- Email: [email protected]
Threshold stresses in amorphous alloys—II. Structural relaxation
Acta mrrull. Vol. 30. pp. 2129 to 2133, 1982 Printed in Great Bntain. All rights reserved
THRESHOLD
OOOI-6160/82;122129-05$03.00/O Copyright 0 1982 Pergamon Press Ltd
STRESSES IN AMORPHOUS STRUCTURAL RELAXATION
ALLOYS-II.
A. 1. TAUB General
Electric
Corporate
Research
(Receiced
and Development,
9 Noren~her
P.O. Box 8, Schenectady,
1981; in revisedform
NY 12301, U.S.A.
21 Muy 1981)
Abstract--Early investigations of structural change in amorphous alloys found stress independent relaxation kinetics. The results of this study indicate that this stress independence only occurs above some stress threshold and that for applied stresses below this critical value the relaxation proceeds at a much slower rate. The existence of this threshold suggests a mechanism for structural relaxation based on shear type rearrangements.
RCsumP--Des etudes anciennes sur le changement de structure dans des alliages amorphes avaient mis en evidence des cinttiques de relaxation independantes de la contrainte. Les risultats de notre etude montrent qu’il n’y a independance de la contrainte qu’au-dessus d’une contrainte seuil et qu’au-dessous de cette valeur critique la relaxation se produit beaucoup plus lentement. Nous presentons un modtle qui rend compte de cette relaxation structurale assist&e par la contrainte. Nous supposons que la relaxation se produit en deux &tapes: un rearrangement atomique de type cisaillement suivi par un effondrement des atomes au tour du volume libre disponible. Cet effondrement permet a la fois une mise en ordre a courte distance et une reduction du volume libre.
Zusammenfassung-Bei friiheren Untersuchungen der strukturellen Anderungen von amorphen Legierungen ergaben sich spannungsunabhangige Relaxationskinetiken. Die Ergebnisse dieser Untersuchung zeigen. daB diese Spannungsunabhlngigkeit nur oberhalb einer Spannungsschwelle auftritt und dab die Relaxation unterhalb dieser Schwelle mit vie1 geringerer Geschwindigkeit ablluft. Ein Model]. welches diese spannungsunterstiitzte strukturelle Relaxation beschreibt. wird entwickelt. Es wird angenommen, daB das Relaxationsereignis iiber einen zweistutigen Prozess ablauft: eine scherartige Atomumlagerung. gefolgt von einem Zusammenriicken der Atome in der NHhe des verfugbaren freien Volumens. Dieses Zusammenriicken erlaubt sowohl die Einstellung der Nahordnung als such die Verringerung des freien Volumens.
INTRODUCTION
EXPERIMENTAL
Structural relaxation has been shown to affect many properties of amorphous alloys (e.g. radial distribution function [ 1.23, Curie temperature [335], elastic modulus [6], flow [779]). Of these properties, the change in flow resistance, as measured by the increase in viscosity, exhibits perhaps the most dramatic changes. Increases in viscosity due to structural change, of greater than five orders of magnitude have been reported [IO]. The temperature dependence of the kinetics of this viscosity relaxation have been examined by numerous investigators [779. I I]. On the other hand, the effect of applied stress on the kinetics has received only cursory attention. This is probably due to the early findings of apparent stress independence [ 11-I 31. However, the establishment of a stress threshold for flow, as described in the previous paper, motivated a re-examination of this question. The results of this new investigation of the stress dependence of structural relaxation. will be presented in this paper. 2129 AM 30,l?-t
The specimens tested were amorphous Fe,,N&P,,B, obtained from Allied Chemical Corporation (Metglas 2826) in the form of ribbons 1.4 m wide x 48 pm thick. The creep tests were performed in tension using the apparatus described previously [ 1 I]. The tests were conducted at constant equivalent shear stress T = o/d’3 where D is the uniaxial tensile stress. The gage length, as defined by the hot zone, was 25.5 cm. During the in sifu preanneals, the specimen was held in tension at 5 MPa to keep it straight. The Hov. observed during these preanneals was negligible. The details of converting the raw data of the tests into measures of stress, strain and strain rate have been described in detail elsewhere [ 1 I]. RESULTS Figure I is a plot of equivalent shear strain = 4’3~ where l is the uniaxial tensile strain, for two
2130
TAUB:
THRESHOLD
STRESSES IN AMORPHOUS
ALLOYS-II
I a b
Fe40Ni40P14B6
(505K)
2‘ELASTIC OL
0
’
I
I
1000
2000 (MINUTES)
TIME
I
3000
4000
Fig. 1. Equivalent shear strain as a function of time, for two as-cast samples of Fe40Ni40PL4B6, creep tested at 505 K. Sample a was held at 505 K for 1 min prior to loading. Sample b was held for 90min. The instantaneous elastic strains are indicated.
samples of as-cast Fe40Ni,aP,,B,, creep tested at 505 K. In test a, the ribbon was heated from room temperature to 505 K (11 min), then held at 505 K for 1 min, at which time the stress was increased from the small straightening load of 5 MPa to the testing stress of 117 MPa. The temperature was then held at 505K and the flow monitored for 3150 min. Also shown in the figure is the strain-time history for a similar test b. The,\only difference in the tests was a 90min hold at 505K prior to increasing the load in test b, compared to 1 min in test a. Figure 2 is a plot of viscosity r~ = r/t, vs time calculated from curves a and b in Fig. 1. After initial transients lasting approximately 200 min, both specimens exhibit a nearly linear increase in viscosity with time, ‘I = r/e + fit(O.9 cc‘.02). This linear increase in the viscosity of amorphous alloys has previously been observed and associated with relaxation of the amorphous structure [7,9]. Furthermore, a recent study of the rate of viscosity increase tj showed that the measured values appear to be independent of the testing method (tensile creep, tensile stress relaxation and bend stress relaxation) [ 111. In Fig. 3, the rates of viscosity increase for samples a and b are shown with the available literature data. The value of 4 for tests a and b are seen to be in agreement with each other and with the available data. The data in Fig. 3, indicate that not only are the kinetics of structural relaxation, as measured by fi, independent of the testing method, but independence of the testing stress is suggested as well. Additional evidence for stress independent relaxation is provided by the tensile stress relaxation, stress-strain rate plots presented in the accompanying paper. In those plots, the isochronal stress-strain rate curves shifted to lower strain rates uniformly with time. If the kinetics of structural change, as measured by the increase in viscosity with time, were stress dependent, then the curves would have rotated as they shifted. Further
evidence for stress independent relaxation are the results of a previous creep investigation of the kinetics of viscosity increase for the alloy Pds2Si,s [12, 13). That study showed that at 5OOK, the rate of viscosity increase is independent of both the testing stress and mid-test stress increases, for equivalent shear stresses in the range 39~ 7 < 55Pa. Referring to Fig. 2, the viscosity-time curve for the 90 min preanneal is seen to lie considerably below that for the 1 min preanneal. Since the only difference in the tests was the specimen load during the first 90 min, this observation implies that during this initial period, the rate of viscosity increase was slower for the specimen loaded to only 5Pa. This observation appears to be in contradiction to the data described above. However, we can show that this apparent contradiction disappears by examining additional viscosity data reported for other alloys annealed under
_
Fs4eNi)ef’t&
-
a- I MINUTE PREANNEAL b-90 MINUTE PREANNEAL
t’l IO’
(505l0
Ill1
I I02 TIME
III1
I I03
I,;1 IO4
1MINUTES)
Fig. 2. Viscosity 4 = r/j as a function of time, calculated from curves a and b in Fig. 1.
-“‘_ LAUD:
THRESHOLD
10'3
STRESSES IN AMORPHOUS
I
I
I
I
2131
ALLOYS-II
I
I
Fe4o”+of’wb
10'2 i
l
l II
Gi- IO
/
E
3 5
5 lO’( )
IO9
-P
STRESS RAWE (YR)
0.
TENSILE CREEP c
SYMBOL I
IO
A
t 100 IO4 II7
0
D
THIS ‘I(
0
DQ FART I
RELAXATION
108 1.4
I
1.6
REF
I
1
1.8
2.0
2.2
2.4
2.6
2.8
103/T tK-‘I Fig. 3. Rate of change of viscosity with time as a function of temperature, as measured in tensile creep, tensile stress relaxation and bend stress relaxation tests. The testing stress ranges are indicated.
both zero and finite loads. The zero load specimens were preannealed under an argon atmosphere, and then creep tested to measure the temperature dependence of the isoconfigurational viscosity. The viscosity at the end of each preanneal q?,, can be determined from the reported isoconfigurational curves. These viscosities and the preanneal temperatures and times are listed in Table 1 for Pds,Si,s[lO, 13) and Pd 75.sCu6Si,6.s [ 14). Since the observed viscosities ‘1,. are orders of magnitude greater than the as-cast viscosities vi [IO] and since these materials have been shown to exhibit a linear viscosity-time dependence [ 1I], the rate of viscosity increase can be calculated as
lower than those under the higher stresses used in Bow tests. Second, at the higher stresses, the relaxation kinetics appear to be stress independent. These two statements, although not conclusive evidence for the existence of a threshold stress for relaxation, are consistent with such a threshold. It is interesting to note that for Fe40Ni40P14B6r this relaxation threshold stress would fall somewhere in the range above 5MPa and below the minimum stress achieved during the stress relaxation tests (50MPa). and that the ilow threshold stress described in the accompanying paper lies within this same range. DISCUSSION
tjcalc _ (VI - qi) _ 2 t, [II . In Table 1, this rate is compared with the actual rates of viscosity increase measured for specimens tested at finite stresses (82MPa for PdSi [7] 133MPa for PdCuSi [ 141. For both alloys, the kinetics of viscosity increase under zero applied stress are clearty slower than those measured under finite stresses. All these observations are summarized by the following two statements. First, under very small applied stress (O-SMPa), the rates of viscosity increase are
We now consider the existence of a threshold stress for structural relaxation. One could account for the low relaxation rate at zero applied stress, compared to the greater rate at nonzero stresses, by assuming that some relaxation events require only thermal activation and that some require both thermal activation and the presence of a local stress greater than some threshold value. However, modeling of the relaxation would be simplified if it was not necessary to make this distinction between stress assisted and stress inde-
Table 1. Comparjson of rates of viscosity increase under zero and nonzero stress conditions Preanneal conditions T(K) t, (h)
Alloy Pd&il~
Cl33
Pd 77.5Cu&i6.5 El41
513 534 552 552
432 181 242 242
If (1015 Pa-s) 7.8 3.3 t.7 1.5
Yle.1e (IO’ Pa) 5.0 5.1 2.0 1.7
(iG?a) 22 [71 16 E71 13 c71 lZ[ll]
2132
TAUB:
THRESHOLD
STRESSES
pendent relaxation events. In fact, the nonzero relaxation rate at zero applied stress can be explained without invoking two types of relaxation mechanisms, if the residual stresses in the specimens are considered. It has been shown by magnetic domain and anisotropy studies that considerable quenched in stresses (7 > lOOMPa) exist in as-cast ribbons [15, 161. Therefore, in the zero applied stress tests, portions of the ribbon were not actually in a zero stress state. The finite relaxation rate observed under zero applied load may be due to the relaxation that occurs in those portions of the specimen subjected to residual stresses (7,,3 greater than the threshold stress (TV). The apparent relaxation rate is small, because 7rer > 7,, in only a small percentage of the material. Trying to determine what the observed i should be in this case is difficult. The situation is complicated by the varying residual stress states that have been observed (e.g. uniaxial tension, biaxial compression [ 171). Furthermore, the residual stresses in ribbons, as determined by magnetic domain observations [lS], have been shown to vary along the ribbon length. Then each specimen will have a different percentage of material with t,,,> T,,, and therefore exhibit a different tjc. This would account for the unsystematic variation in rjc with temperature as reported in Table 1. Since this last result is not easily explained by the original assumption of two types of relaxation events, we will adopt the second suggested criterion and require all relaxation events to be stress assisted. Any model proposed to explain the relaxation must then predict
rj(T,
7)
0
7<70
4(T)
7 >
IN AMORPHOUS
ALLOYS-II
Our new observation of a threshold stress for both structural relaxation and flow provides additional evidence for a shear-type relaxation mechanism. If structural change is accomplished via a series of shear-type atomic rearrangements then a threshold phenomenon similar to that observed for flow would be expected. When the applied stress is less than the threshold value, shear-type rearrangements are limited by energy considerations, so the structural relaxation rate is expected to be small. When the applied stress becomes greater than the threshold value, shear-type rearrangements are permitted, and structural relaxation can proceed. The limited amount of data on the threshold behavior that is available at this time, precludes the development of a more detailed model for relaxation. Of primary importance in understanding the relationship between flow and relaxation, is the need to establish the relative magnitudes of the threshold stresses for both events. More work is also needed to determine if the relaxation is exhibiting a true stress threshold. A true threshold implies that a stress free (both internal, residual and applied stresses) amorphous alloy would exhibit no structural relaxation at elevated temperatures. The fabrication of such a specimen is not feasible at this time. However, if it can be shown that the relaxation rate of a conventional amorphous specimen undergoes a sharp transition at T,,, then a real threshold probably exists. Experiments designed to test for such a change in the rate of viscosity increase are in progress. CONCLUSIONS
= 70 ’
However, the available data is not sufficient to rule out the coexistence of a small, stress independent contribution to the relaxation rate [ ~0.1 rj (T)] as suggested by the original assumption. The concept of stress assisted relaxation is in accord with the results of a previous study of structural relaxation [7], which indicated that flow and relaxation events are similar. In that study, the kinetics of viscosity increase of amorphous Pds2Si1s were explained by a model based on an extension of the free volume model for flow. It was assumed that relaxation is the result of discrete events involving atomic rearrangements. By analogy to flow, these relaxation events were assumed to require thermal activation and were permitted only for certain atomic configurations. The analysis showed that for both flow and relaxation, the values for the thermal activation barriers and for the probability of occurrence of the critical atomic configurations, were similar. Based on these results, it was suggested that a relaxation event consists of a shear-type atomic rearrangement, followed by the collapse of the atoms in their new configuration about the available free volume. This free volume collapse could of course, also produce an increase in local short range order.
The stress dependence of the kinetics relaxation, as measured by the increase with time, have been investigated for Fe4,,N&P,,B, (Metglas 2826). These been correlated with the available data based alloys, with the following results:
of structural in viscosity amorphous results have on two Pd-
(1) The relaxation kinetics appear to be stress independent above some threshold stress zo. Below this threshold, the relaxation proceeds at a slower rate compared to the higher constant value above the threshold. (2) When the residual stresses in the ribbons are considered, the material behavior can be summarized as follows W
7) =
0
7 <
t,,(T)
t(T)
7 ’
70)
The coexistence of a small, stress independent contribution to the relaxation rate [ < 0.11 (T)] is still a possibility. (3) The existence of a stress threshold in both flow and structural relaxation suggests that relaxation occurs via shear-type atomic rearrangements. (4) Additional experiments are needed in order to establish the relative magnitudes ofthe stress thresholds
TAUB: for flow and relation
relaxation.
between
THRESHOLD
Verification
relaxation
rate
STRESSES
of a step function and
stress
near
rc is
also needed. Acknow/edge,l~ents~The author wishes to thank Livingston for a critical reading of the manuscript C. L. Briant for several useful discussions,
Dr J. D. and Dr
REFERENCES T. Egami and T. Ichikawa, Mater Sri. Enyny 32, 293 (1978). T. Egami, J. Muter. Sci. 13, 2587 (1978). H. S. Chen, J. appl. Phys. 49, 4595 (1978). Y. N. Chen and T. Egami, J. appl. Phys. 50, 7615. (1979). A. L. Greer. Thermochimicu Actu 42, 193 (1980). A. Kursumovich and M. Cl. Scott, Appl. Phys ht. 37 ( 1980) 620. A. I. Taub and F. Spaepen. Actu metal/. 28, 1781 (1980).
IN AMORPHOUS
ALLOYS--II
2133
8. J. P. Patterson and D. R. H: Jones, Actu nwtdl. 28. 675 (1980). 9. P. M. Anderson III and A. E. Lord. Mute. Sci. Engrtg 44, 279 (1980). 10. A. I. Taub and F. Spaepen. Script0 mrtull. 13, 195 (1979). 11. A. I. Taub and F. E. Luborsky, Am metall. 29, 1939 (1981). ._ 1L. A. I. Taub and F. Spaepen, Scripta metal/. 13, I 197 (1980). 13. A. I. Taub and F. Spaepen. J. muter. Sci. In press. 14. A. I. Taub and F. Spaepen. Scripts ,nrttrll. 14. 1197 (1980). 15. H. Kronmuller. J. Phys. 41. C8%618 (1980). 16. G. Schroeder, R. Schafer and H. Kronmuller, PhJsicu stums solids 50, 475 (1978). 17. J. D. Livingston, Physicu stutus solid 56. 637 (1979). 18. J. J. Becker, AIP Conf. Proc. 29. 204 (1976). 19. T. Egami. Muter. Rrs. Bull. 13. 557 (1978). 20. F. Spaepen, Actu metull. 25. 407 (1977). 21. T. Takamori, T. Mizoguchi and T. R. McGuire. Muter. Res. Bull. 15, Xl (1980).
THRESHOLD
OOOI-6160/82;122129-05$03.00/O Copyright 0 1982 Pergamon Press Ltd
STRESSES IN AMORPHOUS STRUCTURAL RELAXATION
ALLOYS-II.
A. 1. TAUB General
Electric
Corporate
Research
(Receiced
and Development,
9 Noren~her
P.O. Box 8, Schenectady,
1981; in revisedform
NY 12301, U.S.A.
21 Muy 1981)
Abstract--Early investigations of structural change in amorphous alloys found stress independent relaxation kinetics. The results of this study indicate that this stress independence only occurs above some stress threshold and that for applied stresses below this critical value the relaxation proceeds at a much slower rate. The existence of this threshold suggests a mechanism for structural relaxation based on shear type rearrangements.
RCsumP--Des etudes anciennes sur le changement de structure dans des alliages amorphes avaient mis en evidence des cinttiques de relaxation independantes de la contrainte. Les risultats de notre etude montrent qu’il n’y a independance de la contrainte qu’au-dessus d’une contrainte seuil et qu’au-dessous de cette valeur critique la relaxation se produit beaucoup plus lentement. Nous presentons un modtle qui rend compte de cette relaxation structurale assist&e par la contrainte. Nous supposons que la relaxation se produit en deux &tapes: un rearrangement atomique de type cisaillement suivi par un effondrement des atomes au tour du volume libre disponible. Cet effondrement permet a la fois une mise en ordre a courte distance et une reduction du volume libre.
Zusammenfassung-Bei friiheren Untersuchungen der strukturellen Anderungen von amorphen Legierungen ergaben sich spannungsunabhangige Relaxationskinetiken. Die Ergebnisse dieser Untersuchung zeigen. daB diese Spannungsunabhlngigkeit nur oberhalb einer Spannungsschwelle auftritt und dab die Relaxation unterhalb dieser Schwelle mit vie1 geringerer Geschwindigkeit ablluft. Ein Model]. welches diese spannungsunterstiitzte strukturelle Relaxation beschreibt. wird entwickelt. Es wird angenommen, daB das Relaxationsereignis iiber einen zweistutigen Prozess ablauft: eine scherartige Atomumlagerung. gefolgt von einem Zusammenriicken der Atome in der NHhe des verfugbaren freien Volumens. Dieses Zusammenriicken erlaubt sowohl die Einstellung der Nahordnung als such die Verringerung des freien Volumens.
INTRODUCTION
EXPERIMENTAL
Structural relaxation has been shown to affect many properties of amorphous alloys (e.g. radial distribution function [ 1.23, Curie temperature [335], elastic modulus [6], flow [779]). Of these properties, the change in flow resistance, as measured by the increase in viscosity, exhibits perhaps the most dramatic changes. Increases in viscosity due to structural change, of greater than five orders of magnitude have been reported [IO]. The temperature dependence of the kinetics of this viscosity relaxation have been examined by numerous investigators [779. I I]. On the other hand, the effect of applied stress on the kinetics has received only cursory attention. This is probably due to the early findings of apparent stress independence [ 11-I 31. However, the establishment of a stress threshold for flow, as described in the previous paper, motivated a re-examination of this question. The results of this new investigation of the stress dependence of structural relaxation. will be presented in this paper. 2129 AM 30,l?-t
The specimens tested were amorphous Fe,,N&P,,B, obtained from Allied Chemical Corporation (Metglas 2826) in the form of ribbons 1.4 m wide x 48 pm thick. The creep tests were performed in tension using the apparatus described previously [ 1 I]. The tests were conducted at constant equivalent shear stress T = o/d’3 where D is the uniaxial tensile stress. The gage length, as defined by the hot zone, was 25.5 cm. During the in sifu preanneals, the specimen was held in tension at 5 MPa to keep it straight. The Hov. observed during these preanneals was negligible. The details of converting the raw data of the tests into measures of stress, strain and strain rate have been described in detail elsewhere [ 1 I]. RESULTS Figure I is a plot of equivalent shear strain = 4’3~ where l is the uniaxial tensile strain, for two
2130
TAUB:
THRESHOLD
STRESSES IN AMORPHOUS
ALLOYS-II
I a b
Fe40Ni40P14B6
(505K)
2‘ELASTIC OL
0
’
I
I
1000
2000 (MINUTES)
TIME
I
3000
4000
Fig. 1. Equivalent shear strain as a function of time, for two as-cast samples of Fe40Ni40PL4B6, creep tested at 505 K. Sample a was held at 505 K for 1 min prior to loading. Sample b was held for 90min. The instantaneous elastic strains are indicated.
samples of as-cast Fe40Ni,aP,,B,, creep tested at 505 K. In test a, the ribbon was heated from room temperature to 505 K (11 min), then held at 505 K for 1 min, at which time the stress was increased from the small straightening load of 5 MPa to the testing stress of 117 MPa. The temperature was then held at 505K and the flow monitored for 3150 min. Also shown in the figure is the strain-time history for a similar test b. The,\only difference in the tests was a 90min hold at 505K prior to increasing the load in test b, compared to 1 min in test a. Figure 2 is a plot of viscosity r~ = r/t, vs time calculated from curves a and b in Fig. 1. After initial transients lasting approximately 200 min, both specimens exhibit a nearly linear increase in viscosity with time, ‘I = r/e + fit(O.9 cc‘.02). This linear increase in the viscosity of amorphous alloys has previously been observed and associated with relaxation of the amorphous structure [7,9]. Furthermore, a recent study of the rate of viscosity increase tj showed that the measured values appear to be independent of the testing method (tensile creep, tensile stress relaxation and bend stress relaxation) [ 111. In Fig. 3, the rates of viscosity increase for samples a and b are shown with the available literature data. The value of 4 for tests a and b are seen to be in agreement with each other and with the available data. The data in Fig. 3, indicate that not only are the kinetics of structural relaxation, as measured by fi, independent of the testing method, but independence of the testing stress is suggested as well. Additional evidence for stress independent relaxation is provided by the tensile stress relaxation, stress-strain rate plots presented in the accompanying paper. In those plots, the isochronal stress-strain rate curves shifted to lower strain rates uniformly with time. If the kinetics of structural change, as measured by the increase in viscosity with time, were stress dependent, then the curves would have rotated as they shifted. Further
evidence for stress independent relaxation are the results of a previous creep investigation of the kinetics of viscosity increase for the alloy Pds2Si,s [12, 13). That study showed that at 5OOK, the rate of viscosity increase is independent of both the testing stress and mid-test stress increases, for equivalent shear stresses in the range 39~ 7 < 55Pa. Referring to Fig. 2, the viscosity-time curve for the 90 min preanneal is seen to lie considerably below that for the 1 min preanneal. Since the only difference in the tests was the specimen load during the first 90 min, this observation implies that during this initial period, the rate of viscosity increase was slower for the specimen loaded to only 5Pa. This observation appears to be in contradiction to the data described above. However, we can show that this apparent contradiction disappears by examining additional viscosity data reported for other alloys annealed under
_
Fs4eNi)ef’t&
-
a- I MINUTE PREANNEAL b-90 MINUTE PREANNEAL
t’l IO’
(505l0
Ill1
I I02 TIME
III1
I I03
I,;1 IO4
1MINUTES)
Fig. 2. Viscosity 4 = r/j as a function of time, calculated from curves a and b in Fig. 1.
-“‘_ LAUD:
THRESHOLD
10'3
STRESSES IN AMORPHOUS
I
I
I
I
2131
ALLOYS-II
I
I
Fe4o”+of’wb
10'2 i
l
l II
Gi- IO
/
E
3 5
5 lO’( )
IO9
-P
STRESS RAWE (YR)
0.
TENSILE CREEP c
SYMBOL I
IO
A
t 100 IO4 II7
0
D
THIS ‘I(
0
DQ FART I
RELAXATION
108 1.4
I
1.6
REF
I
1
1.8
2.0
2.2
2.4
2.6
2.8
103/T tK-‘I Fig. 3. Rate of change of viscosity with time as a function of temperature, as measured in tensile creep, tensile stress relaxation and bend stress relaxation tests. The testing stress ranges are indicated.
both zero and finite loads. The zero load specimens were preannealed under an argon atmosphere, and then creep tested to measure the temperature dependence of the isoconfigurational viscosity. The viscosity at the end of each preanneal q?,, can be determined from the reported isoconfigurational curves. These viscosities and the preanneal temperatures and times are listed in Table 1 for Pds,Si,s[lO, 13) and Pd 75.sCu6Si,6.s [ 14). Since the observed viscosities ‘1,. are orders of magnitude greater than the as-cast viscosities vi [IO] and since these materials have been shown to exhibit a linear viscosity-time dependence [ 1I], the rate of viscosity increase can be calculated as
lower than those under the higher stresses used in Bow tests. Second, at the higher stresses, the relaxation kinetics appear to be stress independent. These two statements, although not conclusive evidence for the existence of a threshold stress for relaxation, are consistent with such a threshold. It is interesting to note that for Fe40Ni40P14B6r this relaxation threshold stress would fall somewhere in the range above 5MPa and below the minimum stress achieved during the stress relaxation tests (50MPa). and that the ilow threshold stress described in the accompanying paper lies within this same range. DISCUSSION
tjcalc _ (VI - qi) _ 2 t, [II . In Table 1, this rate is compared with the actual rates of viscosity increase measured for specimens tested at finite stresses (82MPa for PdSi [7] 133MPa for PdCuSi [ 141. For both alloys, the kinetics of viscosity increase under zero applied stress are clearty slower than those measured under finite stresses. All these observations are summarized by the following two statements. First, under very small applied stress (O-SMPa), the rates of viscosity increase are
We now consider the existence of a threshold stress for structural relaxation. One could account for the low relaxation rate at zero applied stress, compared to the greater rate at nonzero stresses, by assuming that some relaxation events require only thermal activation and that some require both thermal activation and the presence of a local stress greater than some threshold value. However, modeling of the relaxation would be simplified if it was not necessary to make this distinction between stress assisted and stress inde-
Table 1. Comparjson of rates of viscosity increase under zero and nonzero stress conditions Preanneal conditions T(K) t, (h)
Alloy Pd&il~
Cl33
Pd 77.5Cu&i6.5 El41
513 534 552 552
432 181 242 242
If (1015 Pa-s) 7.8 3.3 t.7 1.5
Yle.1e (IO’ Pa) 5.0 5.1 2.0 1.7
(iG?a) 22 [71 16 E71 13 c71 lZ[ll]
2132
TAUB:
THRESHOLD
STRESSES
pendent relaxation events. In fact, the nonzero relaxation rate at zero applied stress can be explained without invoking two types of relaxation mechanisms, if the residual stresses in the specimens are considered. It has been shown by magnetic domain and anisotropy studies that considerable quenched in stresses (7 > lOOMPa) exist in as-cast ribbons [15, 161. Therefore, in the zero applied stress tests, portions of the ribbon were not actually in a zero stress state. The finite relaxation rate observed under zero applied load may be due to the relaxation that occurs in those portions of the specimen subjected to residual stresses (7,,3 greater than the threshold stress (TV). The apparent relaxation rate is small, because 7rer > 7,, in only a small percentage of the material. Trying to determine what the observed i should be in this case is difficult. The situation is complicated by the varying residual stress states that have been observed (e.g. uniaxial tension, biaxial compression [ 171). Furthermore, the residual stresses in ribbons, as determined by magnetic domain observations [lS], have been shown to vary along the ribbon length. Then each specimen will have a different percentage of material with t,,,> T,,, and therefore exhibit a different tjc. This would account for the unsystematic variation in rjc with temperature as reported in Table 1. Since this last result is not easily explained by the original assumption of two types of relaxation events, we will adopt the second suggested criterion and require all relaxation events to be stress assisted. Any model proposed to explain the relaxation must then predict
rj(T,
7)
0
7<70
4(T)
7 >
IN AMORPHOUS
ALLOYS-II
Our new observation of a threshold stress for both structural relaxation and flow provides additional evidence for a shear-type relaxation mechanism. If structural change is accomplished via a series of shear-type atomic rearrangements then a threshold phenomenon similar to that observed for flow would be expected. When the applied stress is less than the threshold value, shear-type rearrangements are limited by energy considerations, so the structural relaxation rate is expected to be small. When the applied stress becomes greater than the threshold value, shear-type rearrangements are permitted, and structural relaxation can proceed. The limited amount of data on the threshold behavior that is available at this time, precludes the development of a more detailed model for relaxation. Of primary importance in understanding the relationship between flow and relaxation, is the need to establish the relative magnitudes of the threshold stresses for both events. More work is also needed to determine if the relaxation is exhibiting a true stress threshold. A true threshold implies that a stress free (both internal, residual and applied stresses) amorphous alloy would exhibit no structural relaxation at elevated temperatures. The fabrication of such a specimen is not feasible at this time. However, if it can be shown that the relaxation rate of a conventional amorphous specimen undergoes a sharp transition at T,,, then a real threshold probably exists. Experiments designed to test for such a change in the rate of viscosity increase are in progress. CONCLUSIONS
= 70 ’
However, the available data is not sufficient to rule out the coexistence of a small, stress independent contribution to the relaxation rate [ ~0.1 rj (T)] as suggested by the original assumption. The concept of stress assisted relaxation is in accord with the results of a previous study of structural relaxation [7], which indicated that flow and relaxation events are similar. In that study, the kinetics of viscosity increase of amorphous Pds2Si1s were explained by a model based on an extension of the free volume model for flow. It was assumed that relaxation is the result of discrete events involving atomic rearrangements. By analogy to flow, these relaxation events were assumed to require thermal activation and were permitted only for certain atomic configurations. The analysis showed that for both flow and relaxation, the values for the thermal activation barriers and for the probability of occurrence of the critical atomic configurations, were similar. Based on these results, it was suggested that a relaxation event consists of a shear-type atomic rearrangement, followed by the collapse of the atoms in their new configuration about the available free volume. This free volume collapse could of course, also produce an increase in local short range order.
The stress dependence of the kinetics relaxation, as measured by the increase with time, have been investigated for Fe4,,N&P,,B, (Metglas 2826). These been correlated with the available data based alloys, with the following results:
of structural in viscosity amorphous results have on two Pd-
(1) The relaxation kinetics appear to be stress independent above some threshold stress zo. Below this threshold, the relaxation proceeds at a slower rate compared to the higher constant value above the threshold. (2) When the residual stresses in the ribbons are considered, the material behavior can be summarized as follows W
7) =
0
7 <
t,,(T)
t(T)
7 ’
70)
The coexistence of a small, stress independent contribution to the relaxation rate [ < 0.11 (T)] is still a possibility. (3) The existence of a stress threshold in both flow and structural relaxation suggests that relaxation occurs via shear-type atomic rearrangements. (4) Additional experiments are needed in order to establish the relative magnitudes ofthe stress thresholds
TAUB: for flow and relation
relaxation.
between
THRESHOLD
Verification
relaxation
rate
STRESSES
of a step function and
stress
near
rc is
also needed. Acknow/edge,l~ents~The author wishes to thank Livingston for a critical reading of the manuscript C. L. Briant for several useful discussions,
Dr J. D. and Dr
REFERENCES T. Egami and T. Ichikawa, Mater Sri. Enyny 32, 293 (1978). T. Egami, J. Muter. Sci. 13, 2587 (1978). H. S. Chen, J. appl. Phys. 49, 4595 (1978). Y. N. Chen and T. Egami, J. appl. Phys. 50, 7615. (1979). A. L. Greer. Thermochimicu Actu 42, 193 (1980). A. Kursumovich and M. Cl. Scott, Appl. Phys ht. 37 ( 1980) 620. A. I. Taub and F. Spaepen. Actu metal/. 28, 1781 (1980).
IN AMORPHOUS
ALLOYS--II
2133
8. J. P. Patterson and D. R. H: Jones, Actu nwtdl. 28. 675 (1980). 9. P. M. Anderson III and A. E. Lord. Mute. Sci. Engrtg 44, 279 (1980). 10. A. I. Taub and F. Spaepen. Script0 mrtull. 13, 195 (1979). 11. A. I. Taub and F. E. Luborsky, Am metall. 29, 1939 (1981). ._ 1L. A. I. Taub and F. Spaepen, Scripta metal/. 13, I 197 (1980). 13. A. I. Taub and F. Spaepen. J. muter. Sci. In press. 14. A. I. Taub and F. Spaepen. Scripts ,nrttrll. 14. 1197 (1980). 15. H. Kronmuller. J. Phys. 41. C8%618 (1980). 16. G. Schroeder, R. Schafer and H. Kronmuller, PhJsicu stums solids 50, 475 (1978). 17. J. D. Livingston, Physicu stutus solid 56. 637 (1979). 18. J. J. Becker, AIP Conf. Proc. 29. 204 (1976). 19. T. Egami. Muter. Rrs. Bull. 13. 557 (1978). 20. F. Spaepen, Actu metull. 25. 407 (1977). 21. T. Takamori, T. Mizoguchi and T. R. McGuire. Muter. Res. Bull. 15, Xl (1980).