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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., University of British Columbia, 1968. A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCE in the Department of METALLURGY We accept this thesis' as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA February, 1971 In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the Head of my Department or by his representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Department of Metallurgy The University of British Columbia Vancouver 8, Canada Date May 6, 1971 i ACKNOWLEDGEMENT The author is 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 their helpful discussions and advice. Financial assistance was received in the form of assistant-ships from the Defence Research Board under grants 9535-41 and 7501-02. This financial assistance is gratefully acknowledged. ABSTRACT It has been suggested by others that hot working is an extension of high temperature creep because of the similar observed dependencies of stress, strain rate, temperature and the similar acti vation energies of the two types of deformation. This suggestion has been evaluated for commercial purity aluminum by obtaining stress, -4 strain rate and temperature data in the strain rate range 10 to 10^/second. Published hot compression, hot torsion, and high tempera ture creep work of others is used to provide supplementary data. A combination of the published work of others with the present experi--7 +2 mental work provides data in the strain rate range 10 to 10 /second. From the present analysis, contradictions arise against the theory that hot working is an extension of high temperature creep. First, the method of evaluation of the material constant a in the hyperbolic n' —AH/RT stress-strain rate relation, e = A'T'[sinh (aa)] e , must change in going from creep to hot working. Secondly, the activation energy varies. Those that have suggested that hot working is an extension of high temperature creep found that a and the activation energy were independent of strain rate. Their work is compared to the present analysis and many discrepancies were found. The work in the literature left a data gap in the strain -3 0 rate range 10 to 10 /second. Hot tensile tests and hot rolling tests were used to provide data in this gap. iii TABLE OF CONTENTS Page INTRODUCTION 1 1.1 - Experimental Techniques 2 1.1.1 - Scaled-down Industrial Processes .... 2 1.1.2 - Tensile Tests1.1.3 - Compression Tests 3 1.1.4 - Hot Torsion1.2 - 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 Relationship1.4 - Temperature Dependence 9 1.5 - Recovery Mechanisms 12 1.5.1 - Screw Model 3 1.5.2 - Climb Models .. 14 1.6 - Scope of Present Investigation 15 EXPERIMENTAL 17 2.1 - Material Preparation .. .. 1iv Page 2.1.1..- Rolling Procedure 18 2.1.2 - Load Measurement2.1.3 - Lubrication 18 2.2 - Tensile Testing 20 2.2.1 - Material 22.2.2 - Heating 1 2.2.3 - Testing Procedures 2RESULTS • • • • 23 3.1 - Rolling 23.2 - Tensile Data 24 3.2.1 - Stress Analysis 23.2.2 - Power Law 31 3.2.3 - Exponential Law 33.2.4 - Hyperbolic Sine Relationship 33 DISCUSSION 36 4.1 - Hot Rolling4.2 - Tensile Deformation 37 4.2.1 - True-Stress - True Strain Data 37 4.2.2 - Strain Rate 39 4.2.3 - Stress-Strain 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 - Activation Energy 46 4.2.5 - Zener-Hollomon Parameter 49 CONCLUSIONS 53 BIBLIOGRAPHY 55 VI 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 42 V Evaluation of the Stress Ranges where the Hyperbolic Sine Relation is more than 90% Accurate 47 LIST OF FIGURES vii Figure Page 1 Comparison of stress versus strain curves de rived from different test methods for: (a) low-carbon steel at 1100°C and (b) Fe-25% Cr alloy at 1100°C. Reference (1) .. 4 2 Variation 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, torsion, and creep data. The data is plotted according to a hyperbolic sine relationship. Reference (20). •• 10 4 Experimental set-up for hot rolling. •• •• •• •• 19 5 Typical load trace for hot rolling. # 19 6a Experimental set-up for hot tensile tests . • • . 22 6b Typical load trace for hot tensile testing . • • • 22 7 Variation of strain rate from the entrance plane to the exit plane for rolling according to the relation. The mean strain rate for rolling e, is also shown . . . 25 8 Hot rolling data correlated in terms of the power stress-strain rate relation. Alder and Phillips (10) hot compression data is included for comparison. . . 26 9a Variation of the flow stress with temperature for tests at e = 0.0014 sec.-l at 350°C and 450°C. 27 9b Variation of the flow stress with strain rate for 450°C tests at i = 0.13 sec"! and e = 0.0015 sec.-1 28 10 Steady state stress-strain rate data correlated according to the power stress-strainrate re lations e = Aane-^H/RT. 30 viii Figure Page 11 Steady state stress-strain rate data correlated according to the exponential stress-strain rate, £ = A"e^e" AH/RT_ 32 12 Steady state stress-strain rate data correlated according to the hyperbolic sine relation, e = A"'[sinh (ao) ]n'e-AH/RT. a = 0.3 x 10"3 psi-1. 34 13 Arrhenius plot for tot tensile deformation 35 14 Comparison of load-elongation data for hot tension and hot torsion (12). 38 15 Correlation of stress-strain rate data for hot deformation of commercial purity aluminum accord ing to a power stress-strain rate dependence. Reference 17. .. 41 16 Correlation of hot working data using the structure-corrected Zener-Hollomon parameter and the hyper bolic sine stress function. Reference (1) 51 17 Zener-Hollomon plot using actual experimental acti vation energies 52 1 INTRODUCTION Hot working, in practice, involves large reductions, at 3 high rates of strain (0.1 to 10 /sec), and at temperatures above approximately one-half the absolute melting temperature. It is used extensively in industry because these large reductions can be accom plished at low working stresses without intermediate anneals. The fact that large strains can be achieved with little or no strain harden ing suggests that dynamic softening processes are balancing the strain hardening ^ . For commercial purity aluminum as well as for other pure metals and simple alloys, the flow stress at a particular temperature (2) increases as the rate of deformation is increased . Similarly, if the strain rate is kept constant, the flow stress decreases as the (2) temperature is increased . Therefore, to determine optimum hot work ing conditions the relationship between stress, strain, strain rate and temperature,must be known. The interrelation between these para meters depends on the deformation and recovery mechanisms involved. Considerable attention has been paid to the development of (3-5) tests for evaluation of the hot working parameters . In the ideal hot working experiment, the specimens are deformed uniformly at a constant rate and temperature with a continuous measurement of load or stress. If structural observations are to be made, the specimen must be de formed in a single operation and immediately quenched to avoid structural changes during cooling. In the hot working range of strain rates (3) adiabatic heating may occur but it is usually neglected . The tests used are scaled-down industrial processes, tensile tests, compression (3—6) tests, or hot torsion . 1.1 - Experimental Techniques 1.1.1 - Scaled-down Industrial Processes Scaling down of industrial processes is a useful approach because the mode of deformation in the test and the practical working operation are one and the same. But these processes all involve non-uniformity of deformation and require numerous assumptions in the analysis /in to get true strain rate, strain and stress values. In hot rolling for example, the strain rate changes along the arc of contact. An average strain rate must be assumed. Calculation of the deforming stress is based upon an assumption of sticking friction which may not (8) be constant . The deforming stress cannot be calculated as a function (8) of strain . In extrusion, the strain rate is similarly non-(3-9) uniform , and the stress cannot be precisely calculated. 1.1.2 - Tensile Tests Conventional tensile testing equipment does not provide a suitable strain rate range. For a constant strain rate test, the ex-: da tension rate must be varied as (1/&) (~j^r) » where £ is the gauge length of the specimen, to permit a precise analysis of a, stress E, strain e, at (5,6) (5 6) strain rate and T, temperature ' ' . When tensile testing is done at temperatures above 0.51^, specimens neck typically at 10-30% strain Methods have been devisedto analyze the necked region thus enabling de formation to be carried to true strains of (2). However, these methods are very complex. 1.1.3 - Compression Tests (3-5) Compression tests , normally uniaxial, can be used to evaluate stress up to true strains of 2.3. Test machines that give a (2 9) constant strain rate have been devised, such as Orowan's Cam Plastometer' • However, lubricants must be used to eliminate friction between the platens A ^ • (3-5,10) and the specimen , 1.1.A - Hot Torsion Hot torsion tests on thin-walled tubes give flow curves at -3 3 constant true strain rates in the range 10 to 10 /sec. Strain of (3 11 12) up to 20 can be obtained before fracture ' . For solid torsion specimens the strain and strain rate vary from a maximum at the surface (9) to zero at the centre . Solid specimens are generally used, and only the surface strain rate and stresses examined. This is done on the assumption that the outer layer makes the major stress contribution be cause it work hardens more. This assumption seems justified when con sidering Fig.1(1), after Rossard and Blain, which compares torsion data with tension and compression data. 1.2- Steady State Deformation As can be seen from Fig.l, the flow curves for high tempera ture tension, compression and torsion tests exhibit an initial harden-(2 10 12) ing portion up to a true strain of usually 50-100% ' ' . This Is followed by a region of "steady state" where the stress is essentially independent of strain. The level of this steady state flow stress de creases with increasing temperature and with decreasing strain Such a dependence of flow stress indicates that hot working is a thermally activated process. 4 Fig.l Comparison of stress versus curves derived from different test methods for: (a) low-carbon steel at 1100°C and (b) Fe- 25% Cr alloy at 1100°C. Ref erence (1) . » —8 High temperature creep deformation in the range of 10 to 10 /sec. ' is an example of similar steady state deformation. For constant stress creep, after an initial transient the strain increases linearly with time, 1.3 - Empirical Flow Stress Relationships A number of mathematical expressions have been proposed to describe the relationship between stress and strain rate for high temperature steady state deformation. 1.3.1 - Power Relationship * • -, „. • A n -AH/RT A simple power relationship, e = A^a e , where AH is the apparent activation energy^ for the rate-controlling thermally activated process, has been found to fit available creep data for low (13) stresses . In an intermediate range of stresses, the equation e = ^Q^n nas been found to fit experimental creep data^"^'^^ for a fixed temperature. In this case however, the stress exponent n may,or may not be, a function of temperature, depending on the stress level. For low creep stresses n is constant ^\ for high stresses n is tempera-(3) ture dependent . The factor Aq may also be temperature dependent. (15) For commercial purity aluminum Garofalo reported that n varied from 6.1 to 5 in the temperature range 0.51 to 0.575 T . Fig.2 (Ref.15) illustrates a plot of log a versus log e for some creep data. It illustrates that the power relationship has only limited applicability because at a critical stress value, n for a particular temperature [1] In this paper the term activation energy refers to the apparent activation energy. 6 Fig.2 Variation of log minimum creep rate with (a) log a, (b) a, and (c) log sinh (ao) for aluminum. Refer ence (15). 7 increases. In the presentation of hot working data it is more .N common to apply the equivalent power law a = aQe which is an anomaly according to creep theory,. In this case, both o"o and N are found to be a function of temperature for steady state deformation. The equation has been used to correlate results from compression^'"^'"*"^, torsion^'"^ and extrusiontests. For commercial purity aluminum, N varies from 0.04 to 0.2 in the range 0.55 to 0.9 T (2>10»12>16>17)# m An equation in which the constants are a function of temperature is not useful as an indicator 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 empirically for high stress creep '"'""'^ in commercial purity aluminum and for hot (1 2 6 18) working data at high stresses ' > » . The relationship becomes in valid at high temperatures where the stresses are low, however, and (3) this presents difficulties in the calculation of an activation energy In the case of aluminum and its alloys the parameter A' has (13) been found to be constant at constant temperature. The value of : (13) g has been found to be relatively independent of temperature in the temperature range 0.45 to 0.65 T^ but decreases with increasing tempera ture above the range^^'"*"7. Fig. 2^"^ illustrates how the exponent ial law is only applicable in a limited stress range and fails at low stresses. 1.3.3 - Hyperbolic Sine Relationship Garofalo(13,15) ^as suggested an equation to cover the dependence of steady state creep rate on stress at constant temperature for both high and low stresses. It is of the form e = A'' [sinh (aa)]n where AT' and a are constant and n = n', The product aa is unitless, a in psi ^ and a in psi. If aa> 1.2 (high stresses), the difference . aa between sinh (aa) and ^ is less than 10% and the hyperbolic sine equation is approximated by e = ^—7 e n a°. This is the same as 2n e = A' e^° where ^—7- = A' and a = B/n. The equation e = A' e^° has 2n been shown to satisfy the experimental dependence of creep rate for high n' stresses, so therefore, does e = A''[sinh (aa)] . For aa< 0.8 (low stresses), the difference between sinh (aa) and aa is less than 10% and e = A'1[sinh (aa)]n can be approximated by e = A''an an which re duces to e = Aa11 for 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 relation a = B/n defines a. Therefore, in Garofalo's analysis, creep data at both high stresses (for determination of B ) and at low stresses (for determination of n) must be available for the evaluation of a. Since n = n', n' is also tempera ture dependant. (19) Sellars 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 critical value, his interpretation was inadequately supported. His interpretation would predict a temperature dependence of the activation energy for creep which is not observed experimentally in 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 ' in attempts to analyse hot working test results, have adopted Sellars and Tegart's version of the empirical relationship. They have evaluated the constants a and n' by plotting log e versus sinh aa for various imposed values of a. The value of a that gave a constant value of n' for the temperature range examined was taken as the correct value of a. Wong^^ used this approach to evaluate a for the hot ex trusion of aluminum. He used the relation a = $/n' to evaluate £. The value of nT used by Wong was based on results at his 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 in the same metal. Implying that the hot working of aluminum is an ex tension of high temperature creep, Wong^^ used the hyperbolic sine relationship to construct plots such as Fig.3. Other published work u A i '"• v - u - i • A (1,3,17,20,21) 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 activation energies of the processes. In steady state creep the activation energy is deter mined in the following way. From conventional creep tests the variation of log i with T at constant stress is found. A plot of this variation gives a straight line whose slope yields a value of AH, the experimental acti vation energy, if one assumes for steady state creep constant structure (13) factors which are only stress dependent . That is: ^2f£ = - AH/2.3R 9 T For hot working it is more difficult to conduct a test at constant flow stress over large strains. To evaluate the activation 10 •I J f .'I //./// // Ji ulljJi Ji iii /.ml 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, torsion and creep data. The data is plotted according to a hyperbolic sine relation ship. Reference (20). 11 energy at constant stress thus requires extensive extrapolation, as can be seen from Fig.3. An alternative approach based on the method (22) (19 20 21) of Conrad has been proposed ' ' . One starts with e = A''' ^ ? ^ j [sinh (aa)] e where A''', a, n' are constants independent of temperature and strain rate. AH = RT [ln A'" + n' In sinh (aa) - lne] d AH = RT [ n' - ( • ^ r ^ ) 1 (D (aa) ^ d ln sinh (aa) V 9 ln sinh T d AH = _ RT2 f , (og)^ + RTn' (2) d ln sinh (aa) V 9 ln sinh (aa) J RT t equate (1) and (2) RT r , C? lne -I _ RT2 /3-1/T "\ ,AlL , [n " ^9 ln sinh (aa)^ J - - RT ^ ln sinh (aa) J V + RTn 12 ATT o OT> f 3 log £ "\ /" 3 log [sinh (aa)] ^ Each of the terms in parenthesis is 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, it has been found ' ' ' to fit ex perimental data. TABLE I - Activation Energies AH (kcal/mole) Self Diffusion Hot Working Creep (23) (1) (13) 33 37 33-36 Table I reveals a similarity among the activation energies for creep, hot working,and self diffusion for aluminum. On this basis (1 3 20) it has been concluded ' ' that the rate controlling mechanisms are similar. Various models based upon recovery mechanisms have been pro posed that relate the activation energy of hot working to that of self e va (25) diffusion. They ar  vacancy migration models , climb models and jogged screw models 1.5 - Recovery Mechanisms For high temperature deformation of aluminum, dynamic re-(1,3) covery is considered to be the softening mechanism ' . This is based upon optical, X-ray microbeam and electron microscopy evidence. A number of models have been presented to explain high temperature deformation based upon dynamic recovery. In all of these models the activation energy is that of self diffusion. They are primarily proposed for the creep range of strain rates but since there are simi larities in the case of aluminum between creep and hot working with regard to the microstructural change, the activation energy and the stress-strain rate dependence, the creep theories can be considered for hot working. The rate controlling processes in hot working of aluminum are assumed to be climb and the motion of jogged screw dislocations^7 1,5.1 - Screw Model motion of jogged screw dislocations. The jogs have to move non-con-servatively and create or acquire vacancies. This process will re-^ strain the movement of the jogged dislocations, and must be accomplished by means of self diffusion. The model is based upon the effect of the applied stress moving the jog. A calculation of the speed of the jog as a function of the steady state stress and temperature of the form: The model (25,27) is based upon the diffusion controlled e = Ap D sinh ( s s a b X 2KT ) e -U/KT where A = a constant p = density of mobile screw dislocation s J 3 = constant x a a = applied stress X = average jog spacing b = Burgers Vector D = diffusion Coefficient U = activation Energy p must vary as p a a , which is essentially an adjustment parameter; s s where a is the applied stress. the observed stress dependence of creep rates as given by Garofalo's empirical expression for steady state creep of aluminum. Values of the constants were found to be realistic and the temperature dependence was in the diffusion coefficient. 1.5.2 - Climb Models These models depend upon geometrical patterns of dis locations, the details of which are not accurately known^\ and the (27) models are highly idealized. Weertman proposed a theory based upon the operation of Frank-Read sources on different parallel slip planes. The dislocations climb from adjacent loops and annihilate each other, thus permitting further dislocation 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 = diffusion coefficient T = applied stress N = density of dislocations taking part in climb G = shear modulus k = Boltzman's constant and for both high and low stresses _1 ,2 2 _ /, 3.5. 1.5 CATD .,rv3T b e = __—_ smh [ —r~TT J G b • 8G N2 kT C' = a constant 1.6 - Scope of Present Investigation Past investigations of the hot deformation of commercial purity aluminum (1-3, 10, 12, 14, 17, 20, 21, 28) have been done only in a limited strain rate range. No one researcher has done work in —5 2 the range from creep (10 /sec.) to hot working (10 /sec). In their analysis, prior workers have relied on the publications of other in vestigators to obtain creep or hot working data. Moreover there is a -3 0 data gap in the strain rate range 10 to 10 /sec. In the present -4 work, stress-strain rate data were obtained in the tensile range 10 2 to 10 /sec and beyond. Two types of experiments were used to obtain a strain rate variation of 10"*. Hot rolling, for which earlier published data was not available, was used for strain rates in the range 0.5 to 10 /sec and tensile testing for the range 10 to 10 /sec. The proposition that hot working is an extension of high temperature creep can be better discussed if data are available in the^' strain rate range between creep and hot compression. If the proposition is correct, the same stress-strain rate dependence should be observed -5 2 over the entire range from 10 to 10 /sec. and a common activation energy should apply. EXPERIMENTAL Low strain rate tensile tests were performed at constant crosshead speed in an Instron machine. High strain rate tests were performed on a laboratory size Stanat rolling mill (with 4.1 inch diameter rolls). In both cases the test temperatures were 250, 350 and 450°C. 2.1 - Material Preparation Rolling slabs were cast from Alcan ISCD aluminum with a nominal composition of 99.75% Al, 0.16% Fe, 0.06% Si, and 0.03% maximum total residuals. The melting stock, cast Properzi rod, was melted under reducing conditions to minimize oxide formation. Slabs were cast from 740°C in a carbon coated mould. The cast ingots were 2.5 x 0.625 x 5 inches. In order to control grain size and to eliminate the cast structure, each ingot was cold rolled and annealed. The rolling schedule consisted of a series of 20% cold reductions followed by air anneals at 375°C for 25 minutes until a thickness of 0.200" was reached This gave a VPN hardness of 25, which is typical of the commercial "0" temper hardness of the material. The finished slabs were then cut to 2 inch lengths and end-milled to a width of 2.25 inches. Finally, the slabs were anodized in caustic soda. In the hot rolling experiments the slabs were reduced 50% to 0.100 inch thickness in one pass. Such a large reduction in one pass required that the front edge of the slabs be tapered in order to facilitate the entrance into the roll gap. 18 2.1.1 - Rolling Procedure Figure 4 illustrates the equipment used in rolling. Each specimen was put inside the furnace and soaked over 5 minutes at the desired temperature before being pulled into the roll gap. Rolling was done at 4 peripheral roll speeds - 0.6, 3.66, 7.32 and 14.64 in/sec. In order to lessen the temperature gradient between the slab and the rolls, the rolls were heated by electric resistance elements situated in the roll cores. The mill bearings were cooled with a pressurized circulating oil. The roll temperature was 250°C for all experiments except those in which a roll speed of 0.6 in/sec. was used, in which case the temperature was 350°C. The roll surface temperature was measured by a surface contact thermocouple mounted on the top roll. 2.1.2 - Load Measurement The roll separating force was measured by means of electric resistance strain gauge elements (force washers) situated under the bearing blocks. The strain was measured on a 4-arm strain bridge and re corded on a storage oscilloscope. The scope was triggered by the first increment of load. Figure 5 is a typical recorded load trace. The force washers were individually calibrated in an Instron. Since the load to be measured in rolling was applied to both washers, it was assumed that the individual loads, in calibration, were additive. 2.1.3 - Lubrication The hot rolling of aluminum presents a problem in that 19 Fig.5 Typical load trace for hot rolling. 20 clean aluminum surfaces readily bond to steel rolls. On an in dustrial scale, this is overcome by flood lubrication. On a labora tory scale, lubrication is complicated in that reliable hot rolling load analysis requires the presence of sticking friction over the arc of contact. A compromise must be made by using a lubricant that allows sticking friction to take place but eliminates adhesion. Oil, carbowax, and a colloidal suspension of graphite were tried, but all were found unsuitable. They could not be applied to the rolls in a reproducible manner and the friction force varied. Anodising of the slabs provided the most acceptable solution,in that sticking friction occurred, the conditions were reproducible, and adhesion of the aluminum to the rolls was almost nonexistent. The oxide provided by anodising did not contribute to a reduction in the co efficient of rolling friction, and as such should not be described as a "lubricant". 2.2 - Tensile Testing 2.2.1 - Material Tensile specimens were made from the same ISCD aluminum as used for rolling slabs, but in the form of 3/8 inch diameter rod hot rolled from Properzi rod by the supplier. Specimens were machined with a uniform gauge portion of 0.160 inches diameter and 1.125 inch gauge length. After machining, the specimens were annealed for lh hours at 500°C, and finally cleaned in a phosphoric acid "bright dip" solu tion. 2.2.2 - Heating Figure 6 shows the arrangments for tensile testing. The specimen was loaded into the furnace and grips, then allowed 40 minutes to stabilize before pulling. A thermocouple was situ ated in the furnace at the midpoint of the tensile specimen. 2.2.3 - Testing Procedures Low strain 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 cell was connected to an oscilloscope strain bridge. The load-elongation curve was recorded on the storage scope. Figure 6 illustrates a typical load-elongation curve obtained in this manner. Fig.6 b. Typical load trace for hot tensile testing. RESULTS 23 3.1 - Rolling The roll separating force was converted to an effective (29) material flow stress using Sim's semi-empirical hot rolling formula , P = Kb V R(h^ - h2)' x Q, where P is the roll load, k the mean effective flow stress is plane strain, b the strip width, R the roll radius, h^ the entrance thickness, h^ the exit thickness, and Q is a geometric roll factor. The roll load, P, is the area under the curve of the 56X11 s dd>, where d> entrace ' is the contact angle and s is the normal roll pressure. The geometric factor is a function of R/h^ and the reduction. Tables of calculated (8) Q values are available . The use of a mean effective flow stress is justified because the strain rate decreases along the arc contact (8) and this counteracts strain hardening In the load calculation no correction was made for roll distortion over the arc of contact because roll flattening under the experienced stresses was unlikely to be significant. Sticking friction is assumed with the coefficient of friction, p, a maximum. For plane strain conditions the maximum of p is 0.577 according to Von Mises criterionIn order to compare the rolling data to cam plasto-meter data, all effective rolling stresses were converted to uniaxial (31) stresses using Von Mises Distortion Energy criterion , i.e. in [2] plane strain the effective stress is 1.155 times the uniaxial stress [2] aQ = \ [(ax - a2)2 + (a£ - aj2 + (a3 - o^2 ]h a + a For plane strain oQ = 1 L 2 2 a1-a„ = K= r=7 a = 1.155 a 1 2 V3 o o K = shear stress = mean effective flow stress a = uniaxial stress o 24 Figure 7 gives the variation of strain rate from the entrance plane to exit for rolling according to the relation , _ 2f sin (j) .. ^1 h2 + D (1-cos <j>) 108 e h2 where f = peripheral roll speed <j> = angular distance from the exit D = roll diameter A mean strain rate, as proposed by Larke , had also been shown. It is given: fl ' hl >= fVD(hl - h2 108 6 h^ where f = (IT DN)/60 N = number of revolutions per minute. The hot rolling data is plotted in Fig.8 in terms of linear strain rates and stresses. In this form it is then directly comparable with Alder and Phillips compression data^^ at the same temperatures. 3.2 - Tensile Data 3.2.1 - Stress Analysis True stresses and true strains were calculated from hot tensile load-elongation data assuming uniform elongation. Fig.9a gives the results of two tests at a strain rate of 0.0014/sec. at 350 and 450°C. A steady state region is observed from which a steady state flow stress can be evaluated. The strain rate was evaluated from Fig.7 Variation of strain rate from the entrance plane to the exit plane for rolling according to the relation. The mean strain rate for rolling t is 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 rolling data correlated in terms of the power stress-strain rate relation. Alder and Phillips (10) hot compression data is included for comparison. 2000 L '500 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 in ception of a steady state flow region. The strain rate in testing varied by a maximum of 10% from beginning to the end of the test. The steady state flow stress is strain rate dependent as Fig.9b illustrates for typical tests at two strain rates but constant tempera ture. The steady state stress-strain rate dependence was analyzed in three ways; log £ versus log a in Fig.10; log £ versus a in Fig.11; and log t versus log sinh (aa) in Fig.12. The value of -3 -1 a = 0.3 x 10 psi was used. This value of the material constant, (20) (28) a, was found by Wong and others to best fit test data for the same purity material to a hyperbolic sine relationship. For com-. (2,7,10) . (14) . . , , , . parxson, compression and creep data are included for simi lar purity material. Wong's^^ extrusion data was not included for reasons which will be discussed later. TABLE II - Published hot Working Data for Similar  Composition Aluminum Ref. Composition (%) ^yPe a °f -3 -1 Al Cu Mn Si Fe Deformation X 10 psi 13 99.3 .1 .01 .12 .46 Constanta .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 torsion .31(19) 30 IC3 IO4 tX(psi) Fig.10 Steady state stress-strain rate data correlated according to the power stress-strain rate re lations . . n -AH/RT 3.2.2 - Power Law Figure 10 presents the hot tensile data according to a power law stress-strain rate dependence. The data points fit straight lines of varying slope. Table III lists the slopes. Using the re lation AH = - 2.3R (8 log e/8 1/T)a in the manner suggested by (13) Garofalo an activation energy of 32.5 kcal/mole was obtained for a = 2000 psi, see Fig.13. (14) Lower strain rate data of Servi and Grant for similar purity material is included for comparison to show how in a power function plot the slope changes at a critical stress for a given temperature. Above a critical value of stress n increases. No vari ation in the n value for the tensile results at a given temperature was noticeable because the stress values are above the transition stress levels for Servi and Grant' sresults. 3.2.3 - Exponential Law Figure 11 illustrates the use of the exponential relation to relate the stress and strain rate dependence. Table III lists the 3 values as a function of temperature. An activation energy of 39.5 kcal/mole for hot tensile deformation was obtained using the relation AH = 2.3R ( g - )T ( 9 ) . . An average value —3 3o of 1.57 x 10 psi was used for 3 and -r=r was evaluated at i = 0.00125/sec. 32 !02 0 1-2 3 4 56 7 89 10 cr (ksi) Fig.11 Steady state stress-strain rate data correlated according to the exponential stress-strain rate relation, . ... 3a -AH/RT e = A''e e 3,2.4 - Hyperbolic Sine Relationship The hyperbolic sine dependence of stress and strain rate is illustrated in Fig.12 for the present results. The values of n'are listed in Table III. The activation energy of 38.5 kcal/mole for the process was calculated from the relation AH _ o op / 3 log e \ , 3 log sinh (aa) . AH ~ 2'3R ( 9 log sinh (aa)} T ( 9T/T ~ } e An average value of n = 5.6 was used. TABLE III - The Constants n, n', 3 and AH for Tensile, Compression  and Creep Data of Similar Purity Aluminum Ref. Type %A1 n t(°C) 6 (psi-1) 1 n AH kcal/mole tensile 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 stress-strain rate data correlated according to the hyperbolic sine relation, e = A'"[sinh (aa)]n'e"AH/RT. -3-1 a = 0.3 x 10 psi 35 10 1 1 i i 10"1 - V AH = - 2 3R (? loS ^ ) v3 l'/T ' a = 2000 psi. = 32.5 kcal/mole -2 10 lO"3 lO"4 lO"5 1 i 1 N I 1.2 1.4 1.6 1.8 2.0 1/T, °K_1 x 10-3 Fig.13 Arrhenius plot for hot tensile deformation at ( P lo8 e ) g , ,„ a = 2000 psi. DISCUSSION 36 4.1 - Hot Rolling As can be seen from Fig.8, the fit of the present rolling data to Alder and Phillips data for hot compression at 250°C is good. However, at the higher temperatures the rolling results give 20 to 25% higher stresses than compression data for the same tempera tures. This large difference is attributed to the quenching effect of the rolls rather than the method of evaluating rolling stresses. Three facts substantiate this assumption. First, the 250°C data is within 8% of the hot compression data which is well within the reported accuracy of Sims' method of calculating hot (31 32 33) rolling stresses ' ' . For this temperature of rolling both the slab and the rolls were at the same temperature, 250°C. Secondly, two tests at a strain rate of 0.84/sec. were done with rolls and slab at 350°C. In these two cases the deviation from the com pression data for 350°C was only 10%, still within the reported accur acy of the Sims' method, yet at this lowest roll speed, the effect of air quenching would be highest. Thirdly, the deviation from Alder and Phillips(10) data increased regularly with the difference in temperature between the slab and the rolls. Consequently, the stresses derived from rolling data at 350 and 450°C may be considered erroneous. Only the 250°C data is believed to give reliable working stress re sults. With such limited reliable data, neither an evaluation of the empirical stress-strain rate relationships proposed for hot working nor an activation energy determination for hot rolling is justified. The series of rolling experiments does, however, illustrate the usefulness of hot rolling as a means of evaluating hot working parameters. It also points out the important effect of roll quench ing with a laboratory scale mill. Larger mills permit the rolling of large sections in which case the effect of roll quenching can probably be ignored. For true temperatures in laboratory hot rolling, heated rolls at the desired rolling temperatures must be used. 4.2 - Tensile Deformation 4.2.1 - True Stress - True Strain Data True stresses and strains were derived from load-elonga tion plots assuming uniform elongation occurred until the load began to drop. This assumption seemed justifed when the data was compared with hot torsion data at similar temperatures but slightly different material purity as a in Fig.14. The stress level for the tensile test is higher than that of hot torsion but there are differences in purity and temperature. The lower material purity and test tempera ture may account for the 25% higher steady state stress in the hot tensile test. ' In hot torsion experiments, the attainment of a steady state flow region occurs at a higher strain than for the tensile tests. A shift of the stready state region to higher strains with (13) increasing strain rates also is evident in Fig.9. Others have observed this behaviour. Tensile  9 9.75% Al £ = 0.13 sec"1 T = 45Q°C torsion (12) Torsion Super purity Al' -1 e = 0.5 sec T = 4BQUC 0. 2 0.3 0.4 .ln± Comparison of load-elongation data for hot tension and hot torsion (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 until the onset of steady state flow. Such a variation is small in com parison to the imposed rates, which differ by an order of magni tude. Similar variations occur in evaluating strain rates by either hot torsion, hot rolling, 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 in a flat faced die. Such a large variation is 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 is 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 in the same temperature range. Refer ence may also be made to the results of Wong^2^ whose analysis of Alder and Phillips' hot compression data^^ is given in Table IV. (14) Wong in his analysis chose to use Servi and Grant's creep data for high purity aluminum rather than available data for the (14) commercial purity used in his own extrusion experiments. This was unfortunate, because Wong might have come to different conclusions had he used the creep data for less pure aluminum. 4.2.3.1 - Power Law Dependence A creep rate dependence on a power function of stress is not valid for both high and low stress creep as Fig.10 illustrates. (14) The creep data of Servi and Grant does not give a linear plot of log e versus log a for any temperature. No deviation from linearity on a similar plot occurs for the tensile results presumably because they are all in the high stress region. That is, they lie in the hot working range where the equiva-i *. i ' -N u v * ,(2,6,12,16,17) t . lent relation a = ao e has been found ' to be applicable. Normally in this range a power dependence of stress and strain rate gives linear relationships that are converging as in Fig.15 (Ref.17). The power exponent, n, is commonly found to be temperature dependent (see Table III and IV). For the present tensile data this was not observed as can be seen from the n values listed in Table III. Ex ponent values from both tensile tests and creep tests are similar when the high stress creep range for each temperature is considered. However, in both these cases the exponent values were higher than the (12) 6.1 to 5 usually quoted for aluminum Variations of the exponent, particularly for hot com pression and creep, make the use of a power dependence equation un suitable for relating stress and strain rate at low strain rates to those at high strain rates for high temperature deformation. 41 FLOW STRESS, IOOO psi Fig.15 Correlation of stress-strain rate data for hot deformation of commercial purity aluminum according to a power stress-strain rate dependence. Reference 17. TABLE IV - Wong and Jonas ,(20) Values for the Constants n, n', 3, a, A'' and AH - as determined from their extrusion results and Alder and Phillipshot compression results. T(°C) n (ksi,1) a (ksi 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 listed in Table III for the tensile re sults, varied for the 350 to 450°C tests. The low 3 value for 250°C could indicate that a steady state stress was not obtained at the lower strain rates before necking occurred. The 3 values are com-M - -i, - A * d4) . (2,10) , parable to those reported for creep , compression , and ex-trusion^2^ as listed in Table III and IV. The 3 values calculated by the writer from Alder and Phillips compression results differ from those calculated by Wong and Jonas . They found a constant 3 value of 1.24 ksi \ In the present analysis, 3 was in the range of 0.555 to 0.873 ksi In both cases 3 was temperature independent. Although for the com pression results 3 varied, it did not vary systematically with temperature so it can be said to be temperature independent. 3 (14) values for the creep data were found to be slightly temperature dependent. The magnitude of the range of strain rates plotted in (14) Fig.11 masked the deviation from linearity for the creep data But using a smaller range of strain rate, such as Garofalo, the deviation becomes apparent. As stated before, this is the reason the exponential relationship cannot be used to relate both high and low stress creep data. 4.2.3.3 - Hyperbolic Sine Relationship Use of the hyperbolic relation for the tensile results -3 -1 gave n' values from 4 to 7.6 for a = 0.3 x 10 psi . Such a variation was not reported by Wong and Jonas (*^f or hot extrusion and hot compression} see Table IV. A present re-evaluation of Alder and Phillips data^10^ (see Table III) gives n' values that vary from 4.2 to 6.7, although Wong^^quotes a value of 4.2 for all temperatures. In light of these discrepancies, the variation in the tensile n' value does not appear as questionable. Use of a = 0.3 x 10 3 psi ^ in analyzing the creep dati"^ gave higher values of sinh (aa) than the tensile data for slightly higher temperatures. In order to get a better fit between the two (15) sets of results, a was recalculated using Garofalo's method for -3 -1 low and high stresses. This method gave values of 0.12 x 10 psi , 0.21 x 10-3 psi_1, and 0.27 x 10~3 psi"1 at 260 , 371and4B2°C res pectively. Applying the hyperbolic relationship with these a values gave good fit between the creep and tensile values, see Fig.12. Values of a for the tensile range could not be calculated using a = B/n because the stress levels were too high. In Table III the n' values are, in the tensile to hot working range, approximately temperature independent. Use of the hyperbolic relationship of stress-strain rate made it possible to extrapolate from creep to the hot working range with some effectiveness for similar purity material, see Fig.12. (13) The hyperbolic equation is said to be correct in relating stress and strain rate over large stress ranges because of the equivalence of £ = A''1 [sinh (aa)]n e A^/R^ to e = A'e^a e anc\ e = Aa11. If aa < 0.8, the hyperbolic relation approximates the power relation by less than 10% error, and n' = n. For aa > 1.2, the error is less than 10% between the hyperbolic and the exponential function, and a = B/n or a = B/n' depending upon either Garofalo's^15^ or Sellars and Tegart's^19^ definition. For the tensile results, a must be less than 2500 psi for aa < 0.8. Stress values less than 2500 psi occurred in the 450°C tests where n' =8. • and n' = 7.6, n' = n. For aa >1.2, the 250°C tests are applicable where n'=4, n=6, g = 0.00061 psi-1. These give a = B/n = 0.102 x 10-3 psi_1 and a = g/n' = 0.12 x 10~3 psi-1. —3 —1 (17 19 28) In neither case is a equal to the 0,3 x 10 psi which others ' ' found for the material constant for this purity of aluminum. The hot compression^»-^) an(j creep^4^ results of others were analyzed in the same way to see what a and n' values they gave and to see if they agreed with Wong's best fit values. The results are summarized in Tables IV and V. For no one temperature does the hyperbolic relation approximate the power and exponential expressions by less 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', for compression data^'"^ Sellars and Tegart' s statement that this empirical constant is independent of temperature is substantiated. Garofalo's evaluation, a = g/n gives a's which are temperature de pendent which substantiated his claim. Nothing conclusive can be said about the variation of a (14) values for creep and tensile data with temperature. The stress levels for both the tensile and creep results are in a critical stress range in which the relation a = g/n' cannot be used effectively. For creep, only Garofalo's method^^^ for evaluating a can be used and the stress levels do not satisfy aa > 1,2 for less than 10% error. 46 Instead a = 3/n is used incorrectly at lower stress values. The values for Alder and Phillips compression re sults do not correspond to those found by Wong for the best fit. This is due to the different values of g and n', see Tables III and VI. The value of n' Wong reports for the 250°C line is in error even from visual examination of his plotting of the data^^. (19) Sellars and Tegart limited the usefulness of their findings by saying that a was temperature independent only in the -3 strain rate range they examined which extended only down to 10 /sec. in the case of aluminum. But in order to get the creep data to fit an extrapolation of tensile data or compression data a must be temperature dependent, and the values used are as suggested by Garofalo^1"^. Perhaps a is temperature dependent below a critical value of strain rate. 4.2.4 - Activation Energy Three methods were used to calculate activation energies for the hot tensile deformation of the aluminum. Using a stress-n' —AH/RT strain rate dependence according to e = A''' [sinh (aa) ] e an activation 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 analysis, 32.5 kcal/mole. The activation energies determined from the first two stress-strain rate dependencies are similar as would be suspected as the hyperbolic equation approximates the exponential equation. The difference arises perhaps in the creep determination through the use 9 lo '' ' of ( —) a = 2000 psi. The stress value is possibly in error TABLE V - Evaluation of the Stress Ranges - where the hyperbolic sine relation appoximates the power and experimental relationships by more than 90% accuracy, using the derived values of a, n, n', and 3 as listed in Table III. aa> 1'2 aa < 0.8 T°C n 3 ksi n' a=3/n ksi a=3/n' ksi n r Ref.(10) 250 350 a = 0.3 x. 10-3 psi_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 10_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-for the low strain rate tests at 250°C as a true steady state did not exist. If the 250°C data is ignored, the creep analysis gives an activatipn energy of 38,5 kcal/mole which agrees with the other two values. The calculated activation energy for tensile deformation for the ISCD aluminum, which is approximately 2S composition, agrees „ t. t. . (1,3,13,17,19,20,28,35) . wxth other reported actxvatxon energies »>>»»>> for (35) creep and hot working. Sherby and Dorn report values of 35-36 kcal/mole for high temperature creep of 2S aluminum. Jonas hot (28) and Wong report an activation energy of 37 kcal/mole for hoextrusion and hot compression whereas McQueen, Wong and Jonas quote 41.8 and 44.0 kcal/mole respectively for the same purity material. As the lower value for the hot extrusion is the latest reported by one of the co-authors, this value is believed to be more correct. Since different experimental activation energy values have been quoted for Alder and Phillipshot compression data, a re-evaluation of the activation energy was made here. Using an exponential stress-strain rate dependence it 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 later value with that of Wong and Jonas , AH = 37. In Wong and Jonas' determination of an activation energy, they have taken liberties in arriving at n' for 250°C as was mentioned before. Since the hyperbolic equation is 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 activation energies of 32.7 and 34.4 kcal/mole for exponential and hyperbolic depend encies respectively. Analysis of Servi and Grant's creep data^1^ for 2S aluminum, gave an activation energy of 50 kcal/mole for a constant stress analysis. This compared with the value of 56.8 kcal/mole (35) determined by Sherby and Dorn from this same data. For other 2S aluminum results they found the experimental activation energy (35) to be in the range 35-36 kcal/mole . They attributed the high activation energy in Servi and Grant's case to the heat treatment used . (35) prior to testing The variation in activation energies does not follow any consistent change in composition for the aluminum examined. This would suggest that the activation energy for hot deformation is not purity dependent for the composition variation 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 relate hot working and creep data. Z is a structure factor of the deformed material and is a function of strain ' . The structure associated with a given value of strain is assumed to be a constant for all possible combinations of strain rate and temperature which yield a constant (13) value of Z . . For a constant flow region, as occurs in hot work ing and steady state creep, Z values are constant in the constant flow region. The flow stress is related to the value of Z. At a greater Z, a higher flow stress is needed because few thermally activated events occur per unit strain. This arises from either a low temperature or the shorter time for the event to occur at the 50 (3) (1 20 21) at the higher strain rate . Jonas and others ' ' have used a structure-corrected Zener-Hollomon parameter, Z/A'1', to normalize the slight variations in the composition of the aluminum considered. They have related this structure-factor corrected Zener-Hollomon parameter to the hyperbolic sine stress function as in Fig.16. In the analysis they used a AH = 37.3 kcal/mole. Correct use of the Zener-Hpllomon parameter requires that the same activation energy be used throughout But for the Alder and Phillips data, Jonas and others ^»^^ used a value of AH which differed from the actual experimental value (see Section '4.2.9.). Since Jonas and other ^'^^ have taken this liberty of using the Zener-Hollpmon parameter it was thought advantageous here to present a similar plot to Fig.16 using the various calculated ex-•i • (2,10) (14) perimental activation energies for the compression , creep , and hot tensile data. The values of A''' used are listed in Fig.17 and are comparable to the values of A' 1 ' quoted by Wong^^ as reported in Table IV. The data points fall on a line in Fig.17 which lies almost co-linear with the line in Figure 16. This seems rather remarkable considering the fact that a AH value of 53.4 kcal/mole (13) was used for the creep data . The fit would suggest that use of a Zener-Hollomon plot does not provide conclusive proof for the theory that hot working is an extension of high temperature creep. (14) If for the Servi and Grant creep data a value of 37.3 kcal/mole is used, the data points are orders of magnitude off the line in Fig.16. This casts further doubt on Jonas' use of the ' Zener-Hollomon parameter in his argument. 51 IO' 10' IO' 10' 3f IO' IO IO* io ta 10' ,6* ,d7l A8 10 / SLOPE 4-67 I a .299»l64 psi"1 j Q « 37-3 teaJ/mol« o / IO"2 10"' 10° IO1 10' o + I k » = Creep (14) = Extrusion (20) = Compression (10 = Torsion (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' 10s 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 plot using actual experimental activation energies. 'The data can be inter preted as two. slopes(s61id lines) or one slope (dotted line). S2A T°C A»" sec*1 H kcal/mole • 26.0 io x io19 53.4 371 2,93 x XQir 482 3 x 1014 0 ©11 8*8 x IO9 34.4 a 2S0 8.2 x 102 38.02 350 5.53 x IO10 4S0 6.4S x IO10 A all 5.855 x IO11 38. 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/RT^ can be used to relate the hot working parameters but it 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, it 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. For hot compression it is 37-4 5 kcal/mole. For hot tensile deformation it is 38.5 - 39.5 kcal/mole. For high temperature creep it is 50-57 kcal/mole. 4. Loose use of the Zener-Hollomon relation can give the impression that hot working is an extension of high temperature creep. 5. Hot rolling can be used to evaluate hot working parameters but only when the effect of roll quenching can be ignored. 6. Hot tensile testing on a fixed cross-head speed tensile machine gives hot working data that is comparable to hot compression or hot torsion data. 55 BIBLIOGRAPHY 1. Jonas, J.J., Sellars, C.M. and Tegart, W.J. McG. Metallurgical Reviews, 14, (1969), 1. 2. Arnold, R.R. and Parker, R.J., JIM ., 88, (1959-60), 255. 3. McQueen, H.J., J. Metals, 20, (1968),31. 4. Nicholson, A., Iron and Steel, ^7, (1964), 290, 363. 5. Moore, P., "Deformation Under Hot Working Conditions", I.S.I. Special Report #108 (1968), London, 103. 6. Rossard, C. and Blain, P., Rev. Met., 55, (1958), 573, Publ. IRSID (174a), (1957). 7. Helm, A. and Alexander, J.M. JISI, 207, (1969), 1219. 8. Larke, E.C., "The Rolling of Sheet, Strip, and Plate", Chapman and Hall Ltd., London, (1963). 9. Chandra, T. and Jonas, J.J., to be published. 10. Alder, J.F. and Phillips, V.A., JIM, 83, (1954-55), 80. 11. Rossard, C. and Blain, P., Mem. Scient. Revue, Metall., j>7, (1960) 173-8. 12. Ormerod, H. and Tegart, W.J. McG., JIM, 92, (1963-4), 237. 13. Garofalo, F., "Fundamentals of Creep and Creep Rupture in Metals", Macmillan, N.Y., (1965). 14. Servi, I.S. and Grant, J.J., TAIME, 191, (1951), 909. 15. Garofalo, F., TAIME, 227, (1960), 351. 16. Bailey, J.A. and Singer, A.R.E,, JIM, £2, (1963-4), 404. 17. Jonas, J.J., McQueen, H.J. and Wong, W.A., ibid 5, 49. 18. Hockett, J.E., TAIME, 239, (1967), 969. 19. Sellars, CM. and Tegart, W.J. McG., Mem. Scient. Revue Metall., 63,(1966), 731. 20. Wong, W.A. and Jonas, J.J., TAIME, 242, (1968), 2271. 21. Jonas, J.J. and Immarigeon, J.P., Z. Metallkinde, Bd. 60, (1969), H. 3, 227. 22. Conrad, H., "Iron and Its Dilute Solution", 318. 23. Boulger, F.W., DMIC Report (1966), #226, 15. 24. Weertman, J., J. Appl, Physics, 28, (1957), 362. 25. Barrett, CR. and Nix, W.D., Acta Met. B, (1965), 1247. 26. Raymond, L. and Dorn, J.E., TAIME, 230, (1964), 560. 27. Weertman, J., TAIME, 218, (1960), 207. 28. McQueen, H.J., Wong, W.A. and Jonas, J.J., Can.J. Phys., 45, (1967), 1225. 29. Sims, R.B., Pioc. IME., 207, (1969), 1219. 30. Rowe, G.W., "Principles of Metalworking", Edward Arnold, London, (1965). 31. Dieter, G.E., McGraw-Hill, London, (1961). 32. Helmi, A. and Alexander, J.J., JISI, 207, (1969), 1219. 33. Yanagimoto, S. and Aoki, I., Bulletin of J.SME, 11, (1968), 165. 34. Thomsen, E.G., Yang, CT. and Kobayashi, S., "Mechanics of Plastic Deformation in Metal Processing", The MacMillan Co. N.Y., (1965). 35. Dorn, J.E. and Sherby, O.D., J. Metals, j4, (1952), 959. 36. Dorn, J.Ef, "Mechanical Behavior of Materials at Elevated Temperas tures", McGraw-Hill, N.Y. (1961). 

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