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Internal Friction and Young’s Modulus of Some Rapidly Solidified Al-Si Alloys
N. Tawfik, E.M. Abdel Hady, A. Bastawros
To cite this version:
N. Tawfik, E.M. Abdel Hady, A. Bastawros. Internal Friction and Young’s Modulus of Some Rapidly Solidified Al-Si Alloys. Journal de Physique III, EDP Sciences, 1997, 7 (1), pp.59-65.
�10.1051/jp3:1997110�. �jpa-00249573�
Internal Friction and Young's Modulus of Some Rapidly Solidified Al-Si Alloys
N-L- Tawfik (*), E.M. Abdel Hady and A.M. Bastawros Physics Department, National Research Centre, Dokki, Giza, Egypt
(Received 27 December1995, revised 19 August 1996, accepted 30 September1996)
PACS 62.40 +I Anelasticity, internal friction, stress relaxation and mechanical resonances
PACS.8140.Jj Elasticity and anelasticity, stress-strain relations
Abstract. Al-16 Si, Al-12 5 Si-1 Ni and Al-12 S Si-1 Mg ribbons were prepared by melt spinning. Internal friction was measured in the forced flexural and torsional decay modes
Internal friction increases slowly with the increase in temperature up to a certain temperature, above which the rate of increase is higher. This behaviour is common in all the three alloys, and is more pronounced in the torsional vibration mode than in the flexural vibration mode. The temperatures at which the internal friction shows a significant change in slope are 573, 518 and SS4 K in the flexural mode and 456, 496 and 529 K in the torsional mode for Al-16 Si, Al-Si- Ni and Al-Si-Mg respectively. From the measurement of resonance frequency with temperature, Young~s modulus was calculated The room temperature values are 3.6, 2.1 and 1.4 x10~° N m~~
for Al-16 St, Al-Si-Ni and Al-Si-Mg respectively. These values are m fair agreement with the values deduced from the tensile tests. The variation of Young's modulus with temperature obeys the expression given by Andrews. The temperatures at which In Y
uersus T(K) changes its value
are about 100 degrees above 0.S Tm on the average for the three alloys. A discussion on the relation between the behaviour of internal friction and Young's modulus with temperatures is given.
1. Introduction
Damping in engineering alloys is of importance in the suppression of noise and the extension of fatigue life by reducing the amplitude of vibration under resonant conditions.
Most works on internal friction have been done on dilute solid solution alloys. Some works have been reported on concentrated rapidly solidified alloys [1, 2].
In the present work, we report on the internal friction and resonance frequency measurements from room temperature to 400 °C for melt spun Al-16 Si, Al-12.5 Si-1 Ni and Al-12.5 Si-1 Mg
ribbons.
2. Experimental Method
AI-16 Si, Al-12.5 Si-1 Ni and Al-12.5 Si-1Mg alloys were prepared by melt spinning using the apparatus described in reference [3]. Continuous uniform ribbons of thickness about 25 ~lm and width of1 mm were obtained. Internal friction (Q~~ was measured in both the cantilevered (*) Author for correspondence
@ Les #ditions de Physique 1997
60 JOURNAL DE PHYSIQUE III N°1 flexural and torsional vibrations modes. To prepare the ribbons for internal friction measure- ment in the cantilevered flexural vibration mode, they were first straightened by placing them
between two glass slides in a furnace for 3 hours at 300 °C; then they were furnace cooled.
Measurements were performed under vacuum from room temperature up to about 400 °C at a heating rate of I °C min~~. Internal friction in the flexural mode of vibration was mea-
sured using the resonance method. Samples having free length of about 1.5 cm and thickness 25 ~lm were used. The vibrations were excited electrostatically and the detection was made by
employing a 4 MHz crystal oscillator as described in reference [4]. The change in capacitance between the oscillating foil and a fixed pick up electrode connected in parallel with the collector tuned circuit of the oscillator, produces a corresponding change in the collector current. Inter- nal friction was also measured by the free decay mode using an inverted torsion pendulum [4].
Ribbons having length of about 2 cm were employed. A winged electrode suspended on the foil axis acts as a ground electrode for both electrostatic excitation and pick up. The out put is recorded as a decaying sine wave on the X- t recorder.
3. Results
For the cantilevered mode of flexural vibration, internal friction (Q~~ uers~s temperature was
measured at frequencies ranging from 40 to 120 Hz by changing the vibration length. The variation of (Q~~) with temperature for the different frequencies was similar in shape. Fur- thermore, when a set of measurements from room temperature to the highest temperature
was repeated on the same specimen~ an agreement within experimental uncertainty was found.
This was a result of the thermal treatment (3h at 300 °C) given to the ribbons before perform-
ing the measurements. This treatment was enough to stabilize the structure. Representatives
for the three alloys are shown in Figure 1. Typical values of (Q~~) are about 0.01 at room
temperature and increases to reach values of about 0.05 around 400 °C.
As shown in Figure 1, no internal friction peak is found; instead, the internal friction increases
slowly with the increase in temperature up to a certain temperature beyond which the rise is
more rapid. This temperature depends on the frequency. However, its increase with frequency
is very slow.
Also, the resonance frequency decreases with the increase in temperature, the decrease is slow up a certain temperature beyond which the decrease is faster.
Iiiternal friction was also measured by the decay method employing the torsional vibration mode. The variation of internal friction with temperature at frequencies of about Hz is shown in Figure 2. Typical values of (Q~~) are 0.008 at room temperature, and increase with
temperature to reach values as high as 0.1 near 400 °C. The general behaviour of internal friction with temperature in the torsional vibration mode is similar to that of the flexural mode, but with a more pronounced change of slope.
4. Discussion
A similar behaviour of the variation of internal friction with temperature has been observed in metallic glasses by Morito [1] in metglas 2826. This is a multi-element alloy prepared by rapid
solidification. No distinct internal friction peak was observed.
This rapid rise in internal friction was also observed by Koshimizu and Benoit [5] in their
study of polycrystalline Cu-Zn-Al and Ti-Ni alloys, which occured around the temperature of martensitic transformation. They fitted their results with an equation based on a Landau
theory of first order phase transformation.
0.05 ~
a
~ .
o
c 0.D5
Q
G
~
~ .
~ bl
C .
)
C DOD5
c
0.00
300 4D0 50D to 700
Temperature
Fig. 1. Internal friction Q~~ uersus temperature (flexural vibration mode) a) Al-16 Si, b) Al-12.5 Si-1 Ni and c) Al-12.5 Si-1 Mg. Room temperature frequency: a) 63.5 Hz; b) 70.4 Hz and c) 57.7 Hz.
The present internal friction results, were fitted by a modified form of that given in reference [5], although no phase transformation occurs. The modified expression has the following simple
form:
~ ~~~~
(a + j~+
cx2) ~~~
where x
= 1- (T/Tc), and Tc is the temperature in (K) at which a significant change of the
slope of internal friction with temperature occurs, and a, b and c are temperature independent parameters.
The least square fits are shown as continuous curves in Figures and 2. Extracted values ofTc from the fits of flexural vibration mode are 573, 518 and 554 K for Al-16 Si, Al-12.5 Si-1 Ni and Al-12.5 Si-1 Mg alloys respectively. Tc values obtained from the torsional method are 456, 496 and 529 K for Al-16 Si, Al-Si-Ni and Al-Si-Mg respectively.
Tc values at the low frequencies of the torsional vibration mode are lower than those at the
higher flexural vibration frequencies. The decrease in T~ with frequency goes along with the well known shift of internal friction peaks to low temperatures with the decrease in vibration frequency However, the decrease of more than 100 °C in the case of Al-16 Si seems to be too
large.
Young's modulus Y was calculated from the frequency f, dimensions and density p of the reed using the following expression [6],
f = 0.1615 (~) (2)
' P
~~~
where f is the fundamental frequency of vibration of a cantilevered reed of thickness d and free vibrating length 1.
62 JOURNAL DE PHYSIQUE III N°1
o,io
7
" a)
C
°
~
U
~ 0_05
~
?
C
~ b)
c
30D 400 500 600 700
Temperature (K)
Fig. 2 Internal friction Q~~ uersus temperature (torsional vibration mode). a) Al-16 Si; b) Al-12 S Si-1 Ni and c) Al-12.S Si-1 Mg Room temperature frequency for a), b) and c) is about 1 Hz
Andrews [7] studied the variation of Young's modulus with temperature and deduced the
following equation:
Y = V°Aexp
(/)
(3)m
where V is the specific volume, and A, a and fl are constants which have two sets of values
according to (T/Tm) less or greater than 0.5, Tm is the melting point in (K).
From equation (2), Y is proportional to f2. The variation of the resonance frequency (due
to the change of vibrating specimen dimensions) with temperature is estimated to be less than 0.001% per degree. This is negligible in comparison with the observed frequency variation with
temperature. So, (Y(T)/ Y(293 K)) will be equal to (f(T) / f(293 K))2.
Figure 3 shows In(f(T)/f(293 K))2 uersw T(K) for the flexural vibration results. The torsional results are not included due to the inaccuracies in extracting such low torsional
frequencies values from the damped oscillation curves. Figure 3 shows that equation (3) gives
a reasonable description of the variation of Young's modulus with temperature.
a)
b)
CQ
~m
i~ C)
~
~
~$(
300
64 JOURNAL DE PHYSIQUE III N°1 On the other hand at temperature above (T)), the Si content is more effective than Ni, and Ni is more effective than Mg in preserving the strength at higher temperatures.
For all the three alloys, the internal friction (Q~~) increases slowly with the increase in temperature up to Tc. Above that temperature, the rate of increase of internal friction with the increase in temperature is higher. This can be seen if we consider that for the normally low
stresses used in internal friction experiments and at lower temperatures, the dislocations are unable to breakaway from any of the anchoring points. They just bow out periodically between them. Above certain temperature, the dislocations are partly freed from the anchoring points and thus the bowing out of dislocations increases resulting in more energy dissipation per stress
cycle. Moreover, diffusion and dislocation climb effects contribute to the increase in internal friction at high temperatures
The results also show a high damping capacity for all the three alloys especially at low frequencies.
The elastic modulus was calculated from equation (2). The room temperature values of
Young's modulus of the as melt spun ribbons are 3.6, 2.1 and 1.4 x 10~° N m~2 for Al-16 Si, Al-Si-Ni and Al-Si-Mg respectively. These values compare well with the values extracted from the initial stages of the tensile test [9] being 3, 2.3 and 1.2 x 10~° N m~2 for Al-16 Si, Al-Si-Ni and Al-Si-Mg respectively.
The increase in internal friction and the decrease in Young's modulus are related to each other. This is so since the modulus is a measure of the differential coefficient of the cohesive force between the adjacent atoms, and this is related to the binding energy and hence to the
melting temperature. Cohesive forces decrease with the increase in temperature. To relate that to the increased rise in internal friction above Tc, we refer to the expression given by Lenz and Lucke [10] for the amplitude independent decrement [b] given by:
b = 2~~~~)~~~ (4)
where A is the dislocation density, G is the elastic shear modulus, b is Burger's vector, B is
the viscous damping and Ilk is the elastic compliance per unit length of dislocation
Now, since no fresh dislocations are introduced (low values of applied stress for forced vibra-
tions) then A does not vary. So, the temperature dependence is determined by that of B(T)
and k(T). At low temperatures, B(T) increases slowly [11] with increasing T (larger phonon component). However, as observed, the rapid decrease in Young's modulus above (T)) reflects itself in a rapid increase in the elastic compliance Ilk which gives the observed result of high
internal friction.
A similar behaviour of internal friction and Young's modulus with temperature has been reported in an earlier publication on melt spun Al-Cu and Al-Si eutectic alloys ribbons [2j.
References
[1] Morito N., Internal Friction Study on Structural Relaxation of a Glassy Metal
Fe32N136Cr14P12B6, Mater. So. Eng. 60 (1983) 261
[2] Bastawros A.M., Grais K-I- and Said M.Z., Internal friction and modulus of rapidly solid- ified eutectic Al-Si and Al-Cu ribbons, Egypt. J. Sol. 15 (1992) 114.
[3] Bastawros A-M., Grais K-I- and Said M.Z., Production of thin uniform continuous ribbons by melt quenching, Egypt. J. Sol. 14 (1991) 107.
[4] Bastawros A.M. and Said M.Z., A simple system to measure internal friction and creep, J. Phys. III France 2 (1992)1779.
[5] Koshimizo S. and Benoit W., Internal friction measurements and thermodynamical anal- ysis of a martensitic transformation, J. Phys. Goloq. France 42 (1982) C4-679.
[6] Berry B.S. and Pritchet W.C., Some physical properties of two amorphous metallic alloys,
J. Appl. Phys. 44 (1973) 3122.
[7) Andrews J-P-, Relations between Young's modulus and other physical quantities, Phiios.
Mag. 50 (1925) 665.
[8] Westbrook J H., Trans. Am. Soc. Met. 45 (1953) 221; cited in "Mechanical Metallurgy",
G.E. Dieter, Ed., Second edition jmc Graw-Hill book Company, New ~'ork, 1976) p. 400.
[9] Tawfik N.L., Abdel Hady E.M. and Kassem N.E., Study of melt spun Al-16 Si ribbons on ageing, Submitted for publication.
[10] Lenz D. and Lucke K., Internal friction and ultrasonic attenuation in crystalline solids, D.
Lenz and K. Lucke, Eds., Vol. 2 (Springer Berlin, 1975) p. 48.
[11] Schwarz R.B. and Funk L-L-, Internal friction study of solute segregation to dislocations, Acta Metall. 31 (1983) 299.
