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Effect of cyclic stress reduction on the creep behaviour of Al-40 wt%Zn alloy
ARTICLE IN PRESS
Physica B 388 (2007) 219–225 www.elsevier.com/locate/physb
Effect of cyclic stress reduction on the creep behaviour of Al-40 wt%Zn alloy F. Abd El-Salam, A.M. Abd El-Khalek, R.H. Nada Physics Department, Faculty of Education, Ain Shams University, Cairo, Egypt Received 2 February 2006; received in revised form 21 May 2006; accepted 23 May 2006
Abstract The effect of cyclic stress reduction on the creep behaviour of A1-40 wt% Zn alloy during transformation was investigated. The influence of cyclic stress reduction of increasing amplitudes (18–47%) and frequencies (0.12–0.29 Hz) was systematically examined at various deformation temperatures (573–633 K). Both transient and steady state creep parameters, b, n and s , were found to be higher under cyclic stress reduction condition than under the static condition for the same peak stress. Increasing temperature increased all the measured parameters. Increasing frequency and cyclic stress reduction increased the parameters n and s but decreased b. The frequency was found to be more effective than the cyclic stress reduction amplitude. Activation energies for the transformation temperature region around 603 K, which were found to be independent on either frequency or amplitude of cyclic stress reduction but depend on the temperature range, characterized a dislocation mechanism involving grain boundary sliding or grain migration. r 2006 Elsevier B.V. All rights reserved. PACS: 62.20.Fe; 62.20.Hg; 81.40.Lm Keywords: Cyclic stress reduction; Deformation temperatures; Creep; Amplitude; Frequency
1. Introduction Some of the factors applied to the tested samples may cause hardening by forming a structure in which dislocation mobility is reduced [1]. Hardening may therefore be due to: the interaction of dislocations, interaction of dislocations with impurity, the formation of second-phase particles and ordering [2]. In practice, the application of superimposed timedependent factors in combination with the applied static factors leads to complicated deformation behaviour for some tested phenomena such as creep, fatigue and fracture mode compared with the data of the same samples tested under the same condition without these time dependent factors. The cyclic stress–strain behaviour of Cu single crystals and polycrystals showed curves consisting of three stages centred around a predominant plateau [3]. Corresponding author. Tel.: +20 2 5508201.
E-mail address: [email protected] (A.M. Abd El-Khalek). 0921-4526/$ - see front matter r 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.physb.2006.05.429
The specimens tested under incremental strain amplitudes have the same stress as at conventional constant strain amplitudes. However, the specimens tested at decremental strain amplitudes have a history effect on the stress as compared with those at constant strain amplitudes. When an oscillatory stress is superimposed during plastic deformation, the applied stress decreases [4]. This phenomenon is called the Blaha effect. Strain rate cycling test during the Blaha effect measurement was preformed to separate the effective stress due to weak obstacles, such as an impurity, from that due to dislocation cutting [5]. The stress-dip technique of Ahlquist and Nix [6] was applied to determine both the effective stress, se , which is driving the creep process and the internal back stress, si , which is opposing the creep deformation. The instantaneous strains from a stress drop, D_, and a stress increment, Dþ , were measured for stress changes ranging up to 50% of the initial stress [7]. This study showed that Al–Zn alloys belong to class II solid solution alloys. Transient and steady state stages of Al–Cu samples under the effect of cyclic stress reduction amplitude,
ARTICLE IN PRESS F. Abd El-Salam et al. / Physica B 388 (2007) 219–225
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scy , and constant frequency of 0.2 Hz, were found to be higher than those under static creep condition for the same maximum stress. Such state is described as cyclic creep acceleration, which was observed before in Al–Zn system [8]. In a quenched sample of Al-40 wt%Zn alloy aged in the temperature range [9] up to 498 K, where the spherical or ellipsoidal GP zones can exist, reversion of these zones takes place. It was noticed [10] that the steady creep rate of polycrystalline zinc showed some sensitivity to the strain amplitude of vibrations during the internal friction measurements. The effect of the amplitude of cyclic stress reduction on the creep behaviour of Al-16 wt%Ag alloy, was reported as an acceleration of the steady state rate [11]. The present study aims at investigating the effect of cyclic stress reduction on the creep characteristics of Al-40 wt%Zn alloy during transformation. 2. Experimental procedure Al-40 wt%Zn alloy was prepared by melting pure Al and Zn (99.99) under vacuum in high purity graphite crucible. The ingot was homogenized at 643 K for 24 h, then coldswaged with intermediate anneal into wires of 0.6 mm diameter and 50 mm long. Chemical analysis revealed that specimens composition is very close to the intended alloy composition. According to the phase diagram of the Al–Zn system [12], shown in Fig. 1, after solution heat treatment for 2 h at 643 K the specimens were quenched into cold water kept at 273 K. The accuracy of temperature measurements was of the order of 71 K. A constant load static creep machine was modified so that cyclic and/or static creep tests can be carried out using the same machine. The details of such a modification are described elsewhere [13]. The creep experiments were carried out under a static stress, ss , of 62.3 MPa (peak stress), which was varied by a controlled value ðDsÞ that makes cyclic stress changes from 18% to 47%. This Weight percent zinc 10 20 30 40 50
60
70
80
90
95
600 L
Temperature, °C
500
L+α α or Al
400
382°C
α + α′
300 16 31.6
200
0 Al
88.7
275°C
(95)
β
59.4 (78)
100 0
β+L
α′ + β
α+β
10
20
30
40
50
60
70
Automatic percent zinc
80
90
100 Zn
Fig. 1. The equilibrium phase diagram of Aluminum-Zinc.
62.3 MPa
Stress, σ (MPa)
σmax
σstatic σmin
0 Time, t (s) Fig. 2. Stress–time variation for sinosoidal stress.
means that the three main stress levels have the values; ss : which is the reference value, ðsmax ¼ ss þ DsÞ, ðsmin ¼ ss DsÞ as shown in Fig. 2. This figure shows that the stress magnitude is time dependent. Such cyclic stress with partial unloading has the form of a sinusoidal wave (see Fig. 2), with frequency in the range 0.12–0.29 Hz. Structure investigations were determined from X-ray diffraction patterns obtained for crept samples by using X-ray diffractometer. 3. Experimental results In general, the strain–time relations of Fig. 3 are obtained under a constant stress of 62.3 MPa for Al40 wt%Zn samples at different deformation temperatures from 573 to 633 K in steps of 10 K. This applies to Fig. 3a. Besides, there are specified conditions for Fig. 3(b–h) as follows: Fig. 3(b–e) shows creep relation under the same conditions of Fig. 3a, but with imposed cyclic stress reduction of different frequencies, n ¼ 0:12, 0.18, 0.24, and 0.29 Hz with the same amplitude of cyclic stress reduction, scy (11.2 MPa). In Fig. 3(b,f–h), the creep relations are due to cyclic stress reduction of different amplitudes, scy ¼ 11:2, 15.8, 21.9, and 29.5 MPa at constant frequency, n (0.12 Hz). Under the different conditions investigated, all the strain–time relations of Fig. 3 showed the same normal creep behaviour with different magnitudes for fracture strain and fracture time. A monotonic shift towards higher strains and lower fracture times is observed with increasing the deformation temperature, except for deformation temperature at 603 K. It is also clear from Fig. 3 that the total strain level increases as either the amplitude, scy or the frequency, n, of the cyclic stress reduction increases. Also, both the creep strain and creep rate are enhanced showing the cyclic creep acceleration [13] phenomenon under cyclic stress reduction as compared to static stress of similar peak stress.
ARTICLE IN PRESS F. Abd El-Salam et al. / Physica B 388 (2007) 219–225
90
-2.5
(b)
(a)
573 K 583 K 593 K 603 K 613 K 623 K 633 K
-3.5
60 45
ln εtr
103 . ε
75
30 15
σcy= 0
σcy = 11.2 MPa
ν=0
ν = 0.12 Hz
(c)
-4.5
-5.5
0 100
σcy = 11.2 MPa ν = 0.18 Hz
(a)
(f )
-6.5
3
3.8
103 . ε
80 60
σcy = 11.2 MPa
σcy =15.8 MPa
ν = 0.18 Hz
4.6 5.4 ln [t (s)]
6.2
σcy = 15.8 MPa ν = 0.12 Hz
(b) 7
3
3.8
4.6 5.4 ln [t(s)]
6.2
7
Fig. 4. The relation between ln etr and ln t for different frequencies (n) and amplitudes of cyclic stress reduction (scy ) for representative samples of Al-40 wt% Zn alloy.
40 20
221
ν= 0.12 Hz
0
(d)
100
104.β
80 103 . ε
ν= 0.0 Hz 0.12 Hz 0.18 Hz 0.24 Hz 0.29 Hz
6
(g)
60
4 2
40 σcy = 11.2 MPa
20
σcy = 21.9 MPa ν = 0.12 Hz
ν = 0.24 Hz
0
(a)
(b)
(c)
(d)
0 5
(h)
(e)
100
4
60 40 σcy = 11.2 MPa
20
ν = 0.29 Hz
0
0
15
30 45 60 time (min)
75
3 2
573 K 583 K 593 K 603 K 613 K 623 K 633 K
1 σcy = 29.5 MPa
0
ν = 0.12 Hz
90
0
15
30
45
60
75
50
90
time (min)
σcy= 0.0 MPa 11.2 MPa 15.8 MPa 21.9 MPa 29.5 MPa
40
Fig. 3. Strain–time curves for Al-40 wt%Zn alloy samples at different deformation temperatures, T, under a stress of 62.3 MPa and different frequencies (n) and amplitudes of cyclic stress reduction (scy ).
106.εs
103 . ε
n
80
30 20 10
The transient creep stain tr , which is characterized by a decreasing strain rate, can be described by the relation [14]: tr ¼ o ¼ btn
(1)
where t is the transient creep time (in seconds). The transient creep parameters, n and b, which depend on both the test temperature and the applied stress were calculated from the relation between ln etr and ln t. Fig. 4a demonstrates this relation for different values of n at constant scy (¼11.2 MPa) and Fig. 4b shows the same relation for different values of scy at constant frequency ( ¼ 0.12 Hz). The deformation temperature dependence of b and n is given for samples crept under different frequencies, n, in Fig. 5(a,c,e), and for samples crept under different amplitudes of cyclic stress reduction, scy , in Fig. 5(b,d,f). In Fig. 5, it is observed that the peak values of b and n at 603 K show sudden drop at 613 K followed by further increase at higher temperatures. Increasing either frequency, n or the amplitude of cyclic stress reduction, scy ,
(e)
0 560
(f ) 580
600 T (K)
620
640 560
580
600 T (K)
620
640
Fig. 5. The temperature dependence of the creep parameter b, n and s ; (a,c,e) at different frequencies and (b,d,f) at different amplitudes of cyclic stress reduction.
the level of b values decreased, Fig. 5(a,b), while n values, Fig. 5(c,d), increased. Also, the steady state creep rate, s , values, calculated from the slopes of the linear parts of the creep curves of Fig. 3 and given in Fig. 5e for the samples crept under different frequencies, n, and in Fig. 5f for samples crept under different amplitudes of cyclic stress reduction, scy , increased. In Fig. 5e, a drop in s values takes place at 613 K followed by further increase with increasing the deformation temperature. The general thermally induced behaviour of s in Fig. 5e is similar to that of b and n, Fig. 5(a–d) despite the opposite effect of frequency and/or the amplitude of cyclic stress reduction
ARTICLE IN PRESS F. Abd El-Salam et al. / Physica B 388 (2007) 219–225
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on b compared with n and s . The observed change Db, Dn and Ds due to the factors, T, n, scy , is given in Fig. 6(a,c,e) as temperature dependence of Db, Dn and Ds at constant scy and Fig. 6(b,d,f) for the same relation at constant frequency, n. From Fig. 6, the range of change in these 3
ν=
0.12 Hz 0.18 Hz 0.24 Hz 0.29 Hz
2 1.5
1.2 0.9
1
0.6
0.5
0.3
(a)
0
(b)
0
0 -0.5 -1 -1.5 -2 -2.5 -3 -3.5 (c) -4
-0.5 Δn
-1 -1.5 -2 -2.5 -3
0
0
-5
-2
(d)
-4
-10
106 .Δνs
106 .Δνs
Δn
0
11.2 Mpa 15.8 MPa 21.9 MPa 29.5 MPa
1.5 104.Δβ
104.Δβ
2.5
σcy=
1.8
-15 -20
-6 -8 -10
-25
-12
(e)
-30 560
580
600 T (K)
620
640
(f )
-14 560
580
600 T (K)
620
640
Fig. 6. Temperature dependence of the variations of creep parameter, Db, Dn and Ds ; (a,c,e) at different frequencies and (b,d,f) at different amplitudes of cyclic stress reduction.
parameters at temperatures around 603 K is given in Table 1, and the total change due to the temperature range (573–633 K) of the applied factors is given in Table 2. 4. Discussion The solution of Al–Zn alloys by rapid quenching from the a-phase field produces a very fine structure with grains of very high dislocation density [15]. This suggests that forest hardening is likely to be a dominant strengthening mechanism in these alloys. Such state consists with the high creep resistance reducing the creep strain, , Fig. 3, and n values, Fig. 5(c,d) at low temperatures. In Al–Zn alloys, GP zones are formed on quenching the supersaturated solid solution [16]. Below 498 K, the decomposition of the supersaturated Al–Zn alloy starts with the nucleation and growth of GP zones [17]. The dissolution of these GP zones was revealed above 373 K. Also, the kinetics of formation of GP zones at ambient temperature is drastically reduced when a quenched Al–Zn alloy was reverted at 403 K [16]. For Al–Zn alloy previously aged at low temperature, it was found that annealing above 367 K eliminates all zones and the alloy is therefore reverted. Annealing below 367 K allows partial reversion to take place [18]. Accordingly, the samples tested in the temperature range (573–633 K) and in view of the phase diagram of the Al–Zn alloy [12], the elimination of GP zones and the existence of the mixed ðþaÞ phases or the a-phase is expected in these reverted samples. The reduction in fracture time and the increase of creep strain with increasing the deformation temperature and applying the cyclic stress reduction during creep observed in Fig. 3 are due to the dissolution of the incoherent b-phase in the a-matrix and the increase in the homogeneity
Table 1 The range of change in the creep parameters at temperatures around transformation Temperature (K)
Range for different values of Db 104
593 603 613
D:s 106
Dn
At (n) constant
At ðscy Þ constant
At (n) constant
At ðscy Þ constant
At (n) constant
At ðscy Þ constant
1.3 1.24 1.04
0.7 1.02 0.85
1.39 1.51 1.47
1.16 1.27 1.01
10.5 15.2 12.0
6.8 8.9 8.6
Table 2 The total change in the creep parameters due to the temperature range (573–633 K) of the applied factors Factor
Frequency (n) Cyclic stress reduction, scy
Range of variation for Temperature
Decrease of b 104
Increase of n
Increase of :s 106
60 60
1.28 0.64
1.63 1.18
20.8 4.2
ARTICLE IN PRESS F. Abd El-Salam et al. / Physica B 388 (2007) 219–225
of decreasing or increasing values depending on the net effect of these factors. It is clear that b increases by increasing temperature but decreases with increasing either n or scy , while n and s increase by increasing any of these factors. The effect of temperature depends on the sample composition and is consistent with the nature of creep process being a thermally activated process. From Tables 1 and 2 it is clear that the effect of frequency change generally dominates over that of cyclic stress reduction. For higher values of T, n, and scy , all the effects considerably increase. Although the alternating direction of the cyclic stress reduction is parallel to the applied stress, due to Blaha effect the applied stress decreases [4] leading to the observed decrease of b values. This effect is enhanced by increasing frequency. To determine the activation energy of the transient and steady-state creep stages of Fig. 3, the transient creep parameter b and the steady state creep rate, s , were assumed to vary with the deformation temperature, T, according to the following Arrhenius-type relations [19]; b ¼ constant expðQ=kTÞ,
(2)
s ¼ constant expðQ=kTÞ,
(3)
where Q is the activation energy (in kJ/mol) and k the Boltzmann constant. The energy activating the creep process for both transient and steady state creep stages, respectively, were calculated from the slopes of the straight lines relating ln b and 103/T K1, (Fig. 7a,b) and ln s versus 103/T K1, (Fig. 7c,d). The calculated activation energies from Fig. 7, were found to be independent on either frequency or amplitude of cyclic stress reduction, but showed dependence on the -7 -7.5
ln β
-8 0.0 Hz 0.12 Hz 0.18 Hz 0.24 Hz 0.29 Hz
-8.5 -9 -9.5
15.8 MPa 21.9 MPa 29.5 MPa
(a)
(b)
(c)
(d)
-10 -9.5 -10.5 ln εs
of the distribution of Zn atoms in the a-phase at higher temperatures [1,19]. The external elastic energy due to cyclic stress reduction facilitates the motion of dislocations during creep process which enhances the rate of recovery and shortens the duration of the process [20]. The anomalous behaviour of creep strain level observed at 603 K in Fig. 3, and the associated peak values of the parameters b (Fig. 5a and b) and s (Fig. 5e and f) are due to dynamic strain aging and structure variations that take place in the vicinity of this temperature. Below the transformation temperature, this irregularity at 603 K might be attributed to the coarsening of a (Al) and b (Zn) grains associated with the dissolution of Zn and Al which takes place to satisfy the actual equilibrium composition [1]. The precipitates at grain boundaries or within grains increase creep resistance and lower creep strain at temperatures below 603 K as clear from Fig. 3. Besides, the existing small grains of zinc and aluminum in the matrix formed at lower temperature increase creep resistance and lower the strain level of creep stage, Figs. 3 and 5(a,b,e,f) observed decrease of n, b, and s Fig. 5, with increasing either frequency or the cyclic stress reduction at 613 K is due to a certain degree of fatigue hardening [19]. The enhancement of the primary creep and the higher b values obtained at higher temperatures, shown in Fig. 5(a,b), might be attributed to the reduced crack initiation life associating the existing large grain size at higher deformation temperatures [21] and the fact that the parameter b represents the dependence of the transient strain, tr , on precipitation temperature. Therefore, increasing deformation temperature enables dislocations to overcome the precipitates which act as barriers and increase creep strain. The enhanced transient strain at higher deformation temperatures with the imposed cyclic stress reduction, Fig. 5(c,d), is due to the arrangement and annihilation of some dislocations generated from the new dislocation sources formed in the early stages of creep in the matrix by the applied stress [22]. Above the transformation temperature, 603 K, the b phase begins to transform into the composition of the FCC a-solid solution phase [14,23], which is incoherent with the matrix and has prolonged decomposition time into the stable Zn precipitates [24]. This leads to the final increase of b, n, Fig. 5(a–d), and s , Fig. 5(e,f), with increasing temperature and/or any of the frequency or the amplitude of the cyclic stress reduction. This also indicates an easier motion of the existing dislocations facilitated by either the thermal or mechanical external energy provided to the tested samples [19]. Therefore, vibrations or cyclic stress reduction imposed during creep have marked effect on creep behaviour [25]. The creep parameters b, n and s measured for samples subjected to the effect of temperature, T, frequency, n, and cyclic stress reduction, scy , given in Fig. 5, show behaviours
223
-11.5 -12.5 -13.5 1.55
1.6
1.65
1.7
1000/T (K-1)
1.75
1.55
1.6
1.65
1.7
1.75
1000/T (K-1)
Fig. 7. The relation between both ln b and ln s and 1000/T at: (a,c) different frequencies, and, (b,d) different amplitudes of cyclic stress reduction, for Al-40 wt% Zn alloy samples.
ARTICLE IN PRESS F. Abd El-Salam et al. / Physica B 388 (2007) 219–225
b ¼ bo ðs Þg ,
(4)
where bo is a constant and g is the steady state creep exponent measuring the contribution of the transient mechanism to the steady state creep and measured through the ratio g ¼ ðq ln bÞ=q ln s Þ:. Fig. 8 shows the relation between ln b and ln s , a linear dependence is obtained with a mean value of g ¼ 0:87 for samples crept under different frequencies and 0.93 for samples crept under different amplitude of cyclic stress reduction. The dependence of s on b seems to be due to the decrease of dislocation density to a level that makes the hardening rate at the end of the transient stage converges to recovery rate. So, the steady state creep starts with rates depending on the applied stress. This relatively high value of g which tends to unity confirm again that the mechanism responsible for the transient stage still operates in the steady state stage. The temperature dependence of the lattice parameter (a), the half line width ðD2yÞ of the a-phase and the ratio (c/a) for b-phase are given in Fig. 9. Besides the strain hardening, the hardening caused by Zn atoms represented by their large effect on the distribution of vacancy clusters and the existing precipitate, increase the hardness of the alloy and consequently increase the lattice parameter [27]. At 603 K, the peak value of the lattice parameter (a), Fig. 9a, points to a high deformation level in the alloy with the result of high residual strain corresponds to the peak value in D2y, Fig. 9b. This consists with the minimum -6.5 γ = 0.87
γ = 0.93
ln β
-7 -7.5 0 Hz 0.12 Hz 0.18 Hz 0.24 Hz 0.29 Hz
-8 -8.5
(a) -9 -12
-11
-10 ln εs
4.085
a (10-10 m)
4.08 4.075 4.07 4.065 4.06
(a) 4.055 0.6
Δ2θ (10-3 m)
range of the deformation temperatures being below or above 603 K. Below 603 K, the calculated energies assumed the value 27.5 kJ/mol for the transient creep stage and 30.2 kJ/mol for the steady creep stage. These values are in agreement with the value 29.9 kJ/mol [26], which characterize a dislocation mechanism involving grain boundary sliding or grain migration [14]. Above 603 K, a value of 91.6 kJ/mol was obtained for the transient stage and a value of 88.3 kJ/mol was obtained for the steady stage, respectively. Creep is a continuous process since both transient and steady state creep stages are related to each other by the relation [19]:
0.5
0.4
(b) 0.3 1.86 1.855 1.85 c/a
224
1.845 1.84 1.835
(c) 1.83 560
580
600 T (K)
620
640
Fig. 9. Temperature dependence of the average lattice parameter, a, the half line width, D2y, for the a-phase and c/a for b-phase.
crystallite size indicated through c/a Fig. 9c, for the b-phase (Zn). This state consists with the peak values obtained for b, n and s given in Fig. 5(a–f), respectively. At 613 K, the drop in Figa. 9(a,b) and 5(a–f) which corresponds to decreased lattice parameter indicates the occurrence of a recovery process due to the relief of the internal strains or stresses during the thermally activated growth of the stable incoherent a-phase with larger grains, Fig. 9c. Above 613 K, the dissolution of the a-phase associated with a high concentration of vacancies increases the lattice constant (a), Fig. 9a. Therefore, the formation of the aphase may lead to heterogeneities in the dissolution of the dissolved a-phase atoms in the a-phase showing a solid solution hardening. This increases the internal strain, ðD2yÞ, Fig. 9b, and decreases the ratio, (c/a), Fig. 9c.
15.8 MPa
5. Conclusions
21.9 MPa
(b) -9
-12
29.5 MPa
-11
-10
-9
ln εs
Fig. 8. The relation between ln b and ln s at: (a) different frequencies, and, (b) different amplitudes of cyclic stress reduction, for Al-40 wt% Zn alloy samples.
From experimental results and discussion above, we could conclude: 1. Creep parameters b, n and s showed higher values by increasing temperature. Imposing vibrations of low
ARTICLE IN PRESS F. Abd El-Salam et al. / Physica B 388 (2007) 219–225
frequency and different amplitudes increased n and s but decreased b at different temperatures. 2. The effect of frequency change generally dominates over that of cyclic stress reduction. 3. Activation energies for the transformation temperature region around 603 K, which were found to be independent on either frequency or amplitude of cyclic stress reduction but depend on the temperature range, characterized a dislocation mechanism involving grain sliding or grain migration.
References [1] F. Abd El-Salam, R.H. Nada, A.M. Abd El-Khalek, Physica B 292 (2000) 71. [2] M.M. El-Sayed, F. Abd El-Salam, R. Abd El-Haseeb, Phys. Status Solidi (a) 147 (1995) 401. [3] C.D. Liu, M.N. Bassim, Phys. Status Solidi (a) 149 (1995) 323. [4] T. Ohgaku, N. Takeuchi, Phys. Status Solidi (a) 118 (1990) 153. [5] T. Ohgaku, N. Takeuchi, Phys. Status Solidi (a) 111 (1989) 165. [6] C.N. Ahlquist, W.D. Nix, Scr. Metall. 3 (1969) 679. [7] D.O. Northwood, I.O. Smith, Phys. Stat. Sol. (a) 115 (1989) 125. [8] W. Blum, A. Rosen, A. Cegielska, J.I. Mortin, Acta Metall. 37 (1989) 2439.
225
[9] F. Abd El-Salam, A.M. Ibraheim, A.H. Ammar, Vacuum 48 (1) (1997) 29. [10] R. Kamel, F.A. Bessa, Acta Metall. 13 (1965) 19. [11] G. Graiss, M.A. Mahmoud, Cryst. Res. Technol. 35 (2000) 95. [12] M. Hansen, K. Anderko, Constitution of Binary Alloys, Mc GrowHill, New York, 1958, p. 149. [13] A.F. Abd El-Rehim, Ph.D. Thesis, Physics Department. Ain-Shams University,Cairo, 2004, p. 68. [14] F. Abd El-Salam, M.M. Mostafa, M.M. El-Sayed, R.H. Nada, Phys. Status Solidi (a) 144 (1994) 111. [15] S. Krisknamurtly, S.P. Gupta, Mater. Sci. Eng. 2 (1977) 155. [16] S. Panchanadeeswaran, M.R. Plicha, J.G. Byrne, Phil. Mag. A 49 (1) (1984) 111. [17] G. Wendrock, H. Loffler, O. Kabisch, C.T. Truong, Phys. Status Solidi (a) 91 (1985) 453. [18] C. Panseri, T. Federighi, Acta Metall. 8 (1960) 233. [19] F. Abd El-Salam, A.M. Abd El-Khalek, R.H. Nada, Eur. Phys. J. AP 12 (2000) 159. [20] M.H.N. Beshai, G.H. Deaf, A.M. Abd El-Khalek, G. Graiss, M.A. Kenawy, Phys. Status Solidi (a) 161 (1997) 65. [21] D.J. Morrison, J.C. Moosbrugger, Int. J. Fatifue 19 (1) (1997) 551. [22] H. Jiang, P. Bowen, J.F. Knott, J. Mater Sci. 34 (1999) 719. [23] M. Simeriska, V. Synecek, Acta Metall. 15 (1967) 223. [24] R. Ciach, W. Wereznski, Czech. J. Phys. B 39 (1989) 151. [25] V. Ravi, E. Philofsky, Metall. Trans. 2 (1971) 711. [26] M.M. Mostafa, G.S. Al-Ganainy, Egypt. J. Sol. 28 (1) (2005) 109. [27] F. Abd El-Salam, A. Fawzy, M.T. Mostafa, R.H. Nada, Egypt. J. Sol. 23 (2) (2000) 341.
Physica B 388 (2007) 219–225 www.elsevier.com/locate/physb
Effect of cyclic stress reduction on the creep behaviour of Al-40 wt%Zn alloy F. Abd El-Salam, A.M. Abd El-Khalek, R.H. Nada Physics Department, Faculty of Education, Ain Shams University, Cairo, Egypt Received 2 February 2006; received in revised form 21 May 2006; accepted 23 May 2006
Abstract The effect of cyclic stress reduction on the creep behaviour of A1-40 wt% Zn alloy during transformation was investigated. The influence of cyclic stress reduction of increasing amplitudes (18–47%) and frequencies (0.12–0.29 Hz) was systematically examined at various deformation temperatures (573–633 K). Both transient and steady state creep parameters, b, n and s , were found to be higher under cyclic stress reduction condition than under the static condition for the same peak stress. Increasing temperature increased all the measured parameters. Increasing frequency and cyclic stress reduction increased the parameters n and s but decreased b. The frequency was found to be more effective than the cyclic stress reduction amplitude. Activation energies for the transformation temperature region around 603 K, which were found to be independent on either frequency or amplitude of cyclic stress reduction but depend on the temperature range, characterized a dislocation mechanism involving grain boundary sliding or grain migration. r 2006 Elsevier B.V. All rights reserved. PACS: 62.20.Fe; 62.20.Hg; 81.40.Lm Keywords: Cyclic stress reduction; Deformation temperatures; Creep; Amplitude; Frequency
1. Introduction Some of the factors applied to the tested samples may cause hardening by forming a structure in which dislocation mobility is reduced [1]. Hardening may therefore be due to: the interaction of dislocations, interaction of dislocations with impurity, the formation of second-phase particles and ordering [2]. In practice, the application of superimposed timedependent factors in combination with the applied static factors leads to complicated deformation behaviour for some tested phenomena such as creep, fatigue and fracture mode compared with the data of the same samples tested under the same condition without these time dependent factors. The cyclic stress–strain behaviour of Cu single crystals and polycrystals showed curves consisting of three stages centred around a predominant plateau [3]. Corresponding author. Tel.: +20 2 5508201.
E-mail address: [email protected] (A.M. Abd El-Khalek). 0921-4526/$ - see front matter r 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.physb.2006.05.429
The specimens tested under incremental strain amplitudes have the same stress as at conventional constant strain amplitudes. However, the specimens tested at decremental strain amplitudes have a history effect on the stress as compared with those at constant strain amplitudes. When an oscillatory stress is superimposed during plastic deformation, the applied stress decreases [4]. This phenomenon is called the Blaha effect. Strain rate cycling test during the Blaha effect measurement was preformed to separate the effective stress due to weak obstacles, such as an impurity, from that due to dislocation cutting [5]. The stress-dip technique of Ahlquist and Nix [6] was applied to determine both the effective stress, se , which is driving the creep process and the internal back stress, si , which is opposing the creep deformation. The instantaneous strains from a stress drop, D_, and a stress increment, Dþ , were measured for stress changes ranging up to 50% of the initial stress [7]. This study showed that Al–Zn alloys belong to class II solid solution alloys. Transient and steady state stages of Al–Cu samples under the effect of cyclic stress reduction amplitude,
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scy , and constant frequency of 0.2 Hz, were found to be higher than those under static creep condition for the same maximum stress. Such state is described as cyclic creep acceleration, which was observed before in Al–Zn system [8]. In a quenched sample of Al-40 wt%Zn alloy aged in the temperature range [9] up to 498 K, where the spherical or ellipsoidal GP zones can exist, reversion of these zones takes place. It was noticed [10] that the steady creep rate of polycrystalline zinc showed some sensitivity to the strain amplitude of vibrations during the internal friction measurements. The effect of the amplitude of cyclic stress reduction on the creep behaviour of Al-16 wt%Ag alloy, was reported as an acceleration of the steady state rate [11]. The present study aims at investigating the effect of cyclic stress reduction on the creep characteristics of Al-40 wt%Zn alloy during transformation. 2. Experimental procedure Al-40 wt%Zn alloy was prepared by melting pure Al and Zn (99.99) under vacuum in high purity graphite crucible. The ingot was homogenized at 643 K for 24 h, then coldswaged with intermediate anneal into wires of 0.6 mm diameter and 50 mm long. Chemical analysis revealed that specimens composition is very close to the intended alloy composition. According to the phase diagram of the Al–Zn system [12], shown in Fig. 1, after solution heat treatment for 2 h at 643 K the specimens were quenched into cold water kept at 273 K. The accuracy of temperature measurements was of the order of 71 K. A constant load static creep machine was modified so that cyclic and/or static creep tests can be carried out using the same machine. The details of such a modification are described elsewhere [13]. The creep experiments were carried out under a static stress, ss , of 62.3 MPa (peak stress), which was varied by a controlled value ðDsÞ that makes cyclic stress changes from 18% to 47%. This Weight percent zinc 10 20 30 40 50
60
70
80
90
95
600 L
Temperature, °C
500
L+α α or Al
400
382°C
α + α′
300 16 31.6
200
0 Al
88.7
275°C
(95)
β
59.4 (78)
100 0
β+L
α′ + β
α+β
10
20
30
40
50
60
70
Automatic percent zinc
80
90
100 Zn
Fig. 1. The equilibrium phase diagram of Aluminum-Zinc.
62.3 MPa
Stress, σ (MPa)
σmax
σstatic σmin
0 Time, t (s) Fig. 2. Stress–time variation for sinosoidal stress.
means that the three main stress levels have the values; ss : which is the reference value, ðsmax ¼ ss þ DsÞ, ðsmin ¼ ss DsÞ as shown in Fig. 2. This figure shows that the stress magnitude is time dependent. Such cyclic stress with partial unloading has the form of a sinusoidal wave (see Fig. 2), with frequency in the range 0.12–0.29 Hz. Structure investigations were determined from X-ray diffraction patterns obtained for crept samples by using X-ray diffractometer. 3. Experimental results In general, the strain–time relations of Fig. 3 are obtained under a constant stress of 62.3 MPa for Al40 wt%Zn samples at different deformation temperatures from 573 to 633 K in steps of 10 K. This applies to Fig. 3a. Besides, there are specified conditions for Fig. 3(b–h) as follows: Fig. 3(b–e) shows creep relation under the same conditions of Fig. 3a, but with imposed cyclic stress reduction of different frequencies, n ¼ 0:12, 0.18, 0.24, and 0.29 Hz with the same amplitude of cyclic stress reduction, scy (11.2 MPa). In Fig. 3(b,f–h), the creep relations are due to cyclic stress reduction of different amplitudes, scy ¼ 11:2, 15.8, 21.9, and 29.5 MPa at constant frequency, n (0.12 Hz). Under the different conditions investigated, all the strain–time relations of Fig. 3 showed the same normal creep behaviour with different magnitudes for fracture strain and fracture time. A monotonic shift towards higher strains and lower fracture times is observed with increasing the deformation temperature, except for deformation temperature at 603 K. It is also clear from Fig. 3 that the total strain level increases as either the amplitude, scy or the frequency, n, of the cyclic stress reduction increases. Also, both the creep strain and creep rate are enhanced showing the cyclic creep acceleration [13] phenomenon under cyclic stress reduction as compared to static stress of similar peak stress.
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90
-2.5
(b)
(a)
573 K 583 K 593 K 603 K 613 K 623 K 633 K
-3.5
60 45
ln εtr
103 . ε
75
30 15
σcy= 0
σcy = 11.2 MPa
ν=0
ν = 0.12 Hz
(c)
-4.5
-5.5
0 100
σcy = 11.2 MPa ν = 0.18 Hz
(a)
(f )
-6.5
3
3.8
103 . ε
80 60
σcy = 11.2 MPa
σcy =15.8 MPa
ν = 0.18 Hz
4.6 5.4 ln [t (s)]
6.2
σcy = 15.8 MPa ν = 0.12 Hz
(b) 7
3
3.8
4.6 5.4 ln [t(s)]
6.2
7
Fig. 4. The relation between ln etr and ln t for different frequencies (n) and amplitudes of cyclic stress reduction (scy ) for representative samples of Al-40 wt% Zn alloy.
40 20
221
ν= 0.12 Hz
0
(d)
100
104.β
80 103 . ε
ν= 0.0 Hz 0.12 Hz 0.18 Hz 0.24 Hz 0.29 Hz
6
(g)
60
4 2
40 σcy = 11.2 MPa
20
σcy = 21.9 MPa ν = 0.12 Hz
ν = 0.24 Hz
0
(a)
(b)
(c)
(d)
0 5
(h)
(e)
100
4
60 40 σcy = 11.2 MPa
20
ν = 0.29 Hz
0
0
15
30 45 60 time (min)
75
3 2
573 K 583 K 593 K 603 K 613 K 623 K 633 K
1 σcy = 29.5 MPa
0
ν = 0.12 Hz
90
0
15
30
45
60
75
50
90
time (min)
σcy= 0.0 MPa 11.2 MPa 15.8 MPa 21.9 MPa 29.5 MPa
40
Fig. 3. Strain–time curves for Al-40 wt%Zn alloy samples at different deformation temperatures, T, under a stress of 62.3 MPa and different frequencies (n) and amplitudes of cyclic stress reduction (scy ).
106.εs
103 . ε
n
80
30 20 10
The transient creep stain tr , which is characterized by a decreasing strain rate, can be described by the relation [14]: tr ¼ o ¼ btn
(1)
where t is the transient creep time (in seconds). The transient creep parameters, n and b, which depend on both the test temperature and the applied stress were calculated from the relation between ln etr and ln t. Fig. 4a demonstrates this relation for different values of n at constant scy (¼11.2 MPa) and Fig. 4b shows the same relation for different values of scy at constant frequency ( ¼ 0.12 Hz). The deformation temperature dependence of b and n is given for samples crept under different frequencies, n, in Fig. 5(a,c,e), and for samples crept under different amplitudes of cyclic stress reduction, scy , in Fig. 5(b,d,f). In Fig. 5, it is observed that the peak values of b and n at 603 K show sudden drop at 613 K followed by further increase at higher temperatures. Increasing either frequency, n or the amplitude of cyclic stress reduction, scy ,
(e)
0 560
(f ) 580
600 T (K)
620
640 560
580
600 T (K)
620
640
Fig. 5. The temperature dependence of the creep parameter b, n and s ; (a,c,e) at different frequencies and (b,d,f) at different amplitudes of cyclic stress reduction.
the level of b values decreased, Fig. 5(a,b), while n values, Fig. 5(c,d), increased. Also, the steady state creep rate, s , values, calculated from the slopes of the linear parts of the creep curves of Fig. 3 and given in Fig. 5e for the samples crept under different frequencies, n, and in Fig. 5f for samples crept under different amplitudes of cyclic stress reduction, scy , increased. In Fig. 5e, a drop in s values takes place at 613 K followed by further increase with increasing the deformation temperature. The general thermally induced behaviour of s in Fig. 5e is similar to that of b and n, Fig. 5(a–d) despite the opposite effect of frequency and/or the amplitude of cyclic stress reduction
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on b compared with n and s . The observed change Db, Dn and Ds due to the factors, T, n, scy , is given in Fig. 6(a,c,e) as temperature dependence of Db, Dn and Ds at constant scy and Fig. 6(b,d,f) for the same relation at constant frequency, n. From Fig. 6, the range of change in these 3
ν=
0.12 Hz 0.18 Hz 0.24 Hz 0.29 Hz
2 1.5
1.2 0.9
1
0.6
0.5
0.3
(a)
0
(b)
0
0 -0.5 -1 -1.5 -2 -2.5 -3 -3.5 (c) -4
-0.5 Δn
-1 -1.5 -2 -2.5 -3
0
0
-5
-2
(d)
-4
-10
106 .Δνs
106 .Δνs
Δn
0
11.2 Mpa 15.8 MPa 21.9 MPa 29.5 MPa
1.5 104.Δβ
104.Δβ
2.5
σcy=
1.8
-15 -20
-6 -8 -10
-25
-12
(e)
-30 560
580
600 T (K)
620
640
(f )
-14 560
580
600 T (K)
620
640
Fig. 6. Temperature dependence of the variations of creep parameter, Db, Dn and Ds ; (a,c,e) at different frequencies and (b,d,f) at different amplitudes of cyclic stress reduction.
parameters at temperatures around 603 K is given in Table 1, and the total change due to the temperature range (573–633 K) of the applied factors is given in Table 2. 4. Discussion The solution of Al–Zn alloys by rapid quenching from the a-phase field produces a very fine structure with grains of very high dislocation density [15]. This suggests that forest hardening is likely to be a dominant strengthening mechanism in these alloys. Such state consists with the high creep resistance reducing the creep strain, , Fig. 3, and n values, Fig. 5(c,d) at low temperatures. In Al–Zn alloys, GP zones are formed on quenching the supersaturated solid solution [16]. Below 498 K, the decomposition of the supersaturated Al–Zn alloy starts with the nucleation and growth of GP zones [17]. The dissolution of these GP zones was revealed above 373 K. Also, the kinetics of formation of GP zones at ambient temperature is drastically reduced when a quenched Al–Zn alloy was reverted at 403 K [16]. For Al–Zn alloy previously aged at low temperature, it was found that annealing above 367 K eliminates all zones and the alloy is therefore reverted. Annealing below 367 K allows partial reversion to take place [18]. Accordingly, the samples tested in the temperature range (573–633 K) and in view of the phase diagram of the Al–Zn alloy [12], the elimination of GP zones and the existence of the mixed ðþaÞ phases or the a-phase is expected in these reverted samples. The reduction in fracture time and the increase of creep strain with increasing the deformation temperature and applying the cyclic stress reduction during creep observed in Fig. 3 are due to the dissolution of the incoherent b-phase in the a-matrix and the increase in the homogeneity
Table 1 The range of change in the creep parameters at temperatures around transformation Temperature (K)
Range for different values of Db 104
593 603 613
D:s 106
Dn
At (n) constant
At ðscy Þ constant
At (n) constant
At ðscy Þ constant
At (n) constant
At ðscy Þ constant
1.3 1.24 1.04
0.7 1.02 0.85
1.39 1.51 1.47
1.16 1.27 1.01
10.5 15.2 12.0
6.8 8.9 8.6
Table 2 The total change in the creep parameters due to the temperature range (573–633 K) of the applied factors Factor
Frequency (n) Cyclic stress reduction, scy
Range of variation for Temperature
Decrease of b 104
Increase of n
Increase of :s 106
60 60
1.28 0.64
1.63 1.18
20.8 4.2
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of decreasing or increasing values depending on the net effect of these factors. It is clear that b increases by increasing temperature but decreases with increasing either n or scy , while n and s increase by increasing any of these factors. The effect of temperature depends on the sample composition and is consistent with the nature of creep process being a thermally activated process. From Tables 1 and 2 it is clear that the effect of frequency change generally dominates over that of cyclic stress reduction. For higher values of T, n, and scy , all the effects considerably increase. Although the alternating direction of the cyclic stress reduction is parallel to the applied stress, due to Blaha effect the applied stress decreases [4] leading to the observed decrease of b values. This effect is enhanced by increasing frequency. To determine the activation energy of the transient and steady-state creep stages of Fig. 3, the transient creep parameter b and the steady state creep rate, s , were assumed to vary with the deformation temperature, T, according to the following Arrhenius-type relations [19]; b ¼ constant expðQ=kTÞ,
(2)
s ¼ constant expðQ=kTÞ,
(3)
where Q is the activation energy (in kJ/mol) and k the Boltzmann constant. The energy activating the creep process for both transient and steady state creep stages, respectively, were calculated from the slopes of the straight lines relating ln b and 103/T K1, (Fig. 7a,b) and ln s versus 103/T K1, (Fig. 7c,d). The calculated activation energies from Fig. 7, were found to be independent on either frequency or amplitude of cyclic stress reduction, but showed dependence on the -7 -7.5
ln β
-8 0.0 Hz 0.12 Hz 0.18 Hz 0.24 Hz 0.29 Hz
-8.5 -9 -9.5
15.8 MPa 21.9 MPa 29.5 MPa
(a)
(b)
(c)
(d)
-10 -9.5 -10.5 ln εs
of the distribution of Zn atoms in the a-phase at higher temperatures [1,19]. The external elastic energy due to cyclic stress reduction facilitates the motion of dislocations during creep process which enhances the rate of recovery and shortens the duration of the process [20]. The anomalous behaviour of creep strain level observed at 603 K in Fig. 3, and the associated peak values of the parameters b (Fig. 5a and b) and s (Fig. 5e and f) are due to dynamic strain aging and structure variations that take place in the vicinity of this temperature. Below the transformation temperature, this irregularity at 603 K might be attributed to the coarsening of a (Al) and b (Zn) grains associated with the dissolution of Zn and Al which takes place to satisfy the actual equilibrium composition [1]. The precipitates at grain boundaries or within grains increase creep resistance and lower creep strain at temperatures below 603 K as clear from Fig. 3. Besides, the existing small grains of zinc and aluminum in the matrix formed at lower temperature increase creep resistance and lower the strain level of creep stage, Figs. 3 and 5(a,b,e,f) observed decrease of n, b, and s Fig. 5, with increasing either frequency or the cyclic stress reduction at 613 K is due to a certain degree of fatigue hardening [19]. The enhancement of the primary creep and the higher b values obtained at higher temperatures, shown in Fig. 5(a,b), might be attributed to the reduced crack initiation life associating the existing large grain size at higher deformation temperatures [21] and the fact that the parameter b represents the dependence of the transient strain, tr , on precipitation temperature. Therefore, increasing deformation temperature enables dislocations to overcome the precipitates which act as barriers and increase creep strain. The enhanced transient strain at higher deformation temperatures with the imposed cyclic stress reduction, Fig. 5(c,d), is due to the arrangement and annihilation of some dislocations generated from the new dislocation sources formed in the early stages of creep in the matrix by the applied stress [22]. Above the transformation temperature, 603 K, the b phase begins to transform into the composition of the FCC a-solid solution phase [14,23], which is incoherent with the matrix and has prolonged decomposition time into the stable Zn precipitates [24]. This leads to the final increase of b, n, Fig. 5(a–d), and s , Fig. 5(e,f), with increasing temperature and/or any of the frequency or the amplitude of the cyclic stress reduction. This also indicates an easier motion of the existing dislocations facilitated by either the thermal or mechanical external energy provided to the tested samples [19]. Therefore, vibrations or cyclic stress reduction imposed during creep have marked effect on creep behaviour [25]. The creep parameters b, n and s measured for samples subjected to the effect of temperature, T, frequency, n, and cyclic stress reduction, scy , given in Fig. 5, show behaviours
223
-11.5 -12.5 -13.5 1.55
1.6
1.65
1.7
1000/T (K-1)
1.75
1.55
1.6
1.65
1.7
1.75
1000/T (K-1)
Fig. 7. The relation between both ln b and ln s and 1000/T at: (a,c) different frequencies, and, (b,d) different amplitudes of cyclic stress reduction, for Al-40 wt% Zn alloy samples.
ARTICLE IN PRESS F. Abd El-Salam et al. / Physica B 388 (2007) 219–225
b ¼ bo ðs Þg ,
(4)
where bo is a constant and g is the steady state creep exponent measuring the contribution of the transient mechanism to the steady state creep and measured through the ratio g ¼ ðq ln bÞ=q ln s Þ:. Fig. 8 shows the relation between ln b and ln s , a linear dependence is obtained with a mean value of g ¼ 0:87 for samples crept under different frequencies and 0.93 for samples crept under different amplitude of cyclic stress reduction. The dependence of s on b seems to be due to the decrease of dislocation density to a level that makes the hardening rate at the end of the transient stage converges to recovery rate. So, the steady state creep starts with rates depending on the applied stress. This relatively high value of g which tends to unity confirm again that the mechanism responsible for the transient stage still operates in the steady state stage. The temperature dependence of the lattice parameter (a), the half line width ðD2yÞ of the a-phase and the ratio (c/a) for b-phase are given in Fig. 9. Besides the strain hardening, the hardening caused by Zn atoms represented by their large effect on the distribution of vacancy clusters and the existing precipitate, increase the hardness of the alloy and consequently increase the lattice parameter [27]. At 603 K, the peak value of the lattice parameter (a), Fig. 9a, points to a high deformation level in the alloy with the result of high residual strain corresponds to the peak value in D2y, Fig. 9b. This consists with the minimum -6.5 γ = 0.87
γ = 0.93
ln β
-7 -7.5 0 Hz 0.12 Hz 0.18 Hz 0.24 Hz 0.29 Hz
-8 -8.5
(a) -9 -12
-11
-10 ln εs
4.085
a (10-10 m)
4.08 4.075 4.07 4.065 4.06
(a) 4.055 0.6
Δ2θ (10-3 m)
range of the deformation temperatures being below or above 603 K. Below 603 K, the calculated energies assumed the value 27.5 kJ/mol for the transient creep stage and 30.2 kJ/mol for the steady creep stage. These values are in agreement with the value 29.9 kJ/mol [26], which characterize a dislocation mechanism involving grain boundary sliding or grain migration [14]. Above 603 K, a value of 91.6 kJ/mol was obtained for the transient stage and a value of 88.3 kJ/mol was obtained for the steady stage, respectively. Creep is a continuous process since both transient and steady state creep stages are related to each other by the relation [19]:
0.5
0.4
(b) 0.3 1.86 1.855 1.85 c/a
224
1.845 1.84 1.835
(c) 1.83 560
580
600 T (K)
620
640
Fig. 9. Temperature dependence of the average lattice parameter, a, the half line width, D2y, for the a-phase and c/a for b-phase.
crystallite size indicated through c/a Fig. 9c, for the b-phase (Zn). This state consists with the peak values obtained for b, n and s given in Fig. 5(a–f), respectively. At 613 K, the drop in Figa. 9(a,b) and 5(a–f) which corresponds to decreased lattice parameter indicates the occurrence of a recovery process due to the relief of the internal strains or stresses during the thermally activated growth of the stable incoherent a-phase with larger grains, Fig. 9c. Above 613 K, the dissolution of the a-phase associated with a high concentration of vacancies increases the lattice constant (a), Fig. 9a. Therefore, the formation of the aphase may lead to heterogeneities in the dissolution of the dissolved a-phase atoms in the a-phase showing a solid solution hardening. This increases the internal strain, ðD2yÞ, Fig. 9b, and decreases the ratio, (c/a), Fig. 9c.
15.8 MPa
5. Conclusions
21.9 MPa
(b) -9
-12
29.5 MPa
-11
-10
-9
ln εs
Fig. 8. The relation between ln b and ln s at: (a) different frequencies, and, (b) different amplitudes of cyclic stress reduction, for Al-40 wt% Zn alloy samples.
From experimental results and discussion above, we could conclude: 1. Creep parameters b, n and s showed higher values by increasing temperature. Imposing vibrations of low
ARTICLE IN PRESS F. Abd El-Salam et al. / Physica B 388 (2007) 219–225
frequency and different amplitudes increased n and s but decreased b at different temperatures. 2. The effect of frequency change generally dominates over that of cyclic stress reduction. 3. Activation energies for the transformation temperature region around 603 K, which were found to be independent on either frequency or amplitude of cyclic stress reduction but depend on the temperature range, characterized a dislocation mechanism involving grain sliding or grain migration.
References [1] F. Abd El-Salam, R.H. Nada, A.M. Abd El-Khalek, Physica B 292 (2000) 71. [2] M.M. El-Sayed, F. Abd El-Salam, R. Abd El-Haseeb, Phys. Status Solidi (a) 147 (1995) 401. [3] C.D. Liu, M.N. Bassim, Phys. Status Solidi (a) 149 (1995) 323. [4] T. Ohgaku, N. Takeuchi, Phys. Status Solidi (a) 118 (1990) 153. [5] T. Ohgaku, N. Takeuchi, Phys. Status Solidi (a) 111 (1989) 165. [6] C.N. Ahlquist, W.D. Nix, Scr. Metall. 3 (1969) 679. [7] D.O. Northwood, I.O. Smith, Phys. Stat. Sol. (a) 115 (1989) 125. [8] W. Blum, A. Rosen, A. Cegielska, J.I. Mortin, Acta Metall. 37 (1989) 2439.
225
[9] F. Abd El-Salam, A.M. Ibraheim, A.H. Ammar, Vacuum 48 (1) (1997) 29. [10] R. Kamel, F.A. Bessa, Acta Metall. 13 (1965) 19. [11] G. Graiss, M.A. Mahmoud, Cryst. Res. Technol. 35 (2000) 95. [12] M. Hansen, K. Anderko, Constitution of Binary Alloys, Mc GrowHill, New York, 1958, p. 149. [13] A.F. Abd El-Rehim, Ph.D. Thesis, Physics Department. Ain-Shams University,Cairo, 2004, p. 68. [14] F. Abd El-Salam, M.M. Mostafa, M.M. El-Sayed, R.H. Nada, Phys. Status Solidi (a) 144 (1994) 111. [15] S. Krisknamurtly, S.P. Gupta, Mater. Sci. Eng. 2 (1977) 155. [16] S. Panchanadeeswaran, M.R. Plicha, J.G. Byrne, Phil. Mag. A 49 (1) (1984) 111. [17] G. Wendrock, H. Loffler, O. Kabisch, C.T. Truong, Phys. Status Solidi (a) 91 (1985) 453. [18] C. Panseri, T. Federighi, Acta Metall. 8 (1960) 233. [19] F. Abd El-Salam, A.M. Abd El-Khalek, R.H. Nada, Eur. Phys. J. AP 12 (2000) 159. [20] M.H.N. Beshai, G.H. Deaf, A.M. Abd El-Khalek, G. Graiss, M.A. Kenawy, Phys. Status Solidi (a) 161 (1997) 65. [21] D.J. Morrison, J.C. Moosbrugger, Int. J. Fatifue 19 (1) (1997) 551. [22] H. Jiang, P. Bowen, J.F. Knott, J. Mater Sci. 34 (1999) 719. [23] M. Simeriska, V. Synecek, Acta Metall. 15 (1967) 223. [24] R. Ciach, W. Wereznski, Czech. J. Phys. B 39 (1989) 151. [25] V. Ravi, E. Philofsky, Metall. Trans. 2 (1971) 711. [26] M.M. Mostafa, G.S. Al-Ganainy, Egypt. J. Sol. 28 (1) (2005) 109. [27] F. Abd El-Salam, A. Fawzy, M.T. Mostafa, R.H. Nada, Egypt. J. Sol. 23 (2) (2000) 341.