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A new strain rate change technique for distinguishing between pure metal and alloy type creep behavior
OOOI-6160/87 $3.00+ 0.00 Copyright 0 1987Pergamon Journals Ltd
Acta mernfl.Vol. 35, No. 6, pp. 1391-1400,1987 Printed
in Great
Britain.
All rights reserved
A NEW STRAIN RATE CHANGE TECHNIQUE FOR DISTINGUISHING BETWEEN PURE METAL AND ALLOY TYPE CREEP BEHAVIOR D. L. YANEY,’ J. C. GIBELING’ and W. D. NIX’ ‘Department of Materials Science and Engineering, Stanford University, Stanford, CA 94305 and 2Department of Mechanical Engineering, Division of Materials Science and Engineering, University of California, Davis, CA 95616, U.S.A. (Received
24 February
1986)
Abstract-A
new technique involving strain rate changes has been developed for distinguishing between pure metal and alloy type creep behavior. Both positive and negative strain rate changes were performed on aluminum and Al-5.8 at.% Mg (pure metal and alloy type material respectively) using an Instron electromechanical testing machine. Tests were conducted at 573 K with initial total strain rates of either 4 x 10e5 or 4 x 10-4s-1. Immediately following an order of magnitude change in total strain rate, the plastic strain rate was monitored as a function of stress. The observed transient response for both pure aluminum and Al-S.8 Mg was found to agree with predicted behavior, indicating that the strain rate change test can be used to distinguish between pure metal and alloy type creep behavior. The strain rate change test was also found to be a promising single specimen technique for studying constant structure deformation. The quality of the constant structure data obtained using this technique is shown to depend on the accuracy with which plastic strain rate can be determined. A procedure is described for determining the plastic strain rate with sufficient accuracy to allow the strain rate change test to be used in place of multiple stress reduction tests to study constant structure deformation. RCum-Nous
avons dtvelopp6 une nouvelle technique, impliquant des variations de la vitesse de d&formation, pour distinguer les comportements en fluage d’un m&tal pur et d’un alliage. Nous avons fait varier positivement et nbgativement la vitesse de d&formation de l’aluminium et de Al-5,8 at.% Mg (respectivement un mbtal pur et un alliage), B l’aide d’une machine d’essai &ctromCcanique Instron. Les essais ont 6tt effect&s B 573 K avec des vitesses initiales de dbformation totale de 4 x lo-’ ou de 4 x 1O-4 s-l. Immediatement aprt% une variation d’un ordre de grandeur de la vitesse de d&formation totale, nous avons enregistrb la vitesse de dtformation plastique en fonction de la contrainte. La rbponse transitoire observ6e tant pour l’aluminium pur que pour Al-5,8 Mg est en accord avec le comportement prkdit, ce qui indique que l’essai avec variation de la vitesse de dkformation peut itre utilisb pour diffkrencier les comportements en fluage d’un m&i pur et d’un alliage. L’essai avec variation de la vitesse de d&formation est tgalement une technique prometteuse dans le cas d’un tchantillon unique pour 6tudier la d&formation $ structure constante. La qualit des don&es $ structure constante obtenues B l’aide de cette technique d&end de la pr&ision avec laquelle on peut dbterminer la vitesse de dbformation plastique. Nous d&xivons un pro&d& pour dCterminer la vitesse de d&formation plastique avec assez de p&&ion pour permettre d’utiliser l’essai avec variation de la vitesse de d&formation g la place d’essais multiples de rkduction de la contrainte, dans le but d’ttudier la d&formation B structure constante. Zusammenfassung-Mit einem neu entwickelten Untersuchungsverfahren auf der Grundlage von Wechseln in der Dehnungsrate kann zwischen dem Kriechverhalten reiner Metalle und Legierungen unterschieden werden. Sowohl positive als such negative Wechsel der Dehnungsrate wurden an Aluminium und der Legierung Al-5,8 At.-% Mg (reines Metal1 und typische Legierung also) in einer elektromechanischen Instronmaschine durchgefiihrt. Die Versuche fanden bei 573 K mit anf&glichen Dehnungsraten von 4 x 10m5oder 4 x 1O-4S-I statt. Unmittelbar nach einem Wechsel der Dehnungsrate urn eine GrBBenordnung wurde die plastische Dehnung in Abhangigkeit von der Spannung aufgenommen. Das beobachtete iibergangsverhalten der beiden Metalle stimmte mit dem vorausgesagten Verhalten iiberein. Dieses Ergebnis weist darauf hin, da13dieser Test zur Unterscheidung des Kriechverhaltens von reinen Metallen und Legierungen verwendet werden kann. Es ergab sich aul%xdem, daD dieser Test eine vielversprechende Methode zur untersuchung der Verformung bei konstanter Struktur ist. Die Qualitlt der Ergebnisse bei konstanter Struktur hlngt bei diesem Test von der Genauigkeit ab, mit der die plastische Dehnungsrate bestimmt werden kann. Ein Verfahren wird beschrieben, mit dem diese plastische Dehnungsrate mit ausreichender Genauigkeit bestimmt werden kann, damit die Wechsel in der Dehnungsrate anstelle der Versuche mit mehrfacher Spannungsreduktion zur Untersuchung der Verformung bei konstanter Struktur benutzt werden kSnnen.
1. INTRODUCTION Tests involving
strain rate changes have been used by many investigators for a number of different purposes. Most frequently, the strain rate change test has been used in the study of steady state flow of
materials [l, 21. This is illustrated schematically in Fig. 1. A specimen is deformed at an initial strain rate i, until a steady state flow stress 0, is observed. The
strain rate is then changed to i, and deformation allowed to proceed at this new rate until steady state conditions
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are once
again
achieved.
Since
several
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YANEY et al.: A NEW STRAIN RATE CHANGE TECHNIQUE
Strain
Fig. 1. Schematic stress-strain curve for a strain rate increase in a pure metal.
strain rate changes can typically be performed on a single specimen, this version of the strain rate change test is an efficient means of determining the strain rate dependence of the steady state flow stress of a material at a particular temperature. The strain rate change test has also been used to study deformation under conditions of constant internal structure. Young et al. [3] noted that experimental difficulties are often encountered when the conventional stress-drop test is used to study constant structure flow in pure metals. The transient creep rates following large stress reductions are often quite small and difficult to measure. In addition, for successful analysis of the strain transient, it is necessary to separate the observed creep rate following a stress drop into its elastic, anelastic and plastic components. They attempted to circumvent these difficulties by using the strain rate change test instead of the stress-drop test to study constant structure flow behavior. The method of Young et al. [3] can be described best by assuming that creep of pure polycrystalline metals in the power law regime is adequately represented by an equation of the form kEN
SDAPaN (1)
where, S = structure constant E = dynamic Young’s modulus, 1 = subgrain size, o = applied stress, D = lattice diffusion coefficient, p, N = constant exponents. The exponents p and N are determined using the procedure illustrated in Fig. 1. A sample is deformed to large strain at strain rate i, until steady state is achieved (a = al). The strain rate is then changed and deformation allowed to continue until a new steady state is reached. Immediately following the strain rate change, the “instantaneous resistance to plastic flow at the new strain rate” is measured. On chart recordings of load versus time this is taken as the stress corresponding to the sudden change in slope that occurs at (r = u2. Thus, according to Young et al. [3],
6, and a2 refer to the flow stress of the same structure at two different total imposed strain rates, namely i, and i,. From Fig. 1, it can be seen that the steady state stress exponent is given by the expression
It is assumed that the substructure is completely characterized by the subgrain size, 1. Thus, the constant structure stress exponent can be written as
Since subgrain size is typically assumed to be inversely proportional to the steady state flow stress, p is simply equal to N - n. Since the work of Young et al. [3] in the mid1970’s, the development of high speed computer aided data acquisition techniques has eliminated most of the experimental difficulties associated with interpreting the results of stress-drop tests. Thus, today, multiple stress reduction tests are the preferred method for studying the constant structure flow behavior of materials. In the present investigation, computer aided data collection techniques have been applied to the more conventional strain rate change test. As a result, a number of problems associated with using the method of Young et al. [3] to study constant structure behavior have become apparent. In the sections that follow, a new technique for studying constant structure behavior using the strain rate change test is described. This technique is independent of any theoretical picture of plastic flow. It is shown that by monitoring the variation in plastic strain rate with stress, it is possible to use the strain rate change test to distinguish between pure metal and alloy type creep behavior. The results of strain rate change tests performed on pure aluminum and Al-5.8 at.%Mg (pure metal and solid solution strengthened alloy, respectively) are presented and shown to conform to expected behavior.
YANEY et al.:
A NEW STRAIN KATE CHANGE TECHNIQUE
9
Time
Isecl
(4
1747
‘..,
-
‘. .-_, ‘. ‘_ ‘.
‘._ ‘.. 1745
2
-
12
I
.. .. .
10-a nn,sec
-
.. ‘.
. . .
;
1745
Cal
t...~.~~~~‘~~~~~~.~~‘~~.~~~~~~‘~.,.~.~~.’ 19 5
20.4
20.0
Time
20
0
21.2
(set)
@I
Fig. 2. Crosshead displacement vs time for: (a) a crosshead speed increase
and (b) a crosshead
speed decrease.
2. EXPERIMENTAL
The materials used in this investigation were Al (99.999%) and Al-5.8 at.%Mg. Cylindrical compression specimens 5.08 mm (0.2 in) in diameter and 7.62mm (0.3 in) in length were prepared from these materials. After machining, all specimens were annealed in air at 723 K for one hour and air cooled. Strain rate change tests were conducted in air at 573 K using an Instron model 1125 electromechanical testing machine. The total imposed true strain rate was either 4 x 10m5or 4 x 10m4s-’ and both positive and negative strain rate changes of an order of magnitude were performed. Samples were deformed between polished alumina plattens with boron nitride used as a lubricant. Heating was accomplished by a split shell resistance furnace. Although measured loads never exceeded 2220 N (500 lb), existing compression test fixtures necessitated the use of a 44.5 kN (10,000 lb) capacity Instron load cell to measure load. Thus, the major source of noise in the load signal was the high grain setting on the load cell amplifier. In order to characterize the ability of the Instron testing machine to perform the desired crosshead speed changes, the following procedure was used. A plexiglass sample 25.4 mm (1 .OOin) in length and 19.1 mm (0.751 in) in diameter was loaded in compression at an initial crosshead speed of 2.12 x 1O-4
1393
mm/s (5 x low4 in/min). After loading to approx. 1780 N (400 lb), the crosshead speed was increased to 2.12 x 10m3mm/s (5 x 10e3 in/min). During the course of the crosshead speed change, crosshead displacement was measured as a function of time using a Unimeasure 80 transducer (described elsewhere [4]) in conjunction with a Hewlett-Packard 3456A digital voltmeter. Typical plots of crosshead displacement vs time are shown in Fig. 2. The displacement resolution was 0.02pm and the time resolution was 0.025 s. This procedure was also used to characterize machine response during the crosshead speed decrease from 2.12 x 10e3 to 2.12 x 10m4 mm/s. A Hewlett-Packard model 3054A data acquisition system was used to collect data during all tests, with the first 60 points following a change in strain rate collected at a rate of five readings per second. This system was also used to control the crosshead speed of the Instron. As a result, it was possible to vary the crosshead speed as desired during the course of a test to either maintain a constant total imposed true strain or perform a strain rate change. The total imposed true strain rate, i, is related to crosshead speed by the following equation ir= 8/L,
(4)
where, 8 = crosshead speed, L, = current total length of the sample. Thus, in order to maintain a constant total true strain rate it is necessary to calculate the current length of the sample at frequent intervals during the course of a test and then used equation (4) to calculate the crosshead speed necessary to maintain the desired total imposed true strain rate. At any point in a test, the current total length of the sample is given by the expression
L,=L,-Ax+P/K,
(5)
where, L,= initial length of the sample, Ax = total deflection of the crosshead since the beginning of the test, P = magnitude of the current load, K,,, = machine stiffness at load P. The total crosshead deflection, Ax was measured using an Instron clip-on extensometer with a maximum deflection of 6.35 mm (0.25 in). In order to measure machine stiffness, the test specimen was replaced by a ceramic cylinder 19.05 mm (0.75 in) in diameter and 25.4 mm (1 in) in length. Crosshead deflection was then monitored as a function of load for an imposed crosshead speed of 4.23 x 10-4mm/s (0.001 in/min) and a test temperature of 573 K. The crosshead speeds used in the strain rate change tests ranged from 1.72 x 10e4 mm/s (6.78 x 10m6in/s) to 3.05 x 10m3mm/s (1.2 x 10m4in/s). The machine stiffness was found to be independent of crosshead speed within this range. However, the machine stiffness was found to depend on load. The loaddisplacement values collected during the spring constant test were fitted to a fifth order polynomial and the K,,, value used in equation (4) is that value corresponding to the current load, P. Finally, it
YANEY et al.:
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A NEW STRAIN RATE CHANGE TECHNIQUE
20
1 Aluminum . 573 K
Ial ~~~‘~~~~‘~~~~‘~~~~~~~~~I~~~~
0 0
10
20
30
Percent
True
40
50
60
Strain
(4
20-....,....,....,....,....,....
1 Alumirium . 573 K ;ii 15%.
4 x
lo-
Fig. 4. Normalized strain rate vs modulus compensated stress for pure aluminum and Al-MB alloys.
4 x
Is-‘)
m-5
15-11
I 0
_
lb1 _
~~~~‘~..~~~~~~I~~~~‘.~“‘~“’ 0 i0 20
30
Percent
True
40
50
60
Strain
(b)
Al-5.8 -573 K
at.%Mg
ICI ~~~~.~~..I~~~~~~~~~I~~~~~~~.~I~~~~~~~..I~
0 0
10
20
Percent
True
30
40
Strain
(4
Fig. 3.True stress vs percent true strain for: (a) a strain rate increase test in pure aluminum, (b) a strain rate decrease test in pure aluminum and (c) both a strain rate increase and a strain rate decrease test in Al-5.8 at.%Mg. All tests conducted at 573 K. The imposed total true strain rate in all tests was either 4 x 10m5or 4 x 10-4s-1.
should be noted that the crosshead speed was not continuously variable. It could be incremented only in steps corresponding to 0.1% of the selected pushbutton speed. However, this step size was sufficiently small that the strain rate varied by no more than 2.5% from the desired value before a correction was made.
3. EXPERIMENTAL
RESULTS
Typical stress-strain curves for positive and negative changes in strain rate in pure aluminum are shown in Fig. 3(a) and (b) respectively. Note that because of the large amount of strain required to reach steady state, both at the beginning of the test and after a strain rate change, only one strain rate change experiment could be performed on any given sample. Values of steady state flow stress and strain rate are plotted in Fig. 4 and shown to agree quite well with creep test results of other investigators ]4,51. Figure 3(c) shows a typical stress-strain curve for strain rate change experiments performed on Al5.8 Mg. The steady state flow stress values obtained are plotted in Fig. 4 and shown to agree quite well with results of other investigators [6, 7J. Unlike pure aluminum, where elevated temperature deformation is characterized by extensive subgrain development, microstructure evolution in Al-Mg alloys deformed in the Class I regime is characterized by the development of a homogeneous distribution of dislocation loops [7]. As a result, large amounts of strain are not required for the Al-Mg alloy to reach steady state. However, because annealing before testing produces samples with relatively low dislocation densities, a yield point is frequently observed at the beginning of a test as well as immediately following a strain rate increase in the AI-Mg alloy. Only after significant dislocation multiplication occurs does the stress required to cause deformation at a constant strain rate approach the steady state value. For similar reasons, a minimum in flow stress is observed following a strain rate decrease for Al-S.8 Mg at 573 K. This can be seen in Fig. 3(c). Steady state deformation at a total strain rate of 4 x 1O-4 s-r produces a dislocation density which is significantly higher than
YANEY et
al.:
A NEW STRAIN RATE CHANGE TECHNIQUE
Fig. 5. Schematic illustration of the Instron testing machine and sample.
that which would characterize steady state deformation at the lower strain rate (4 x 10e5 SK’). Thus, until dislocation annihilation occurs, the flow stress observed at the new strain rate is less than the steady state value.
1395
where, k = crosshead speed, P = loading rate, E = Young’s modulus of the sample, A, = initial area of the sample, L, = initial length of the sample, L, = unloaded length of the sample. Using equation (7), the plastic strain rate can be computed at any point during the experiment. It is important to note that both the plastic strain rate and the stress vary continuously during the transient following a change in total strain rate. The plastic strain rate approaches the total strain rate only when the loading rate is small (i.e. during steady state deformation). Thus, the analysis described above differs considerably from that of Young et al. [3] in which the total strain rate is assumed to be equal to the plastic strain rate even immediately after a strain rate change. The measurement of the plastic strain rate as a function of stress following a strain rate change permits one to distinguish between pure metal and alloy type creep behavior, as shown schematically in Fig. 6. Consider first the case of a pure metal in
Pure Metal Type
4. TECHNIQUE FOR DISTINGUISHING BETWEEN PURE METAL AND ALLOY TYPE CREEP BEHAVIOR In order to distinguish between pure metal and alloy type creep behavior, plastic strain rate was monitored as a function of stress during the deformation transient following a strain rate change. The observed variation was then compared with the known variation of plastic strain rate with stress for steady state deformation. In this section, the procedure for determining plastic strain rate is outlined and the expected variations of plastic strain rate with stress following strain rate changes in both pure metal and alloy type materials are discussed. As noted by Johnston and Gilman [8] in 1959, and later by Holbrook et al. [9], a proper interpretation of tension or compression tests requires that the coupling between specimen and testing machine be taken into account. Thus, as shown in Fig. 5, the testing system used in this investigation consists of two components: (1) the Instron testing machine which deforms elastically and (2) the specimen which deforms both elastically and plastically. The total imposed true strain rate, i, is simply the sum of three terms c, = i,,, machine + i,,, sample + i,,, sample
LOG(Stress)
Alloy Type
(6)
where &,mach,ne= rate at which the machine deforms elastically expressed as a strain rate, CE,,samp,e = elastic strain rate of the sample, iP,,samp,e = plastic strain rate of the sample. Or equivalently, as shown by Holbrook et al. [9]
1
a
(7)
b
LOG(Stress)
Fig. 6. Schematic illustration of the expected variation in log (plastic strain rate) with log (stress) following strain rate Increases and decreases in: (a) pure metals and (b) alloy type materials.
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YANEY et al.:
A NEW STRAIN RATE CHANGE TECHNIQUE
which steady state deformation occurs in the power law regime. When the strain rate is increased, the behavior shown schematically in Fig. 6(a) should be observed. Immediately after a change in total imposed true strain rate, no sudden change in plastic strain rate should be observed, i.e. the plastic strain rate should not change discontinuously. If flow is thermally activated, the plastic strain rate depends only on the stress, temperature and structure and not on the stress rate. Since neither the stress nor the structure change instantaneously and the temperature is held constant, no sudden change in plastic strain rate should be observed immediately following a change in imposed total strain rate. In terms of the elements shown in Fig. 5, the strain rate can change instantaneously only for the two elastic elements; the plastic strain rate of the element represented by the dashpot cannot change abruptly. The observed variation of plastic strain rate with stress following a strain rate increase should differ considerably from the known variation of plastic strain rate with stress for steady state deformation. For a pure metal, deformation in the power law regime is characterized by the formation of well developed subgrains with a characteristic dimension, 1, which varies inversely with steady state flow stress. Thus, for the case of a strain rate increase, the structure initially present after steady state deformation at the lower strain rate is “softer” than the structure which is characteristic of steady state flow at any higher plastic strain rate. As a result, the flow stress during the transient is expected to be temporarily less than the flow stress predicted from steady state data at the same plastic strain rate. Only after sufficient microstructural refinement has occurred should a return to steady state behavior be observed. For the case of a strain rate decrease in a pure metal, plastic strain rate continuity should once again be observed immediately following the change in total imposed strain rate. However, as the deformation transient proceeds, the stress is expected to be greater than that characteristic of steady state deformation at the same plastic strain rate. The structure formed by steady state deformation at the initial high strain rate is “stronger” than the structure characteristic of steady state flow at the lower strain rate. Thus, until microstructural softening occurs, the stress will be greater than that predicted from steady state data at the same plastic strain rate. Finally, it should be noted that for the short period of time following a strain rate increase or decrease when the structure is essentially constant, it may be possible to study constant structure flow behavior using the strain rate change test. Young et al. [3], characterized the relationship between strain rate and stress at constant structure by a power law relationship, and obtained a constant structure stress exponent of about 8 for pure aluminum using the strain rate change test. However, more recent stress drop experiments by Gibeling [lo] and Gibeling and Nix
[1I] have shown that for small stress changes (such as those seen at the beginning of a strain rate change experiment), the constant structure stress exponents in pure metals may be much larger than eight. As mentioned earlier, microstructural evolution in alloy type materials is characterized by the development of a homogeneous distribution of dislocation loops. This differs considerably from microstructural evolution in pure metals in which subgrains are formed. Thus, pure metals and alloy type materials should respond quite differently to changes in total imposed strain rate. The expected responses of an alloy type material to increases and decreases in total strain rate are shown in Fig. 6(b). For purposes of illustration, the steady state stress exponent for materials exhibiting alloy type behavior is assumed to have a value of approximately three. This is commonly observed in Al-Mg alloys deformed in the Class I regime. If flow is again assumed to be thermally activated, then plastic strain rate continuity should be observed immediately following a strain rate change in alloy type materials as well. As the deformation transient proceeds, the variation in plastic strain rate with stress should differ from the variation in plastic strain rate with stress predicted from steady state behavior. For a strain rate increase in an alloy type material, the dislocation density is initially lower than that characteristic of steady state deformation at any higher strain rate. Thus, the observed stress should be greater than that predicted by the steady state relation during the transient. Only after dislocation multiplication has had a chance to occur should a return to steady state behavior be observed. Analogously, for the case of a strain rate decrease, the dislocation density is initially too high. Thus, until dislocation annihilation occurs, the stress observed at a given plastic strain rate should be less than that associated with steady state deformation at the same strain rate. Finally, it should be possible to determine the constant structure stress exponent for alloy type materials using the strain rate change test. Stress drop experiments of Mills et al. [7] indicate that a constant structure exponent of approximately two should be observed in Class I alloys. This is shown in Fig. 6(b). 5. OBSERVED BEHAVIOR-COMPARISON WITH EXPECTED RESULTS
Log-log plots of plastic strain rate versus stress for both increases and decreases in total strain rate for pure aluminum are shown in Fig. 7(a) and (b) respectively. Similar plots for strain rate change tests performed on the Al-5.8 Mg alloy are shown in Fig. 8(a) and (b). In all cases, the observed transient behaviors for both aluminum and Al-5.8 Mg are in excellent agreement with the qualitative predictions shown in Fig. 6. These results demonstrate that the strain rate change test can successfully distinguish between pure metal and alloy type creep behavior.
YANEY
et al.:
A NEW STRAIN
RATE
CHANGE
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TECHNIQUE
from anelastic deformation was calculated for all points following a strain rate decrease in pure aluminum. The results of this calculation indicate that for a strain rate decrease in pure aluminum, the anelastic strain rate is always two orders of magnitude less than the plastic strain rate. Thus, for pure aluminum there is no need to modify equation (6) to take anelastic deformation into account. Furthermore, since anelastic deformation is always a smaller fraction of the total deformation in Al-Mg alloys than in pure aluminum, the contribution of anelastic processes to the total strain rate in the Al-5.8 Mg alloy was not taken into account.
Aluminum 573 K
5.1. Plastic strain rate continuity
I 0
1.0
.9
LOG[Stress.
1 1
12
MPa)
Previously it was noted that if flow is thermally activated, the plastic strain rate must be continuous
10-j
Al-5.8 Aluminum
1
573 K Strain
573 K
strain RateDecrease 10-5
lb1
1.0
.9
LOG(Stress,
1.1
1.2
1.E
1.9
MPa)
(4 lo+T
Fig. 7. Log (plastic strain rate) vs log (stress) following: (a) a strain rate increase and (b) a strain rate decrease in pure aluminum. Circles represent transient behavior and squares represent steady state behavior.
The contribution of anelastic deformation to the total strain rate has not yet been considered. Since large anelastic strains have been observed in pure aluminum [4], it is necessary to determine the effect of including in equation (6) a term corresponding to the anelastic strain rate on the calculation of the plastic strain rate. Previously, Gibeling [lo] showed that the anelastic response-of pure aluminum to a stress reduction from 9.6 to 0.96 MPa at 573 K could be successfully described by a rheological model. In this model, two Voigt elements, one with a linear dashpot and one with a power law dashpot with a stress exponent of two are placed in series. Assuming that the anelastic deformation which occurs during the strain rate changes can also be described using this model, the contribution to the total strain rate
1.7
LOG(Stress,
MPal
@I
Increase
1.6
1.5 .8
Rate
at.%Mg
Al-5.8 573 K Strain
10-5
1.5
Rate
at.%Mg Decrease
Ibl :
:
1.6
1.7
LOGEtress,
1.8
’
1.9
MPa)
@I
Fig. 8. Log (plastic strain rate) vs log (stress) following: (a) a strain rate increase and (b) a strain rate decrease in Al-5.8 at.%Mg. Circles represent transient behavior and squares represent steady state behavior.
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YANEY ef al.: A NEW STRAIN RATE CHANGE TECHNIQUE
following a change in crosshead speed. However, the calculated plastic strain rates immediately following strain rate increases for both materials are abnormally low. In fact, the plastic strain rate calculated 0.2 s after the strain rate increase in pure aluminum is negative, erroneously indicating that the sample (which was being tested in compression) was increasing in length following the increase in crosshead speed. It should be noted that although contributions to deformation from mechanically activated strain cannot be ruled out, they cannot be responsible for the apparent discontinuities in plastic strain rate. If mechanically activated strain contributed to deformation during the period of high stress rates following an increase in crosshead speed, the plastic strain rate observed would be greater, not less than the initial steady state strain rate. Thus, since calculations similar to those used by Gibeling et al. [12] indicate that a resolution time of 0.2 s should be sufficient to observe plastic strain rate continuity in aluminum and Al-S.8 Mg, factors other than athermal flow must be responsible for this discrepancy. Instead, it is believed that the inherent inaccuracy in Km as well as possible difficulties in quickly establishing the new crosshead speed are responsible for the apparent discontinuity in plastic strain rate following an increase in total strain rate. During steady state deformation, the dominant term in equation (7) is the total strain rate 8/L,. However, immediately following a strain rate increase, the first and second terms in equation (7), k/L, and P/k;, L, respectively, are of approximately equal magnitude. In addition, they are both more than an order of magnitude greater than the third term, pL,IEA, L,. Thus, the calculated value of i, immediately following a strain rate increase is strongly dependent upon the difference between two terms of comparable magnitude, and any error in either J? or K,,, will greatly affect the calculated value of i,. In fact, only an 11 percent increase in & is needed to confirm plastic strain rate continuity following a strain rate increase in the Al-5.8 Mg alloy. For pure aluminum, a 21% increase in K,,, is required to observe strain rate continuity. However, these are not unreasonable corrections in light of the fact that the greatest inaccuracies in K,,, occur at the low loads at which these materials were tested. It should be noted that although direct knowledge of & was required in this investigation in order to compute plastic strain rates, such knowledge would not have been required if it had been possible to measure sample length directly during testing. By measuring sample displacement independently, the plastic strain rate can be determined simply by subtracting the elastic strain rate of the sample from the total strain rate measured at the sample. If the tests had been conducted in tension (rather than compression) and the sample displacements had been measured directly across the gauge length, the plastic strain rates could have been calculated with much
greater accuracy than was possible in the present experiments. With regard to possible uncertainties in crosshead speed, Fig. 2(a) shows the variation in crosshead displacement with time for a crosshead speed increase from 2.12 x 1O-4 to 2.12 x lo-‘mm/s. For approx. 0.2 s after the speed change is initiated, the actual crosshead speed is approx. 1.3 times the desired speed. Thus, for the first data point collected following a strain rate increase, the assumed crosshead speed may be less than the actual value, thereby adding to the inaccuracies in i,. Although inaccuracies in J? and Km greatly affect the values of plastic strain rate calculated immediately following an increase in crosshead speed, the same is not true for a decrease in the crosshead speed. After a decrease in strain rate, the dominant term in equation (7) is the second term, P/k L,. This term is approximately an order of magnitude greater than either of the other two terms and determination of i, no longer depends on the difference between two terms of comparable magnitude. Thus, accurate knowledge of K,,, is not nearly as critical as for the case of strain rate increase. With reference to the accuracy with which crosshead speed is known, Fig. 2(b) shows the variation in crosshead displacement with time following a crosshead speed decrease from 2.12 x 10m3to 2.12 x 10m4 mm/s. For approx. 0.4 s following the speed change, the actual crosshead speed is less than the assumed value. However, the relative unimportance of the 8/Lp term minimizes the error introduced by the possible uncertainty in crosshead speed. 5.2. Constant structure behavior Despite the difficulties associated with accurately determining i, immediately following a strain rate change, it is quite clear from Figs 7 and 8 that the plastic strain rate does not equal the total strain rate immediately following a strain rate change as assumed implicitly by Young et al. [3]. Furthermore, with improved time resolution, it is now clear that there is no single stress which corresponds to a material’s “instantaneous resistance to flow” at the new strain rate. As a result, the procedure we have described here must be used to study constant structure behavior using the strain rate change test. Recently, Gibeling and Nix [1 l] used high resolution stress drop creep tests to study the constant structure flow behavior of pure aluminum at 673 K. Although a power law relationship of the form ccs= Ad.’ was found to adequately describe the constant structure behavior for large stress drops, this relationship was found to be inappropriate for describing the constant structure behavior following small stress reductions. For small stress drops, the apparent constant structure exponent was observed to increase to a value of about 10 indicating that the constant structure data could be better described by an exponential relationship.
YANEY et al.:
1399
A NEW STRAIN RATE CHANGE TECHNIQUE
structure conditions (i.e. constant .c?,, and 8), a plot of log i, vs u should yield a straight line. In Fig. 9(a) and (b), the logarithm of the plastic strain rate is plotted vs stress for strain rate increases and decreases, respectively, in pure aluminum. For both increases and decreases in strain rate, the exponential relationship of equation (8) is obeyed for approximately the first 0.024.03% strain following the change in strain rate. At larger strains, a deviation from linearity is observed indicating a change in structure. We note that the maximum change in stress associated with constant structure deformation in these tests is quite small, approx. 5%. According to equation (8), the slope, /3 of a log (E’,)u plot for constant structure is equal to AF/(2.303) kT6. If 8 is assumed to be Strain RateIncrease lal 1o-5 5 : : 5 : : : : : linearly proportional to the steady state flow stress 7.0 9.0 11.0 13.0 associated with formation of the initial structure (a,), Stress (MPa) then fl should be inversely proportional to the product To,, (AF is assumed to be independent of (4 temperature). Thus, the value of j? obtained for the 1o-3 strain rate increase for pure aluminum should be Aluminum greater than the value of /I obtained for the strain rate 573 K decrease at the same temperature, since the steady state flow stress reached prior to the strain rate increase was less than the steady state flow stress attained prior to the strain rate reduction. As shown in Fig. 9, this is what was observed, indicating that the results of the strain rate change tests on pure aluminum are internally consistent. The constant structure data obtained for pure aluminum in this investigation can also be compared to the constant structure data of other investigators [ 11, 131. This comparison is summarized in Table 1. When the data for the strain rate decrease are comStrain Rate Decrease lb1 pared with data for stress drops at 573 and 673 K, lo+ : : : /I is found to vary approximately with l/Tu,, as 7.0 9.0 11.0 13.0 expected. However, the value of p obtained for the Stress (MPa) strain rate increases is much higher than would be @I expected from the corresponding value of l/To,. Fig. 9. Log (plastic strain rate) vs stress for: (a) a strain rate Several possible explanations for this discrepancy can increase and (b) a strain rate decrease in pure aluminum at be found. The structure parameter, 8, may not scale 573 K. linearly with the steady state flow stress associated with formation of the initial structure. Also, the high value of /l obtained for the strain rate increase may Following the suggestions of Gibeling and Nix [l 11, reflect contributions to deformation from athermal the theory of obstacle controlled glide can be used to mechanisms. As noted earlier, the stress rate followdescribe the constant structure flow behavior of pure ing the increase in strain rate in pure aluminum is metals in terms of an exponential relationship
i,=toexp[~(l-;)I
(8)
where i, = pre-exponential term that depends on stress and structure, AF = Helmholtz free energy for activation of dislocation glide, k = Boltzmann’s constant, T = absolute temperature, rr = stress, d = structure parameter. It should be noted that this relationship, unlike a simple power law relationship, adequately describes constant structure flow behavior for small changes in stress, such as those immediately following a strain rate change. Then, under constant
Table
1. Exponential
law constant
structure
/Y[= AF/(2,303)kZZ] (MPa-‘) Strain rate increase (this investigation)
573 K
Stress drop 673 K Gibeling and Nix [ll] Stress drop 573 K Raymond and Dom Strain rate decrease (this investigation)
behavior W&l (K-’ MPa-I)
1.7
2.28 x 1O-4
1.0
3.10 x 10-q
0.7
2.53 x 10m4
0.62
1.42 x lo-*
[13]
573 K
1400
YANEY er al.:
A NEW STRAIN RATE CHANGE TECHNIQUE
quite high, 1.1 MPa/s. In addition, Konig and Blum [14], studying Al-l 1 wt%Zn at 523 K, observed that even for the same initial stress (and structure), the constant structure exponent, /I, was higher for stress increases than for stress decreases provided the initial stress was sufficiently high. With regard to the constant structure behavior of alloy type materials, Mills et aI. [7] showed that a power law relationship of the form, t,, = Aa* can be used to describe the constant structure behavior of Al-5.5 at.%Mg tested at 573 K in the Class I regime. Unfortunately, the result of these high resolution stress reduction creep tests could not be duplicated using the strain rate change test. For the strain rate increase test, problems associated with the measurement of i, at the beginning of the transient made determination of a constant structure exponent difficult. For the strain rate decrease, a constant structure exponent greater than two was obtained. This lack of agreement with previous experiments is probably a reflection of the inaccuracy inherent in determining i, using the method of this investigation. By modifying the experimental procedure as described in Section 5.1 so that the plastic strain rate following a change in crosshead speed can be more accurately determined, it should be possible to duplicate the constant structure results of multiple stress reduction tests using a single strain rate change test.
the present investigation for aluminum are consistent with an exponential law for thermally activated glide, and are in general agreement with previous results. However, experimental uncertainties made a precise determination of plastic strain rates difficult early in the transient. As a consequence, only a qualitative comparison could be made between the constant structure behavior of Al-5.8 at.%Mg determined from strain rate change tests and previous stress change experiments. Further, plastic strain rate continuity was confirmed only for strain rate decrease tests. It is suggested that direct measurements of specimen strain should enable single specimen strain rate change tests to be used to make a qualitative distinction between pure metal and alloy type behavior. In addition, these tests should provide a quantitative measure of constant structure deformation.
REFERENCES 1. J. W. Edington, K. N. Melton and C. P. Cutler, Prog. Mater. Sci. 21, 61 (1976). 2. A. K. Ghosh, Superplastic Forming of Structural Allovs
(edited by N. ET Paton and C. I? Hamilton), p. 85. Conf. Proc. Metall. Sot. A.I.M.E. (1982). 3. C. M. Young, S. L. Robinson and b. D: Sherby, Acta metall. 23, 633 (1975). 4. J. C. Gibeling and W. D. Nix, Acta metall. 29, 1769 (1981).
6. CONCLUSIONS
The continuous variation of plastic strain rate with stress following increases and decreases in total strain rate has been analyzed. The results of experiments on pure aluminum and Al-5.8 at.%Mg tested at 573 K demonstrate that strain rate change tests can be used to make a qualitative distinction between pure metal and alloy type deformation. The high resolution measurements made in the present investigation also indicate that constant structure behavior can be determined from the plastic strain rate versus stress data obtained at small strains immediately following a change in total strain rate. This interpretation is fundamentally different from previous analysis based on the determination of an instantaneous resistance to flow at the new imposed strain rate. The constant structure results obtained in
5. I. S. Servi and N. J. Grant, Trans. Am. Inst. Min. Engrs 191, 909 (1951). 6. K. Kucharova, I. Sax1 and J. Cadek. Acta metall. 22. 465 (1964). 7. M. J. Mills, J. C. Gibeling and W. D. Nix, Acta metall. 33, 1503 (1985). 8. W. G. Johnston and J. J. Gilman, J. appl. Phys. 30, 129 (1959).
9. J. H. Holbrook, J. C. Swearengen and R. W. Rohde, Mechanical Testing .for Deformation Model Develooment, ASTM STP 765 (edited by R. W. Rhode and
J. C. Swearengen), D. 80 (1982). 10. J. C. Gibeling,Ph:D: dissertation, Stanford Univ. Calif. (1979). 11. J. C. Gibeling and W. D. Nix, Proc. 6th Int. Co& on the Strength of Metals and Alloys (edited by R. C. Gifkins), p. 613. Pergamon Press, Oxford (1982). 12. J. C. Gibeling, J. H. Holbrook and W. D. Nix, Acta metall. 32, 1287 (1984). 13. L. Raymond and J. E. Dom, Trans. Am. Inst. Min. Engrs 230, 560 (1964).
14. G. Konig and W. Blum, Acta metall. 25, 1531 (1977).
Acta mernfl.Vol. 35, No. 6, pp. 1391-1400,1987 Printed
in Great
Britain.
All rights reserved
A NEW STRAIN RATE CHANGE TECHNIQUE FOR DISTINGUISHING BETWEEN PURE METAL AND ALLOY TYPE CREEP BEHAVIOR D. L. YANEY,’ J. C. GIBELING’ and W. D. NIX’ ‘Department of Materials Science and Engineering, Stanford University, Stanford, CA 94305 and 2Department of Mechanical Engineering, Division of Materials Science and Engineering, University of California, Davis, CA 95616, U.S.A. (Received
24 February
1986)
Abstract-A
new technique involving strain rate changes has been developed for distinguishing between pure metal and alloy type creep behavior. Both positive and negative strain rate changes were performed on aluminum and Al-5.8 at.% Mg (pure metal and alloy type material respectively) using an Instron electromechanical testing machine. Tests were conducted at 573 K with initial total strain rates of either 4 x 10e5 or 4 x 10-4s-1. Immediately following an order of magnitude change in total strain rate, the plastic strain rate was monitored as a function of stress. The observed transient response for both pure aluminum and Al-S.8 Mg was found to agree with predicted behavior, indicating that the strain rate change test can be used to distinguish between pure metal and alloy type creep behavior. The strain rate change test was also found to be a promising single specimen technique for studying constant structure deformation. The quality of the constant structure data obtained using this technique is shown to depend on the accuracy with which plastic strain rate can be determined. A procedure is described for determining the plastic strain rate with sufficient accuracy to allow the strain rate change test to be used in place of multiple stress reduction tests to study constant structure deformation. RCum-Nous
avons dtvelopp6 une nouvelle technique, impliquant des variations de la vitesse de d&formation, pour distinguer les comportements en fluage d’un m&tal pur et d’un alliage. Nous avons fait varier positivement et nbgativement la vitesse de d&formation de l’aluminium et de Al-5,8 at.% Mg (respectivement un mbtal pur et un alliage), B l’aide d’une machine d’essai &ctromCcanique Instron. Les essais ont 6tt effect&s B 573 K avec des vitesses initiales de dbformation totale de 4 x lo-’ ou de 4 x 1O-4 s-l. Immediatement aprt% une variation d’un ordre de grandeur de la vitesse de d&formation totale, nous avons enregistrb la vitesse de dtformation plastique en fonction de la contrainte. La rbponse transitoire observ6e tant pour l’aluminium pur que pour Al-5,8 Mg est en accord avec le comportement prkdit, ce qui indique que l’essai avec variation de la vitesse de dkformation peut itre utilisb pour diffkrencier les comportements en fluage d’un m&i pur et d’un alliage. L’essai avec variation de la vitesse de d&formation est tgalement une technique prometteuse dans le cas d’un tchantillon unique pour 6tudier la d&formation $ structure constante. La qualit des don&es $ structure constante obtenues B l’aide de cette technique d&end de la pr&ision avec laquelle on peut dbterminer la vitesse de dbformation plastique. Nous d&xivons un pro&d& pour dCterminer la vitesse de d&formation plastique avec assez de p&&ion pour permettre d’utiliser l’essai avec variation de la vitesse de d&formation g la place d’essais multiples de rkduction de la contrainte, dans le but d’ttudier la d&formation B structure constante. Zusammenfassung-Mit einem neu entwickelten Untersuchungsverfahren auf der Grundlage von Wechseln in der Dehnungsrate kann zwischen dem Kriechverhalten reiner Metalle und Legierungen unterschieden werden. Sowohl positive als such negative Wechsel der Dehnungsrate wurden an Aluminium und der Legierung Al-5,8 At.-% Mg (reines Metal1 und typische Legierung also) in einer elektromechanischen Instronmaschine durchgefiihrt. Die Versuche fanden bei 573 K mit anf&glichen Dehnungsraten von 4 x 10m5oder 4 x 1O-4S-I statt. Unmittelbar nach einem Wechsel der Dehnungsrate urn eine GrBBenordnung wurde die plastische Dehnung in Abhangigkeit von der Spannung aufgenommen. Das beobachtete iibergangsverhalten der beiden Metalle stimmte mit dem vorausgesagten Verhalten iiberein. Dieses Ergebnis weist darauf hin, da13dieser Test zur Unterscheidung des Kriechverhaltens von reinen Metallen und Legierungen verwendet werden kann. Es ergab sich aul%xdem, daD dieser Test eine vielversprechende Methode zur untersuchung der Verformung bei konstanter Struktur ist. Die Qualitlt der Ergebnisse bei konstanter Struktur hlngt bei diesem Test von der Genauigkeit ab, mit der die plastische Dehnungsrate bestimmt werden kann. Ein Verfahren wird beschrieben, mit dem diese plastische Dehnungsrate mit ausreichender Genauigkeit bestimmt werden kann, damit die Wechsel in der Dehnungsrate anstelle der Versuche mit mehrfacher Spannungsreduktion zur Untersuchung der Verformung bei konstanter Struktur benutzt werden kSnnen.
1. INTRODUCTION Tests involving
strain rate changes have been used by many investigators for a number of different purposes. Most frequently, the strain rate change test has been used in the study of steady state flow of
materials [l, 21. This is illustrated schematically in Fig. 1. A specimen is deformed at an initial strain rate i, until a steady state flow stress 0, is observed. The
strain rate is then changed to i, and deformation allowed to proceed at this new rate until steady state conditions
1391
are once
again
achieved.
Since
several
1392
YANEY et al.: A NEW STRAIN RATE CHANGE TECHNIQUE
Strain
Fig. 1. Schematic stress-strain curve for a strain rate increase in a pure metal.
strain rate changes can typically be performed on a single specimen, this version of the strain rate change test is an efficient means of determining the strain rate dependence of the steady state flow stress of a material at a particular temperature. The strain rate change test has also been used to study deformation under conditions of constant internal structure. Young et al. [3] noted that experimental difficulties are often encountered when the conventional stress-drop test is used to study constant structure flow in pure metals. The transient creep rates following large stress reductions are often quite small and difficult to measure. In addition, for successful analysis of the strain transient, it is necessary to separate the observed creep rate following a stress drop into its elastic, anelastic and plastic components. They attempted to circumvent these difficulties by using the strain rate change test instead of the stress-drop test to study constant structure flow behavior. The method of Young et al. [3] can be described best by assuming that creep of pure polycrystalline metals in the power law regime is adequately represented by an equation of the form kEN
SDAPaN (1)
where, S = structure constant E = dynamic Young’s modulus, 1 = subgrain size, o = applied stress, D = lattice diffusion coefficient, p, N = constant exponents. The exponents p and N are determined using the procedure illustrated in Fig. 1. A sample is deformed to large strain at strain rate i, until steady state is achieved (a = al). The strain rate is then changed and deformation allowed to continue until a new steady state is reached. Immediately following the strain rate change, the “instantaneous resistance to plastic flow at the new strain rate” is measured. On chart recordings of load versus time this is taken as the stress corresponding to the sudden change in slope that occurs at (r = u2. Thus, according to Young et al. [3],
6, and a2 refer to the flow stress of the same structure at two different total imposed strain rates, namely i, and i,. From Fig. 1, it can be seen that the steady state stress exponent is given by the expression
It is assumed that the substructure is completely characterized by the subgrain size, 1. Thus, the constant structure stress exponent can be written as
Since subgrain size is typically assumed to be inversely proportional to the steady state flow stress, p is simply equal to N - n. Since the work of Young et al. [3] in the mid1970’s, the development of high speed computer aided data acquisition techniques has eliminated most of the experimental difficulties associated with interpreting the results of stress-drop tests. Thus, today, multiple stress reduction tests are the preferred method for studying the constant structure flow behavior of materials. In the present investigation, computer aided data collection techniques have been applied to the more conventional strain rate change test. As a result, a number of problems associated with using the method of Young et al. [3] to study constant structure behavior have become apparent. In the sections that follow, a new technique for studying constant structure behavior using the strain rate change test is described. This technique is independent of any theoretical picture of plastic flow. It is shown that by monitoring the variation in plastic strain rate with stress, it is possible to use the strain rate change test to distinguish between pure metal and alloy type creep behavior. The results of strain rate change tests performed on pure aluminum and Al-5.8 at.%Mg (pure metal and solid solution strengthened alloy, respectively) are presented and shown to conform to expected behavior.
YANEY et al.:
A NEW STRAIN KATE CHANGE TECHNIQUE
9
Time
Isecl
(4
1747
‘..,
-
‘. .-_, ‘. ‘_ ‘.
‘._ ‘.. 1745
2
-
12
I
.. .. .
10-a nn,sec
-
.. ‘.
. . .
;
1745
Cal
t...~.~~~~‘~~~~~~.~~‘~~.~~~~~~‘~.,.~.~~.’ 19 5
20.4
20.0
Time
20
0
21.2
(set)
@I
Fig. 2. Crosshead displacement vs time for: (a) a crosshead speed increase
and (b) a crosshead
speed decrease.
2. EXPERIMENTAL
The materials used in this investigation were Al (99.999%) and Al-5.8 at.%Mg. Cylindrical compression specimens 5.08 mm (0.2 in) in diameter and 7.62mm (0.3 in) in length were prepared from these materials. After machining, all specimens were annealed in air at 723 K for one hour and air cooled. Strain rate change tests were conducted in air at 573 K using an Instron model 1125 electromechanical testing machine. The total imposed true strain rate was either 4 x 10m5or 4 x 10m4s-’ and both positive and negative strain rate changes of an order of magnitude were performed. Samples were deformed between polished alumina plattens with boron nitride used as a lubricant. Heating was accomplished by a split shell resistance furnace. Although measured loads never exceeded 2220 N (500 lb), existing compression test fixtures necessitated the use of a 44.5 kN (10,000 lb) capacity Instron load cell to measure load. Thus, the major source of noise in the load signal was the high grain setting on the load cell amplifier. In order to characterize the ability of the Instron testing machine to perform the desired crosshead speed changes, the following procedure was used. A plexiglass sample 25.4 mm (1 .OOin) in length and 19.1 mm (0.751 in) in diameter was loaded in compression at an initial crosshead speed of 2.12 x 1O-4
1393
mm/s (5 x low4 in/min). After loading to approx. 1780 N (400 lb), the crosshead speed was increased to 2.12 x 10m3mm/s (5 x 10e3 in/min). During the course of the crosshead speed change, crosshead displacement was measured as a function of time using a Unimeasure 80 transducer (described elsewhere [4]) in conjunction with a Hewlett-Packard 3456A digital voltmeter. Typical plots of crosshead displacement vs time are shown in Fig. 2. The displacement resolution was 0.02pm and the time resolution was 0.025 s. This procedure was also used to characterize machine response during the crosshead speed decrease from 2.12 x 10e3 to 2.12 x 10m4 mm/s. A Hewlett-Packard model 3054A data acquisition system was used to collect data during all tests, with the first 60 points following a change in strain rate collected at a rate of five readings per second. This system was also used to control the crosshead speed of the Instron. As a result, it was possible to vary the crosshead speed as desired during the course of a test to either maintain a constant total imposed true strain or perform a strain rate change. The total imposed true strain rate, i, is related to crosshead speed by the following equation ir= 8/L,
(4)
where, 8 = crosshead speed, L, = current total length of the sample. Thus, in order to maintain a constant total true strain rate it is necessary to calculate the current length of the sample at frequent intervals during the course of a test and then used equation (4) to calculate the crosshead speed necessary to maintain the desired total imposed true strain rate. At any point in a test, the current total length of the sample is given by the expression
L,=L,-Ax+P/K,
(5)
where, L,= initial length of the sample, Ax = total deflection of the crosshead since the beginning of the test, P = magnitude of the current load, K,,, = machine stiffness at load P. The total crosshead deflection, Ax was measured using an Instron clip-on extensometer with a maximum deflection of 6.35 mm (0.25 in). In order to measure machine stiffness, the test specimen was replaced by a ceramic cylinder 19.05 mm (0.75 in) in diameter and 25.4 mm (1 in) in length. Crosshead deflection was then monitored as a function of load for an imposed crosshead speed of 4.23 x 10-4mm/s (0.001 in/min) and a test temperature of 573 K. The crosshead speeds used in the strain rate change tests ranged from 1.72 x 10e4 mm/s (6.78 x 10m6in/s) to 3.05 x 10m3mm/s (1.2 x 10m4in/s). The machine stiffness was found to be independent of crosshead speed within this range. However, the machine stiffness was found to depend on load. The loaddisplacement values collected during the spring constant test were fitted to a fifth order polynomial and the K,,, value used in equation (4) is that value corresponding to the current load, P. Finally, it
YANEY et al.:
1394
A NEW STRAIN RATE CHANGE TECHNIQUE
20
1 Aluminum . 573 K
Ial ~~~‘~~~~‘~~~~‘~~~~~~~~~I~~~~
0 0
10
20
30
Percent
True
40
50
60
Strain
(4
20-....,....,....,....,....,....
1 Alumirium . 573 K ;ii 15%.
4 x
lo-
Fig. 4. Normalized strain rate vs modulus compensated stress for pure aluminum and Al-MB alloys.
4 x
Is-‘)
m-5
15-11
I 0
_
lb1 _
~~~~‘~..~~~~~~I~~~~‘.~“‘~“’ 0 i0 20
30
Percent
True
40
50
60
Strain
(b)
Al-5.8 -573 K
at.%Mg
ICI ~~~~.~~..I~~~~~~~~~I~~~~~~~.~I~~~~~~~..I~
0 0
10
20
Percent
True
30
40
Strain
(4
Fig. 3.True stress vs percent true strain for: (a) a strain rate increase test in pure aluminum, (b) a strain rate decrease test in pure aluminum and (c) both a strain rate increase and a strain rate decrease test in Al-5.8 at.%Mg. All tests conducted at 573 K. The imposed total true strain rate in all tests was either 4 x 10m5or 4 x 10-4s-1.
should be noted that the crosshead speed was not continuously variable. It could be incremented only in steps corresponding to 0.1% of the selected pushbutton speed. However, this step size was sufficiently small that the strain rate varied by no more than 2.5% from the desired value before a correction was made.
3. EXPERIMENTAL
RESULTS
Typical stress-strain curves for positive and negative changes in strain rate in pure aluminum are shown in Fig. 3(a) and (b) respectively. Note that because of the large amount of strain required to reach steady state, both at the beginning of the test and after a strain rate change, only one strain rate change experiment could be performed on any given sample. Values of steady state flow stress and strain rate are plotted in Fig. 4 and shown to agree quite well with creep test results of other investigators ]4,51. Figure 3(c) shows a typical stress-strain curve for strain rate change experiments performed on Al5.8 Mg. The steady state flow stress values obtained are plotted in Fig. 4 and shown to agree quite well with results of other investigators [6, 7J. Unlike pure aluminum, where elevated temperature deformation is characterized by extensive subgrain development, microstructure evolution in Al-Mg alloys deformed in the Class I regime is characterized by the development of a homogeneous distribution of dislocation loops [7]. As a result, large amounts of strain are not required for the Al-Mg alloy to reach steady state. However, because annealing before testing produces samples with relatively low dislocation densities, a yield point is frequently observed at the beginning of a test as well as immediately following a strain rate increase in the AI-Mg alloy. Only after significant dislocation multiplication occurs does the stress required to cause deformation at a constant strain rate approach the steady state value. For similar reasons, a minimum in flow stress is observed following a strain rate decrease for Al-S.8 Mg at 573 K. This can be seen in Fig. 3(c). Steady state deformation at a total strain rate of 4 x 1O-4 s-r produces a dislocation density which is significantly higher than
YANEY et
al.:
A NEW STRAIN RATE CHANGE TECHNIQUE
Fig. 5. Schematic illustration of the Instron testing machine and sample.
that which would characterize steady state deformation at the lower strain rate (4 x 10e5 SK’). Thus, until dislocation annihilation occurs, the flow stress observed at the new strain rate is less than the steady state value.
1395
where, k = crosshead speed, P = loading rate, E = Young’s modulus of the sample, A, = initial area of the sample, L, = initial length of the sample, L, = unloaded length of the sample. Using equation (7), the plastic strain rate can be computed at any point during the experiment. It is important to note that both the plastic strain rate and the stress vary continuously during the transient following a change in total strain rate. The plastic strain rate approaches the total strain rate only when the loading rate is small (i.e. during steady state deformation). Thus, the analysis described above differs considerably from that of Young et al. [3] in which the total strain rate is assumed to be equal to the plastic strain rate even immediately after a strain rate change. The measurement of the plastic strain rate as a function of stress following a strain rate change permits one to distinguish between pure metal and alloy type creep behavior, as shown schematically in Fig. 6. Consider first the case of a pure metal in
Pure Metal Type
4. TECHNIQUE FOR DISTINGUISHING BETWEEN PURE METAL AND ALLOY TYPE CREEP BEHAVIOR In order to distinguish between pure metal and alloy type creep behavior, plastic strain rate was monitored as a function of stress during the deformation transient following a strain rate change. The observed variation was then compared with the known variation of plastic strain rate with stress for steady state deformation. In this section, the procedure for determining plastic strain rate is outlined and the expected variations of plastic strain rate with stress following strain rate changes in both pure metal and alloy type materials are discussed. As noted by Johnston and Gilman [8] in 1959, and later by Holbrook et al. [9], a proper interpretation of tension or compression tests requires that the coupling between specimen and testing machine be taken into account. Thus, as shown in Fig. 5, the testing system used in this investigation consists of two components: (1) the Instron testing machine which deforms elastically and (2) the specimen which deforms both elastically and plastically. The total imposed true strain rate, i, is simply the sum of three terms c, = i,,, machine + i,,, sample + i,,, sample
LOG(Stress)
Alloy Type
(6)
where &,mach,ne= rate at which the machine deforms elastically expressed as a strain rate, CE,,samp,e = elastic strain rate of the sample, iP,,samp,e = plastic strain rate of the sample. Or equivalently, as shown by Holbrook et al. [9]
1
a
(7)
b
LOG(Stress)
Fig. 6. Schematic illustration of the expected variation in log (plastic strain rate) with log (stress) following strain rate Increases and decreases in: (a) pure metals and (b) alloy type materials.
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which steady state deformation occurs in the power law regime. When the strain rate is increased, the behavior shown schematically in Fig. 6(a) should be observed. Immediately after a change in total imposed true strain rate, no sudden change in plastic strain rate should be observed, i.e. the plastic strain rate should not change discontinuously. If flow is thermally activated, the plastic strain rate depends only on the stress, temperature and structure and not on the stress rate. Since neither the stress nor the structure change instantaneously and the temperature is held constant, no sudden change in plastic strain rate should be observed immediately following a change in imposed total strain rate. In terms of the elements shown in Fig. 5, the strain rate can change instantaneously only for the two elastic elements; the plastic strain rate of the element represented by the dashpot cannot change abruptly. The observed variation of plastic strain rate with stress following a strain rate increase should differ considerably from the known variation of plastic strain rate with stress for steady state deformation. For a pure metal, deformation in the power law regime is characterized by the formation of well developed subgrains with a characteristic dimension, 1, which varies inversely with steady state flow stress. Thus, for the case of a strain rate increase, the structure initially present after steady state deformation at the lower strain rate is “softer” than the structure which is characteristic of steady state flow at any higher plastic strain rate. As a result, the flow stress during the transient is expected to be temporarily less than the flow stress predicted from steady state data at the same plastic strain rate. Only after sufficient microstructural refinement has occurred should a return to steady state behavior be observed. For the case of a strain rate decrease in a pure metal, plastic strain rate continuity should once again be observed immediately following the change in total imposed strain rate. However, as the deformation transient proceeds, the stress is expected to be greater than that characteristic of steady state deformation at the same plastic strain rate. The structure formed by steady state deformation at the initial high strain rate is “stronger” than the structure characteristic of steady state flow at the lower strain rate. Thus, until microstructural softening occurs, the stress will be greater than that predicted from steady state data at the same plastic strain rate. Finally, it should be noted that for the short period of time following a strain rate increase or decrease when the structure is essentially constant, it may be possible to study constant structure flow behavior using the strain rate change test. Young et al. [3], characterized the relationship between strain rate and stress at constant structure by a power law relationship, and obtained a constant structure stress exponent of about 8 for pure aluminum using the strain rate change test. However, more recent stress drop experiments by Gibeling [lo] and Gibeling and Nix
[1I] have shown that for small stress changes (such as those seen at the beginning of a strain rate change experiment), the constant structure stress exponents in pure metals may be much larger than eight. As mentioned earlier, microstructural evolution in alloy type materials is characterized by the development of a homogeneous distribution of dislocation loops. This differs considerably from microstructural evolution in pure metals in which subgrains are formed. Thus, pure metals and alloy type materials should respond quite differently to changes in total imposed strain rate. The expected responses of an alloy type material to increases and decreases in total strain rate are shown in Fig. 6(b). For purposes of illustration, the steady state stress exponent for materials exhibiting alloy type behavior is assumed to have a value of approximately three. This is commonly observed in Al-Mg alloys deformed in the Class I regime. If flow is again assumed to be thermally activated, then plastic strain rate continuity should be observed immediately following a strain rate change in alloy type materials as well. As the deformation transient proceeds, the variation in plastic strain rate with stress should differ from the variation in plastic strain rate with stress predicted from steady state behavior. For a strain rate increase in an alloy type material, the dislocation density is initially lower than that characteristic of steady state deformation at any higher strain rate. Thus, the observed stress should be greater than that predicted by the steady state relation during the transient. Only after dislocation multiplication has had a chance to occur should a return to steady state behavior be observed. Analogously, for the case of a strain rate decrease, the dislocation density is initially too high. Thus, until dislocation annihilation occurs, the stress observed at a given plastic strain rate should be less than that associated with steady state deformation at the same strain rate. Finally, it should be possible to determine the constant structure stress exponent for alloy type materials using the strain rate change test. Stress drop experiments of Mills et al. [7] indicate that a constant structure exponent of approximately two should be observed in Class I alloys. This is shown in Fig. 6(b). 5. OBSERVED BEHAVIOR-COMPARISON WITH EXPECTED RESULTS
Log-log plots of plastic strain rate versus stress for both increases and decreases in total strain rate for pure aluminum are shown in Fig. 7(a) and (b) respectively. Similar plots for strain rate change tests performed on the Al-5.8 Mg alloy are shown in Fig. 8(a) and (b). In all cases, the observed transient behaviors for both aluminum and Al-5.8 Mg are in excellent agreement with the qualitative predictions shown in Fig. 6. These results demonstrate that the strain rate change test can successfully distinguish between pure metal and alloy type creep behavior.
YANEY
et al.:
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RATE
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from anelastic deformation was calculated for all points following a strain rate decrease in pure aluminum. The results of this calculation indicate that for a strain rate decrease in pure aluminum, the anelastic strain rate is always two orders of magnitude less than the plastic strain rate. Thus, for pure aluminum there is no need to modify equation (6) to take anelastic deformation into account. Furthermore, since anelastic deformation is always a smaller fraction of the total deformation in Al-Mg alloys than in pure aluminum, the contribution of anelastic processes to the total strain rate in the Al-5.8 Mg alloy was not taken into account.
Aluminum 573 K
5.1. Plastic strain rate continuity
I 0
1.0
.9
LOG[Stress.
1 1
12
MPa)
Previously it was noted that if flow is thermally activated, the plastic strain rate must be continuous
10-j
Al-5.8 Aluminum
1
573 K Strain
573 K
strain RateDecrease 10-5
lb1
1.0
.9
LOG(Stress,
1.1
1.2
1.E
1.9
MPa)
(4 lo+T
Fig. 7. Log (plastic strain rate) vs log (stress) following: (a) a strain rate increase and (b) a strain rate decrease in pure aluminum. Circles represent transient behavior and squares represent steady state behavior.
The contribution of anelastic deformation to the total strain rate has not yet been considered. Since large anelastic strains have been observed in pure aluminum [4], it is necessary to determine the effect of including in equation (6) a term corresponding to the anelastic strain rate on the calculation of the plastic strain rate. Previously, Gibeling [lo] showed that the anelastic response-of pure aluminum to a stress reduction from 9.6 to 0.96 MPa at 573 K could be successfully described by a rheological model. In this model, two Voigt elements, one with a linear dashpot and one with a power law dashpot with a stress exponent of two are placed in series. Assuming that the anelastic deformation which occurs during the strain rate changes can also be described using this model, the contribution to the total strain rate
1.7
LOG(Stress,
MPal
@I
Increase
1.6
1.5 .8
Rate
at.%Mg
Al-5.8 573 K Strain
10-5
1.5
Rate
at.%Mg Decrease
Ibl :
:
1.6
1.7
LOGEtress,
1.8
’
1.9
MPa)
@I
Fig. 8. Log (plastic strain rate) vs log (stress) following: (a) a strain rate increase and (b) a strain rate decrease in Al-5.8 at.%Mg. Circles represent transient behavior and squares represent steady state behavior.
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following a change in crosshead speed. However, the calculated plastic strain rates immediately following strain rate increases for both materials are abnormally low. In fact, the plastic strain rate calculated 0.2 s after the strain rate increase in pure aluminum is negative, erroneously indicating that the sample (which was being tested in compression) was increasing in length following the increase in crosshead speed. It should be noted that although contributions to deformation from mechanically activated strain cannot be ruled out, they cannot be responsible for the apparent discontinuities in plastic strain rate. If mechanically activated strain contributed to deformation during the period of high stress rates following an increase in crosshead speed, the plastic strain rate observed would be greater, not less than the initial steady state strain rate. Thus, since calculations similar to those used by Gibeling et al. [12] indicate that a resolution time of 0.2 s should be sufficient to observe plastic strain rate continuity in aluminum and Al-S.8 Mg, factors other than athermal flow must be responsible for this discrepancy. Instead, it is believed that the inherent inaccuracy in Km as well as possible difficulties in quickly establishing the new crosshead speed are responsible for the apparent discontinuity in plastic strain rate following an increase in total strain rate. During steady state deformation, the dominant term in equation (7) is the total strain rate 8/L,. However, immediately following a strain rate increase, the first and second terms in equation (7), k/L, and P/k;, L, respectively, are of approximately equal magnitude. In addition, they are both more than an order of magnitude greater than the third term, pL,IEA, L,. Thus, the calculated value of i, immediately following a strain rate increase is strongly dependent upon the difference between two terms of comparable magnitude, and any error in either J? or K,,, will greatly affect the calculated value of i,. In fact, only an 11 percent increase in & is needed to confirm plastic strain rate continuity following a strain rate increase in the Al-5.8 Mg alloy. For pure aluminum, a 21% increase in K,,, is required to observe strain rate continuity. However, these are not unreasonable corrections in light of the fact that the greatest inaccuracies in K,,, occur at the low loads at which these materials were tested. It should be noted that although direct knowledge of & was required in this investigation in order to compute plastic strain rates, such knowledge would not have been required if it had been possible to measure sample length directly during testing. By measuring sample displacement independently, the plastic strain rate can be determined simply by subtracting the elastic strain rate of the sample from the total strain rate measured at the sample. If the tests had been conducted in tension (rather than compression) and the sample displacements had been measured directly across the gauge length, the plastic strain rates could have been calculated with much
greater accuracy than was possible in the present experiments. With regard to possible uncertainties in crosshead speed, Fig. 2(a) shows the variation in crosshead displacement with time for a crosshead speed increase from 2.12 x 1O-4 to 2.12 x lo-‘mm/s. For approx. 0.2 s after the speed change is initiated, the actual crosshead speed is approx. 1.3 times the desired speed. Thus, for the first data point collected following a strain rate increase, the assumed crosshead speed may be less than the actual value, thereby adding to the inaccuracies in i,. Although inaccuracies in J? and Km greatly affect the values of plastic strain rate calculated immediately following an increase in crosshead speed, the same is not true for a decrease in the crosshead speed. After a decrease in strain rate, the dominant term in equation (7) is the second term, P/k L,. This term is approximately an order of magnitude greater than either of the other two terms and determination of i, no longer depends on the difference between two terms of comparable magnitude. Thus, accurate knowledge of K,,, is not nearly as critical as for the case of strain rate increase. With reference to the accuracy with which crosshead speed is known, Fig. 2(b) shows the variation in crosshead displacement with time following a crosshead speed decrease from 2.12 x 10m3to 2.12 x 10m4 mm/s. For approx. 0.4 s following the speed change, the actual crosshead speed is less than the assumed value. However, the relative unimportance of the 8/Lp term minimizes the error introduced by the possible uncertainty in crosshead speed. 5.2. Constant structure behavior Despite the difficulties associated with accurately determining i, immediately following a strain rate change, it is quite clear from Figs 7 and 8 that the plastic strain rate does not equal the total strain rate immediately following a strain rate change as assumed implicitly by Young et al. [3]. Furthermore, with improved time resolution, it is now clear that there is no single stress which corresponds to a material’s “instantaneous resistance to flow” at the new strain rate. As a result, the procedure we have described here must be used to study constant structure behavior using the strain rate change test. Recently, Gibeling and Nix [1 l] used high resolution stress drop creep tests to study the constant structure flow behavior of pure aluminum at 673 K. Although a power law relationship of the form ccs= Ad.’ was found to adequately describe the constant structure behavior for large stress drops, this relationship was found to be inappropriate for describing the constant structure behavior following small stress reductions. For small stress drops, the apparent constant structure exponent was observed to increase to a value of about 10 indicating that the constant structure data could be better described by an exponential relationship.
YANEY et al.:
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structure conditions (i.e. constant .c?,, and 8), a plot of log i, vs u should yield a straight line. In Fig. 9(a) and (b), the logarithm of the plastic strain rate is plotted vs stress for strain rate increases and decreases, respectively, in pure aluminum. For both increases and decreases in strain rate, the exponential relationship of equation (8) is obeyed for approximately the first 0.024.03% strain following the change in strain rate. At larger strains, a deviation from linearity is observed indicating a change in structure. We note that the maximum change in stress associated with constant structure deformation in these tests is quite small, approx. 5%. According to equation (8), the slope, /3 of a log (E’,)u plot for constant structure is equal to AF/(2.303) kT6. If 8 is assumed to be Strain RateIncrease lal 1o-5 5 : : 5 : : : : : linearly proportional to the steady state flow stress 7.0 9.0 11.0 13.0 associated with formation of the initial structure (a,), Stress (MPa) then fl should be inversely proportional to the product To,, (AF is assumed to be independent of (4 temperature). Thus, the value of j? obtained for the 1o-3 strain rate increase for pure aluminum should be Aluminum greater than the value of /I obtained for the strain rate 573 K decrease at the same temperature, since the steady state flow stress reached prior to the strain rate increase was less than the steady state flow stress attained prior to the strain rate reduction. As shown in Fig. 9, this is what was observed, indicating that the results of the strain rate change tests on pure aluminum are internally consistent. The constant structure data obtained for pure aluminum in this investigation can also be compared to the constant structure data of other investigators [ 11, 131. This comparison is summarized in Table 1. When the data for the strain rate decrease are comStrain Rate Decrease lb1 pared with data for stress drops at 573 and 673 K, lo+ : : : /I is found to vary approximately with l/Tu,, as 7.0 9.0 11.0 13.0 expected. However, the value of p obtained for the Stress (MPa) strain rate increases is much higher than would be @I expected from the corresponding value of l/To,. Fig. 9. Log (plastic strain rate) vs stress for: (a) a strain rate Several possible explanations for this discrepancy can increase and (b) a strain rate decrease in pure aluminum at be found. The structure parameter, 8, may not scale 573 K. linearly with the steady state flow stress associated with formation of the initial structure. Also, the high value of /l obtained for the strain rate increase may Following the suggestions of Gibeling and Nix [l 11, reflect contributions to deformation from athermal the theory of obstacle controlled glide can be used to mechanisms. As noted earlier, the stress rate followdescribe the constant structure flow behavior of pure ing the increase in strain rate in pure aluminum is metals in terms of an exponential relationship
i,=toexp[~(l-;)I
(8)
where i, = pre-exponential term that depends on stress and structure, AF = Helmholtz free energy for activation of dislocation glide, k = Boltzmann’s constant, T = absolute temperature, rr = stress, d = structure parameter. It should be noted that this relationship, unlike a simple power law relationship, adequately describes constant structure flow behavior for small changes in stress, such as those immediately following a strain rate change. Then, under constant
Table
1. Exponential
law constant
structure
/Y[= AF/(2,303)kZZ] (MPa-‘) Strain rate increase (this investigation)
573 K
Stress drop 673 K Gibeling and Nix [ll] Stress drop 573 K Raymond and Dom Strain rate decrease (this investigation)
behavior W&l (K-’ MPa-I)
1.7
2.28 x 1O-4
1.0
3.10 x 10-q
0.7
2.53 x 10m4
0.62
1.42 x lo-*
[13]
573 K
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YANEY er al.:
A NEW STRAIN RATE CHANGE TECHNIQUE
quite high, 1.1 MPa/s. In addition, Konig and Blum [14], studying Al-l 1 wt%Zn at 523 K, observed that even for the same initial stress (and structure), the constant structure exponent, /I, was higher for stress increases than for stress decreases provided the initial stress was sufficiently high. With regard to the constant structure behavior of alloy type materials, Mills et aI. [7] showed that a power law relationship of the form, t,, = Aa* can be used to describe the constant structure behavior of Al-5.5 at.%Mg tested at 573 K in the Class I regime. Unfortunately, the result of these high resolution stress reduction creep tests could not be duplicated using the strain rate change test. For the strain rate increase test, problems associated with the measurement of i, at the beginning of the transient made determination of a constant structure exponent difficult. For the strain rate decrease, a constant structure exponent greater than two was obtained. This lack of agreement with previous experiments is probably a reflection of the inaccuracy inherent in determining i, using the method of this investigation. By modifying the experimental procedure as described in Section 5.1 so that the plastic strain rate following a change in crosshead speed can be more accurately determined, it should be possible to duplicate the constant structure results of multiple stress reduction tests using a single strain rate change test.
the present investigation for aluminum are consistent with an exponential law for thermally activated glide, and are in general agreement with previous results. However, experimental uncertainties made a precise determination of plastic strain rates difficult early in the transient. As a consequence, only a qualitative comparison could be made between the constant structure behavior of Al-5.8 at.%Mg determined from strain rate change tests and previous stress change experiments. Further, plastic strain rate continuity was confirmed only for strain rate decrease tests. It is suggested that direct measurements of specimen strain should enable single specimen strain rate change tests to be used to make a qualitative distinction between pure metal and alloy type behavior. In addition, these tests should provide a quantitative measure of constant structure deformation.
REFERENCES 1. J. W. Edington, K. N. Melton and C. P. Cutler, Prog. Mater. Sci. 21, 61 (1976). 2. A. K. Ghosh, Superplastic Forming of Structural Allovs
(edited by N. ET Paton and C. I? Hamilton), p. 85. Conf. Proc. Metall. Sot. A.I.M.E. (1982). 3. C. M. Young, S. L. Robinson and b. D: Sherby, Acta metall. 23, 633 (1975). 4. J. C. Gibeling and W. D. Nix, Acta metall. 29, 1769 (1981).
6. CONCLUSIONS
The continuous variation of plastic strain rate with stress following increases and decreases in total strain rate has been analyzed. The results of experiments on pure aluminum and Al-5.8 at.%Mg tested at 573 K demonstrate that strain rate change tests can be used to make a qualitative distinction between pure metal and alloy type deformation. The high resolution measurements made in the present investigation also indicate that constant structure behavior can be determined from the plastic strain rate versus stress data obtained at small strains immediately following a change in total strain rate. This interpretation is fundamentally different from previous analysis based on the determination of an instantaneous resistance to flow at the new imposed strain rate. The constant structure results obtained in
5. I. S. Servi and N. J. Grant, Trans. Am. Inst. Min. Engrs 191, 909 (1951). 6. K. Kucharova, I. Sax1 and J. Cadek. Acta metall. 22. 465 (1964). 7. M. J. Mills, J. C. Gibeling and W. D. Nix, Acta metall. 33, 1503 (1985). 8. W. G. Johnston and J. J. Gilman, J. appl. Phys. 30, 129 (1959).
9. J. H. Holbrook, J. C. Swearengen and R. W. Rohde, Mechanical Testing .for Deformation Model Develooment, ASTM STP 765 (edited by R. W. Rhode and
J. C. Swearengen), D. 80 (1982). 10. J. C. Gibeling,Ph:D: dissertation, Stanford Univ. Calif. (1979). 11. J. C. Gibeling and W. D. Nix, Proc. 6th Int. Co& on the Strength of Metals and Alloys (edited by R. C. Gifkins), p. 613. Pergamon Press, Oxford (1982). 12. J. C. Gibeling, J. H. Holbrook and W. D. Nix, Acta metall. 32, 1287 (1984). 13. L. Raymond and J. E. Dom, Trans. Am. Inst. Min. Engrs 230, 560 (1964).
14. G. Konig and W. Blum, Acta metall. 25, 1531 (1977).