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Analysis of the steady state hot deformation of aluminum 1971

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ANALYSIS OF THE STEADY STATE HOT DEFORMATION OF ALUMINUM by GEORGE ALLAN BARCLAY B.A.Sc., Uni v e r s i t y of 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 thesis' as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA February, 1971 In p r e s e n t i n g t h i s t h e s i s i n p a r t i a l f u l f i l m e n t o f the r e q u i r e m e n t s f o r an advanced deg ree a t the U n i v e r s i t y o f B r i t i s h C o l u m b i a , I a g r e e t h a t t he L i b r a r y s h a l l make i t f r e e l y a v a i l a b l e f o r r e f e r e n c e and s t u d y . I f u r t h e r a g r ee t h a t p e r m i s s i o n f o r e x t e n s i v e c o p y i n g of t h i s t h e s i s f o r s c h o l a r l y p u r p o s e s may be g r a n t e d by t he Head o f my Depar tment o r by h i s r e p r e s e n t a t i v e s . I t i s u n d e r s t o o d t h a t c o p y i n g o r p u b l i c a t i o n o f t h i s t h e s i s f o r f i n a n c i a l g a i n s h a l l not be a l l o w e d w i t h o u t my w r i t t e n p e r m i s s i o n . Depar tment o f Metallurgy The U n i v e r s i t y o f B r i t i s h C o l u m b i a V a n c o u v e r 8, Canada Date May 6, 1971 i ACKNOWLEDGEMENT The author i s grateful for the advice and encouragement given by his research director, Dr. J.A Lund. Thanks are also ex- tended to fellow graduate students and technicians for th e i r h e l p f u l discussions and advice. Financial assistance was received i n the form of assistant- 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 It has been suggested by others that hot working i s an extension of high temperature creep because of the s i m i l a r observed dependencies of s t r e s s , s t r a i n rate, temperature and the s i m i l a r a c t i - v ation energies of the two types of deformation. This suggestion has been evaluated f o r commercial p u r i t y aluminum by obtaining s t r e s s , -4 s t r a i n rate and temperature data i n the s t r a i n rate range 10 to 10^/second. Published hot compression, hot t o r s i o n , and high tempera- ture creep work of others i s used to provide supplementary data. A combination of the published work of others with the present experi- -7 +2 mental work provides data i n the s t r a i n rate range 10 to 10 /second. From the present an a l y s i s , contradictions a r i s e against the theory that hot working i s an extension of high temperature creep. F i r s t , the method of evaluation of the material constant a i n the hyperbolic 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 ' T ' [ s i n h ( a a ) ] e , must change i n going from creep to hot working. Secondly, the a c t i v a t i o n energy v a r i e s . Those that have suggested that hot working i s an extension of high temperature creep found that a and the a c t i v a t i o n energy were independent of s t r a i n rate. Their work i s compared to the present analysis and many discrepancies were found. The work i n the l i t e r a t u r e l e f t a data gap i n the s t r a i n -3 0 rate range 10 to 10 /second. Hot t e n s i l e tests and hot r o l l i n g tests were used to provide data i n t h i s gap. i i i TABLE OF CONTENTS Page INTRODUCTION 1 1.1 - Experimental Techniques 2 1.1.1 - Scaled-down I n d u s t r i a l Processes . . . . 2 1.1.2 - Tensi l e Tests 2 1.1.3 - Compression Tests 3 1.1.4 - Hot Torsion 3 1.2 - Steady State Deformation 3 1.3 - Empirical Flow Stress Relationships 5 1.3.1 - Power Relationship 5 1.3.2 - Exponential Relationship 7 1.3.3 - Hyperbolic Sine Relationship 7 1.4 - Temperature Dependence 9 1.5 - Recovery Mechanisms 12 1.5.1 - Screw Model 13 1.5.2 - Climb Models .. 1 4 1.6 - Scope of Present Investigation 15 EXPERIMENTAL 1 7 2.1 - Ma t e r i a l Preparation .. .. 17 i v 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 2.2 - Te n s i l e Testing 2 0 2.2.1 - Ma t e r i a l 20 2.2.2 - Heating 21 2.2.3 - Testing Procedures 21 RESULTS • • • • 23 3.1 - R o l l i n g 2 3 3.2 - Tensi l e Data 2 4 3.2.1 - Stress Analysis 24 3.2.2 - Power Law 31 3.2.3 - Exponential Law 31 3.2.4 - Hyperbolic Sine Relationship 33 DISCUSSION 36 4.1 - Hot R o l l i n g 36 4.2 - Te n s i l e Deformation 37 4.2.1 - True-Stress - True S t r a i n Data 37 4.2.2 - S t r a i n Rate 39 4.2.3 - St r e s s - S t r a i n Rate Dependence 39 V Page 4.2.3.1 - Power Law Dependence . . . . .. 40 4.2.3.2 - Exponential Law 43 4.2.3.3 - Hyperbolic Sine Relationship »'• 43 4.2.4 - A c t i v a t i o n Energy 46 4.2.5 - Zener-Hollomon Parameter 49 CONCLUSIONS 53 BIBLIOGRAPHY 55 V I LIST OF TABLES Table Page I Activation Energies AH (kcal/mole) II Published Hot Working Data for Similar Composition Aluminum 29 III The Constants n, n', 6 and AH for Tensile, Compression and Creep Data of similar Purity Aluminum IV Wong and Jonas' Values for the Constants n, n', 8, a, A " and AH 4 2 V Evaluation of the Stress Ranges where the Hyperbolic Sine Relation is more than 90% Accurate 47 LIST OF FIGURES v i i Figure Page 1 Comparison of stress versus s t r a i n curves de- ri v e d from d i f f e r e n t test methods f o r : (a) low- carbon s t e e l at 1100°C and (b) Fe-25% Cr a l l o y at 1100°C. Reference (1) .. 4 2 V a r i a t i o n of log minimum creep rate with (a) log a, (b) a, and (c) log sinh (ao) for aluminum. Reference (15). 6 3 Wong and Jonas's extrusion data plotted with others 'hot' compression, t o r s i o n , and creep data. The data i s p l o t t e d according to a hyperbolic sine r e l a t i o n s h i p . Reference (20). •• 10 4 Experimental set-up f o r hot r o l l i n g . •• •• •• •• 19 5 T y p i c a l load trace f o r hot r o l l i n g . # 19 6a Experimental set-up for hot t e n s i l e tests . • • . 22 6b T y p i c a l load trace f o r hot t e n s i l e t e s t i n g . • • • 22 7 V a r i a t i o n of s t r a i n rate from the entrance plane to the e x i t plane f o r r o l l i n g according to the r e l a t i o n . The mean s t r a i n rate for r o l l i n g e, i s also shown . . . 25 8 Hot r o l l i n g data correlated i n terms of the power s t r e s s - s t r a i n rate r e l a t i o n . Alder and P h i l l i p s (10) hot compression data i s included f o r comparison. . . 26 9a V a r i a t i o n of the flow stress with temperature for tests at e = 0.0014 s e c . - l at 350°C and 450°C. 27 9b V a r i a t i o n of the flow stress with s t r a i n rate for 450°C tests at i = 0.13 s e c " ! and e = 0.0015 s e c . - 1 28 10 Steady state s t r e s s - s t r a i n rate data correlated according to the power s t r e s s - s t r a i n r a t e re- l a t i o n s e = A a n e - ^ H / R T . 30 v i i i Figure Page 11 Steady state s t r e s s - s t r a i n rate data correlated according to the exponential s t r e s s - s t r a i n rate, £ = A " e ^ e " AH/RT_ 32 12 Steady state s t r e s s - s t r a i n rate data correlated according to the hyperbolic sine r e l a t i o n , e = A " ' [ s i n h (ao) ] n ' e - A H / R T . a = 0.3 x 10"3 p s i - 1 . 34 13 Arrhenius p l o t for tot t e n s i l e deformation 35 14 Comparison of load-elongation data for hot tension and hot t o r s i o n (12). 3 8 15 C o r r e l a t i o n of s t r e s s - s t r a i n rate data for hot deformation of commercial p u r i t y aluminum accord- ing to a power s t r e s s - s t r a i n rate dependence. Reference 17. .. 41 16 C o r r e l a t i o n of hot working data using the s t r u c t u r e - corrected Zener-Hollomon parameter and the hyper- b o l i c sine stress function. Reference (1) 51 17 Zener-Hollomon pl o t using actual experimental a c t i - v a t i o n energies 52 1 INTRODUCTION Hot working, i n p r a c t i c e , involves large reductions, at 3 high rates of s t r a i n (0.1 to 10 / s e c ) , and at temperatures above approximately one-half the absolute melting temperature. It i s used extensively i n industry because these large reductions can be accom- plish e d at low working stresses without intermediate anneals. The fac t that large s t r a i n s can be achieved with l i t t l e or no s t r a i n harden- ing suggests that dynamic softening processes are balancing the s t r a i n hardening ^ . For commercial p u r i t y aluminum as w e l l as f o r other pure metals and simple a l l o y s , the flow stress at a p a r t i c u l a r temperature (2) increases as the rate of deformation i s increased . S i m i l a r l y , i f the s t r a i n rate i s kept constant, the flow stress decreases as the (2) temperature i s increased . Therefore, to determine optimum hot work- ing conditions 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 rate and temperature,must be known. The i n t e r r e l a t i o n between these para- meters depends on the deformation and recovery mechanisms involved. Considerable attention has been paid to the development of (3-5) tests f o r evaluation of the hot working parameters . In the i d e a l hot working experiment, the specimens are deformed uniformly at a constant rate and temperature with a continuous measurement of load or s t r e s s . If s t r u c t u r a l observations are to be made, the specimen must be de- formed i n a s i n g l e operation and immediately quenched to avoid s t r u c t u r a l changes during cooling. In the hot working range of s t r a i n rates (3) adiabatic heating may occur but i t i s usually neglected . The t e s t s used are scaled-down i n d u s t r i a l processes, t e n s i l e t e s t s , compression (3—6) t e s t s , or hot t o r s i o n . 1.1 - Experimental Techniques 1.1.1 - Scaled-down I n d u s t r i a l Processes Scaling down of i n d u s t r i a l processes i s a use f u l approach because the mode of deformation i n the test and the p r a c t i c a l working operation are one and the same. But these processes a l l involve non- uniformity of deformation and require numerous assumptions i n the analysis / i n to get true s t r a i n rate, s t r a i n and stress values. In hot r o l l i n g f o r example, the s t r a i n rate changes along the arc of contact. An average s t r a i n rate must be a s s u m e d . C a l c u l a t i o n of the deforming stress i s based upon an assumption of s t i c k i n g f r i c t i o n which may not (8) be constant . The deforming stress cannot be calculated as a function (8) of s t r a i n . In extrusion, the s t r a i n rate i s s i m i l a r l y non- (3-9) uniform , and the stress cannot be p r e c i s e l y c a l c u l a t e d . 1.1.2 - Te n s i l e Tests Conventional t e n s i l e t e s t i n g equipment does not provide a s u i t a b l e s t r a i n rate range. For a constant s t r a i n rate t e s t , the ex- : da tension rate must be vari e d as (1/&) (~ĵ r) » where £ i s the gauge length of the specimen, to permit a precise analysis of a, stress E, s t r a i n e, at (5,6) (5 6) s t r a i n rate and T, temperature ' ' . When t e n s i l e t e s t i n g i s done at temperatures above 0.51^, specimens neck t y p i c a l l y at 10-30% s t r a i n Methods have been d e v i s e d t o analyze the necked region thus enabling de- formation to be ca r r i e d to true s t r a i n s of (2). However, these methods are very complex. 1.1.3 - Compression Tests (3-5) Compression tests , normally u n i a x i a l , can be used to evaluate stress up to true s t r a i n s of 2.3. Test machines that give a (2 9) constant s t r a i n rate have been devised, such as Orowan's Cam Plastometer' • However, lubricants must be used to eliminate f r i c t i o n between the platens A ^ • (3-5,10) and the specimen , 1.1.A - Hot Torsion Hot t o r s i o n tests on thin-walled tubes give flow curves at -3 3 constant true s t r a i n rates i n the range 10 to 10 /sec. S t r a i n of (3 11 12) up to 20 can be obtained before f r a c t u r e ' . For s o l i d t o r s i o n specimens the s t r a i n and s t r a i n r a t e vary from a maximum at the surface (9) to zero at the centre . S o l i d specimens are generally used, and only the surface s t r a i n rate and stresses examined. This i s done on the assumption that the outer layer makes the major stress contribution be- cause i t work hardens more. This assumption seems j u s t i f i e d when con- s i d e r i n g Fig.1(1), a f t e r Rossard and B l a i n , which compares t o r s i o n data with tension and compression data. 1.2- Steady State Deformation As can be seen from F i g . l , the flow curves f o r high tempera- ture tension, compression and t o r s i o n tests exhibit an i n i t i a l harden- (2 10 12) ing portion up to a true s t r a i n of usually 50-100% ' ' . This Is followed by a region of "steady s t a t e " where the stress i s e s s e n t i a l l y independent of s t r a i n . The l e v e l of t h i s steady state flow stress de- creases with increasing temperature and with decreasing s t r a i n Such a dependence of flow stress indicates that hot working i s a thermally activated process. 4 F i g . l Comparison of stress versus curves derived 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 at 1100°C and (b) Fe- 25% Cr a l l o y at 1100°C. Ref- erence (1) . » —8 High temperature creep deformation i n the range of 10 to 10 /sec. ' i s an example of s i m i l a r steady state deformation. For constant stress creep, a f t e r an i n i t i a l transient the s t r a i n increases l i n e a r l y with time, 1.3 - Empirical Flow Stress Relationships A number of mathematical expressions have been proposed to describe the r e l a t i o n s h i p between stress and s t r a i n rate f or high temperature steady state deformation. 1.3.1 - Power Relationship * • -, „ . • 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 ^ for the r a t e - c o n t r o l l i n g thermally activated process, has been found to f i t a v a i l a b l e creep data for low (13) stresses . In an intermediate range of stresses, the equation e = ^ Q ^ n n a s been found to f i t experimental creep d a t a ^ " ^ ' ^ ^ for a f i x e d temperature. In t h i s case however, the stress exponent n may,or may not be, a function of temperature, depending on the stress l e v e l . For low creep stresses n i s constant ̂ \ f o r high stresses n i s tempera- (3) ture dependent . The f a c t o r A q may also be temperature dependent. (15) For commercial p u r i t y aluminum Garofalo reported that n varied from 6.1 to 5 i n the temperature range 0.51 to 0.575 T . Fig.2 (Ref.15) i l l u s t r a t e s a p l o t of log a versus log e for some creep data. I t i l l u s t r a t e s that the power r e l a t i o n s h i p has only l i m i t e d a p p l i c a b i l i t y because at a c r i t i c a l s tress value, n f o r a p a r t i c u l a r temperature [1] In 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 a c t i v a t i o n energy. 6 Fig.2 V a r i a t i o n of log minimum creep rate with (a) log a, (b) a, and (c) log sinh (ao) f o r aluminum. Refer- ence (15). 7 increases. In the presentation of hot working data i t i s more .N common to apply the equivalent power law a = a Qe which i s an anomaly according to creep theory,. In t h i s case, both o"o and N are found to be a function of temperature f o r steady state deformation. The equation has been used to c o r r e l a t e r e s u l t s from compression^'"^'"*"^, t o r s i o n ^ ' " ^ and e x t r u s i o n t e s t s . For commercial p u r i t y aluminum, N v a r i e s from 0.04 to 0.2 i n the range 0.55 to 0.9 T ( 2 > 1 0 » 1 2 > 1 6 > 1 7 ) # m An equation i n which the constants are a function of temperature i s not useful as an i n d i c a t o r of the deformation mechanism. 1.3.2 - Exponential Relationship A . i -a . . i 3a ,-AH/RT n . . . An exponential law, e = A e e , applies e m p i r i c a l l y for high stress creep '"'""'̂  i n commercial p u r i t y aluminum and for hot (1 2 6 18) working data at high stresses ' > » . The r e l a t i o n s h i p becomes i n - v a l i d at high temperatures where the stresses are low, however, and (3) th i s presents d i f f i c u l t i e s i n the 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 of aluminum and i t s a l l o y s the parameter A' has (13) been found to be constant at constant temperature. The value of : (13) g has been found to be r e l a t i v e l y independent of temperature i n the temperature range 0.45 to 0.65 T^ but decreases with increasing tempera- ture above the r a n g e ^ ^ ' " * " 7 . F i g . 2^"^ i l l u s t r a t e s how the exponent- i a l law i s only applicable i n a l i m i t e d stress range and f a i l s at low stresses. 1.3.3 - Hyperbolic Sine Relationship Garofalo(13,15) ^ a s suggested an equation to cover the dependence of steady state creep rate on stress at constant temperature f o r both high and low stresses. I t i s of the form e = A'' [sinh ( a a ) ] n where A T' and a are constant and n = n', The product aa i s u n i t l e s s , a i n p s i ^ and a i n p s i . If aa> 1.2 (high s t r e s s e s ) , the d i f f e r e n c e . aa between sinh (aa) and ^ i s le s s than 10% and the hyperbolic sine equation i s approximated by e = ^ — 7 e n a ° . This i s the same as 2 n e = A' e^° where ^—7- = A' and a = B/n. The equation e = A' e^° has 2 n been shown to s a t i s f y the experimental dependence of creep rate f o r high n' stresses, so therefore, does e = A''[sinh (aa)] . For aa< 0.8 (low s t r e s s e s ) , the d i f f e r e n c e between sinh (aa) and aa i s le s s than 10% and e = A ' 1 [ s i n h ( a a ) ] n can be approximated by e = A''a n an which re- duces to e = Aa 1 1 f o r low stresses and A''a11 = A and n = n'. In Garofalo's empirical equation n', and to a small extent B, are functions of temperature, The r e l a t i o n a = B/n defines a. Therefore, i n Garofalo's a n a l y s i s , creep data at both high stresses (for determination of B ) and at low stresses (for determination of n) must be a v a i l a b l e f o r the evaluation of a. Since n = n', n' i s also tempera- ture dependant. (19) S e l l a r s and Tegart doubt Garofalo's findings that a and n' are temperature dependent. They suggest that since the data of Garofalo were in.a narrow stress range on both sides of the c r i t i c a l value, h i s i n t e r p r e t a t i o n was inadequately supported. His i n t e r p r e t a t i o n would predict 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 experimentally i n the considered stress range. —AH/RT n' They therefore propose the equation e = A''' e [sinh (aa)] and (18) a = B/n' where A''', a, and n', are independent of temperature. (1,3,12,17,20,21) , , _ , . Others ' i n attempts to analyse hot working test r e s u l t s , have adopted S e l l a r s and Tegart's version of the empirical r e l a t i o n s h i p . They have evaluated the constants a and n' by p l o t t i n g log e versus sinh aa f o r various imposed values of a. The value of a that gave a constant value of n' f o r the temperature range examined was taken as the correct value of a. Wong^^ used t h i s approach to evaluate a f o r the hot ex- tr u s i o n of aluminum. He used the r e l a t i o n a = $/n' to evaluate £. The value of n T used by Wong was based on r e s u l t s at h i s highest ex- perimental temperature. The values of n' and a thus obtained for ex- trusion were found to compare to those for high temperature creep i n the same metal. Implying that the hot working of aluminum i s an ex- tension of high temperature creep, Wong^^ used the hyperbolic sine r e l a t i o n s h i p to construct p l o t s such as F i g . 3 . Other published work u A i '"• v - u - i • A ( 1 , 3 , 1 7 , 2 0 , 2 1 ) has drawn analogies between hot working and creep 1.4 - Temperature Dependence A comparison of the temperature dependence of hot working and creep can also be made through the apparent a c t i v a t i o n energies of the processes. In steady state creep the a c t i v a t i o n energy i s deter- mined i n the following way. From conventional creep t e s t s the v a r i a t i o n of log i with T at constant stress i s found. A p l o t of t h i s v a r i a t i o n gives a st r a i g h t l i n e whose slope y i e l d s a value of AH, the experimental a c t i - v ation energy, i f one assumes f o r steady state creep constant structure ( 1 3 ) factors which are only stress dependent . That i s : ^ 2 f £ = - AH /2.3R 9 T For hot working i t i s more d i f f i c u l t to conduct a test at constant flow stress over large s t r a i n s . To evaluate the a c t i v a t i o n 10 •I J f .'I //./// // Ji ulljJi Ji iii / . m l IK W 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 extrusion data plotted with others 'hot' compression, tor s i o n and creep data. The data i s p lotted according to a hyperbolic sine r e l a t i o n - ship. Reference (20). 11 energy at constant stress thus requires extensive extrapolation, as can be seen from Fig.3. An a l t e r n a t i v e approach based on the method (22) (19 20 21) of Conrad has been proposed ' ' . One s t a r t s with e = A''' ^ ? ^ j [sinh (aa)] e where A''', a, n' are constants independent of temperature and s t r a i n rate. AH = RT [ l n A ' " + n' In sinh (aa) - lne] d A H = RT [ n' - ( • ^ r ^ ) 1 (D (aa) ^ d l n sinh (aa) V 9 l n sinh T d AH = _ R T 2 f , ( o g ) ^ + RTn' (2) d l n sinh (aa) V 9 l n sinh (aa) J RT t equate (1) and (2) RT r , C? lne -I _ R T 2 /3-1/T "\ ,AlL , [ n " ^9 l n sinh ( a a ) ^ J - - RT ^ l n sinh (aa) J V + R T n 12 ATT o OT> f 3 log £ "\ /" 3 log [sinh (aa)] ^ Each of the terms i n parenthesis i s a slope which can be determined from experimental data. The above analysis can be applied to any function of stress but the hyperbolic one has been used by (1 3 19 20) others because, as noted above, i t has been found ' ' ' to f i t ex- perimental data. TABLE I - A c t i v a t i o n Energies AH (kcal/mole) Self D i f f u s i o n Hot Working Creep (23) (1) (13) 33 37 33-36 Table I reveals a s i m i l a r i t y among the a c t i v a t i o n energies for creep, hot working,and s e l f d i f f u s i o n f o r aluminum. On t h i s basis (1 3 20) i t has been concluded ' ' that the rate c o n t r o l l i n g mechanisms are s i m i l a r . Various models based upon recovery mechanisms have been pro-posed that r e l a t e the a c t i v a t i o n energy of hot working to that of s e l f e va (25) d i f f u s i o n . They ar cancy migration models , climb models and jogged screw models 1.5 - Recovery Mechanisms For high temperature deformation of aluminum, dynamic re- (1,3) covery i s considered to be the softening mechanism ' . This i s based upon o p t i c a l , X-ray microbeam and ele c t r o n microscopy evidence. A number of models have been presented to explain high temperature deformation based upon dynamic recovery. In a l l of these models the a c t i v a t i o n energy i s that of s e l f d i f f u s i o n . They are pr i m a r i l y proposed f o r the creep range of s t r a i n rates but since there are simi - l a r i t i e s i n the case of aluminum between creep and hot working with regard to the microstructural change, the a c t i v a t i o n energy and the s t r e s s - s t r a i n rate dependence, the creep theories can be considered f o r hot working. The rate c o n t r o l l i n g processes i n hot working of aluminum are assumed to be climb and the motion of jogged screw d i s l o c a t i o n s ^ 7 1,5.1 - Screw Model motion of jogged screw d i s l o c a t i o n s . The jogs have to move non-con- s e r v a t i v e l y and create or acquire vacancies. This process w i l l re-^ s t r a i n the movement of the jogged d i s l o c a t i o n s , and must be accomplished by means of s e l f d i f f u s i o n . The model i s based upon the e f f e c t of the applied stress moving the jog. A c a l c u l a t i o n of the speed of the jog as a function of the steady state stress and temperature of the form: The model (25,27) i s based upon the d i f f u s i o n c o n t r o l l e d e = Ap D sinh ( s s a b X 2KT ) e -U/KT where A = a constant p = density of mobile screw d i s l o c a t i o n s J 3 = constant x a a = applied stress X = average jog spacing b = Burgers Vector D = d i f f u s i o n C o e f f i c i e n t U = a c t i v a t i o n Energy p must vary as p a a , which i s e s s e n t i a l l y an adjustment parameter; s s where a i s the applied s t r e s s . the observed stress dependence of creep rates as given by Garofalo's empirical expression f o r steady state creep of aluminum. Values of the constants were found to be r e a l i s t i c and the temperature dependence was i n the d i f f u s i o n c o e f f i c i e n t . 1.5.2 - Climb Models These models depend upon geometrical patterns of d i s - l o c a t i o n s , the d e t a i l s of which are not accurately known^\ and the (27) models are highly i d e a l i z e d . Weertman proposed a theory based upon the operation 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 planes. The d i s l o c a t i o n s climb from adjacent loops and a n n i h i l a t e each other, thus permitting further d i s l o c a t i o n loops to be emitted from the sources. For low stresses Weertman proposed: 3 This equation has been compared by Barret and Nix (25) to b 2 N 2 G 9 C X 15 where C = constant D = d i f f u s i o n c o e f f i c i e n t T = applied stress N = density of d i s l o c a t i o n s taking part i n climb G = shear modulus k = Boltzman's constant and f o r both high and low stresses _1 ,2 2 _ /, 3.5. 1.5 C A T D . , r v 3 T b e = _ _ — _ smh [ — r ~ T T J G b • 8G N 2 kT C' = a constant 1.6 - Scope of Present Investigation Past in v e s t i g a t i o n s of the hot deformation of commercial p u r i t y aluminum (1-3, 10, 12, 14, 17, 20, 21, 28) have been done only i n a l i m i t e d s t r a i n rate range. No one researcher has done work i n —5 2 the range from creep (10 /sec.) to hot working (10 / s e c ) . In t h e i r a n a l y s i s , p r i o r workers have r e l i e d on the publications of other i n - v e s t i g a t o r s to obtain creep or hot working data. Moreover there i s a -3 0 data gap i n the s t r a i n rate range 10 to 10 /sec. In the present -4 work, s t r e s s - s t r a i n rate data were obtained i n the t e n s i l e range 10 2 t o 10 / s e c and beyond. Two types of experiments were used to obtain a s t r a i n rate v a r i a t i o n of 10"*. Hot r o l l i n g , f o r which e a r l i e r published data was not a v a i l a b l e , was used f o r s t r a i n rates i n the range 0.5 to 10 / s e c and t e n s i l e testing f o r the range 10 to 10 /sec. The proposition that hot working i s an extension of high temperature creep can be better discussed i f data are a v a i l a b l e i n the^' s t r a i n rate range between creep and hot compression. If the proposition i s c o r r e c t , the same s t r e s s - s t r a i n rate dependence should be observed -5 2 over the en t i r e range from 10 to 10 /sec. and a common a c t i v a t i o n energy should apply. EXPERIMENTAL Low s t r a i n rate t e n s i l e tests were performed at constant crosshead speed i n an Instron machine. High s t r a i n rate t e s t s were performed on a laboratory s i z e Stanat r o l l i n g m i l l (with 4.1 inch diameter r o l l s ) . In both cases the test temperatures were 250, 350 and 450°C. 2.1 - Material Preparation R o l l i n g slabs were cast from Alcan ISCD aluminum with a nominal composition 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 . The melting stock, cast Properzi rod, was melted under reducing conditions to minimize oxide formation. Slabs were cast from 740°C i n a carbon coated mould. The cast ingots were 2.5 x 0.625 x 5 inches. In order to control grain s i z e and to eliminate the cast structure, each ingot was cold r o l l e d and annealed. The r o l l i n g schedule consisted of a serie s of 20% cold reductions followed by a i r anneals at 375°C f o r 25 minutes u n t i l a thickness of 0.200" was reached This gave a VPN hardness of 25, which i s t y p i c a l of the commercial "0" temper hardness of the material. The f i n i s h e d slabs were then cut to 2 inch lengths and end-milled to a width of 2.25 inches. F i n a l l y , the slabs were anodized i n caustic soda. In the hot r o l l i n g experiments the slabs were reduced 50% to 0.100 inch thickness i n one pass. Such a large reduction i n one pass required that the front edge of the slabs be tapered i n order to f a c i l i t a t e the entrance into the r o l l gap. 18 2.1.1 - R o l l i n g Procedure Figure 4 i l l u s t r a t e s the equipment used i n r o l l i n g . Each specimen was put in s i d e the furnace and soaked over 5 minutes at the desired temperature before being pulled into the r o l l gap. R o l l i n g was done at 4 peripheral r o l l speeds - 0.6, 3.66, 7.32 and 14.64 in/sec. In order to lessen the temperature gradient between the slab and the r o l l s , the r o l l s were heated by e l e c t r i c resistance elements situated i n the r o l l cores. The m i l l bearings were cooled with a pressurized c i r c u l a t i n g o i l . The r o l l temperature was 250°C fo r a l l experiments except those i n which a r o l l speed of 0.6 in/sec. was used, i n which case the temperature was 350°C. The r o l l surface temperature was measured by a surface contact thermocouple mounted on the top r o l l . 2.1.2 - Load Measurement The r o l l separating force was measured by means of e l e c t r i c resistance s t r a i n gauge elements (force washers) situated under the bearing blocks. The s t r a i n was measured on a 4-arm s t r a i n bridge and re- corded on a storage o s c i l l o s c o p e . The scope was triggered by the f i r s t increment of load. Figure 5 i s a t y p i c a l recorded load trace. The force 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. Since the load to be measured i n r o l l i n g was applied to both washers, i t was assumed that the i n d i v i d u a l loads, i n c a l i b r a t i o n , were a d d i t i v e . 2.1.3 - Lu b r i c a t i o n The hot r o l l i n g of aluminum presents a problem i n that 19 Fig.5 T y p i c a l load trace for hot r o l l i n g . 20 clean aluminum surfaces 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 ale, t h i s i s overcome by fl o o d l u b r i c a t i o n . On a labora- tory s c a l e , l u b r i c a t i o n i s complicated i n that r e l i a b l e hot r o l l i n g load analysis requires the presence of 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 using a l u b r i c a n t that allows s t i c k i n g f r i c t i o n to take place but eliminates adhesion. O i l , carbowax, and a c o l l o i d a l suspension of graphite were t r i e d , but a l l were found unsuitable. They could not be applied to the r o l l s i n a reproducible manner and the f r i c t i o n force v a r i e d . Anodising of the slabs provided the most acceptable s o l u t i o n , i n that s t i c k i n g f r i c t i o n occurred, the conditions were reproducible, and adhesion of the aluminum to the r o l l s was almost nonexistent. The oxide provided by anodising did not contribute to a reduction i n the co- e f f i c i e n t of r o l l i n g f r i c t i o n , and as such should not be described as a " l u b r i c a n t " . 2.2 - Tensi l e Testing 2.2.1 - M a t e r i a l Ten s i l e specimens were made from the same ISCD aluminum as used f o r r o l l i n g slabs, but i n the form of 3/8 inch diameter rod hot r o l l e d from Properzi rod by the suppl i e r . Specimens were machined with a uniform gauge portion of 0.160 inches diameter and 1.125 inch gauge length. A f t e r machining, the specimens were annealed f or lh hours at 500°C, and f i n a l l y cleaned i n a phosphoric acid "bright d i p " s o l u - t i o n . 2.2.2 - Heating Figure 6 shows the arrangments f o r t e n s i l e t e s t i n g . The specimen was loaded into the furnace and g r i p s , then allowed 40 minutes to s t a b i l i z e before p u l l i n g . A thermocouple was s i t u - ated i n the furnace at the midpoint of the t e n s i l e specimen. 2.2.3 - Testing Procedures Low s t r a i n rate tests were conducted at 0.01, 0.1, and 1 inch/min. cross head speeds. The load and elongation were recorded autographically on the Instron chart. Crosshead speeds greater than approximately 5 inch/min. were found to be above the slewing speed of the chart recorder. In order to get a load-elongation curve at a cross head speed of 10 inch/min., the load c e l l was connected to an o s c i l l o s c o p e s t r a i n bridge. The load-elongation curve was recorded on the storage scope. Figure 6 i l l u s t r a t e s a t y p i c a l load-elongation curve obtained i n t h i s manner. Fig.6 b. Typical load trace for hot t e n s i l e t e s t i n g . RESULTS 23 3.1 - R o l l i n g The r o l l separating force was converted to an e f f e c t i v e (29) material flow stress using Sim's semi-empirical hot r o l l i n g formula , P = Kb V R(h^ - h 2)' x Q, where P i s the r o l l load, k the mean e f f e c t i v e flow stress i s plane s t r a i n , b the s t r i p width, R the r o l l radius, h^ the entrance thickness, h^ the ex i t thickness, and Q i s a geometric r o l l f a c t o r . The r o l l load, P, i s the area under the curve of the 56X11 s dd>, where d> entrace ' i s the contact angle and s i s the normal r o l l pressure. The geometric f a c t o r i s a function of R/h^ and the reduction. Tables of calculated (8) Q values are a v a i l a b l e . The use of a mean e f f e c t i v e flow stress i s j u s t i f i e d because the s t r a i n rate decreases along the arc contact (8) and t h i s counteracts s t r a i n hardening In the load c a l c u l a t i o n no cor r e c t i o n was made for r o l l d i s t o r t i o n over the arc of contact because r o l l f l a t t e n i n g under the experienced stresses was u n l i k e l y to be s i g n i f i c a n t . S t i c k i n g f r i c t i o n i s assumed with the c o e f f i c i e n t of f r i c t i o n , p, a maximum. For plane s t r a i n conditions the maximum of p i s 0.577 according to Von Mises c r i t e r i o n I n order to compare the r o l l i n g data to cam plas t o - meter data, a l l e f f e c t i v e r o l l i n g stresses were converted to u n i a x i a l (31) stresses using 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] plane s t r a i n the e f f e c t i v e stress i s 1.155 times the u n i a x i a l stress [2] a Q = \ [ ( a x - a 2 ) 2 + ( a £ - aj2 + ( a 3 - o^2 ]h a + a For plane s t r a i n o Q = 1 L 2 2 a 1 - a „ = K = r=7 a = 1.155 a 1 2 V3 o o K = shear stress = mean e f f e c t i v e flow stress a = u n i a x i a l stress o 24 Figure 7 gives the v a r i a t i o n of s t r a i n rate from the entrance plane to e x i t f o r r o l l i n g according to the r e l a t i o n , _ 2f s i n (j) .. ^1 h 2 + D (1-cos <j>) 1 0 8 e h 2 where f = peripheral r o l l speed <j> = angular distance from the e x i t D = r o l l diameter A mean s t r a i n rate, as proposed by Larke , had also been shown. I t i s given: fl ' h l > = f V D ( h l - h 2 1 0 8 6 h^ where f = (IT DN)/60 N = number of revolutions per minute. The hot r o l l i n g data i s p l o t t e d i n Fig.8 i n terms of l i n e a r s t r a i n rates and stresses. In t h i s form i t i s then d i r e c t l y comparable with Alder 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 stresses and true s t r a i n s were calculated from hot t e n s i l e load-elongation data assuming uniform elongation. Fig.9a gives the r e s u l t s of two tests at a s t r a i n rate of 0.0014/sec. at 350 and 450°C. A steady state region i s observed from which a steady state flow stress can be evaluated. The s t r a i n rate was evaluated from Fig.7 V a r i a t i o n of s t r a i n rate from the entrance plane to the e x i t plane for r o l l i n g according to the r e l a t i o n . The mean s t r a i n rate f o r r o l l i n g t i s also shown, ' I 350 °C rftfi • • AAA • • • / AA m Qn • AAA/AA f250°C A /A& ROLLING DATA A250°C • 350°C o450°C • ALDER a PHILLIPS 8 10 12 cr(ksi) 14 16 Fig.8 Hot r o l l i n g data correlated i n terms of the power s t r e s s - s t r a i n rate r e l a t i o n . Alder and P h i l l i p s (10) hot compression data i s included for comparison.  2 0 0 0 L ' 5 0 0 to Q. 1000 e= . 0015 sec" 1 e = .13 sec 1 -0 T= 45 0°C 500 .02 .04 .06 .08 .10 .12 .14 16 € Fig.9b. Variation of the flow stress with strain rate for 450°C test at £ = 0.13 sec. ^ and i = 0.0015 sec. ^, oo 29 the cross head speed and the instantaneous gauge length at the i n - ception of a steady state flow region. The s t r a i n rate i n te s t i n g v a r i e d by a maximum of 10% from beginning to the end of the t e s t . The steady state flow stress i s s t r a i n rate 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 tests at two s t r a i n rates but constant tempera- ture. The steady state s t r e s s - s t r a i n rate dependence was analyzed i n three ways; log £ versus log a i n Fig.10; log £ versus a i n Fig.11; and log t versus log sinh (aa) i n Fig.12. The value of -3 -1 a = 0.3 x 10 p s i was used. This value of the material constant, (20) (28) a, was found by Wong and others to best f i t t e s t data for the same p u r i t y material to a hyperbolic sine r e l a t i o n s h i p . For com- . (2,7,10) . (14) . . , , , . parxson, compression and creep data are included f o r si m i - l a r p u r i t y m a t e r i a l . Wong's^^ extrusion data was not included f o r reasons which w i l l be discussed l a t e r . TABLE II - Published hot Working Data f o r Similar Composition Aluminum Ref. Composition (%) ^yP e a ° f -3 -1 A l Cu Mn S i Fe Deformation X 10 p s i 13 99.3 .1 .01 .12 .46 Con s t a n t a .12(250°C) . creep .21(350°C) .27(450°C) 2 99.45 .02 - .12 .31 compression .20(19) 17 99.0 compression .30 9 99.2 .1 .02 .2 .46 compression .3 (19) 11 99.99 hot t o r s i o n .31(19) 30 IC3 IO4 tX(psi) Fig.10 Steady state s t r e s s - s t r a i n rate data correlated according to the power s t r e s s - s t r a i n rate re- l a t i o n s . . n -AH/RT 3.2.2 - Power Law Figure 10 presents the hot t e n s i l e data according to a power law s t r e s s - s t r a i n rate dependence. The data points f i t s t r a i g h t l i n e s of varying slope. Table I I I l i s t s the slopes. Using the re- l a t i o n AH = - 2.3R (8 log e/8 1/T)a i n the manner suggested by (13) Garofalo an a c t i v a t i o n energy of 32.5 kcal/mole was obtained f o r a = 2000 p s i , see Fig.13. (14) Lower s t r a i n rate data of Servi and Grant f o r s i m i l a r p u r i t y material i s included for comparison to show how i n a power function p l o t the slope changes at a c r i t i c a l stress f o r a given temperature. Above a c r i t i c a l value of stress n increases. No v a r i - ation i n the n value for the t e n s i l e r e s u l t s at a given temperature was noticeable because the stress values are above the t r a n s i t i o n stress l e v e l s f o r Servi and Grant' s r e s u l t s . 3.2.3 - Exponential Law Figure 11 i l l u s t r a t e s the use of the exponential r e l a t i o n to r e l a t e the stress and s t r a i n rate dependence. Table I I I l i s t s the 3 values as a function of temperature. An a c t i v a t i o n energy of 39.5 kcal/mole f o r hot t e n s i l e deformation was obtained using the r e l a t i o n AH = 2.3R ( g - ) T ( 9 ) . . An average value —3 3o of 1.57 x 10 p s i was used f o r 3 and -r=r was evaluated at i = 0.00125/sec. 3 2 ! 0 2 0 1 - 2 3 4 5 6 7 8 9 10 cr ( k s i ) Fig.11 Steady state s t r e s s - s t r a i n rate data correlated according to the exponential s t r e s s - s t r a i n rate r e l a t i o n , . ... 3a -AH/RT e = A''e e 3,2.4 - Hyperbolic Sine Relationship The hyperbolic sine dependence of stress and s t r a i n rate i s i l l u s t r a t e d i n Fig.12 f o r the present r e s u l t s . The values of n'are l i s t e d i n Table I I I . The a c t i v a t i o n energy of 38.5 kcal/mole f or the process was calculated from the r e l a t i o n AH _ o o p / 3 log e \ , 3 log sinh (aa) . A H ~ 2 ' 3 R ( 9 log sinh ( aa) } T ( 9T/T ~ } e An average value of 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 of Similar P u r i t y Aluminum Ref. Type %A1 n t(°C) 6 ( p s i - 1 ) 1 n AH kcal/mole t e n s i l e 99.7 6 250 .00061 4 39.5 /• 3a (e a e ) 5.4 350 .00099 5 38.5 (E a sinh (aa) 8 450 .0033 7.6 32.5 (constant a ) 10 compression 99.2 26.4 250 .000873 6.7 45.7 3a (e a e ) 11.2 350 .000555 4.2 38.82(e a sinh (aa) 7.5 450 .000587 4.2 36.8 (20) 6.35 550 .000815 4.8 44.0 (3) 2 compression 99.5 9.5 300 .000463 3.5 32.7 3a (e a e ) • 7.6 400 .00056 4.05 34.5 (e a sinh (aa) 7.0 500 .00079 5 14 creep 99.3 8.23 260 .0011 9.64 50 (constant a ) 8.43 371 .0024 8.5 2.0 482 .0034 5.1 31.6 (e a sinh (aa) 18 compression 99.0 10.6 400 .00064 4.7 54.3 200 .00146 11.2 10 10" 10' sin h(ao-) io 10" Fig.12 Steady state s t r e s s - s t r a i n rate data correlated according to the hyperbolic sine r e l a t i o n , e = A ' " [ s i n h ( a a ) ] n ' e " A H / R T . - 3 - 1 a = 0.3 x 10 p s i 35 10 1 1 i i 10" 1 - V AH = - 2 3R ( ? l o S ^ ) v3 l'/T ' a = 2000 p s i . = 32.5 kcal/mole -2 10 l O " 3 l O " 4 l O " 5 1 i 1 N I 1.2 1.4 1.6 1.8 2.0 1/T, ° K _ 1 x 1 0 - 3 Fig.13 Arrhenius p l o t for hot t e n s i l e deformation at ( P l o 8 e ) g , ,„ a = 2000 p s i . DISCUSSION 36 4.1 - Hot Rolling As can be seen from Fig.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 for hot compression at 250°C i s good. However, at the higher temperatures the r o l l i n g results give 20 to 25% higher stresses than compression data for the same tempera- tures. This large difference i s attributed to the quenching effect of the r o l l s rather than the method of evaluating r o l l i n g stresses. Three facts substantiate this assumption. F i r s t , the 250°C data i s within 8% of the hot compression data which i s well within the reported accuracy of Sims' method of calculating 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 tests at a s t r a i n rate of 0.84/sec. were done with r o l l s and slab at 350°C. In these two cases the deviation from the com- pression data for 350°C was only 10%, s t i l l within the reported accur- acy of the Sims' method, yet at th i s lowest r o l l speed, the effect of a i r quenching would be highest. Thirdly, the deviation from Alder and P h i l l i p s ( 1 0 ) data increased regularly with the difference 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 stress re- s u l t s . With such limited r e l i a b l e data, neither an evaluation of the empirical s t r e s s - s t r a i n rate relationships proposed for hot working nor an activation energy determination for hot r o l l i n g i s j u s t i f i e d . The serie s of r o l l i n g experiments does, however, i l l u s t r a t e the usefulness of hot r o l l i n g as a means of evaluating hot working parameters. It also points out the important e f f e c t of r o l l quench- ing with a laboratory scale m i l l . Larger m i l l s permit the r o l l i n g of large sections i n which case the e f f e c t of r o l l quenching can probably be ignored. For true temperatures i n laboratory hot r o l l i n g , heated r o l l s at the desired r o l l i n g temperatures must be used. 4.2 - Te n s i l e Deformation 4.2.1 - True Stress - True S t r a i n Data True stresses and s t r a i n s were derived from load-elonga- t i o n p l o t s assuming uniform elongation occurred u n t i l the load began to drop. This assumption seemed j u s t i f e d when the data was compared with hot t o r s i o n data at s i m i l a r temperatures but s l i g h t l y d i f f e r e n t material p u r i t y as a i n Fig.14. The stress l e v e l f o r the t e n s i l e test i s higher than that of hot t o r s i o n but there are differences i n pur i t y and temperature. The lower material p u r i t y and tes t tempera- ture may account f o r the 25% higher steady state stress i n the hot t e n s i l e t e s t . ' In hot t o r s i o n experiments, the attainment of a steady state flow region occurs at a higher s t r a i n than f o r the t e n s i l e t e s t s . A s h i f t of the stready state region to higher s t r a i n s with (13) increasing s t r a i n rates also i s evident i n Fig.9. Others have observed t h i s behaviour. T e n s i l e 9 9.75% A l £ = 0.13 s e c " 1 T = 45Q°C torsion (12) T o r s i o n Super p u r i t y A l ' -1 e = 0.5 sec T = 4BQ UC 0. 2 0.3 0.4 . l n ± Comparison of load-elongation data f or hot tension and hot t o r s i o n (12). 39 4.2.2 - Strain Rate A constant strain rate was not imposed during testing. The strain rate in fact decreased by 10% from the beginning u n t i l the onset of steady state flow. Such a variation i s small in com- parison to the imposed rates, which diff e r by an order of magni- tude. Similar variations occur i n evaluating strain rates by either hot torsion, hot ro l l i n g , or hot extrusion. The strain rate evalu- ation here is believed to be at.:least as accurate as those in pre- vious reported work for compression and torsion. In contrast, the validity of the mean strain rate values quoted for extrusion through (9 34) a square die is questionable. In fact, Jonas and other ' state that the strain rate varies by as much as 2-3 orders of magnitude for extrusion i n a f l a t faced die. Such a large variation i s not per- missable when investigating high temperature strain rate sensitivity. Figure 10 compares the tensile data of the present work to Servi and Grant' s creep data for similar temperatures and simi- lar purity material. There i s reasonable agreement between the two sets of data in the region of overlapping strain rates, except at the lowest test temperatures, 4.2.3 - Stress Strain Rate Dependence When considering the stress-strain rate dependence of hot tensile deformation, comparison can be made with results reported * u- u - - A u - • (2,10,18) for high temperature creep and hot compression for material of similar purity and i n the same temperature range. Refer- ence may also be made to the results of Wong^2^ whose analysis of Alder and P h i l l i p s ' hot compression d a t a ^ ^ i s given in Table IV. (14) Wong i n h i s analysis chose to use Servi and Grant's creep data f o r high p u r i t y aluminum rather than a v a i l a b l e data f o r the (14) commercial p u r i t y used i n his own extrusion experiments. This was unfortunate, because Wong might have come to d i f f e r e n t conclusions had he used the creep data f o r less pure aluminum. 4.2.3.1 - Power Law Dependence A creep rate dependence on a power function of stress i s not v a l i d f o r both high and low stress creep as Fig.10 i l l u s t r a t e s . (14) The creep data of Servi and Grant does not give a l i n e a r p l o t of log e versus log a f o r any temperature. No deviation from l i n e a r i t y on a s i m i l a r p l o t occurs f o r the t e n s i l e r e s u l t s presumably because they are a l l i n the high stress region. That i s , they l i e i n the hot working range where the equiva- i *. i ' - N u v * ,(2,6,12,16,17) t . lent r e l a t i o n a = a o e has been found ' to be applicab l e . Normally i n t h i s range a power dependence of stress and s t r a i n rate gives l i n e a r r e l a t i o n s h i p s that are converging as i n Fig.15 (Ref.17). The power exponent, n, i s commonly found to be temperature dependent (see Table I II and IV). For the present t e n s i l e data t h i s was not observed as can be seen from the n values l i s t e d i n Table I I I . Ex- ponent values from both t e n s i l e tests and creep tests are s i m i l a r when the high stress creep range f o r each temperature i s considered. However, i n both these cases the exponent values were higher than the (12) 6.1 to 5 usually quoted f o r aluminum Variations of the exponent, p a r t i c u l a r l y f o r hot com- pression and creep, make the use of a power dependence equation un- suit a b l e f o r r e l a t i n g stress and s t r a i n rate at low s t r a i n rates to those at high s t r a i n rates f o r high temperature deformation. 41 FLOW STRESS, IOOO psi Fig.15 Co r r e l a t i o n of s t r e s s - s t r a i n rate data f o r hot deformation of commercial p u r i t y aluminum according to a power s t r e s s - s t r a i n rate dependence. Reference 17. TABLE IV - Wong and Jonas ,(20) Values for the Constants n, n', 3, a, A'' and AH - as determined from t h e i r extrusion r e s u l t s and Alder and P h i l l i p s h o t compression r e s u l t s . T(°C) n ( k s i , 1 ) a ( k s i v ) AH A ' " x 10 10 Ref. 320 376 445 490 555 616 13.7 8.1 6.7 5.2 4.7 4.1 4.0 4.0 4.0 4.0 4.0 4.0 1.24 1.24 1.24 1.24 1.24 1.24 .3 .3 ,3 ,3 .3 .3 37.4 .28 2 2.34 2.34 2.51 extrusion 250 350 450 550 24.4 11.2 7.7 6.5 4.2 4.2 4.2 4.2 1.24 1.24 1.24 1.24 ,3 .3 .3 .3 36.8 2.51 2.34 2.40 2.51 Hot compression ho 4.2.3.2 - Exponential Law Values of 3, as l i s t e d i n Table I I I f o r the t e n s i l e r e - s u l t s , v a r i e d f o r the 350 to 450°C t e s t s . The low 3 value f o r 250°C could i n d i c a t e that a steady state stress was not obtained at the lower s t r a i n rates before necking occurred. The 3 values are com- M - - i , - A * d 4 ) . (2,10) , parable to those reported f o r creep , compression , and ex- t r u s i o n ^ 2 ^ as l i s t e d i n Table I II and IV. The 3 values calculated by the wr i t e r from Alder and P h i l l i p s compression r e s u l t s d i f f e r from those calculated by Wong and Jonas . They found a constant 3 value of 1.24 k s i \ In the present a n a l y s i s , 3 was i n the range of 0.555 to 0.873 k s i In both cases 3 was temperature independent. Although f o r the com- pression r e s u l t s 3 v a r i e d , i t did not vary systematically with temperature so i t can be said to be temperature independent. 3 (14) values f o r the creep data were found to be s l i g h t l y temperature dependent. The magnitude of the range of s t r a i n rates p l o t t e d i n (14) Fig.11 masked the deviation from l i n e a r i t y f o r the creep data But using a smaller range of s t r a i n rate, such as G a r o f a l o , the deviation becomes apparent. As stated before, t h i s i s the reason the exponential r e l a t i o n s h i p cannot be used to r e l a t e both high and low stress creep data. 4.2.3.3 - Hyperbolic Sine Relationship Use of the hyperbolic relation f o r the t e n s i l e r e s u l t s -3 -1 gave n' values from 4 to 7.6 f o r a = 0.3 x 10 p s i . Such a v a r i a t i o n was not reported by Wong and Jonas ( * ^ f o r hot extrusion and hot c o m p r e s s i o n } see Table IV. A present re-evaluation of Alder and P h i l l i p s d a t a ^ 1 0 ^ (see Table III) gives n' values that vary from 4.2 to 6.7, although Wong^^quotes a value of 4.2 f o r a l l temperatures. In l i g h t of these discrepancies, the v a r i a t i o n i n the t e n s i l e n' value does not appear as questionable. Use of a = 0.3 x 10 3 p s i ^ i n analyzing the creep d a t i " ^ gave higher values of sinh (aa) than the t e n s i l e data f o r s l i g h t l y higher temperatures. In order to get a better f i t between the two (15) sets of r e s u l t s , a was recalculated using Garofalo's method f o r -3 -1 low and high stresses. This method gave values of 0.12 x 10 p s i , 0.21 x 1 0 - 3 p s i _ 1 , and 0.27 x 10~ 3 p s i " 1 at 2 6 0 , 371and4B2°C res- p e c t i v e l y . Applying the hyperbolic r e l a t i o n s h i p with these a values gave good f i t between the creep and t e n s i l e values, see Fig.12. Values of a f o r the t e n s i l e range could not be calculated using a = B/n because the stress l e v e l s were too high. In Table I I I the n' values are, i n the t e n s i l e to hot working range, approximately temperature independent. Use of the hyperbolic 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 rate made i t possible to extrapolate from creep to the hot working range with some effectiveness f o r s i m i l a r p u r i t y material, see Fig.12. (13) The hyperbolic equation i s said to be correct i n r e l a t i n g stress and s t r a i n rate over large stress ranges because of the equivalence of £ = A'' 1 [sinh ( a a ) ] n e A^/ R^ t o e = A'e^ a e anc\ e = Aa 1 1. If aa < 0.8, the hyperbolic r e l a t i o n approximates the power r e l a t i o n by le s s than 10% e r r o r , and n' = n. For aa > 1.2, the error i s le s s than 10% between the hyperbolic and the exponential function, and a = B/n or a = B/n' depending upon either G a r o f a l o ' s ^ 1 5 ^ or S e l l a r s and T e g a r t ' s ^ 1 9 ^ d e f i n i t i o n . For the t e n s i l e r e s u l t s , a must be le s s than 2500 p s i f o r aa < 0.8. Stress values le s s than 2500 p s i occurred i n the 450°C te s t s where n' = 8 . • and n' = 7.6, n' = n. For aa >1.2, the 250°C te s t s are applicable where n ' = 4 , n = 6 , g = 0.00061 p s i - 1 . These give a = B/n = 0.102 x 1 0 - 3 p s i _ 1 and a = g/n' = 0.12 x 10~3 p s i - 1 . —3 —1 (17 19 28) In neither case i s a equal to the 0,3 x 10 p s i which others ' ' found f o r the material constant f o r t h i s p u r i t y of aluminum. The hot compression^»-^) a n ( j c r e e p ^ 4 ^ r e s u l t s of others were analyzed i n the same way to see what a and n' values they gave and to see i f they agreed with Wong's best f i t values. The r e s u l t s are summarized i n Tables IV and V. For no one temperature does the hyperbolic r e l a t i o n approximate the power and exponential expressions by l e s s than 10% error at both low and high stresses. As a con- sequence, n' values are probably subject to some error. When considering the values of a, using a = g/n', f o r compression d a t a ^ ' " ^ S e l l a r s and Tegart' s statement that t h i s empirical constant i s independent of temperature i s substantiated. Garofalo's evaluation, a = g/n gives a's which are temperature de- pendent which substantiated h i s c l a i m . Nothing conclusive can be said about the v a r i a t i o n of a (14) values f o r creep and t e n s i l e data with temperature. The stress l e v e l s f o r both the t e n s i l e and creep r e s u l t s are i n a c r i t i c a l s tress range i n which the r e l a t i o n a = g/n' cannot be used e f f e c t i v e l y . For creep, only Garofalo's method^^^ f o r evaluating a can be used and the stress l e v e l s do not s a t i s f y aa > 1,2 for less than 10% error. 46 Instead a = 3/n i s used i n c o r r e c t l y at lower stress values. The values for Alder and P h i l l i p s compression re- s u l t s do not correspond to those found by Wong f o r the best f i t . This i s due to the d i f f e r e n t values of g and n', see Tables I I I and VI. The value of n' Wong reports f o r the 250°C l i n e i s i n error even from v i s u a l examination of his p l o t t i n g of the d a t a ^ ^ . (19) S e l l a r s and Tegart l i m i t e d the usefulness of t h e i r findings by saying that a was temperature independent only i n the -3 s t r a i n rate range they examined which extended only down to 10 /sec. i n the case of aluminum. But i n order to get the creep data to f i t an extrapolation of t e n s i l e data or compression data a must be temperature dependent, and the values used are as suggested by Garo f a l o ^ 1 " ^ . Perhaps a i s temperature dependent below a c r i t i c a l value of s t r a i n rate. 4.2.4 - A c t i v a t i o n Energy Three methods were used to ca l c u l a t e a c t i v a t i o n energies fo r the hot t e n s i l e deformation of the aluminum. Using a s t r e s s - n' —AH/RT s t r a i n rate dependence according to e = A''' [sinh (aa) ] e an a c t i v a t i o n energy of 39.5 kcal/mole was obtained; using i = A'' 3a —AH/RT e e ,38.5 kcal/mole; and using a creep type a n a l y s i s , 32.5 kcal/mole. The a c t i v a t i o n energies determined from the f i r s t two s t r e s s - s t r a i n rate dependencies are s i m i l a r as would be suspected as the hyperbolic equation approximates the exponential equation. The difference a r i s e s perhaps i n the creep determination through the use 9 l o '' ' of ( — ) a = 2000 p s i . The stress value i s possibly i n error TABLE V - Evaluation of the Stress Ranges - where the hyperbolic sine r e l a t i o n appoximates the power and experimental relationships by more than 90% accuracy, using the derived values of a, n, n', and 3 as l i s t e d i n Table I I I . a a > 1 ' 2 aa < 0.8 T°C n 3 k s i 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 p s i _ 1 26.4 .873 6.7 0.33 .13 450 11.2 .555 4.2 0.50 .13 550 6.3 4.8 -3 Ref. (14) 260 a = .12 x 10 a values not 8.23 9.64 . -3 371 a = .21 x 10 high enough 8.43 8.5 482 a = .27 x 1 0 _ 3 2.0 5.1 Ref.(2) 300 a = .3 x 10~ 3 9.5 1.1 3.5 .15 .31 a values too high 400 7.6 2.4 4.05 .32 .6 500 7.0 3.4 5 .49 .68 250 Tensile 6 .61 4 .102 .12 350 - 450 7.6 8.0 -o- f o r the low s t r a i n rate tests at 250°C as a true steady state did not e x i s t . If the 250°C data i s ignored, the creep analysis gives an a c t i v a t i p n energy of 38,5 kcal/mole which agrees with the other two values. The calculated a c t i v a t i o n energy f o r t e n s i l e deformation for the ISCD aluminum, which i s approximately 2S composition, agrees „ t . t . . (1,3,13,17,19,20,28,35) . wxth other reported actxvatxon energies » > > » » > > f o r (35) creep and hot working. Sherby and Dorn report values of 35-36 kcal/mole f o r high temperature creep of 2S aluminum. Jonas hot (28) and Wong report an a c t i v a t i o n energy of 37 kcal/mole f o r extrusion and hot compression whereas McQueen, Wong and Jonas quote 41.8 and 44.0 kcal/mole r e s p e c t i v e l y f o r the same p u r i t y m a t e r i a l . As the lower value f o r the hot extrusion i s the l a t e s t reported by one of the co-authors, t h i s value i s believed to be more co r r e c t . Since d i f f e r e n t experimental a c t i v a t i o n energy values have been quoted f o r Alder and P h i l l i p s h o t compression data, a re-evaluation of the a c t i v a t i o n energy was made here. Using an exponential s t r e s s - s t r a i n rate dependence i t was found that AH = 45.7; using a hyperbolic dependence, AH = 38.82. The former value agrees with the value of 44, determined by McQueen, Wong, (28) (20) and Jonas and the l a t e r value with that of Wong and Jonas , AH = 37. In Wong and Jonas' determination of an a c t i v a t i o n energy, they have taken l i b e r t i e s i n a r r i v i n g at n' f o r 250°C as was mentioned before. Since the hyperbolic equation i s an approxi- mation of the exponential equation, the value of 45.7 kcal/mole would not be subject to as much as error . (2) Arnold and Parker's data gave a c t i v a t i o n energies of 32.7 and 34.4 kcal/mole for exponential and hyperbolic depend- encies r e s p e c t i v e l y . Analysis of Servi and Grant's creep d a t a ^ 1 ^ f o r 2S aluminum, gave an a c t i v a t i o n energy of 50 kcal/mole for a constant stress a n a l y s i s . This compared with the value of 56.8 kcal/mole (35) determined by Sherby and Dorn from t h i s same data. For other 2S aluminum r e s u l t s they found the experimental a c t i v a t i o n energy (35) to be i n the range 35-36 kcal/mole . They a t t r i b u t e d the high a c t i v a t i o n energy i n Servi and Grant's case to the heat treatment used . (35) p r i o r 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 energies does not follow any consistent change i n composition f o r the aluminum examined. This would suggest that the a c t i v a t i o n energy for hot deformation i s not p u r i t y dependent for the composition v a r i a t i o n considered. 4.2.5 - Zener-Hollomon Parameter Jonas and others 3 »20»21) have used a form of the _i_ AH/RT Zener-Hollomon parameter, Z = e e , to r e l a t e hot working and creep data. Z i s a structure f a c t o r of the deformed material and i s a function of s t r a i n ' . The structure associated with a given value of s t r a i n i s assumed to be a constant for a l l possible combinations of s t r a i n rate and temperature which y i e l d a constant (13) value of Z . . For a constant flow region, as occurs i n hot work- ing and steady state creep, Z values are constant i n the constant flow region. The flow stress i s r e l a t e d to the value of Z. At a greater Z, a higher flow stress i s needed because few thermally activated events occur per unit s t r a i n . This a r i s e s from e i t h e r a low temperature or the shorter time for the event to occur at the 50 (3) (1 20 21) at the higher s t r a i n rate . Jonas and others ' ' have used a structure-corrected Zener-Hollomon parameter, Z/A'1', to normalize the s l i g h t v a r i a t i o n s i n the composition of the aluminum considered. They have rel a t e d t h i s s t r u c t u r e - f a c t o r corrected Zener-Hollomon parameter to the hyperbolic sine s t r e s s function as i n Fig.16. In the analysis they used a AH = 37.3 kcal/mole. Correct use of the Zener-Hpllomon parameter requires that the same a c t i v a t i o n energy be used throughout But f o r the Alder and P h i l l i p s data, Jonas and others ̂ » ^ ^ used a value of AH which d i f f e r e d from the actual experimental value (see Section '4.2.9.). Since Jonas and other ̂ ' ^ ^ have taken t h i s l i b e r t y of using the Zener-Hollpmon parameter i t was thought advantageous here to present a s i m i l a r p l o t to Fig.16 using the various calculated ex- •i • (2,10) (14) perimental a c t i v a t i o n energies for the compression , creep , and hot t e n s i l e data. The values of A''' used are l i s t e d i n Fig.17 and are comparable to the values of A' 1 ' quoted by Wong^^ as reported i n Table IV. The data points f a l l on a l i n e i n Fig.17 which l i e s almost c o - l i n e a r with the l i n e i n Figure 16. This seems rather remarkable considering the fac t that a AH value of 53.4 kcal/mole (13) was used f o r the creep data . The f i t would suggest that use of a Zener-Hollomon pl o t does not provide conclusive proof f o r the theory that hot working i s an extension of high temperature creep. (14) If f o r the Servi and Grant creep data a value of 37.3 kcal/mole i s used, the data points are orders of magnitude off the l i n e i n Fig.16. This casts further doubt on Jonas' use of the ' Zener-Hollomon parameter i n h i s argument. 51 IO' 10' IO' 10' 3f IO' IO IO* io- ta 10' ,6* ,d7l A8 10 / S L O P E 4 - 6 7 I a .299»l64 p s i " 1 j Q « 37 -3 teaJ/mol« o / IO"2 10"' 10° IO1 10' o + I k » = Creep (14) = E x t r u s i o n (20) = Compression (10 = T o r s i o n (12) Sinh (cc cr) Fig.16 Correlation of hot working data using the structure- corrected Ziner-Hollomon parameter and the hyperbolic sine stress function. Reference (1). 52 10 1 10' I0 : 10' io- 10' N 10" 10' 10 s 10 4 • SERVI a GRANT (14) o ARNOLD 8 PARKER(?) • ALDER 8 PHILLIPS (10) A INSTRON DATA 9 i' 10 10 I0U 10' sin h[aa) 10 io Fig.17 Zener-Hollomon pl o t using actual experimental a c t i v a t i o n energies. 'The data can be i n t e r - preted as two. slopes(s61id l i n e s ) or one slope (dotted l i n e ) . S2A T°C A » " s e c * 1 H k c a l / m o l e • 26.0 i o x i o 1 9 53.4 371 2,93 x XQir 4 8 2 3 x 1 0 1 4 0 © 1 1 8*8 x I O 9 34.4 a 2 S 0 8.2 x 1 0 2 3 8 . 0 2 350 5.53 x I O 1 0 4 S 0 6.4S x I O 1 0 A a l l 5.855 x I O 1 1 3 8 . S 53 CONCLUSIONS 1. It has been suggested by others that hot working is 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 in 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 in the stress-strain rate relation must change in going from creep to hot working. Secondly, the activation energy is found to vary. 2. A hyperbolic sine relationsip £ = •A''* [sinh (aa)]" e ̂H/RT̂ can be used to relate the hot working parameters but i t is 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 critical value of strain rate, i t is possible to ex- trapolate approximately from high temperature creep to hot working, n' 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 in the strain rate range considered. 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