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Internal damping due to dislocation movements induced by thermal expansion mismatch between matrix and particles in metal matrix composites
Scripta METALLURGICA et MATERIALIA
Vol. 28, pp. 1047-1052, 1993 Printed in the U.S.A.
Pergamon Press Ltd. All rights reserved
INTERNAL DAMPING DUE TO DISLOCATION MOVEMENTS INDUCED BY THERMAL EXPANSION MISMATCH BETWEEN MATRIX AND PARTICLES IN METAL MATRIX COMPOSITES C. Girard, G. Lormand, R. Foug~res, A. Vincent GEMPPM - U R A 341 - I N S A - Bat 303 69621 Villeurbanne cedex france
(Received January 19, 1993) (Revised February 16, 1993) Introduction
In metal matrix composites (MMCs), the mechanical behaviour of the reinforcement-matrix interface is an important parameter because it governs the load transfer from matrix to particles, from which the mechanical properties of these materials are derived (1). Therefore, it would be useful to set out an experimental method able to characterize the interface and the adjacent matrix behaviours. Thus, a study has been undertaken by means of internal damping (I.D.) measurements, which are well known to be very sensitive for studying irreversible displacements at the atomic scale. More especially, this investigation is based on the fact that, during cooling of MMCs, stress concentrations originating from differences in coefficients of thermal expansion (C.T.E.) of matrix and particles should induce dislocation movements in the matrix surrounding the reinforcement; that is, local microplastic strains occur (2,3). Therefore, during I.D. measurements vs temperature these movements should contribute to MMCs I.D. in a process similar to those involved around first order phase transitions in solids (4,5,6). The aim of this paper is to present, in the case of M/SiC particulate composites, new developments of this approach that had previously led to promising results in the case of A1-Si alloys (7). Exoerimental Procedure
This study was carried out mainly on an A1/12 vol% SiC composite produced by the powder metallurgy route (hot isostatic pressing)). Sizes of SiC particles were in the range 10-15ttm. In order to investigate on the one hand the effects linked with the presence of particles and on the other hand the influence of the matrix yield strength, some experiments were also carried out on the unreinforced Al and on a 7075 alloy/15 vol.% SiC composite elaborated by the Osprey method (ALCAN supplier), respectively. The latter alloy was solution treated at 470°C for 4h and then aged for 24h at 160°C. The specimens had a gauge length of 48mm and a cross section of 5x0.3mm2. The I.D. measurements were performed on a computer controlled torsion pendulum of inverted type, able to work in the frequency range 0.3-1.5Hz with these specimens. The I.D. of the specimen was characterized by the logarithmic decrement, 8, of the freely decaying oscillations of the pendulum. The measurements were carried out, with various cooling rates in the range 5 0 - 2 0 0 K / h , w i t h i n the temperature domain 430-50K. Prior to each cooling experiment the sample was maintained at the starting temperature, 430K or 385K for 12 hours. Unless specified, the surface shear strain amplitude was 5x10-6. Exoerimental Results
I.D. durin~ coolln~ - Influence of coolin~ rato The-I.D. spectra for an AI/SiC spe-cimen in the annealed state are presented in Fig. 1. A typical I.D. 1047 0956-716X/93 $6.00 + .00 Copyright (c) 1993 Pergamon Press Ltd.
1048
INTERNAL DAMPING
1.0e-1.
1.0e-l-
8.0e-2.
8.0e-2-
6.0e-2.
6
8
.
0
Vol.
e
-
2
28, No.
~
e
4.0e-2.
8 "°"71
2.0e-2. 0.0e+0
2 * J
100
"
"
200 300 Temperature (K)
,
400
Fig. 1: Logarithmic decrement vs temperature for various cooling rates: curves a, b, c, d correspond to I'F I = 200,100, 50, and 0 K/h, respectively, for M/SiC composite. Curve e corresponds to IT I = 200K/h for the unreinforced AI matrix. Oscillation frequency at 430K is 0.37Hz.
500
.
\ 0
e
-
/ 2
~
0.0e+0
100
200 300 Temperature (K)
400
500
Fig. 2: Influence of oscillation frequency on logarithmic decrement vs temperature: curves a, b, c correspond to 0.37,1,1.SHz at 430K, respectively. IT I = 200K/h. A1/SiC composite.
spectrum (for example, see curve a) exhibits a rapid decrease of the high temperature background with decreasing temperature, and a broad, poorly defined maximum situated around 190K. Note that the phenomenon is perfectly reproducible when the specimen is heated up to 430K and tested again. Moreover, this phenomenon is only slightly affected by the strain amplitude, whose influence has been tested in the range lx10 "6 - 10x10-6. In addition, from Fig.1 it can be seen that, over a wide temperature range, 380-100K, the I.D. appears to be enhanced as the cooling rate JTI is increased from 50K/h to 200K/h. Moreover, to get a reference spectrum in conditions close to the limit rate ITI = 0, isothermal measurements were performed in steps of 20K over the whole range 430-100K : following each temperature decrement, the temperature was kept constant during 30 min before the measurement, in order to enable I.D. to reach a constant value. This spectrum is labeled d in Fig. 1. Finally, in order to establish what is linked with the presence of particles in the MMC, the I.D. spectrum for the unreinforced AI matrix, produced in conditions similar to those used for the reinforced case, has been also reported in Fig. 1 (curve e). The I.D. appears to remain smaller than for the reinforced material except in the high temperature domain. Moreover, note that the I.D. is almost independent on I'll for this unreinforced material. Influence of oscillation freauencv As illustrated in Fig. 2, the I.D. is enhanced over the whole temperature domain of the broad maximum when the oscillation frequency of the pendulum is decreased from 1.5Hz to 0.37Hz. Influence of matrix nature For this comparative study, the specimens were tested from 430K to 50K. The I.D. spectrum for the 7075/SIC is shown in Fig. 3 (curve a) : a low temperature broad maximum is also observed, but it is less high than that obtained for the M/SiC composite whose I.D. spectrum in the same domain is given in Fig.4 (curve a). Moreover, as for the reinforced AI, it has been observed that the I.D. is temperature rate dependent in the temperature domain of the broad maximum. As shown in Fig. 3 and 4 (curves b), the I.D. measured during heating exhibits a quite different behaviour with respect to cooling : the low temperature side of the I.D. spectra is strongly lowered but conversely the high temperature side is enhanced. Thus, on heating the specimen, the broad maximum
9
Vol.
28, No.
9
INTERNAL DAMPING
1049
1.0e-1.
3.0e-2.
8.0e-2
a
2.0e-2
6.0e-2 4.0e-2-
1.0e-2.
2.0e-2. O.Oe+O 50
0.0e+0 150 250 350 Temperature (K)
Fig. 3 : Influence of matrix nature. Curves a, b and c correspond to cooling from 430K, heating from 50K and cooling ~ o m 300K, respectively. 7075A1/SIC composite. IT I = 200K/h. Oscillation frequency at 430K is 0.33Hz.
i
50
450
150 250 350 Temperature (K)
i
450
Fig. 4: Curves a and b correspond to cooling from 430K to 50K and heating from 50K to 430K, respectively. M/SiC composite. Oscillation frequency at 430K is 0.37Hz.
of the A1/SiC composite appears to be shifted towards a higher temperature and its height is reduced. Moreover, in the case of the 7075/SIC composite, the low temperature maximum is not at all present on heating. Finally, note that when an incomplete thermal cycle is carried out, the subsequent I.D. spectrum is markedly changed. This is best illustrated in Fig. 3: spectrum c has been obtained on cooling the specimen from 300K, subsequently to an interruption of the heating stage of the thermal cycle at this temperature. The primary conclusion derived from these results is that the MMCs exhibit temperature rate and frequency dependent I.D. that is linked with the presence of particles.
a specific
Discussion
A simple model for I.D. In microheterogeneous materials, I.D. may result from contributions due to each phase and from specific contributions linked with the interaction between particles and matrix. In our case, the contribution from SiC itself can be ruled out because it is expected to remain perfectly elastic. Then, in A1 based alloys reinforced with SiC, I.D. should result from the usual relaxational mechanisms of the matrix and from specific mechanisms that occur at the interface or in the adjacent matrix. Since the cooling rate influence appears to be suppressed in the unreinforced material, and the relaxational mechanisms of the matrix are known to be independent on IT I, the IT I effect is undoubtedly caused by some of the latter mechanisms, whose contribution to I.D. will be hereafter noted St. The contributions that are usually independent on IT I, including matrix contributions and other contributions due to the interaction between the applied stress and the particle (8,9,10), will be noted 8B. Since the fundamental properties of the low temperature I.D. maximum of the investigated composites appear to be similar to those previously observed around first order phase transition in solids (4,5,6), related mechanisms are likely to be responsible for both phenomena. In the case of phase transformations, I.D. has been explained in terms of inelastic strains associated to the second phase growth : (i) the constrained strain linked with the transformation shape mismatch between the matrix and the new phase particle, (ii) the local plastic strain that may relax the internal stresses induced by the former mismatch. Similarly, from previous studies on composite materials, we believe that ~ are linked with the dynamic relaxation of thermal stresses that are generated in the vicinity of the reinforcement upon cooling due to the C.T.E. mismatch between matrix and particles (2,3,11). Moreover, in the AI/SiC composite and in the investigated temperature range, this relaxation process is expected to occur by punching out of
I050
Vol. 28, No. 9
INTERNAL DAMPING
Driving stress profile in the glide plane
1.0e-1. 8.0e-2.
Dislocation
6.0e-2.
~ 4.0e-: 2.0e-~ ,
a Particle Matrix
~
b
0.0e+0
Distance from a particle
Fig. 5: Schematic of the dislocation movement in the vicinity of a particle, a - position of the dislocation at an arbitrary instant, b - new position at a later instant (temperature has been decreased and hence the internal stress has been increased, but for clarity the friction stress evolution has been neglected).
100
200
300
Temperature
400
500
(IO
Fig. 6: Differential spectra 8t vs T derived from Fig. I by subtracting the background contribution from the total damping measured at various cooling rates: curves a, b and c correspond to 200, 100 and 50K/h, respectively.
dislocation loops from particle-matrix interface. This displacement of each dislocation, which is mainly governed by the thermally induced stress field, is schematized in Fig.5: when the critical stress, zf, to move the dislocation in the matrix is reached, the dislocation is driven away from the particle as the internal stresses are increased on cooling the specimen. Then the I.D. associated with this mechanism can be derived from the general expression for the logarithmic decrement: [1]
8~=AW= I I(~dEp 2W 2W
with W the maximal elastic energy stored in the material during a stress cycle, a = (~0 sincot the macroscopic oscillating stress, ~ the macroscopic non-elastic strain. In a similar way to that proposed for phase transformation I.D. (4, 5, 6), let it be considered that, during an I.D. experiment, the increment of the macroscopic non-elastic strain is proportional to the applied stress, thus leading to:
[2]
d~p=kader
where dET = Aa.dT is the variation of the transformation strain (11) associated with the C.T.E. mismatch Aix between particles and matrix during a temperature change dT, and k is a function that can be considered as quasi constant over a period of oscillationbut that varies gently with the internal state of the material. According to these assumptions eq. [1] can be easilyintegrated,thus leading to : S T = k Aa ao21T I P / 4 W Note that it is difficultto establishthe complete expression of the function k because this requires one to know the detailsof the mechanism that operates at the microscopic level. A similar difficultyhas been also encountered in the case of phase transformations. However, in the case of I.D. measured during plastic deformation of metals, a model based on thermally activated motion of dislocations has been
Vol.
28, No.
9
INTERNAL DAMPING
1051
proposed by various authors (12, 13). In our case k is expected to be a complex function of the particle size and shape, the critical stress xf and the internal stress field xi around particles such that k = 0 when anywhere in the matrix xi < xf. Discussion of experimental results General features of 8 t I.D.: From eq. [3] it can be seen that this simple model predicts, as models for phase transformations, a linear dependence of I.D. vs I T I and P. This relationship between 8T a n d IT I can be tested by processing the experimental data in the following way. From eq. [3] it appears that 8T is expected to vanish at ITI = 0. Therefore, the spectrum d in Fig. 1 would represent 8B. Then by assuming that 8B is not affected by the occurrence of the mechanisms responsible for ~ , one can determine this latter contribution 8"i" from our experimental results by subtracting 8B from & T h e spectra thus obtained are shown in Fig. 6 in the case of cooling. It can be seen that the linear dependence of ~ upon I "~I, deduced from eq. [3], is reasonably satisfied over a wide domain of temperatures. Note that the same behaviour has been also verified in the case of heating. A similar approach applied to the frequency dependence has also led us to a reasonable agreement with a linear dependence of 5"i" on the period of the pendulum oscillation. In addition, the weak influence of the strain amplitude on I.D. of composites, which has been mentioned in the section "Experimental Results", is in good agreement with the model. Indeed, since W varies as C~o2, 8 "i" is expected to be independent of amplitude of measurement. Finally, the low I.D. in the 7075/SIC composite, with respect to that in the A1/SiC composite, can be explained readily. Indeed, the proportionality factor k defined in eq. [2] is expected to decrease when the critical stress xf is increased: as above mentioned it has to reach the limit value k=0 when xf is so high that the matrix remains perfectly elastic. I.D. on cooling: The shape of the spectra 8"1"shown in Fig. 6 can be explained as follows. During the time spent at 430K, prior to each experiment, the thermal stresses around SiC particles are expected to be relaxed, at least in the case of the A1/SiC composite. Consequently, k = 0 during the beginning of cooling since no dislocation displacement can occur when "~i<'cf. When the thermal stress in the vicinity of particles becomes larger than xf, the mechanism becomes operative. This occurs around 390K, in the case of the A1/SiC composite. Then, 8T increases rapidly with decreasing T, presumably because k increases due to an increase of the density of dislocations involved in the phenomenon, especially by dislocation emission from the interface (2). The fact that 8T goes through a maximum could arise from various mechanisms that tend to reduce the phenomenon with decreasing the temperature further: (i) an increase of zf due to both a forest type hardening in the vicinity of particles (2, 15) and a reduction of the intrinsic mobility of dislocation, and (ii) an interaction between the plastic zones around neighbouring particles. I.D. on heating: Finally, in consideration of the proposed mechanism of I.D., the fact that the I.D. spectrum on heating exhibits a shape quite different from that on cooling (see Fig. 3 and 4) can be explained readily. Indeed, in the first stage of the heating experiment the pre-existing internal stress field, induced by cooling the sample down to 100 K, is expected to be quasielasticaUy reduced below xf and so most of the present dislocations become immobile. This explains the fact that, in the range 100-250K, the I.D. measured on heating remains markedly lower than that measured on cooling. In the high temperature domain, internal stresses increase again and tend again to exceed the friction stress. Then, the fact the I.D. level on heating becomes higher than that on cooling is not surprising. However, the appearance of a maximum on heating in the case of the A1/SiC composite is more difficult to explain. Finally, note that the proposed interpretation is quite consistent with the low I.D. level observed for the uncomplete spectrum on cooling from 300K (Fig. 3 curve c). Indeed, on the one hand the internal stress field established on heating from 50K to 300K is expected to be reduced during the beginning of cooling and on the other hand the local hardening around particles that was induced by the first cooling from 430 to 50K was not annealing at 300K: both effects are expected to reduce the function k in eq. [3].
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INTERNAL DAMPING
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Conclusions
This study of I.D. as a function of temperature in M/SiC composites has shown that an important contribution to I.D. is linked with dislocation movements induced by the thermal stresses due to the C.T.E. mismatch between the AI matrix and SiC particles. A simple model has been proposed to explain the main features of the observed phenomena; that is, ST varies as the temperature rate IT I and the period of oscillation P. Moreover, 8 t evolutions vs temperature are governed in a complex manner by the variations of the thermal internal stress field, the dislocation density and the dislocation mobility in the vicinity of particles. Further studies are still required to calibrate these I.D. effects against the characteristics of particles, matrix and interface. However I.D. measurements already appear to be a promising tool for studying dislocation movements that are linked with thermally induced stress variations in the vicinity of particles. Acknowledgements
This work was supported by the A4rospatiale Society (Suresnes laboratory), which is gratefully acknowledged. We are also very grateful to P. Fond~res (Villetaneuse University) for elaborating the M/SiC composite. References
1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15.
C.S. Lee, Y.H. Kim, T. Lim and K.S. Hart, Script. Metall., 25, 613 (1991). R. Hamann and tL Foug~res, Proceeding of Riso International Symposium on Materials Science XII, p. 373, Eds N. Hansen, D. Jensen, J. Leffers, H. Lilholt, T. Lorentzen, A.S. Pedersen, O.B. Pedersen and B. Ralph (1991). D.C. Dunan and A. Mortensen, Acta. Metall. Mater., vol. 39, 2, 127 (1991). J.F. Delorme, R. Schmid, M. Robin and P. F. Gobin, J. Phys., 32 C2-101 (1971). V.S. Postnikov, S.A. Gridnev, B.M. Darinskii and I.M. Sharshakov, Nuevo cim., vol. 33B, 1, 324 (1976). O. Mercier, K.N. Melton and Y.de Preville, Acta Metall. Mater., vol. 27, 1467 (1979). X. Zhou, R. Foug~res and A. Vincent, J. Phys. ]]I France 2, nov., 2185 (1992). M. Okabe, T. Mori and T. Mura, Phil. Mag., vol. 44, 1, 1 (1981). M. Kohen, G. Fantozzi, F. Fouquet, Proceeding of ICIFUAS IV, Eds D. Lenz and K. Lficke, Springer Verlag, vol.1, 276 (1975). G.. Schoeck, Physica Status Solidi, Vol.32, 651 (1969). P.J. Withers, W.M. Stobbs and O.B. Pedersen, Acta Metall. Mater., vol 37, 11, 3061 (1989). H. Munstedt, Z. MetaUkunde, Vol. 65,530 (1974). G. Kaiser and W Pechhold, Acta Metall. Mater., vol. 17, 527 (1969). A.S. Nowick and B.S. Berry, Anelastic relaxation in crystalline solids, Academic Press New York and London (1972). R.J. Arsenault, L. Wang and C.K Feng, Acta. Metall., vol. 39, 1, 47 (1991).
9
Vol. 28, pp. 1047-1052, 1993 Printed in the U.S.A.
Pergamon Press Ltd. All rights reserved
INTERNAL DAMPING DUE TO DISLOCATION MOVEMENTS INDUCED BY THERMAL EXPANSION MISMATCH BETWEEN MATRIX AND PARTICLES IN METAL MATRIX COMPOSITES C. Girard, G. Lormand, R. Foug~res, A. Vincent GEMPPM - U R A 341 - I N S A - Bat 303 69621 Villeurbanne cedex france
(Received January 19, 1993) (Revised February 16, 1993) Introduction
In metal matrix composites (MMCs), the mechanical behaviour of the reinforcement-matrix interface is an important parameter because it governs the load transfer from matrix to particles, from which the mechanical properties of these materials are derived (1). Therefore, it would be useful to set out an experimental method able to characterize the interface and the adjacent matrix behaviours. Thus, a study has been undertaken by means of internal damping (I.D.) measurements, which are well known to be very sensitive for studying irreversible displacements at the atomic scale. More especially, this investigation is based on the fact that, during cooling of MMCs, stress concentrations originating from differences in coefficients of thermal expansion (C.T.E.) of matrix and particles should induce dislocation movements in the matrix surrounding the reinforcement; that is, local microplastic strains occur (2,3). Therefore, during I.D. measurements vs temperature these movements should contribute to MMCs I.D. in a process similar to those involved around first order phase transitions in solids (4,5,6). The aim of this paper is to present, in the case of M/SiC particulate composites, new developments of this approach that had previously led to promising results in the case of A1-Si alloys (7). Exoerimental Procedure
This study was carried out mainly on an A1/12 vol% SiC composite produced by the powder metallurgy route (hot isostatic pressing)). Sizes of SiC particles were in the range 10-15ttm. In order to investigate on the one hand the effects linked with the presence of particles and on the other hand the influence of the matrix yield strength, some experiments were also carried out on the unreinforced Al and on a 7075 alloy/15 vol.% SiC composite elaborated by the Osprey method (ALCAN supplier), respectively. The latter alloy was solution treated at 470°C for 4h and then aged for 24h at 160°C. The specimens had a gauge length of 48mm and a cross section of 5x0.3mm2. The I.D. measurements were performed on a computer controlled torsion pendulum of inverted type, able to work in the frequency range 0.3-1.5Hz with these specimens. The I.D. of the specimen was characterized by the logarithmic decrement, 8, of the freely decaying oscillations of the pendulum. The measurements were carried out, with various cooling rates in the range 5 0 - 2 0 0 K / h , w i t h i n the temperature domain 430-50K. Prior to each cooling experiment the sample was maintained at the starting temperature, 430K or 385K for 12 hours. Unless specified, the surface shear strain amplitude was 5x10-6. Exoerimental Results
I.D. durin~ coolln~ - Influence of coolin~ rato The-I.D. spectra for an AI/SiC spe-cimen in the annealed state are presented in Fig. 1. A typical I.D. 1047 0956-716X/93 $6.00 + .00 Copyright (c) 1993 Pergamon Press Ltd.
1048
INTERNAL DAMPING
1.0e-1.
1.0e-l-
8.0e-2.
8.0e-2-
6.0e-2.
6
8
.
0
Vol.
e
-
2
28, No.
~
e
4.0e-2.
8 "°"71
2.0e-2. 0.0e+0
2 * J
100
"
"
200 300 Temperature (K)
,
400
Fig. 1: Logarithmic decrement vs temperature for various cooling rates: curves a, b, c, d correspond to I'F I = 200,100, 50, and 0 K/h, respectively, for M/SiC composite. Curve e corresponds to IT I = 200K/h for the unreinforced AI matrix. Oscillation frequency at 430K is 0.37Hz.
500
.
\ 0
e
-
/ 2
~
0.0e+0
100
200 300 Temperature (K)
400
500
Fig. 2: Influence of oscillation frequency on logarithmic decrement vs temperature: curves a, b, c correspond to 0.37,1,1.SHz at 430K, respectively. IT I = 200K/h. A1/SiC composite.
spectrum (for example, see curve a) exhibits a rapid decrease of the high temperature background with decreasing temperature, and a broad, poorly defined maximum situated around 190K. Note that the phenomenon is perfectly reproducible when the specimen is heated up to 430K and tested again. Moreover, this phenomenon is only slightly affected by the strain amplitude, whose influence has been tested in the range lx10 "6 - 10x10-6. In addition, from Fig.1 it can be seen that, over a wide temperature range, 380-100K, the I.D. appears to be enhanced as the cooling rate JTI is increased from 50K/h to 200K/h. Moreover, to get a reference spectrum in conditions close to the limit rate ITI = 0, isothermal measurements were performed in steps of 20K over the whole range 430-100K : following each temperature decrement, the temperature was kept constant during 30 min before the measurement, in order to enable I.D. to reach a constant value. This spectrum is labeled d in Fig. 1. Finally, in order to establish what is linked with the presence of particles in the MMC, the I.D. spectrum for the unreinforced AI matrix, produced in conditions similar to those used for the reinforced case, has been also reported in Fig. 1 (curve e). The I.D. appears to remain smaller than for the reinforced material except in the high temperature domain. Moreover, note that the I.D. is almost independent on I'll for this unreinforced material. Influence of oscillation freauencv As illustrated in Fig. 2, the I.D. is enhanced over the whole temperature domain of the broad maximum when the oscillation frequency of the pendulum is decreased from 1.5Hz to 0.37Hz. Influence of matrix nature For this comparative study, the specimens were tested from 430K to 50K. The I.D. spectrum for the 7075/SIC is shown in Fig. 3 (curve a) : a low temperature broad maximum is also observed, but it is less high than that obtained for the M/SiC composite whose I.D. spectrum in the same domain is given in Fig.4 (curve a). Moreover, as for the reinforced AI, it has been observed that the I.D. is temperature rate dependent in the temperature domain of the broad maximum. As shown in Fig. 3 and 4 (curves b), the I.D. measured during heating exhibits a quite different behaviour with respect to cooling : the low temperature side of the I.D. spectra is strongly lowered but conversely the high temperature side is enhanced. Thus, on heating the specimen, the broad maximum
9
Vol.
28, No.
9
INTERNAL DAMPING
1049
1.0e-1.
3.0e-2.
8.0e-2
a
2.0e-2
6.0e-2 4.0e-2-
1.0e-2.
2.0e-2. O.Oe+O 50
0.0e+0 150 250 350 Temperature (K)
Fig. 3 : Influence of matrix nature. Curves a, b and c correspond to cooling from 430K, heating from 50K and cooling ~ o m 300K, respectively. 7075A1/SIC composite. IT I = 200K/h. Oscillation frequency at 430K is 0.33Hz.
i
50
450
150 250 350 Temperature (K)
i
450
Fig. 4: Curves a and b correspond to cooling from 430K to 50K and heating from 50K to 430K, respectively. M/SiC composite. Oscillation frequency at 430K is 0.37Hz.
of the A1/SiC composite appears to be shifted towards a higher temperature and its height is reduced. Moreover, in the case of the 7075/SIC composite, the low temperature maximum is not at all present on heating. Finally, note that when an incomplete thermal cycle is carried out, the subsequent I.D. spectrum is markedly changed. This is best illustrated in Fig. 3: spectrum c has been obtained on cooling the specimen from 300K, subsequently to an interruption of the heating stage of the thermal cycle at this temperature. The primary conclusion derived from these results is that the MMCs exhibit temperature rate and frequency dependent I.D. that is linked with the presence of particles.
a specific
Discussion
A simple model for I.D. In microheterogeneous materials, I.D. may result from contributions due to each phase and from specific contributions linked with the interaction between particles and matrix. In our case, the contribution from SiC itself can be ruled out because it is expected to remain perfectly elastic. Then, in A1 based alloys reinforced with SiC, I.D. should result from the usual relaxational mechanisms of the matrix and from specific mechanisms that occur at the interface or in the adjacent matrix. Since the cooling rate influence appears to be suppressed in the unreinforced material, and the relaxational mechanisms of the matrix are known to be independent on IT I, the IT I effect is undoubtedly caused by some of the latter mechanisms, whose contribution to I.D. will be hereafter noted St. The contributions that are usually independent on IT I, including matrix contributions and other contributions due to the interaction between the applied stress and the particle (8,9,10), will be noted 8B. Since the fundamental properties of the low temperature I.D. maximum of the investigated composites appear to be similar to those previously observed around first order phase transition in solids (4,5,6), related mechanisms are likely to be responsible for both phenomena. In the case of phase transformations, I.D. has been explained in terms of inelastic strains associated to the second phase growth : (i) the constrained strain linked with the transformation shape mismatch between the matrix and the new phase particle, (ii) the local plastic strain that may relax the internal stresses induced by the former mismatch. Similarly, from previous studies on composite materials, we believe that ~ are linked with the dynamic relaxation of thermal stresses that are generated in the vicinity of the reinforcement upon cooling due to the C.T.E. mismatch between matrix and particles (2,3,11). Moreover, in the AI/SiC composite and in the investigated temperature range, this relaxation process is expected to occur by punching out of
I050
Vol. 28, No. 9
INTERNAL DAMPING
Driving stress profile in the glide plane
1.0e-1. 8.0e-2.
Dislocation
6.0e-2.
~ 4.0e-: 2.0e-~ ,
a Particle Matrix
~
b
0.0e+0
Distance from a particle
Fig. 5: Schematic of the dislocation movement in the vicinity of a particle, a - position of the dislocation at an arbitrary instant, b - new position at a later instant (temperature has been decreased and hence the internal stress has been increased, but for clarity the friction stress evolution has been neglected).
100
200
300
Temperature
400
500
(IO
Fig. 6: Differential spectra 8t vs T derived from Fig. I by subtracting the background contribution from the total damping measured at various cooling rates: curves a, b and c correspond to 200, 100 and 50K/h, respectively.
dislocation loops from particle-matrix interface. This displacement of each dislocation, which is mainly governed by the thermally induced stress field, is schematized in Fig.5: when the critical stress, zf, to move the dislocation in the matrix is reached, the dislocation is driven away from the particle as the internal stresses are increased on cooling the specimen. Then the I.D. associated with this mechanism can be derived from the general expression for the logarithmic decrement: [1]
8~=AW= I I(~dEp 2W 2W
with W the maximal elastic energy stored in the material during a stress cycle, a = (~0 sincot the macroscopic oscillating stress, ~ the macroscopic non-elastic strain. In a similar way to that proposed for phase transformation I.D. (4, 5, 6), let it be considered that, during an I.D. experiment, the increment of the macroscopic non-elastic strain is proportional to the applied stress, thus leading to:
[2]
d~p=kader
where dET = Aa.dT is the variation of the transformation strain (11) associated with the C.T.E. mismatch Aix between particles and matrix during a temperature change dT, and k is a function that can be considered as quasi constant over a period of oscillationbut that varies gently with the internal state of the material. According to these assumptions eq. [1] can be easilyintegrated,thus leading to : S T = k Aa ao21T I P / 4 W Note that it is difficultto establishthe complete expression of the function k because this requires one to know the detailsof the mechanism that operates at the microscopic level. A similar difficultyhas been also encountered in the case of phase transformations. However, in the case of I.D. measured during plastic deformation of metals, a model based on thermally activated motion of dislocations has been
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proposed by various authors (12, 13). In our case k is expected to be a complex function of the particle size and shape, the critical stress xf and the internal stress field xi around particles such that k = 0 when anywhere in the matrix xi < xf. Discussion of experimental results General features of 8 t I.D.: From eq. [3] it can be seen that this simple model predicts, as models for phase transformations, a linear dependence of I.D. vs I T I and P. This relationship between 8T a n d IT I can be tested by processing the experimental data in the following way. From eq. [3] it appears that 8T is expected to vanish at ITI = 0. Therefore, the spectrum d in Fig. 1 would represent 8B. Then by assuming that 8B is not affected by the occurrence of the mechanisms responsible for ~ , one can determine this latter contribution 8"i" from our experimental results by subtracting 8B from & T h e spectra thus obtained are shown in Fig. 6 in the case of cooling. It can be seen that the linear dependence of ~ upon I "~I, deduced from eq. [3], is reasonably satisfied over a wide domain of temperatures. Note that the same behaviour has been also verified in the case of heating. A similar approach applied to the frequency dependence has also led us to a reasonable agreement with a linear dependence of 5"i" on the period of the pendulum oscillation. In addition, the weak influence of the strain amplitude on I.D. of composites, which has been mentioned in the section "Experimental Results", is in good agreement with the model. Indeed, since W varies as C~o2, 8 "i" is expected to be independent of amplitude of measurement. Finally, the low I.D. in the 7075/SIC composite, with respect to that in the A1/SiC composite, can be explained readily. Indeed, the proportionality factor k defined in eq. [2] is expected to decrease when the critical stress xf is increased: as above mentioned it has to reach the limit value k=0 when xf is so high that the matrix remains perfectly elastic. I.D. on cooling: The shape of the spectra 8"1"shown in Fig. 6 can be explained as follows. During the time spent at 430K, prior to each experiment, the thermal stresses around SiC particles are expected to be relaxed, at least in the case of the A1/SiC composite. Consequently, k = 0 during the beginning of cooling since no dislocation displacement can occur when "~i<'cf. When the thermal stress in the vicinity of particles becomes larger than xf, the mechanism becomes operative. This occurs around 390K, in the case of the A1/SiC composite. Then, 8T increases rapidly with decreasing T, presumably because k increases due to an increase of the density of dislocations involved in the phenomenon, especially by dislocation emission from the interface (2). The fact that 8T goes through a maximum could arise from various mechanisms that tend to reduce the phenomenon with decreasing the temperature further: (i) an increase of zf due to both a forest type hardening in the vicinity of particles (2, 15) and a reduction of the intrinsic mobility of dislocation, and (ii) an interaction between the plastic zones around neighbouring particles. I.D. on heating: Finally, in consideration of the proposed mechanism of I.D., the fact that the I.D. spectrum on heating exhibits a shape quite different from that on cooling (see Fig. 3 and 4) can be explained readily. Indeed, in the first stage of the heating experiment the pre-existing internal stress field, induced by cooling the sample down to 100 K, is expected to be quasielasticaUy reduced below xf and so most of the present dislocations become immobile. This explains the fact that, in the range 100-250K, the I.D. measured on heating remains markedly lower than that measured on cooling. In the high temperature domain, internal stresses increase again and tend again to exceed the friction stress. Then, the fact the I.D. level on heating becomes higher than that on cooling is not surprising. However, the appearance of a maximum on heating in the case of the A1/SiC composite is more difficult to explain. Finally, note that the proposed interpretation is quite consistent with the low I.D. level observed for the uncomplete spectrum on cooling from 300K (Fig. 3 curve c). Indeed, on the one hand the internal stress field established on heating from 50K to 300K is expected to be reduced during the beginning of cooling and on the other hand the local hardening around particles that was induced by the first cooling from 430 to 50K was not annealing at 300K: both effects are expected to reduce the function k in eq. [3].
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Conclusions
This study of I.D. as a function of temperature in M/SiC composites has shown that an important contribution to I.D. is linked with dislocation movements induced by the thermal stresses due to the C.T.E. mismatch between the AI matrix and SiC particles. A simple model has been proposed to explain the main features of the observed phenomena; that is, ST varies as the temperature rate IT I and the period of oscillation P. Moreover, 8 t evolutions vs temperature are governed in a complex manner by the variations of the thermal internal stress field, the dislocation density and the dislocation mobility in the vicinity of particles. Further studies are still required to calibrate these I.D. effects against the characteristics of particles, matrix and interface. However I.D. measurements already appear to be a promising tool for studying dislocation movements that are linked with thermally induced stress variations in the vicinity of particles. Acknowledgements
This work was supported by the A4rospatiale Society (Suresnes laboratory), which is gratefully acknowledged. We are also very grateful to P. Fond~res (Villetaneuse University) for elaborating the M/SiC composite. References
1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15.
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