s s but the h y p e r b o l i c one has been used (1 3 19  o t h e r s because, as noted perimental  be  above, i t has been found  ' '  by  20) '  to f i t ex-  data.  TABLE I - A c t i v a t i o n E n e r g i e s AH  Self Diffusion  (kcal/mole)  Hot Working  (23)  Creep  (1)  33  (13)  37  33-36  T a b l e I r e v e a l s a s i m i l a r i t y among the a c t i v a t i o n f o r c r e e p , hot working,and s e l f d i f f u s i o n f o r aluminum. (1 3 i t has been concluded  ' '  On  energies this basis  20) t h a t the r a t e c o n t r o l l i n g mechanisms are  similar. V a r i o u s models based upon r e c o v e r y mechanisms have been p r o posed t h a t r e l a t e the a c t i v a t i o n energy of hot working to t h a t of s e l f diffusion. jogged  1.5  They a r ee vacancy va m i g r a t i o n models  screw models  , climb models  (25)  - Recovery Mechanisms F o r h i g h temperature d e f o r m a t i o n  of aluminum, dynamic re-  and  covery i s c o n s i d e r e d t o be the s o f t e n i n g mechanism  (1,3) ' .  This i s  based upon o p t i c a l , X-ray microbeam and e l e c t r o n m i c r o s c o p y e v i d e n c e . A number o f models have been p r e s e n t e d t o e x p l a i n h i g h temperature d e f o r m a t i o n based upon dynamic r e c o v e r y .  In a l l  the a c t i v a t i o n energy i s t h a t o f s e l f d i f f u s i o n .  o f t h e s e models They a r e p r i m a r i l y  proposed f o r the creep range o f s t r a i n r a t e s but s i n c e t h e r e a r e s i m i larities  i n the case o f aluminum between creep and hot working w i t h  r e g a r d t o the m i c r o s t r u c t u r a l change, t h e a c t i v a t i o n energy and t h e s t r e s s - s t r a i n r a t e dependence, t h e creep t h e o r i e s can be c o n s i d e r e d f o r h o t working. The r a t e c o n t r o l l i n g p r o c e s s e s i n hot working o f aluminum are assumed  to be climb and the motion o f j o g g e d screw  dislocations^  7  1,5.1 - Screw Model The model  (25,27)  i s based upon the d i f f u s i o n  motion o f jogged screw d i s l o c a t i o n s .  controlled  The j o g s have t o move non-con-  s e r v a t i v e l y and c r e a t e o r a c q u i r e v a c a n c i e s .  T h i s p r o c e s s w i l l re-^  s t r a i n the movement o f the jogged d i s l o c a t i o n s , and must be accomplished by means o f s e l f  diffusion.  The model i s based upon the e f f e c t of the  a p p l i e d s t r e s s moving the j o g .  A c a l c u l a t i o n o f the speed of the j o g  as a f u n c t i o n o f the s t e a d y s t a t e s t r e s s and temperature o f t h e form:  e  s  = Ap  s  D sinh (  a b X ) 2KT  -U/KT e  where  A p  = a s  constant  = d e n s i t y of mobile  screw d i s l o c a t i o n  J  3 = constant x a  p  s  a  = applied stress  X  = average j o g s p a c i n g  b  = Burgers  D  = diffusion  U  = a c t i v a t i o n Energy  must v a r y as p  s  Vector Coefficient  a a 3 , which i s e s s e n t i a l l y an adjustment parameter;  where a i s the a p p l i e d s t r e s s . T h i s e q u a t i o n has been compared by B a r r e t and the observed  Nix  s t r e s s dependence of creep r a t e s as g i v e n by  e m p i r i c a l e x p r e s s i o n f o r steady s t a t e creep of aluminum. the c o n s t a n t s were found was  i n the d i f f u s i o n  1.5.2  - Climb  to be r e a l i s t i c  and  (25)  to  Garofalo's Values  of  the temperature dependence  coefficient.  Models  These models depend upon g e o m e t r i c a l p a t t e r n s of l o c a t i o n s , the d e t a i l s  dis-  of which are not a c c u r a t e l y k n o w n ^ \ and  the  (27) models are h i g h l y i d e a l i z e d . Weertman  proposed a t h e o r y based upon  the o p e r a t i o n of Frank-Read sources on d i f f e r e n t p a r a l l e l s l i p The  planes.  d i s l o c a t i o n s climb from a d j a c e n t l o o p s and a n n i h i l a t e each o t h e r ,  thus p e r m i t t i n g f u r t h e r d i s l o c a t i o n loops to be emitted from the sources.  For low s t r e s s e s Weertman proposed: 9  X  C b  2  N  2  G  15  where  and  C  =  constant  D  = diffusion coefficient  T  = applied  stress  N  = density  of d i s l o c a t i o n s t a k i n g p a r t  G  = shear modulus  k  = Boltzman's c o n s t a n t  f o r both high  =  e  and _1 C _ _ G  low  ,2 2 _ T D — _ b  A  - Scope of P r e s e n t  /, 3.5. 1.5 v 3 T b [ —r~TT 8G N kT  . ,  r  smh •  in a the  (1-3,  a constant  Investigation  10,  12,  14,  l i m i t e d s t r a i n r a t e range. range  from creep  (10  —5  17, No  to o b t a i n  20, one  d e f o r m a t i o n of 21,  on  has (10  2  done work i n  /sec).  In t h e i r  the p u b l i c a t i o n s of o t h e r i n -  creep or hot working d a t a .  i n the s t r a i n r a t e range 10  commercial  have been done o n l y  researcher  -3 data gap  28)  /sec.) to hot working  a n a l y s i s , p r i o r workers have r e l i e d vestigators  J  2  Past i n v e s t i g a t i o n s of the hot p u r i t y aluminum  climb  stresses  C' =  1.6  in  Moreover t h e r e  is a  0 to 10  /sec.  In the  present -4  work, s t r e s s - s t r a i n r a t e d a t a were o b t a i n e d i n the  t e n s i l e range  10  2 to  10  /sec  and  beyond.  Two  types of experiments were used to  a s t r a i n r a t e v a r i a t i o n of 10"*.  Hot  d a t a was  not  a v a i l a b l e , was  10  and  t e n s i l e t e s t i n g f o r the  /sec  The  proposition  r o l l i n g , f o r which e a r l i e r  used f o r s t r a i n r a t e s range 10  i n the  to 10  s t r a i n r a t e range between creep and  hot  i f d a t a are  compression.  published  range 0.5  to  /sec.  t h a t hot working i s an e x t e n s i o n  temperature creep can be b e t t e r d i s c u s s e d  obtain  of  high  a v a i l a b l e i n the^' I f the  proposition  is correct,  the  same s t r e s s - s t r a i n r a t e dependence s h o u l d be -5  over the e n t i r e range from 10 energy  should  apply.  observed  2 to 10 / s e c . and a common a c t i v a t i o n  EXPERIMENTAL  Low s t r a i n r a t e t e n s i l e t e s t s were performed a t crosshead speed i n an I n s t r o n machine.  High s t r a i n r a t e t e s t s were  performed on a l a b o r a t o r y s i z e Stanat r o l l i n g m i l l diameter r o l l s ) . and  constant  (with 4.1  inch  In both cases the t e s t temperatures were 250, 350  450°C.  2.1 - M a t e r i a l  Preparation  R o l l i n g s l a b s were c a s t from A l c a n  ISCD aluminum w i t h a  nominal c o m p o s i t i o n of 99.75% A l , 0.16% Fe, 0.06% S i , and 0.03% maximum t o t a l r e s i d u a l s . melted under r e d u c i n g  The m e l t i n g  conditions  stock,  c a s t P r o p e r z i r o d , was  to m i n i m i z e o x i d e f o r m a t i o n .  were c a s t from 740°C i n a carbon coated mould.  Slabs  The c a s t i n g o t s were  2.5 x 0.625 x 5 i n c h e s . In o r d e r  t o c o n t r o l g r a i n s i z e and to e l i m i n a t e  the c a s t  s t r u c t u r e , each i n g o t was c o l d r o l l e d and annealed.  The r o l l i n g  s c h e d u l e c o n s i s t e d of a s e r i e s of 20% c o l d r e d u c t i o n s  followed  anneals a t 375°C f o r 25 minutes u n t i l a t h i c k n e s s T h i s gave a VPN hardness  of 0.200" was reached  of 25, which i s t y p i c a l of the commercial "0"  temper hardness of the m a t e r i a l . 2 inch lengths  by a i r  and e n d - m i l l e d  The f i n i s h e d s l a b s were then c u t t o  t o a w i d t h of 2.25 i n c h e s .  F i n a l l y , the  s l a b s were anodized i n c a u s t i c soda. In the hot r o l l i n g experiments t h e s l a b s were reduced 50% to 0.100 i n c h t h i c k n e s s pass r e q u i r e d  i n one p a s s .  Such a l a r g e r e d u c t i o n  that the f r o n t edge of the s l a b s be tapered  f a c i l i t a t e the e n t r a n c e i n t o the r o l l  gap.  i n one  i n o r d e r to  18  2.1.1  - R o l l i n g Procedure Figure  specimen was  4 i l l u s t r a t e s the equipment  put i n s i d e the f u r n a c e  d e s i r e d temperature b e f o r e b e i n g was  done at 4 p e r i p h e r a l r o l l In order  s l a b and the r o l l s ,  p u l l e d i n t o t h e r o l l gap.  speeds - 0.6,  3.66,  cores.  circulating o i l .  The r o l l  was  used, i n which case the temperature was  the top  between the  resistance  speed of 0.6  350°C.  contact  in/sec.  The r o l l  cooled 250°C in/sec. surface  thermocouple mounted on  roll.  2.1.2  - Load Measurement The r o l l  separating  r e s i s t a n c e s t r a i n gauge elements bearing  blocks.  corded  on a s t o r a g e  first  and 14.64  temperature was  a l l experiments except those i n which a r o l l  measured by a s u r f a c e  Rolling  The m i l l b e a r i n g s were  for  temperature was  7.32  the r o l l s were heated by e l e c t r i c the r o l l  Each  and soaked over 5 minutes a t the  to l e s s e n the temperature g r a d i e n t  elements s i t u a t e d i n with a pressurized  used i n r o l l i n g .  The s t r a i n was  f o r c e was measured by means o f e l e c t r i c ( f o r c e washers) s i t u a t e d under the measured on a 4-arm s t r a i n b r i d g e  oscilloscope.  increment of l o a d .  Figure  The scope was  and r e -  t r i g g e r e d by the  5 i s a t y p i c a l recorded  load  trace.  The f o r c e washers were i n d i v i d u a l l y c a l i b r a t e d i n an Instron. washers,  Since i t was  the l o a d to be measured i n r o l l i n g was assumed t h a t the i n d i v i d u a l l o a d s ,  a p p l i e d to b o t h  i n c a l i b r a t i o n , were  additive.  2.1.3  - Lubrication The hot r o l l i n g o f aluminum p r e s e n t s  a problem i n t h a t  19  Fig.5  T y p i c a l load t r a c e f o r hot  rolling.  20  c l e a n aluminum s u r f a c e s r e a d i l y bond to s t e e l r o l l s .  On an i n -  d u s t r i a l s c a l e , t h i s i s overcome by f l o o d l u b r i c a t i o n . tory s c a l e , l u b r i c a t i o n i s complicated  On a l a b o r a -  i n that r e l i a b l e hot r o l l i n g  l o a d a n a l y s i s r e q u i r e s the presence o f s t i c k i n g f r i c t i o n over the arc of contact.  A compromise must be made by u s i n g a l u b r i c a n t t h a t  allows  f r i c t i o n t o take p l a c e but e l i m i n a t e s  sticking Oil,  carbowax, and a c o l l o i d a l s u s p e n s i o n  t r i e d , but a l l were found u n s u i t a b l e .  adhesion. o f g r a p h i t e were  They c o u l d n o t be a p p l i e d t o  the r o l l s  i n a r e p r o d u c i b l e manner and the f r i c t i o n f o r c e v a r i e d .  Anodising  of t h e s l a b s p r o v i d e d  t h e most a c c e p t a b l e  that s t i c k i n g f r i c t i o n occurred,  solution,in  the c o n d i t i o n s were r e p r o d u c i b l e , and  a d h e s i o n of the aluminum t o the r o l l s was almost n o n e x i s t e n t .  The o x i d e  p r o v i d e d by a n o d i s i n g d i d n o t c o n t r i b u t e t o a r e d u c t i o n i n t h e c o e f f i c i e n t of r o l l i n g  friction,  and as such should n o t be d e s c r i b e d as  a "lubricant".  2.2 - T e n s i l e T e s t i n g 2.2.1 - M a t e r i a l T e n s i l e specimens were made from the same ISCD aluminum as used f o r r o l l i n g s l a b s , but i n the form of 3/8 i n c h diameter r o d hot r o l l e d from P r o p e r z i r o d by t h e s u p p l i e r . with  a uniform  gauge l e n g t h .  gauge p o r t i o n of 0.160 i n c h e s diameter and 1.125 i n c h A f t e r machining, the specimens were annealed f o r lh hours  at 500°C, and f i n a l l y c l e a n e d tion.  Specimens were machined  i n a phosphoric  acid "bright d i p " solu-  2.2.2 - H e a t i n g F i g u r e 6 shows the arrangments f o r t e n s i l e  testing.  The specimen was loaded i n t o the f u r n a c e and g r i p s , then a l l o w e d 40 minutes ated  to s t a b i l i z e b e f o r e p u l l i n g .  A thermocouple  i n the f u r n a c e a t the midpoint of the t e n s i l e  2.2.3 - T e s t i n g  was  situ-  specimen.  Procedures  Low s t r a i n r a t e t e s t s were conducted 1 inch/min. c r o s s head speeds.  a t 0.01, 0.1, and  The l o a d and e l o n g a t i o n were r e c o r d e d  a u t o g r a p h i c a l l y on the I n s t r o n c h a r t . Crosshead  speeds g r e a t e r than a p p r o x i m a t e l y 5 inch/min.  were found to be above the s l e w i n g speed of the c h a r t r e c o r d e r . In o r d e r t o get a l o a d - e l o n g a t i o n curve a t a c r o s s head speed of 10 inch/min., the l o a d c e l l was connected t o an o s c i l l o s c o p e bridge.  strain  The l o a d - e l o n g a t i o n curve was r e c o r d e d on the s t o r a g e scope.  F i g u r e 6 i l l u s t r a t e s a t y p i c a l l o a d - e l o n g a t i o n curve o b t a i n e d i n t h i s manner.  F i g . 6 b.  T y p i c a l l o a d t r a c e f o r hot  tensile testing.  23  RESULTS  3.1 - R o l l i n g The r o l l  s e p a r a t i n g f o r c e was c o n v e r t e d t o an e f f e c t i v e  (29) m a t e r i a l f l o w s t r e s s u s i n g Sim's s e m i - e m p i r i c a l hot r o l l i n g P = Kb V R ( h ^ - h ) ' x Q, where P i s t h e r o l l 2  formula  ,  l o a d , k t h e mean e f f e c t i v e  f l o w s t r e s s i s p l a n e s t r a i n , b the s t r i p w i d t h , R the r o l l  r a d i u s , h^  the e n t r a n c e t h i c k n e s s , h ^ the e x i t t h i c k n e s s , and Q i s a geometric roll is  factor.  the  The r o l l  l o a d , P, i s the a r e a under t h e curve of the  5  6X11  entrace c o n t a c t a n g l e and s i s the normal r o l l p r e s s u r e .  f a c t o r i s a f u n c t i o n o f R/h^ and the r e d u c t i o n . Q values are a v a i l a b l e  (8)  .  s dd>, where d> ' The geometric  T a b l e s of c a l c u l a t e d  The use o f a mean e f f e c t i v e f l o w  i s j u s t i f i e d because the s t r a i n r a t e decreases  stress  a l o n g the a r c c o n t a c t  (8) and t h i s c o u n t e r a c t s s t r a i n In  hardening  the l o a d c a l c u l a t i o n no c o r r e c t i o n was made f o r r o l l  d i s t o r t i o n over t h e a r c o f c o n t a c t because r o l l f l a t t e n i n g under t h e e x p e r i e n c e d s t r e s s e s was u n l i k e l y t o be s i g n i f i c a n t .  Sticking  friction  i s assumed w i t h the c o e f f i c i e n t of f r i c t i o n , p, a maximum. F o r p l a n e s t r a i n c o n d i t i o n s t h e maximum of p i s 0.577 a c c o r d i n g t o Von Mises c r i t e r i o n I n  o r d e r t o compare the r o l l i n g d a t a t o cam p l a s t o -  meter d a t a , a l l e f f e c t i v e r o l l i n g  s t r e s s e s were c o n v e r t e d t o u n i a x i a l (31) s t r e s s e s u s i n g Von Mises D i s t o r t i o n Energy c r i t e r i o n , i.e. i n [2] p l a n e s t r a i n the e f f e c t i v e s t r e s s i s 1.155 times the u n i a x i a l s t r e s s [2] a  Q  = \ [(a - a ) x  + (a -  2  2  £  a For plane s t r a i n o a  2  - a „ = K = r=7 1 2 V3 1  K a  Q  =  aj +a  2  1  + ( a - o^  2  3  L  2  a  o  = 1.155 a  o  = shear s t r e s s = mean e f f e c t i v e f l o w o  = uniaxial  ]  stress  stress  h  24  Figure entrance  plane  7 g i v e s the v a r i a t i o n of s t r a i n r a t e from  to e x i t f o r r o l l i n g  , _  2f s i n (j) h + D (1-cos  .. <j>)  2  where  f = peripheral r o l l <j> = angular D = roll  a c c o r d i n g to the  1  0  8  relation  ^1 h  e  2  speed  d i s t a n c e from the  exit  diameter  A mean s t r a i n r a t e , as proposed by L a r k e is  the  , had  a l s o been shown.  It  given:  >= where f =  f  V  fl D (  ' h  l  - h  1  h 0  8  2  6  l  h^  (IT DN)/60  N = number of r e v o l u t i o n s per minute. The  hot r o l l i n g  l i n e a r s t r a i n r a t e s and  d a t a i s p l o t t e d i n F i g . 8 i n terms of  s t r e s s e s . In t h i s form i t i s then d i r e c t l y  comparable w i t h A l d e r and  P h i l l i p s compression d a t a ^ ^  at the same  temperatures.  3.2  - T e n s i l e Data 3.2.1  - Stress Analysis True s t r e s s e s and  t r u e s t r a i n s were c a l c u l a t e d from hot  t e n s i l e l o a d - e l o n g a t i o n data assuming uniform g i v e s the r e s u l t s of two and  450°C.  A steady  elongation.  Fig.9a  t e s t s at a s t r a i n r a t e of 0.0014/sec. at  s t a t e r e g i o n i s observed from which a  s t a t e f l o w s t r e s s can be  evaluated.  The  s t r a i n r a t e was  350  steady  evaluated  from  Fig.7  V a r i a t i o n of s t r a i n r a t e from the entrance plane to the e x i t plane f o r r o l l i n g a c c o r d i n g to the r e l a t i o n . The mean s t r a i n r a t e f o r r o l l i n g t i s a l s o shown, '  I  rftfi  ••  AAA  • • • / AA m Qn • AAA/AA f250°C  350 °C  A /A& ROLLING DATA A250°C • 350°C o450°C • ALDER a PHILLIPS 8  Fig.8  10 12 cr(ksi)  14  16  Hot r o l l i n g d a t a c o r r e l a t e d i n terms of the power s t r e s s - s t r a i n r a t e r e l a t i o n . A l d e r and P h i l l i p s (10) h o t compression d a t a i s i n c l u d e d f o r comparison.  e = .13 sec 2000  to Q.  L  1  -0  '500 e= . 0015  sec"  1  1000  T= 45 0 ° C  500  .02  .04  .06  .08  .10  .12  .14  16  € Fig.9b.  Variation of the flow stress with s t r a i n rate for 450°C test at  £ = 0.13  sec. ^ and i = 0.0015 sec. ^,  oo  29 the c r o s s head speed and the i n s t a n t a n e o u s gauge l e n g t h at the i n c e p t i o n of a steady s t a t e f l o w r e g i o n .  The s t r a i n r a t e i n t e s t i n g  v a r i e d by a maximum of 10% from b e g i n n i n g t o t h e end of t h e t e s t . The  steady s t a t e f l o w s t r e s s i s s t r a i n r a t e dependent as Fig.9b  i l l u s t r a t e s f o r t y p i c a l t e s t s a t two s t r a i n r a t e s but c o n s t a n t temperature. The  steady s t a t e s t r e s s - s t r a i n r a t e dependence was  a n a l y z e d i n t h r e e ways; l o g £ v e r s u s l o g a i n F i g . 1 0 ; l o g £ v e r s u s a i n F i g . 1 1 ; and l o g t v e r s u s l o g s i n h  (aa) i n F i g . 1 2 .  The v a l u e of  -3 -1 a = 0.3 x 10 p s i was used. T h i s v a l u e of t h e m a t e r i a l c o n s t a n t , (20) (28) a, was found by Wong and o t h e r s to best f i t t e s t data f o r the same p u r i t y m a t e r i a l to a h y p e r b o l i c s i n e r e l a t i o n s h i p . .  (2,7,10)  parxson, compression  .  (14) .  and creep  lar purity material.  .  F o r com, , , .  data a r e i n c l u d e d f o r s i m i -  W o n g ' s ^ ^ e x t r u s i o n d a t a was n o t i n c l u d e d f o r  reasons which w i l l be d i s c u s s e d l a t e r .  TABLE I I - P u b l i s h e d hot Working Data f o r S i m i l a r Composition Aluminum  Ref.  Composition  (%)  Al  Cu  Mn  Si  Fe  ^yP ° Deformation  99.3  .1  .01  .12  .46  Constanta  .12(250°C) .  creep  .21(350°C)  e  a  f  13  X 10  -3 -1 psi  .27(450°C) 2 17 9 11  99.45  .02  -  .12  .31  99.0 99.2 99.99  .1  .02  .2  .46  compression  .20(19)  compression  .30  compression  .3 (19)  hot t o r s i o n  .31(19)  30  IC  IO  3  4  tX(psi)  Fig.10  Steady s t a t e s t r e s s - s t r a i n r a t e d a t a c o r r e l a t e d a c c o r d i n g to the power s t r e s s - s t r a i n r a t e r e lations . . n -AH/RT  3.2.2  - Power  Law  F i g u r e 10 p r e s e n t s the hot t e n s i l e data a c c o r d i n g to a power law s t r e s s - s t r a i n r a t e dependence. l i n e s of v a r y i n g s l o p e . l a t i o n AH = - 2.3R  Table I I I l i s t s  (8 l o g e/8  1/T)a  The  data p o i n t s f i t s t r a i g h t  the s l o p e s .  Using  the r e -  i n the manner suggested  by  (13) Garofalo  an a c t i v a t i o n energy of 32.5  a = 2000 p s i , see  k c a l / m o l e was  obtained f o r  Fig.13. (14)  Lower s t r a i n r a t e data of S e r v i and Grant p u r i t y m a t e r i a l i s i n c l u d e d f o r comparison to show how f u n c t i o n p l o t the s l o p e changes at a c r i t i c a l temperature.  for similar i n a power  stress f o r a given  Above a c r i t i c a l v a l u e of s t r e s s n i n c r e a s e s .  No  vari-  a t i o n i n the n v a l u e f o r the t e n s i l e r e s u l t s at a g i v e n temperature was  n o t i c e a b l e because the s t r e s s v a l u e s are above the  transition  s t r e s s l e v e l s f o r S e r v i and G r a n t ' s r e s u l t s . 3.2.3  - Exponential  Law  F i g u r e 11 i l l u s t r a t e s the use of the e x p o n e n t i a l to  r e l a t e the s t r e s s and  s t r a i n r a t e dependence.  the 3 v a l u e s as a f u n c t i o n of temperature. 39.5  kcal/mole  f o r hot t e n s i l e deformation was  r e l a t i o n AH = 2.3R of  1.57  x 10  —3  An  ( g  p s i was  i = 0.00125/sec.  -)  T  (  3o  used f o r 3 and -r=r  was  Table I I I l i s t s  a c t i v a t i o n energy of obtained using  ) . .  9  relation  the  An average v a l u e  e v a l u a t e d at  32  !02  0  1  -  2  3  4  cr  Fig.11  7  5 6  8 9  10  (ksi)  Steady s t a t e s t r e s s - s t r a i n r a t e d a t a c o r r e l a t e d a c c o r d i n g to the e x p o n e n t i a l stress-strain rate r e l a t i o n , . ... 3a -AH/RT e = A''e e  3,2.4 -  Hyperbolic Sine  The h y p e r b o l i c is illustrated listed  Relationship  s i n e dependence of s t r e s s and s t r a i n  i n Fig.12 f o r t h e p r e s e n t r e s u l t s .  i n Table I I I .  rate  The v a l u e s o f n'are  The a c t i v a t i o n energy o f 38.5 k c a l / m o l e f o r t h e  p r o c e s s was c a l c u l a t e d from the r e l a t i o n AH _ o o p / 3 l o g e A  H  ~ ' 2  3  R  (  9 log sinh  \ (aa) T }  , 3 log sinh 9T/T  (  (aa) . ~  e  }  An average v a l u e o f n = 5.6 was used. TABLE I I I - The Constants n, n', 3 and AH f o r T e n s i l e , Compression and Creep Data o f S i m i l a r P u r i t y Aluminum Ref.  Type  2  18  t(°C) 6 ( p s i  - 1  ) n  1  AH k c a l / m o l e  /•  3a  250  .00061  4  39.5  5.4  350  .00099  5  38.5 (E a s i n h (aa)  8  450  .0033  7.6  32.5 (constant  compression 99.2 26.4  250  .000873  6.7  11.2  350  .000555  4.2  45.7 (e a e ) 38.82(e a s i n h (aa)  7.5  450  .000587  4.2  36.8 (20)  6.35  550  .000815  4.8  44.0 (3)  9.5  300  .000463  7.6  400  .00056  32.7 (e a e ) 4.05 34.5 (e a s i n h (aa)  7.0  500  .00079  5  8.23  260  .0011  9.64 50  8.43  371  .0024  8.5  2.0  482  .0034  5.1  10.6  400  .00064  4.7  54.3  200  .00146  11.2  99.7  compression 99.5  •  14  n 6  tensile  10  %A1  creep  99.3  compression 99.0  )  (e a e a  )  3a  3a  3.5  (constant  a  )  31.6 (e a s i n h (aa)  10  10"  io  10'  sin h(ao-)  Fig.12  10"  Steady s t a t e s t r e s s - s t r a i n r a t e d a t a c o r r e l a t e d a c c o r d i n g to the h y p e r b o l i c s i n e r e l a t i o n , e = A'"[sinh  a = 0.3 x 10  (aa)] 'e"  - 3 - 1 psi  n  A H / R T  .  35  10  1  1  10"  -  1  i  i  V S ^ ) AH = - 2 3R ( 3 l'/T ' a = 2000 p s i . ?  l o  v  = 32.5 k c a l / m o l e 10  -2  lO"  3  lO"  4  lO"  5  1 1.2  1  i 1.6  1.4  1.8  1/T, ° K Fig.13  Arrhenius plot  ( P  8 e ) g , ,„  _ 1  x 10  N  I 2.0  - 3  f o r hot t e n s i l e d e f o r m a t i o n a t  l o  a = 2000 p s i .  36  DISCUSSION  4.1 - Hot R o l l i n g As can be seen from F i g . 8 , the f i t of the present r o l l i n g data to Alder and P h i l l i p s  data f o r hot compression at 250°C i s  good. However, at the higher temperatures the r o l l i n g r e s u l t s give 20 to 25% higher stresses than compression data f o r the same temperatures.  This large d i f f e r e n c e i s a t t r i b u t e d to the quenching e f f e c t  of the r o l l s rather than the method of evaluating r o l l i n g s t r e s s e s . Three f a c t s substantiate t h i s assumption.  F i r s t , the  250°C data i s w i t h i n 8% of the hot compression data which i s w e l l w i t h i n the reported accuracy of Sims' method of c a l c u l a t i n g hot (31 32 33) r o l l i n g stresses  '  '  . For t h i s temperature of r o l l i n g both  the slab and the r o l l s were at the same temperature, 250°C. Secondly, two t e s t s at a s t r a i n r a t e of 0.84/sec. were done w i t h r o l l s and slab at 350°C.  I n these two cases the d e v i a t i o n from the com-  pression data f o r 350°C was only 10%, s t i l l w i t h i n the reported accuracy of the Sims' method, yet at t h i s lowest r o l l speed, the e f f e c t of a i r quenching would be highest. and P h i l l i p s  ( 1 0 )  T h i r d l y , the d e v i a t i o n from Alder  data increased r e g u l a r l y with the d i f f e r e n c e i n  temperature between the slab and the r o l l s .  Consequently, the stresses  derived from r o l l i n g data at 350 and 450°C may be considered erroneous. Only the 250°C data i s believed to give r e l i a b l e working s t r e s s r e sults. With such l i m i t e d r e l i a b l e data, neither an evaluation of the e m p i r i c a l s t r e s s - s t r a i n rate r e l a t i o n s h i p s proposed f o r hot working nor an a c t i v a t i o n energy determination f o r hot r o l l i n g i s  justified. the  The s e r i e s of r o l l i n g experiments does, however, i l l u s t r a t e  u s e f u l n e s s o f h o t r o l l i n g as a means of e v a l u a t i n g h o t working  parameters. ing of  I t a l s o p o i n t s out t h e important e f f e c t o f r o l l  with a laboratory scale m i l l .  L a r g e r m i l l s permit the r o l l i n g  l a r g e s e c t i o n s i n which case the e f f e c t o f r o l l  p r o b a b l y be i g n o r e d .  quench-  quenching can  F o r t r u e temperatures i n l a b o r a t o r y hot r o l l i n g ,  heated r o l l s a t t h e d e s i r e d r o l l i n g  temperatures must be used.  4.2 - T e n s i l e Deformation 4.2.1 - True S t r e s s - True S t r a i n Data True s t r e s s e s and s t r a i n s were d e r i v e d from l o a d - e l o n g a t i o n p l o t s assuming u n i f o r m e l o n g a t i o n o c c u r r e d u n t i l the l o a d began to  drop.  T h i s assumption seemed j u s t i f e d when the d a t a was compared  w i t h h o t t o r s i o n d a t a a t s i m i l a r temperatures b u t s l i g h t l y m a t e r i a l p u r i t y as a i n F i g . 1 4 .  different  The s t r e s s l e v e l f o r t h e t e n s i l e  t e s t i s h i g h e r than t h a t o f h o t t o r s i o n but t h e r e a r e d i f f e r e n c e s i n p u r i t y and temperature.  The lower m a t e r i a l p u r i t y  and t e s t  tempera-  t u r e may account f o r the 25% h i g h e r steady s t a t e s t r e s s i n the h o t tensile test. ' In  h o t t o r s i o n experiments, the attainment of a steady  s t a t e f l o w r e g i o n o c c u r s a t a h i g h e r s t r a i n than f o r the t e n s i l e tests.  A s h i f t o f t h e s t r e a d y s t a t e r e g i o n to h i g h e r s t r a i n s w i t h (13)  i n c r e a s i n g s t r a i n rates also i s evident i n Fig.9. observed t h i s b e h a v i o u r .  Others  have  Tensile 9 9.75% £  =  0.13  T  =  45Q°C  Al  sec"  1  torsion (12) Torsion Super p u r i t y A l '  0. 2  e  =  0.5  T  =  4BQ C  sec  -1  U  0.3  .ln±  Comparison of l o a d - e l o n g a t i o n data f o r hot t e n s i o n and hot t o r s i o n (12).  0.4  39  4.2.2 - Strain Rate A constant s t r a i n rate was not imposed during t e s t i n g . The s t r a i n rate i n fact decreased by 10% from the beginning u n t i l the onset of steady state flow.  Such a v a r i a t i o n i s small i n com-  parison to the imposed rates, which d i f f e r by an order of magnitude.  Similar variations occur i n evaluating s t r a i n rates by either  hot t o r s i o n , hot r o l l i n g , or hot extrusion.  The s t r a i n rate evalu-  ation here i s believed to be at.:least as accurate as those i n previous reported work f o r compression and torsion.  In contrast, the  v a l i d i t y of the mean s t r a i n rate values quoted f o r extrusion through (9 34)  a square die i s questionable.  In f a c t , Jonas and other  '  state  that the s t r a i n rate varies by as much as 2-3 orders of magnitude f o r extrusion i n a f l a t faced die.  Such a large v a r i a t i o n i s not per-  missable when investigating high temperature  s t r a i n rate s e n s i t i v i t y .  Figure 10 compares the t e n s i l e data of the present work to Servi and Grant' s  creep data for similar temperatures  and simi-  l a r purity material. There i s reasonable agreement between the two sets of data i n the region of overlapping s t r a i n rates, except at the lowest test  temperatures,  4.2.3 - Stress Strain Rate Dependence When considering the s t r e s s - s t r a i n rate dependence of hot t e n s i l e deformation, comparison can be made with results reported * u- u temperature for high  creep  A hot u - compression • (2,10,18)f o r and  material of similar purity and i n the same temperature  range.  Refer-  ence may also be made to the results of Wong^ ^ whose analysis of 2  Alder and P h i l l i p s ' hot compression d a t a ^ ^ i s given i n Table IV.  Wong i n h i s a n a l y s i s  chose t o use S e r v i and Grant's  (14)  creep  d a t a f o r h i g h p u r i t y aluminum r a t h e r than a v a i l a b l e d a t a f o r t h e (14) commercial  purity  used i n h i s own e x t r u s i o n experiments.  This  was u n f o r t u n a t e , because Wong might have come t o d i f f e r e n t c o n c l u s i o n s had he used the creep d a t a f o r l e s s pure aluminum. 4.2.3.1 - Power Law Dependence A creep r a t e dependence on a power f u n c t i o n o f s t r e s s i s not v a l i d  f o r both h i g h and low s t r e s s creep as Fig.10  illustrates.  (14) The  creep data o f S e r v i and Grant  does not g i v e a l i n e a r p l o t o f  l o g e v e r s u s l o g a f o r any temperature. No d e v i a t i o n from l i n e a r i t y on a s i m i l a r p l o t o c c u r s f o r the t e n s i l e r e s u l t s presumably  because  they a r e a l l i n the h i g h s t r e s s  r e g i o n . That i s , they l i e i n the hot working range where the e q u i v a i *. i ' - u v * ,(2,6,12,16,17) . N  t  lent relation a = a Normally  o  e  has been found  '  t o be a p p l i c a b l e .  i n t h i s range a power dependence of s t r e s s and s t r a i n  g i v e s l i n e a r r e l a t i o n s h i p s t h a t a r e c o n v e r g i n g as i n Fig.15 The power exponent, n, i s commonly found to be temperature (see T a b l e I I I and I V ) .  rate  (Ref.17). dependent  F o r the p r e s e n t t e n s i l e d a t a t h i s was not  observed as can be seen from the n v a l u e s l i s t e d  i n T a b l e I I I . Ex-  ponent v a l u e s from both t e n s i l e t e s t s and creep t e s t s a r e s i m i l a r when the h i g h s t r e s s creep range f o r each temperature  i s considered.  However, i n both these cases t h e exponent v a l u e s were h i g h e r than the (12) 6.1 t o 5 u s u a l l y quoted f o r aluminum V a r i a t i o n s of the exponent, p a r t i c u l a r l y f o r h o t comp r e s s i o n and c r e e p , make the use o f a power dependence e q u a t i o n uns u i t a b l e f o r r e l a t i n g s t r e s s and s t r a i n r a t e at low s t r a i n r a t e s to those a t h i g h s t r a i n r a t e s f o r h i g h temperature  deformation.  41  FLOW  Fig.15  STRESS,  IOOO psi  C o r r e l a t i o n of s t r e s s - s t r a i n r a t e d a t a f o r hot deformation o f commercial p u r i t y aluminum a c c o r d i n g t o a power s t r e s s - s t r a i n r a t e dependence. Reference 17.  TABLE IV - Wong and Jonas  ,(20)  Values f o r the Constants n, n', 3, a, A''  from t h e i r e x t r u s i o n r e s u l t s  T(°C)  n  (ksi, ) 1  and A l d e r and P h i l l i p s h o t  a  (ksi  v)  AH  and AH - as determined compression  A'"  x  10  320  13.7  4.0  1.24  .3  .28  376  8.1  4.0  1.24  .3  2  445  6.7  4.0  1.24  ,3  2.34  490  5.2  4.0  1.24  ,3  2.34  555  4.7  4.0  1.24  .3  2.51  616  4.1  4.0  1.24  .3  250  24.4  4.2  1.24  ,3  350  11.2  4.2  1.24  .3  2.34  450  7.7  4.2  1.24  .3  2.40  550  6.5  4.2  1.24  .3  2.51  37.4  36.8  2.51  results.  10  Ref.  extrusion  Hot  compression  ho  4.2.3.2 - E x p o n e n t i a l Law V a l u e s of 3, as l i s t e d i n T a b l e I I I f o r t h e t e n s i l e r e s u l t s , v a r i e d f o r t h e 350 t o 450°C t e s t s . could i n d i c a t e that  The low 3 v a l u e f o r 250°C  a steady s t a t e s t r e s s was n o t o b t a i n e d a t t h e  lower s t r a i n r a t e s b e f o r e n e c k i n g o c c u r r e d .  The 3 v a l u e s a r e com-  M - i , - A * d4) . (2,10) , p a r a b l e t o those r e p o r t e d f o r creep , compression , and extrusion^ ^ 2  as l i s t e d  i n T a b l e I I I and I V .  The 3 v a l u e s c a l c u l a t e d by the w r i t e r from A l d e r and P h i l l i p s compression  results  Wong and Jonas  They found a c o n s t a n t 3 v a l u e o f 1.24 k s i \  .  d i f f e r from those c a l c u l a t e d by  In t h e present a n a l y s i s , 3 was i n t h e range o f 0.555 t o 0.873 k s i In both cases 3 was temperature  independent.  A l t h o u g h f o r t h e com-  p r e s s i o n r e s u l t s 3 v a r i e d , i t d i d not vary s y s t e m a t i c a l l y with temperature  so i t can be s a i d t o be temperature  v a l u e s f o r t h e creep data  (14)  independent.  were found t o be s l i g h t l y  3  temperature  dependent. The magnitude of t h e range of s t r a i n r a t e s p l o t t e d i n F i g . 1 1 masked t h e d e v i a t i o n from l i n e a r i t y f o r t h e creep d a t a  (14)  But u s i n g a s m a l l e r range o f s t r a i n r a t e , such as G a r o f a l o , t h e d e v i a t i o n becomes apparent.  As s t a t e d b e f o r e , t h i s i s the r e a s o n  the e x p o n e n t i a l r e l a t i o n s h i p cannot be used t o r e l a t e both h i g h and low s t r e s s creep d a t a .  4.2.3.3 - H y p e r b o l i c Sine R e l a t i o n s h i p Use of t h e h y p e r b o l i c relation f o r t h e t e n s i l e -3 gave n' v a l u e s from 4 to 7.6 f o r a = 0.3 x 10  results  -1 psi .  v a r i a t i o n was not r e p o r t e d by Wong and Jonas ( * ^ f  o  r  Such a  hot e x t r u s i o n  and hot c o m p r e s s i o n  }  see T a b l e IV.  A l d e r and P h i l l i p s d a t a ^ ^  (see T a b l e I I I ) g i v e s n' v a l u e s t h a t v a r y  1 0  from 4.2  to 6.7,  temperatures.  A p r e s e n t r e - e v a l u a t i o n of  a l t h o u g h W o n g ^ ^ q u o t e s a v a l u e of 4.2  for a l l  In l i g h t of these d i s c r e p a n c i e s , the v a r i a t i o n i n the  t e n s i l e n' v a l u e does not appear as q u e s t i o n a b l e . Use  of a = 0.3  x 10  p s i ^ i n a n a l y z i n g the creep  3  dati"^  gave h i g h e r v a l u e s of s i n h (aa) than the t e n s i l e d a t a f o r s l i g h t l y h i g h e r temperatures.  In o r d e r t o get a b e t t e r f i t between the two (15) s e t s of r e s u l t s , a was r e c a l c u l a t e d u s i n g G a r o f a l o ' s method for -3 low and h i g h s t r e s s e s .  0.21  x 10  - 3  pectively.  psi  _ 1  ,  T h i s method gave v a l u e s of 0.12  and 0.27  x 10~  3  -1  x 10  psi  p s i " at 2 6 0 , 371and4B2°C  ,  res-  1  A p p l y i n g the h y p e r b o l i c r e l a t i o n s h i p w i t h these a v a l u e s  gave good f i t between the creep and  t e n s i l e v a l u e s , see  Fig.12.  Values of a f o r the t e n s i l e range c o u l d not be c a l c u l a t e d u s i n g a = B/n because the s t r e s s l e v e l s were too h i g h . I n T a b l e I I I the n' v a l u e s a r e , i n the t e n s i l e t o hot working range, a p p r o x i m a t e l y  temperature  independent.  Use o f  the  h y p e r b o l i c r e l a t i o n s h i p of s t r e s s - s t r a i n r a t e made i t p o s s i b l e to e x t r a p o l a t e from creep t o the hot working range w i t h some e f f e c t i v e n e s s f o r s i m i l a r p u r i t y m a t e r i a l , see F i g . 1 2 . (13) The h y p e r b o l i c e q u a t i o n i s s a i d t o be c o r r e c t r e l a t i n g s t r e s s and s t r a i n r a t e over l a r g e s t r e s s ranges  of the e q u i v a l e n c e of £ = A'' e = A'e^  a  e  approximates F o r aa  > 1.2,  anc  \  1  e = Aa . 11  [sinh ( a a ) ]  n  I f aa < 0.8,  e  A  ^/ ^  in because  R  t o  the h y p e r b o l i c r e l a t i o n  the power r e l a t i o n by l e s s than 10% e r r o r , and n' = n. the e r r o r i s l e s s than 10% between the h y p e r b o l i c and  the e x p o n e n t i a l f u n c t i o n , and a = B/n  or a = B/n'  depending upon  e i t h e r G a r o f a l o ' s ^ ^ o r S e l l a r s and T e g a r t ' s ^ ^ d e f i n i t i o n . 1 5  For  1 9  the t e n s i l e r e s u l t s , a must be l e s s than 2500 p s i f o r aa <  0.8.  S t r e s s v a l u e s l e s s than 2500 p s i o c c u r r e d i n the 450°C t e s t s where n' = 8 . • and n' = 7.6,  n' = n.  a p p l i c a b l e where n ' = 4 , a = B/n  = 0.102  x 10  - 3  For aa  n=6, psi  _  1  >1.2,  the 250°C t e s t s  g = 0.00061 p s i  and a = g/n'  In n e i t h e r case i s a e q u a l to the 0,3  - 1  —3  These g i v e  x 10~  = 0.12  x 10  .  are  psi  3  .  - 1  —1 (17 19 28) psi which o t h e r s ' '  found f o r the m a t e r i a l c o n s t a n t f o r t h i s p u r i t y of aluminum. The hot c o m p r e s s i o n ^ » - ^ ) were a n a l y z e d i n the same way  a  n  (  j  c  p^ ^ 4  r  e  e  r e s u l t s of o t h e r s  to see what a and n' v a l u e s they gave  and t o see i f they agreed w i t h Wong's b e s t f i t v a l u e s . are summarized i n T a b l e s IV and V.  F o r no one  h y p e r b o l i c r e l a t i o n approximate the power and  The  temperature  results does the  exponential expressions  by l e s s than 10% e r r o r a t both low and h i g h s t r e s s e s .  As a  con-  sequence, n' v a l u e s are p r o b a b l y s u b j e c t t o some e r r o r . When c o n s i d e r i n g the v a l u e s of a, u s i n g a = compression  data^'"^  S e l l a r s and T e g a r t ' s  e m p i r i c a l c o n s t a n t i s independent Garofalo's evaluation, a =  g/n  pendent which s u b s t a n t i a t e d h i s Nothing  of temperature  statement  g/n',  for  that t h i s  i s substantiated.  g i v e s a's which are temperature  de-  c l a i m .  c o n c l u s i v e can be s a i d about the v a r i a t i o n of a  (14) v a l u e s f o r creep  and  t e n s i l e d a t a w i t h temperature.  l e v e l s f o r both the t e n s i l e and range i n which the r e l a t i o n a =  The  stress  creep r e s u l t s are i n a c r i t i c a l g/n'  cannot be used  stress  effectively.  For c r e e p , o n l y G a r o f a l o ' s m e t h o d ^ ^ ^ f o r e v a l u a t i n g a can be used the s t r e s s l e v e l s do not s a t i s f y aa > 1,2  f o r l e s s than 10%  error.  and  46  Instead a =  3/n i s used i n c o r r e c t l y a t lower s t r e s s v a l u e s . The v a l u e s f o r A l d e r and P h i l l i p s  compression r e -  s u l t s do not correspond to those found by Wong fit.  T h i s i s due t o  and V I .  f o r the best  t h e d i f f e r e n t v a l u e s of g and n', see T a b l e s I I I  The v a l u e of n' Wong r e p o r t s f o r t h e 250°C l i n e i s i n e r r o r  even from v i s u a l examination S e l l a r s and  of h i s p l o t t i n g of the d a t a ^ ^ .  Tegart  (19)  l i m i t e d the usefulness of t h e i r  f i n d i n g s by s a y i n g t h a t a was temperature  independent  only i n the -3  s t r a i n r a t e range they examined which extended in  t h e case of aluminum.  o n l y down t o 10 / s e c .  But i n o r d e r t o g e t t h e creep d a t a t o f i t  an e x t r a p o l a t i o n o f t e n s i l e d a t a or compression temperature  dependent, and the v a l u e s used a r e as suggested by  Garofalo^ "^. 1  value of s t r a i n 4.2.4  Perhaps a i s temperature  dependent below a c r i t i c a l  rate.  - A c t i v a t i o n Energy Three methods were used  for  d a t a a must be  to c a l c u l a t e a c t i v a t i o n  t h e hot t e n s i l e d e f o r m a t i o n of t h e aluminum.  Using a s t r e s s -  s t r a i n r a t e dependence a c c o r d i n g t o e = A''' [ s i n h an a c t i v a t i o n energy 3a e  energies  n' —AH/RT (aa) ] e  of 39.5 k c a l / m o l e was o b t a i n e d ; u s i n g i = A''  —AH/RT e  kcal/mole.  , 3 8 . 5 kcal/mole;  and u s i n g a creep type a n a l y s i s , 32.5  The a c t i v a t i o n e n e r g i e s determined  s t r e s s - s t r a i n r a t e dependencies  from  the f i r s t two  a r e s i m i l a r as would be s u s p e c t e d as  the h y p e r b o l i c e q u a t i o n approximates  the exponential equation.  The  d i f f e r e n c e a r i s e s perhaps i n the creep d e t e r m i n a t i o n through t h e use 9 lo '' ' of (— ) a = 2000 p s i . The s t r e s s v a l u e i s p o s s i b l y i n e r r o r  TABLE V - E v a l u a t i o n of the S t r e s s Ranges - where the h y p e r b o l i c s i n e r e l a t i o n appoximates the power and e x p e r i m e n t a l r e l a t i o n s h i p s by more than 90% a c c u r a c y , u s i n g the d e r i v e d v a l u e s of a, n, n', and 3 as l i s t e d i n T a b l e I I I . a a >  T°C  n  3 ksi  1  '  aa < 0.8  2  n'  a=3/n k s i  a=3/n' k s i  n  r  Ref.(10) 250 350  a = 0.3 x. 1 0  - 3  450  psi  _  1  26.4  .873  6.7  0.33  .13  11.2  .555  4.2  0.50  .13  550  6.3  4.8  a v a l u e s not  8.23  9.64  h i g h enough  8.43  8.5  2.0  5.1  -3 Ref. (14) 260 .  a = .12 x 10  371  a = .21 x 10  482  a = .27 x 1 0  300 400  a = .3 x 1 0 ~  Ref.(2)  -3  500 250 350 450  Tensile  _ 3  3  9.5 7.6  1.1 2.4  3.5 4.05  .15 .32  .31 .6  7.0  3.4  5  .49  .68  4  .102  .12  6  .61  a v a l u e s too high  7.6  8.0  -o-  f o r the low s t r a i n r a t e t e s t s a t 250°C as a t r u e not e x i s t .  state did  I f the 250°C d a t a i s i g n o r e d , the creep a n a l y s i s g i v e s  an a c t i v a t i p n energy two  steady  of 38,5  kcal/mole which agrees w i t h the o t h e r  values. The  c a l c u l a t e d a c t i v a t i o n energy  for tensile  f o r the ISCD aluminum, which i s a p p r o x i m a t e l y  deformation  2S c o m p o s i t i o n ,  agrees  „ . . . (1,3,13,17,19,20,28,35) . wxth o t h e r r e p o r t e d a c t x v a t x o n e n e r g i e s » > > » » > > f t  creep and  hot working.  35-36 k c a l / m o l e and Wong  t  Sherby and Dorn  f o r h i g h temperature  (35)  of 37 k c a l / m o l e  Jonas  f o r hot  whereas McQueen, Wong and  quote 41.8  and  r e s p e c t i v e l y f o r the same p u r i t y  material.  As the lower v a l u e f o r the hot e x t r u s i o n i s the  kcal/mole  r e p o r t e d by one of the  Jonas  (28)  e x t r u s i o n and hot compression 44.0  r  r e p o r t v a l u e s of  creep of 2S aluminum.  r e p o r t an a c t i v a t i o n energy  o  latest  c o - a u t h o r s , t h i s v a l u e i s b e l i e v e d t o be  more c o r r e c t . S i n c e d i f f e r e n t e x p e r i m e n t a l a c t i v a t i o n energy have been quoted  f o r A l d e r and P h i l l i p s h o t  a r e - e v a l u a t i o n of the a c t i v a t i o n energy was  compression  made h e r e .  e x p o n e n t i a l s t r e s s - s t r a i n r a t e dependence i t was AH = 45.7;  u s i n g a h y p e r b o l i c dependence, AH  v a l u e agrees w i t h the v a l u e of 44, and Jonas AH = 37. energy, was  (28)  and  data,  Using  The  former  by McQueen, Wong,  the l a t e r v a l u e w i t h t h a t of Wong and Jonas  In Wong and  Jonas'  d e t e r m i n a t i o n of an  (20)  ,  activation  they have taken l i b e r t i e s i n a r r i v i n g a t n' f o r  mentioned b e f o r e .  an  found t h a t  = 38.82.  determined  values  250°C as  S i n c e the h y p e r b o l i c e q u a t i o n i s an a p p r o x i -  mation of the e x p o n e n t i a l e q u a t i o n , the v a l u e of 45.7 would not be s u b j e c t to as much as  error.  kcal/mole  A r n o l d and P a r k e r ' s d a t a of 32.7 encies  and  34.4  kcal/mole  (2)  gave a c t i v a t i o n  energies  f o r e x p o n e n t i a l and h y p e r b o l i c depend-  respectively. A n a l y s i s of S e r v i and G r a n t ' s  creep d a t a ^ ^ 1  aluminum, gave an a c t i v a t i o n energy of 50 k c a l / m o l e stress analysis.  f o r 2S  f o r a constant  T h i s compared w i t h the v a l u e of 56.8  kcal/mole  (35) determined  by Sherby and Dorn  from t h i s same d a t a .  2S aluminum r e s u l t s they found the e x p e r i m e n t a l  For  other  a c t i v a t i o n energy  (35) to be i n the range 35-36 kcal/mole  .  a c t i v a t i o n energy i n S e r v i and G r a n t ' s prior  They a t t r i b u t e d the h i g h  case t o the heat treatment  used  . (35) to t e s t i n g The v a r i a t i o n i n a c t i v a t i o n e n e r g i e s does not f o l l o w  any  c o n s i s t e n t change i n c o m p o s i t i o n f o r the aluminum examined.  T h i s would suggest  t h a t the  a c t i v a t i o n energy f o r hot  i s not p u r i t y dependent f o r the c o m p o s i t i o n v a r i a t i o n  4.2.5  deformation considered.  - Zener-Hollomon Parameter Jonas and  others  3  »20»21) have used a form of  the  _i_ AH/RT Zener-Hollomon parameter, Z = e e creep d a t a .  , to r e l a t e hot working  and  Z i s a s t r u c t u r e f a c t o r o f the deformed m a t e r i a l and  i s a f u n c t i o n of s t r a i n  '  .  The  structure associated with a  g i v e n v a l u e of s t r a i n i s assumed to be a c o n s t a n t f o r a l l p o s s i b l e combinations  of s t r a i n r a t e and  temperature  which y i e l d a c o n s t a n t  (13) v a l u e of Z i n g and  . . For a c o n s t a n t f l o w r e g i o n , as o c c u r s i n hot work-  steady s t a t e creep, Z v a l u e s are constant i n the c o n s t a n t  flow r e g i o n . g r e a t e r Z,  The  flow stress i s related  a higher  flow s t r e s s i s needed because few  a c t i v a t e d events o c c u r per u n i t s t r a i n . low temperature  to the v a l u e o f Z.  At a  thermally  T h i s a r i s e s from e i t h e r a  o r the s h o r t e r time f o r the event  t o o c c u r a t the  at the h i g h e r s t r a i n r a t e  (3)  .  Jonas and o t h e r s  (1 20 21) ' ' have used  50  a s t r u c t u r e - c o r r e c t e d Zener-Hollomon parameter, Z/A' ', t o n o r m a l i z e 1  the s l i g h t v a r i a t i o n s i n the c o m p o s i t i o n of t h e aluminum c o n s i d e r e d . They have r e l a t e d t h i s s t r u c t u r e - f a c t o r c o r r e c t e d Zener-Hollomon parameter t o the h y p e r b o l i c s i n e s t r e s s f u n c t i o n as i n F i g . 1 6 .  In  the a n a l y s i s they used a AH = 37.3 k c a l / m o l e . C o r r e c t use of the Zener-Hpllomon parameter r e q u i r e s t h a t the same a c t i v a t i o n energy be used throughout A l d e r and P h i l l i p s  But f o r the  d a t a , Jonas and o t h e r s ^ » ^ ^  used  AH which d i f f e r e d from the a c t u a l e x p e r i m e n t a l v a l u e '4.2.9.).  S i n c e Jonas and o t h e r ^ ' ^ ^  a value of  (see S e c t i o n  have taken t h i s l i b e r t y o f  u s i n g the Zener-Hollpmon parameter i t was thought  advantageous here  to p r e s e n t a s i m i l a r p l o t t o Fig.16 u s i n g the v a r i o u s c a l c u l a t e d ex•i • (2,10) (14) p e r i m e n t a l a c t i v a t i o n e n e r g i e s f o r the compression , creep , and hot t e n s i l e d a t a .  The v a l u e s o f A''' used a r e l i s t e d  and a r e comparable t o the v a l u e s o f A' ' quoted 1  i n T a b l e IV. almost  by W o n g ^ ^ as r e p o r t e d  The data p o i n t s f a l l on a l i n e i n Fig.17 which  c o - l i n e a r w i t h t h e l i n e i n F i g u r e 16.  remarkable  i n Fig.17  This  lies  seems r a t h e r  c o n s i d e r i n g t h e f a c t t h a t a AH v a l u e o f 53.4 k c a l / m o l e (13)  was used f o r the creep data  .  The f i t would suggest  t h a t use o f a  Zener-Hollomon p l o t does not p r o v i d e c o n c l u s i v e proof f o r t h e t h e o r y t h a t h o t working i s an e x t e n s i o n o f h i g h temperature (14) I f f o r t h e S e r v i and Grant 37.3  kcal/mole  i s used,  the l i n e i n F i g . 1 6 . '  creep.  creep d a t a a v a l u e o f  the d a t a p o i n t s a r e o r d e r s of magnitude o f f  T h i s casts f u r t h e r doubt on Jonas' use of the  Zener-Hollomon parameter i n h i s argument.  51  IO'  10'  IO'  10'  3f  IO'  IO  o +  IO*  I  k  io-  /  SLOPE  I a .299»l6 p s i " j  ta  Q « 37-3  »  4-67 4  = = = =  C r e e p (14) E x t r u s i o n (20) C o m p r e s s i o n (10 T o r s i o n (12)  1  teaJ/mol«  10'  ,6*  o  /  ,dl 7  A8  10  IO"  2  10"'  10°  IO  Sinh (cc cr)  Fig.16  1  10'  Correlation of hot working data using the structurecorrected Ziner-Hollomon parameter and the hyperbolic sine stress function. Reference (1).  52  10  1  10'  I0  :  10'  io-  10'  N  10"  10'  10  10  s  • SERVI a GRANT (14) o ARNOLD 8 PARKER(?) • ALDER 8 PHILLIPS (10) A INSTRON DATA  4  9  10  i'  10  I0  U  10'  sin h[aa)  Fig.17  10  io  Zener-Hollomon p l o t u s i n g a c t u a l e x p e r i m e n t a l a c t i v a t i o n energies. 'The data can be i n t e r p r e t e d as two. s l o p e s ( s 6 1 i d l i n e s ) o r one s l o p e (dotted l i n e ) .  S2A  T°C  A » "  sec*  26.0  i o  i o  371  2 , 9 3 x XQ  482  3  0  ©11  8*8  x  IO  9  a  2S0  8.2  x  10  2  350  5.53  x  4S0  6.4S  x  all  5.855  •  A  x  1  1  H  9  kcal/mole 53.4  ir  x  1 0  x  1  4  34.4 38.02  I O  1  0  I O  1  0  I O  1  1  38. S  53  CONCLUSIONS  1.  It has been suggested by others that hot working i s an ex^  tension of high temperature creep because of the similar observed interdependencies of stress, strain-rate and temperature, and the similar activation energies of the two types of deformation. The present analysis of data for material of approximately 2S aluminum -7 +2 -1 composition i n the strain rate range 10 to 10 sec. provides evidence that  opposes this suggestion. First, the method of evalu-r  ation.of the constant a i n the stress-strain rate relation must change i n going from creep to hot working.  Secondly, the activation  energy i s found to vary.  2.  A hyperbolic sine relationsip £ = •A''* [sinh (aa)]"  e ^H/RT^  can be used to relate the hot working parameters but i t i s only an approximation of power and exponential stress-strain rate dependencies. The constants  a  and n' are variable.  If a becomes temperature de-  pendent below some c r i t i c a l value of strain rate, i t i s possible to extrapolate approximately from high temperature creep to hot working, is slightly temperature dependent.  3.  On the basis of prior and present work, the apparent acti-  vation energy for hot deformation varies from 37 to 57 kcal/mole i n the strain rate range considered. For hot compression i t i s 37-4 5 kcal/mole.  For hot tensile deformation i t i s 38.5 - 39.5 kcal/mole.  For high temperature creep i t i s 50-57 kcal/mole.  n'  4.  Loose use of t h e Zener-Hollomon r e l a t i o n can g i v e  the i m p r e s s i o n t h a t hot working i s an e x t e n s i o n o f h i g h  temperature  creep.  5.  Hot r o l l i n g  can be used t o e v a l u a t e hot working  but o n l y when the e f f e c t of r o l l quenching can be  6.  Hot t e n s i l e t e s t i n g  o r hot t o r s i o n  data.  ignored.  on a f i x e d cross-head  machine g i v e s hot working data t h a t i s comparable  parameters  speed  tensile  to hot compression  55  BIBLIOGRAPHY  1. J o n a s , J . J . , S e l l a r s , C.M. Reviews,  14,  2. A r n o l d , R.R.  and T e g a r t , W.J.  Metallurgical  (1969), 1. and P a r k e r , R.J.,  JIM  3. McQueen, H.J., J . M e t a l s , 20, 4. N i c h o l s o n , A., 5. Moore, P.,  McG.  ., 88,  (1959-60),  255.  (1968),31.  I r o n and S t e e l , ^ 7 ,  (1964), 290,  363.  "Deformation Under Hot Working C o n d i t i o n s " , I . S . I .  S p e c i a l Report #108  (1968), London,  103.  6. R o s s a r d , C. and B l a i n , P., Rev. Met., IRSID (174a),  (1958), 573, P u b l .  (1957).  7. Helm, A. and A l e x a n d e r , J.M. 8. L a r k e , E.C.,  55,  J I S I , 207,  (1969),  1219.  "The R o l l i n g of Sheet, S t r i p , and P l a t e " , Chapman  and H a l l L t d . , London,  (1963).  9. Chandra, T. and Jonas, J . J . , t o be p u b l i s h e d . 10. A l d e r , J . F . and P h i l l i p s , V.A.,  JIM, 83,  (1954-55),  80.  11. R o s s a r d , C. and B l a i n , P., Mem.  S c i e n t . Revue, M e t a l l . , j>7, (1960)  173-8. 12. Ormerod, H. and T e g a r t , W.J. 13. G a r o f a l o , F., "Fundamentals M a c m i l l a n , N.Y.,  McG.,  JIM, 92,  (1963-4),  237.  of Creep and Creep Rupture i n M e t a l s " ,  (1965).  14. S e r v i , I.S. and Grant, J . J . , TAIME, 191, 15. G a r o f a l o , F., TAIME, 227,  (1960),  (1951),  909.  351.  16. B a i l e y , J.A. and S i n g e r , A.R.E,, JIM, £ 2 ,  (1963-4),  17. Jonas, J . J . , McQueen, H.J. and Wong, W.A.,  i b i d 5,  18. H o c k e t t , J.E., TAIME, 239,  (1967),  969.  404. 49.  19. S e l l a r s , C M . 63,(1966), 20. Wong, W.A.  and T e g a r t , W.J.  McG.,  Mem.  S c i e n t . Revue M e t a l l . ,  731. and Jonas, J . J . , TAIME, 242,  (1968),  2271.  21. Jonas, J . J . and Immarigeon, J.P., Z. M e t a l l k i n d e , Bd. 60, H. 3,  (1969),  227.  22. Conrad, H.,  " I r o n and I t s D i l u t e S o l u t i o n " ,  23. B o u l g e r , F.W.,  DMIC Report  (1966), #226, 15.  24. Weertman, J . , J . A p p l , P h y s i c s , 28, 25. B a r r e t t , C R .  318.  and N i x , W.D.,  (1957),  A c t a Met.  B,  26. Raymond, L . and Dorn, J . E . , TAIME, 230,  362.  (1965),  (1964),  1247.  560.  27. Weertman, J . , TAIME, 218,  (1960),  28. McQueen, H.J.,  and Jonas, J . J . , Can.J. Phys.,  (1967),  Wong, W.A.  207. 45,  1225.  29. Sims, R.B.,  P i o c . IME.,  30. Rowe, G.W.,  "Principles  207,  (1969),  1219.  of Metalworking", Edward A r n o l d , London,  (1965). 31. D i e t e r , G.E.,  M c G r a w - H i l l , London,  (1961).  32. Helmi, A. and A l e x a n d e r , J . J . , J I S I , 207,  (1969),  1219.  33. Yanagimoto, S. and A o k i , I . , B u l l e t i n of J.SME, 11, 34. Thomsen, E.G.,  Yang, C T .  and Kobayashi, S.,  (1968),  "Mechanics  Deformation i n M e t a l P r o c e s s i n g " , The M a c M i l l a n Co. N.Y., 35. Dorn, J.E. and Sherby, O.D.,  J . M e t a l s , j4, (1952),  165.  of P l a s t i c (1965).  959.  36. Dorn, J . E , "Mechanical Behavior of M a t e r i a l s a t E l e v a t e d Temperas f  t u r e s " , M c G r a w - H i l l , N.Y.  (1961).  

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