Effect of cyclic stress reduction on the creep parameters of Al–Si alloy with Ag and Sn additions

Materials Science and Engineering A 552 (2012) 486–492

Contents lists available at SciVerse ScienceDirect

Materials Science and Engineering A journal homepage: www.elsevier.com/locate/msea

Effect of cyclic stress reduction on the creep parameters of Al–Si alloy with Ag and Sn additions R.H. Nada a , F. Abd El-Salam a , A.M. Abd El-Khalek a,b,∗ , L.A. Wahab c , H.Y. Zahran a a b c

Department of Physics, Faculty of Education, Ain Shams University, Cairo, Egypt Department of Physics, Faculty of Science, University of Tabuk, Tabuk, Saudi Arabia National Centre for Radiation Research and Technology, Nasr-City, Cairo, Egypt

a r t i c l e

i n f o

Article history: Received 24 March 2012 Received in revised form 22 April 2012 Accepted 12 May 2012 Available online 31 May 2012 PACS: 61.72Lk 61.72Ss 61.72Yx Keywords: Static stress Stress reduction Cyclic creep Transient creep Steady state creep Spheroidization

a b s t r a c t Strain time measurements for Al–3 wt.%Si, Al–3 wt.%Si–1 wt.%Ag and Al–3 wt.%Si–1 wt.%Sn alloys were performed under static peak stress ( s = 83.2 MPa), cyclic stress reduction  cy (0–3.48 MPa) and frequency  (0–0.38 Hz) at different working temperatures Tw from 413 to 493 K. The creep curves were obtained under both static stress,  s (with  =  cy = 0), and then with superimposed cyclic stress at either: constant frequency ( = 0.38 Hz) and different  cy values (hereafter specified as a-state), or at constant value of cyclic stress reduction ( cy = 3.48 MPa) and different frequency values (here after, b-state). The observed improved tensile ductility and softening with Ag addition, was due to the partial precipitation of Si attaching to the reticulate boundaries of the Ag phases. The improved mechanical properties with Sn addition were rendered to the spheroidization of Sn phases around Si particles forming the peritectictype island structure. The high value of  ratio relating ˇ and ε˙ st may point to a single mechanism operating in both creep stages. © 2012 Elsevier B.V. All rights reserved.

1. Introduction During sample testing the applied factors may cause hardening by forming a structure in which dislocation mobility is reduced. Such hardening may be due to: the formation of second-phase particles, ordering and interaction of dislocations with impurity atoms [1]. When an oscillatory stress is superimposed during plastic deformation, the applied stress decreases. This phenomenon is called Blaha effect [2]. A sample subjected to cyclic stress of sinusoidal variation for the amplitude of vibration stress,  a , the value  cy = 2 a is called the stress variation or the range of stress. If the mean stress,  m , is zero, then completely reversed stresses are produced. The creep of metals and alloys under cyclic stress reduction amplitude,  cy , and constant frequency, were found to be higher than those under static creep condition for the same maximum

stress. The response that develops is described as “cyclic creep acceleration”, which was observed before in Al–Zn system [3,4]. In aluminum alloys, particularly of the high strength, ageharden able types occupy a position of importance. To improve the strength of aluminum, without losing ductility, the metal is alloyed with several alloying elements. The excellent mechanical properties of Al–Si and Al–Sn alloys led to their extensive use in engineering applications [3]. Marked effect of Ag content in Al–Ag alloys used in industry on either the kinetics of aging or the identification of the properties formed during the aging process was reported [5,6]. The present work aims at studying the effect of cyclic stress reduction on the static creep behavior of Al–3 wt.%Si base alloy and its tertiary alloys containing 1 wt.% of either Ag or Sn. From a technical viewpoint, this is justifiable since cyclic stress reductions have serious effect on creep properties of loaded materials.

2. Experimental procedure ∗ Corresponding author at: Department of Physics, Faculty of Education, Ain Shams University, Cairo, Egypt. Tel.: +20 2 25500415; fax: +20 2 25500415. E-mail address: Asaad [email protected] (A.M. Abd El-Khalek). 0921-5093/$ – see front matter © 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.msea.2012.05.074

Concerning the Al–Si phase diagram, given in Fig. 1, the solubility of Si (in wt.%Si) in Al is 1.3 at 823 K, 0.29 at 673 K and 0.008 at 523 K [7]. The solubility of Ag (in wt.%Ag) in Al is 55.6 at 839 K,

R.H. Nada et al. / Materials Science and Engineering A 552 (2012) 486–492

487

All the strain–time relations show the same normal creep behavior. Increasing temperature, cyclic stress reduction  cy and/or frequency  increased the total level of strain, ε. The strain level for alloy B is higher than those for alloys (A and C). Both the creep strain and creep rate are enhanced showing the cyclic creep acceleration [11]. The transient creep strain εtr which is characterized by a decreasing strain rate is given as [12]; εtr = ε − εo = ˇt n

Fig. 1. Phase diagram of Al–Si system.

49.4 at 799 K, 28 at 773 K and 8 at 673 K [8]. The limit of solubility of Sn (in wt.%Sn) in Al is 0.06 at 833 K, just below 0.05 at 803 K, and for higher or lower temperatures the solubility sharply decreases (0.045 at 673 K) [9]. Al, Si, Ag and Sn of purity 99.99% were used to prepare the binary base alloy Al–3 wt.%Si (hereafter alloy A) and ternary alloys of Al–3 wt.%Si–1 wt.%Ag (alloy B) and Al–3 wt.%Si–1 wt.%Sn (alloy C). The alloys were prepared by melting separately at 1123 K in high purity clean graphite crucible. The ingots were homogenized at 823 K for 53 h, under vacuum of 10−3 Torr. A part of each ingot was cold drawn to wire of 0.7 mm diameter, and a part was rolled into sheet for electron microscope investigation. Chemical analysis revealed the specimen’s composition considered here besides traces of Fe, Mn and Cu. All specimens were aged for 2 h at 673 K then quenched into iced water to have an identical thermomechanical history. Micrographs of sheets from all the tested samples were investigated by using a JEOL 1200 Ex II transmission electron microscope working at 70 kV and a twin jet machine for ultimate thinning down to perforation. The solution used was 10% perchloric acid and 90% ethanol at 273 K. The voltage and current applied were around 10–25 V and 0.1–0.3 mA, respectively. The tensile testing unit used in the present work is similar to that used elsewhere [10]. The sample in wire form with 0.7 mm diameter and 4.5 cm long was used. For creep measurements a static stress  s (peak stress) of 83.2 MPa at different working temperatures from 413 to 493 K in steps of 20 K. The strain–time (ε–t) relations at different working temperatures Tw , for all the tested alloys, were obtained for both the static creep,  s (with  =  cy = 0), and dynamic creep with superimposed cyclic stress applied with the static creep at either constant frequency ( = 0.38 Hz, different  cy values from 0 to 3.48 MPa, hereafter specified as, a-state), or at constant value of cyclic stress reduction ( cy = 3.48 MPa, different frequency values from 0 to 0.38 Hz, hereafter, b-state). The static creep parameters are always involved in all the figures of both states (a and b), for comparison. 3. Experimental results Fig. 2 shows the strain–time (ε–t) curves for the tested samples at 413 K, under different values of cyclic stress reduction  cy or frequency . as representative examples for, a-state, and b-state.

(1)

where the transient creep time t, n the time exponent, and ˇ the creep constant, are the transient creep parameters which depend on temperature and the applied stress. The relation between ln εtr and ln t for all the tested samples at different temperatures, different  cy and  values are given in Fig. 3. At 413 K, Fig. 3a is a representative example for ln εtr and ln t relation under, a-state and Fig. 3b for, b-state. It is observed that increasing Tw ,  cy and/or  decreased n, Fig. 4a, and increased ˇ, Fig. 4b. Also, alloy C has the highest n values and alloy B with Ag has the lowest n values, while the reverse behavior is observed with ˇ values. The steady state creep rate ε˙ st , is obtained under different values of  cy from Fig. 2a, and under different values of  from Fig. 2b. The cyclic stress reduction,  cy , dependence of ε˙ st is given at different temperatures in Fig. 4c, as representative example. The transient creep parameter ˇ and the steady state creep rate ε˙ st were found [13] to vary with working temperature, Tw , following respectively, the Arrhenius-type relations. ˇ = const. · exp

 −Q 

and ε˙ st = const. · exp

(2)

KTw

 −Q  KTw

,

(3)

where Q is the activation energy (in kJ/mol) and K is Boltzmann constant. The activation energies for both creep stages under different values of  cy and/or  were calculated for the transient stage from the slopes of the straight lines relating ln ˇ and (1000/Tw ) K−1 , Fig. 5a, and for the steady state stage from ln ε˙ st and (1000/Tw ) K−1 , Fig. 5b, as representative examples, for the tested alloys. The transient and the steady creep stages are related to each other by the relation:  ˇ = ˇo (ε˙ st ) ,

(4)

where ˇo is a constant and  is the steady state creep exponent which measures the contribution of the transient creep mechanism to the steady state creep. The relation between ln ˇ and ln ε˙ st under ( = 0.38 Hz) or ( cy = 3.48 MPa) are obtained for the tested alloys. Fig. 6, is a representative example for the ln ˇ and ln ε˙ st relation under ( = 0.38 Hz) and different,  cy . Each data point shows the values of ln ˇ and ln ε˙ st at certain working temperature. The slope of the straight line in Fig. 6, for the tested alloys gives the value of the ratio . The high  values obtained, around 0.95, ensure the high relationship between creep stages and support the view that creep is a continuous process. 4. Discussion The solidified monotectoid Al–3 wt.%Si alloy consists generally, as a hypoeutectic alloy, Fig. 1, of primary aluminum dendrites in a eutectic matrix [14]. The fineness of the dendrites depends mainly on the diffusion and concentration of solute atoms [15]. The two phases Al and Si characterizing the microstructure of Al–Si alloys are a combination of a high strength-brittle phase

488

R.H. Nada et al. / Materials Science and Engineering A 552 (2012) 486–492

0.12

0.12 static 1.74MPa 3.48MPa

strain(ε)

0.1 0.08

0.87MPa 2.6MPa

0.08

0.06

0.06

0.04

0.04

0.02

( I)

0

strain(ε)

20

40

0

60

0

0.12

0.12

0.1

0.1

0.08

0.08

0.06

0.06

0.04

0.04

0.02

strain(ε)

20

40

60

0.02

(II)

(II)

0

0

0.12

0.12

0.1

0.1

0.08

0.08

0.06

0.06

0.04

0.04 0.02

0.02 0

0.18Hz 0.33Hz

0.02

(I)

0

static 0.25Hz 0.38Hz

0.1

(III) 0

20

40

60

time(min)

(a)

0 0

(III) 20

40

60

time(min)

(b)

Fig. 2. The strain time (ε–t) curves for the tested samples at 413 K, under different values of cyclic stress reduction  cy , a(I–III) (a-state), or different frequency , b(I–III) (b-state), as representative examples.

(Si) and a low strength-ductile phase (Al) [16]. The nature of the components of the tested alloy depends mainly on their degree of solubility in each other [8–10]. The strength of binary alloy increases with increasing second phase content, which decreases the mobility of dislocations. This also goes to any element added to the alloy components. Heating a quenched alloy at temperatures below the line of solubility limit gives rise to controlled precipitation of the second phase with a high level of ductility and fine structure [17]. It was found [18] that the nucleation of precipitates in Al–Si alloys was enhanced by preaging quenched specimens near room temperature. Such enhancement can be attributed to the formed loops which act as precipitation centers for Si atoms, thus stabilizing them.

In terms of the elastic strains imposed by solute atoms of different sizes from solvent atoms, the solute atoms can be regarded as point defects. The compliance mismatch between Al matrix and Si leads to significant load transfer to the brittle Si particles, which crack rather than decoher [19]. For alloy B, in the micrograph, Fig. 7B, the white phases are the matrix ˛(Al) most of which belong to dendrite crystal. The gray reticulate phases are inhomogeneous structure of Ag fine and coarse particles of GP zones and metastable   phase both of which form thick boundaries for the enveloped dendrite crystals of the ˛(Al) matrix. The black phases are Si phases. The fine Ag particles in the GPZ seem to be preferred sites for Si precipitation. This is clear in Fig. 7B where Si precipitates are almost partially attached to the aggregated Ag particles, specially on the reticulate boundaries forming peritectic-type island structure. This may stabilize

R.H. Nada et al. / Materials Science and Engineering A 552 (2012) 486–492

-7

static 1.74MPa 3.48MPa

ln

ε tr

-6

-7

0.87MPa 2.6MPa

-5

-4 ( I) 3.8

ln ε tr

0.18Hz 0.33Hz

-5

-3 4.8

5.8

6.8

( I) -3 3.8

-7

-7

-6

-6

-5

-5

-4

-4 (II) 3.8

4.8

5.8

6.8

3.8 -7

-6

-6

-5

-5

-4

-4 (III) 3.8

4.8

ln t(s)

5.8

5.8

6.8

(a)

6.8

(II)

-7

-3

4.8

-3

-3

ε tr

static 0.25Hz 0.38Hz

-6

-4

ln

489

4.8

5.8

6.8

(III)

-3 3.8

4.8

5.8

6.8

ln t(s)

(b)

Fig. 3. The relation between ln εtr and ln t for all the tested samples at 413 K: (a) I–III different  cy , a-state and (b) I–III different, , b-state, as representative examples.

some Si and Ag particles and consequently lower their hardening effect and impart softening for the alloy, Figs. 2 and 4, and makes it of low creep resistance specially at high temperature. Although, the presence of silver is expected to harden the alloy B, the observations in Fig. 4, shows continuous softening behavior for the samples of alloy B more than that for the alloys (A and C). It may be that the Ag precipitate particles, with Y(Ag) [Young’s modulus of Ag] = 80.5 GN m−2 , and the second phase Si with Y(Si) = 103 GN m−2 , are more harder than the matrix, Y(Al) = 71 GN m−2 , and the difference in ductility makes the whole structure similar to that of a non-Newtonian fluid containing rigid particles [20], which rotate practically without deformation while the soft phase, Al, undergo plastic deformation performing accommodation between both by sliding along the interfaces [21]. Accordingly, the Al–3 wt.%Si–1 wt.%Sn, consists of ˛(Al), Si and ˇ(Sn) phases, and according to rules of equilibrium diagram, it can be inferred that this system should belong to ternary eutectic system [22].

In the Al–Si–Sn alloys all the secondary particles, Si and Sn, had significantly different values of elastic moduli and nanohardness than the Al matrix, and Si particles still harder than Al and Sn, which give a clear indication of variation in mechanical properties [23] when receiving similar amounts of work hardening. Homogenization phenomenon for Al–Si–Sn alloys is mainly the spheroidization of Si and Sn phases. The gathering and spheroidization of second phases will decrease the interface energy of the system [22]. The eutectic phases in the boundary of ˛(Al) phases melt at the homogenization temperature so that the diffusion and movement of the boundary becomes easier leading to the dendrite structure on solidification. During gathering, the shape of Sn phase depends on interface energy value between itself and other solid phases. The possible equilibrium shape of Sn and Si will be either Sn attached to Si or Sn enveloping Si, with the later having the lowest interface energy. After homogenization the spheroidized Si particles are enveloped in ˇ(Sn) layers forming peritictic-type island

490

R.H. Nada et al. / Materials Science and Engineering A 552 (2012) 486–492

0.7

(a)

1600

(b)

1400 0.6

1200

β x 10

n

-5

1000

0.5

800 600 400

0.4

200 0.3

0

25

2

4

x10 -5

2

4

6

σ cyclic (Mpa)

413K 433K

15

453K

st

.

0

(c)

20

ε

0

6

10

473K

5

493K

0 0

1

2

3

4

σ cyclic (MPa)

5

6

Fig. 4. The cyclic stress reduction,  cy , dependence of the creep parameters: (a) n, (b) ˇ, and (c) ε˙ st , at different working temperatures, as representative examples.

structure. It was reported [22] that high volume fraction and uniform structure can be formed when the Sn/Si ratio is in the range of 3–4. In Fig. 7C, the lack of Sn content relative to Si content in the tested alloy C reflects the inhomogeneous structure formed. There are just dispersions of few density of ˇ(Sn) (gray) around the course Si precipitates (black) which are not enveloped in ˇ(Sn) phases indicating a decreased volume fraction of the peritectic-type island structure. Also, the low concentration of Sn forms thin Sn layer around Si particles and Sn is widely dispersed within the matrix leaving

-2

unenveloped Si particles. These coarse Si particles which are harder than the matrix, besides the dispersed Sn particles increase the hardness of the alloy. In terms of solid solubility of Si, Ag and Sn (in wt.%) in Al at the aging temperature (673 K), Si: 0.29, Ag: 8 and Sn: 0.045 will exist in the Al matrix in alloy B (Al–Si–Ag) and in alloys C (Al–Si–Sn), besides the 99.71 wt.%Si precipitate. It is therefore expected that the volume fraction of the peritectic-type island structure in alloys C will increase leading to the improved mechanical parameters in Figs. 2a and b and 4, over those for alloys (A and B).

-4

(a)

-4

static

0.87 Mpa

1.74 Mpa

2.6 Mpa

-6

-8

ε. ln

ln β

st

3.48 Mpa

-6

-8

-10

(b)

-10

-12

2

2.2

2.4

-1

1000/T (K )

2.6

-14

2

2.2

2.4

-1

2.6

1000/T (K )

Fig. 5. The relation between: (a) ln ˇ and (1000/Tw ) K−1 , for the transient stage, (b) ln ε˙ st and (1000/Tw ) K−1 , for the steady state stage, under constant frequency and different  cy values, a-state, as representative examples for the tested alloys.

R.H. Nada et al. / Materials Science and Engineering A 552 (2012) 486–492

4-

ln β

5-

static

Mpa 0.87

Mpa 2.6

Mpa 3.48

11-

12-

Mpa 1.74

6-

7-

8-

8-

9-

10-

ln ε.st

13-

Fig. 6. ln ˇ vs. ln ε˙ st under constant frequency,  = 0.38 Hz and different  cy values, as representative example.

In the working temperature range, the solubility of Si, Ag and Sn in the Al matrix decreases on decreasing temperature and consequently the quantity of the precipitates increase in the matrix causing the corresponding increase in the hardening parameters at 413 K. Above this temperature coarsening of the precipitates takes place and the number of the precipitated particles decrease leading to the reduction of strength observed at 493 K, Fig. 4, as reported previously [24], specially for alloy B where the course GPZ and   plates, which are known to be less effective as barriers for moving dislocations [11], are formed. Sn as an alloying element can increase the strength by solution strengthening and refine the dendrite and grain size in Al alloys. At 413 K the decreased solubility of Si and Sn in the Al matrix increases

491

the free precipitated ratio of Si and Sn in the matrix. These precipitates increase the strength of the alloy because Frank–Reed sources are supposed to cause hardening due to the subsequent formation of dislocation pile-ups at grain boundaries, as those observed in Fig. 7A. When the average particle size of Sn is so small the relative tendency to crack initiation is reduced. This consists with the increased values of n, Fig. 4a, and the decrease of both ˇ, Fig. 4b and ε˙ st , c. The additional consequence of the Sn addition is the formation of a rather undesirable microstructure, i.e., a much coarser and less uniform microstructure containing a plate-like dendritic structure branched out during solidification. These coarse dendrites are rather nonuniformaly distributed and are composed of highly concentrated, mechanically strong, finely dispersed, small Si particles imbedded in the ˇ(Sn) phase, which increase hardening due to the decrease of the mobile dislocation density which makes the alloy brittle and more harder [25]. Increasing aging temperature to 493 K increases the degree of solubility of Si and Sn in the Al matrix and consequently decreases the free Si and Sn precipitates [7]. This facilitates the mobility of dislocations which leads to the softening behavior observed from the decrease of the parameter n, Fig. 4a and the increased values of ˇ, Fig. 4b and ε˙ st , c, respectively. This increase of softening by increasing the aging temperature may be rendered to the dependence of the number and lifetime of the stabilized loops on the aging temperature which enhances Si atoms diffusion when increased and consequently more softening is observed due to the dislocation activity [26], induced by thermal growth of precipitates which facilitate dislocation motion between the less number of the large precipitates. This softening discloses the higher dislocation mobility, which is a thermally activated process.

Fig. 7. Room temperature electron micrographs for samples of the tested alloys aged at 673 K for 2 h (18,000×).

492

R.H. Nada et al. / Materials Science and Engineering A 552 (2012) 486–492

Table 1 The average values of the activation energy Q (for ˇ values) at constant  cy = 3.48 MPa, and constant  = 0.38 Hz. Parameter’s values

Q (kJ/mol) Alloy A

 cy = 3.48 MPa  = 0.38 Hz

56.59 58.2

Alloy B

Alloy C

45.12 51.2

60.86 63.42

Table 2 The average values of the activation energy Q (for ε˙ st values) at constant  cy = 3.48 MPa, and constant  = 0.38 Hz. Parameter’s values

Q (kJ/mol) Alloy A

 cy = 3.48 MPa  = 0.38 Hz

calculated activation energy (kJ/mol) (Tables 1 and 2), by increasing working temperature,  cy and/or , reaching values near to (50 kJ/mol) which can be attributed to dislocation glide [24]. It is clear from Tables 1 and 2 that Q values are higher for alloy C, and lower for alloy B, the softest alloy. The dependence of ε˙ st on ˇ seems to be due to the decrease in the dislocation density to a level that makes the hardening rate at the end of the transient stage converges to the recovery rate. So, the steady state creep starts with rates depending on the applied stress. The relatively high values of  which tend to unity (0.95) confirm that the mechanism responsible for the transient stage still operates in the steady state creep stage.

63.88 64.3

Alloy B

Alloy C

56.3 60

64.36 61.8

The softening behavior due to Ag addition, which is clear from Figs. 2 and 4 can be explained on the basis that silver addition inhibits the uncontrolled growth of the high strength large structure during the solidification of the binary alloy. It is believed that such small addition of Ag (1 wt.%) goes primarily into solution within the Al phase. It appears that Ag promotes a higher nucleation density of solid phases during solidification. The high density and apparent random relative positioning of these solid phase nuclei cause them to immediately impinge upon one another and prevent the formation of the high strength large plate-like structure. Thus, the ternary alloy B samples will be softer than alloys A and C. From cyclic stress reduction data, a high creep resistance of alloys (A and C) is observed, as reflected by the lower values of ε, Fig. 2; ˇ, Fig. 4b; ε˙ st , Fig. 4c, and the higher values of n, Fig. 4a and Q shown in Tables 1 and 2, as compared with those of alloy B. The enhancement of the primary creep decrease of n, Fig. 4a, and the higher ˇ values, Fig. 4b, and ε˙ st values, Fig. 4c, obtained at higher temperatures might be attributed to the reduced crack initiation life associating the existing grain size at higher temperatures [27]. This enhancement with the imposed cyclic stress reduction might be due to the arrangement and annihilation of dislocations generated from the new dislocation sources formed in early stages of creep in the matrix by the applied stress [28]. The driving force for both the arrangement and annihilation of these dislocations will be that exerted by the effecting stress and the role of the effective energy, which can be estimated as half the stress times the corresponding strain, such that the effective mobile dislocations move parallel to the direction of stress. This consists with the fact that the parameter ˇ represents the dependence of the transient strain, εtr , on the amount of precipitate which decreases, and the precipitate particle size increases with increasing temperature, enables dislocations to overcome these precipitates, and so increase creep strain [12]. The activation energy Q values calculated from Fig. 5, and given in Tables 1 and 2, show some dependence on both  cy and  besides the main dependence on the working temperature. The effect of the external cyclic stress reduction and the applied frequency can be considered as a matter of stored energy in the sample, which reduces the external thermal energy needed to complete the creep run. An increase of this stored energy produces a reduction in the

5. Conclusions 1. Ag addition softened the alloy and improved the tensile ductility. 2. The Sn phases gathered and spheroidized around the Si particles during homogenization. 3. The peritectic-type island structure formed improved the mechanical properties and the increased Sn content caused increased hardening. 4. Cyclic creep acceleration was observed allover the working temperature range, associated with a marked effect on the creep parameters. 5. The high value of  ratio relating ε˙ st and ˇ shows that a single mechanism operates in both creep stages. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24] [25] [26] [27] [28]

F. Abd El-Salam, R.H. Nada, A.M. Abd El-Khalek, Physics B 292 (2000) 71. T. Ohgaku, N. Takeuchi, Phys. Status Solidi A 118 (1990) 153. A.R. Blum, A. Cegielska, J.I. Mortin, Acta Metall. 37 (1989). R.H. Nada, F. Abd El-Salam, L.A. Wahab, H.Y. Zahran, Mater. Sci. Eng. A 532 (2012) 249–254. R.M. Aikin, M.R. Plichta, Acta Metall. 38 (1990) 77. K. Ohashi, T. Fujita, K. Kaneko, Z. Horita, T.G. Langdon, Mater. Sci. Eng. A 437 (2006) 240–247. W.L. Fink, H. Freche, Trans. AIME 111 (1934) 304–317. G.V. Raynor, D.W. Wakeman, Philos. Mag. 40 (1949) 404–417. A.H. Sulley, H.K. Hardy, T.H. Heal, J. Inst. Met. 76 (1950) 269–281. Sh.M. Abd El-Aziz, Ph.D. Thesis, Faculty of Education, Ain Shams University, 2007, pp. 25, 34, 59–61. F. Abd El-Salam, M.M. Mostafa, L.A. Wahab, M.T. Mostafa, Sh.M. Abd El-Aziz, Mater. Sci. Eng. A 474 (2008) 230–235. F. Abd El-Salam, A.M. Abd El-Khalek, R.H. Nada, Physica B 388 (2007) 219. F. Abd El-Salam, A.M. Abd El-Khalek, R.H. Nada, Eur. Phys. J. AP12 (2000) 159. H.A. Abdel Salam, M.M. Farag, Second Cairo University MDP Conference, Cairo, Egypt, December 27–29, 1982. T. Okamoto, K. Kishetake, J. Cryst. Growth 24 (1975) 137–146. A.M.A. Mohamed, F.H. Samuel, A.M. Samuel, H.W. Doty, S. Valtierra, Metall. Mater. Trans. A 39A (2008) 490–500. S. Krishnamurthy, S.P. Gupta, Mater. Sci. Eng. 30 (1997) 155–165. M.S. Rosenbaum, D. Turnbull, Acta Metall. 10 (1958) 653. M.R. Joyce, S. Syngellakis, P.A.S. Reed, Mater. Sci. Technol. 20 (2004) 47. M. Suery, B.B. Baudelet, Philos. Mag. 41 (1980) 41. E.H. Toscano, Scr. Metall. 17 (1983) 309. G.C. Yuan, Z.J. Li, Y.X. Lou, X.M. Zhang, Mater. Sci. Eng. A280 (2000) 108–115. M.S. Ali, P.A.S. Reed, S. Syngellakis, A. Moffat, C. Perrin, Mater. Sci. Forum 519–521 (2006) 1071–1076. O. Ozawa, H. Kimura, Mater. Sci. Eng. 8 (1971) 327. F. Abd El-Salam, M.T. Mostafa, R.H. Nada, A.M. Abd El-Khalek, Egypt. J. Solids 24 (1) (2001) 67. G. Sharma, R.V. Ramanujan, T.R.G. Kutty, G.P. Tiwari, Mater. Sci. Eng. A 278 (2000) 106–112. D.J. Morrison, J.C. Mossbrugger, Int. J. Fatigue 19 (1) (1997) 551. H. Jiang, P. Bowen, J.F. Knott, J. Mater. Sci. 34 (1999) 719.