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Effect of calcium addition on the microstructure and compressive deformation behaviour of 7178 aluminium alloy
Materials and Design 32 (2011) 2803–2812
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Effect of calcium addition on the microstructure and compressive deformation behaviour of 7178 aluminium alloy D.P. Mondal a,⇑, Nidhi Jha a, Anshul Badkul a, S. Das a, M.S. Yadav a, Prabhash Jain b a b
Advanced Materials and Processes Research Institute (CSIR LAB), Bhopal 462 064, India University Institute of Technology, Barkatullah University, Bhopal 462 026, India
a r t i c l e
i n f o
Article history: Received 6 August 2010 Accepted 31 December 2010 Available online 8 January 2011 Keywords: A. Non-ferros metals and alloys E. Mechanical F. Microstructure
a b s t r a c t Aluminium 7178 alloys containing 1% calcium are used to study the effect of calcium addition on their microstructure and compressive deformation behaviour. The compressive deformation behaviour of aluminium alloy containing 1% calcium is studied at varying strain rates (102–10/s). The material is prepared using stir casting technique. The yield stress, flow stress and elastic limit are measured from the true stress–strain graph. The strain rate sensitivity and strain-hardening exponent was also determined for each material at different strain rates. Its microstructural characterization reveals that Ca particles act as grain refiners for primary base alloy and helps in improving the strength of the virgin alloy. An empirical relationship has been proposed to predict the flow curve of the alloys as a function of strain and strain rate. Ó 2011 Elsevier Ltd. All rights reserved.
1. Introduction Aluminium and its alloys have potential applications in aerospace and automotive industry because of its higher specific strength and stiffness [1–3]. Pure aluminium is relatively a soft material. For applications requiring greater mechanical strength, it is generally alloyed with other elements such as copper, magnesium, manganese, iron, silicon and zinc. Strake [4] reviewed in detail the effect of different alloying elements on the microstructure and mechanical behaviour of aluminium and its alloys. Zhongxia et al. [5] reported that addition of rare earth metals like Sc, Zr and Ti, in small quantities refined the microstructure and thus improved the strength of Al–5Mg alloy significantly. Thompson and Zinkham [6] also examined that addition of alloying elements like Zr, Cr and Fe in a 7075 Aluminium alloy results in different kinds of inter-metallic phases of various size ranges which results in microstructural refinement and influences in age hardening characteristics as well as recrystallisation and grain growth. The inter-metallic precipitates also causes for higher strength and fatigue crack growth resistance. Heusler and Schneider [7] examined that addition of Mg, Na and Sr in small quantities influenced the eutectic transformation of Al–Si cast alloys and modified silicon morphologies to a great extent and thus improve its strength and toughness. It is further reported by Dash and Makhlouf [8] that the castability of Al–Si alloys improved, hydrogen absorption decreased and microstructure got refined and modified due to addition of Mg, ⇑ Corresponding author. Tel.: +91 755 2418952. E-mail address: [email protected] (D.P. Mondal). 0261-3069/$ - see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.matdes.2010.12.056
Mn, Cu, Sr and Ti. All these factors lead to higher strength and ductility. The 7178 series alloys based on Al–Zn–Mg system have unique combination of desirable characteristics including low density, high strength and fracture toughness [9]. Increased strength of these alloys was achieved through the formation of finer inter-metallic precipitates with increasing Zn, Mg and Cu concentration [10]. However, improved mechanical properties require a strict control on alloy preparation and processing aiming to achieve refined and modified microstructure along with generation of fine coherent precipitates. Elements like Ti [8], Cr [6], Zr [6] and Sc [5], and component like TiB2 [11] are used for obtaining refined microstructure. Calcium has been used by Mihriban and Pekguleryuz as an important alloying element in magnesium alloys to improve their high temperature strength vis-a-vis creep resistance [12]. It was examined by these investigators that Ca offers a thermally stable second phase Mg2Ca and thus significantly improved the elevated temperature strength and creep property. Ca added Mg–Al alloy becomes a promising low cost magnesium alloy for improved heat resistant and elevated temperature creep resistant automobile engine component applications [13]. It was reported that the addition of small amount of Ca into Mg–Al alloys can result in refinement of grain-structure and thus increasing their mechanical properties [14,15]. It was also examined by Drits et al. [16] that addition of Ca in Mg-alloys not only refined the microstructure and improved its creep resistance but also improved its high temperature oxidation resistance. In this context, it is suspicious that calcium can also be used as grain refiner for Al–Zn–Mg alloy. But this aspect, to the best of our knowledge had been overlooked so far.
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Silicon when added to aluminium alloys to increase the mechanical properties led to coarse microstructures containing coarse Si needle which in due course caused inherent brittleness and poor workability [17]. Calcium has been used as a modifier of the silicon eutectic phase in Al–Si cast alloys [18]. It was reported that the addition of Ca in Al–Si alloys modified the needle shaped silicon to fibrous type of silicon or fine silicon particles [19], which finally led to the improvement in strength and toughness [20]. It is noted from Al–Ca phase diagram (as shown in Fig. 1) that it has high eutectic temperature (613 °C). This makes it suitable for higher temperature applications with increased strength. In this context, it is interesting to understand the effect of calcium addition on the microstructure and compressive deformation behaviour of 7178 alloys under varying strain rates. Attempts have been made for empirical prediction of flow curves as a function of strain rate and strain for Ca added 7178 alloys. 2. Experimental 2.1. Material synthesis and microstructure 7178 alloy is prepared through stir casting technique. This technique involves melting of 7178 aluminium alloy ingot in an electrical resistance furnace.7178 alloy normally contains Si 0.4 wt.%, Fe 0.5 wt.%, Cu 1.75 wt.%, Mn 0.3 wt.%, Mg 2.5 wt.%, Cr 0.2 wt.%, Zn 6.3 wt.% and remaining Al. After maintaining the temperature between 750 and 800 °C, a vortex was created using a mechanical stirrer. Calcium granular is added to the melt with continued stirring. Stirring was continued for about 10 min after addition of calcium particles for uniform distribution in the melt. The melt temperature was then maintained at 800 °C for half an hour, so that Ca particles
got dissolved into the melt. Castings were prepared by pouring the melt into preheated cast iron moulds of cylindrical shapes. From these castings, samples of 10 mm diameter and 15 mm length were prepared for microstructural examination. For microstructural characterization, the samples were polished using standard metallographic technique and etched with Keller’s reagent. Before examination under SEM, samples were sputtered with gold. 2.2. Compressive deformation Compression tests were performed on a Universal Testing Machine (BISS, Bangalore India make of 50 KN capacity) at room temperature and at varying strain rates (0.01/s, 0.1/s,1/s and 10/s). For the compression test samples of 10 mm diameter and 15 mm length were prepared form the castings. The surfaces of the specimens were polished mechanically prior to testing and were lubricated with thin molybdenum sulphide coating so as to reduce the friction between the specimen surface and the compression test plates. The density of all the samples was determined and it was noted that the average density of Ca added samples was 2.7 ± 0.02 g/cc and that of 7178 alloy was 2.83 g/cc. The true stress–true strain graph was plotted during the testing using the built in software. Different data related to compressive deformation have been determined from the analysis of true stress–strain curves. 3. Results 3.1. Material and microstructure Fig. 2a shows the microstructure of 7178 alloy exhibiting the dendrites of aluminium. The dendrites are highly elongated. The
Fig. 1. Phase diagram of Al–Ca system.
D.P. Mondal et al. / Materials and Design 32 (2011) 2803–2812
addition of 1 wt.% calcium in the alloy also provides dendritic structures, but less elongated and relatively finer (Fig. 2b). Additionally, Fig. 2b shows the presence of Al4Ca inter-metallic precipitates (marked arrow) along the grain boundary. Higher magnification micrograph of 7178 alloy without Ca addition (Fig. 2c) shows the presence of eutectic phase in the inter-dendritic region (marked arrow). This signifies that addition of Ca suppresses the formation of eutectic phase along the inter-dendritic region. Fig. 2d reveals that there are two different types of shapes of the particles (precipitates): fibrous and particulates. Generally fibrous types of precipitates (marked arrow) are present along the interdendritic region and particulate type precipitates (marked P) are present within the arms of dendrite. Particulate type precipitates
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are generally Al2Ca which have significantly higher melting point and they act as a nucleating agent of dendrites, where as fibrous type (generally Al4Ca, Mg2Ca) opposes the growth of dendrites. The microstructure of 7178 alloy with Ca addition also reveals that a large amount of submicron precipitates are formed within the dendritic arms (Fig. 2e), but no such precipitates are observed in 7178 alloy without Ca addition. The average dendritic spacing in 7178 alloy with and without Ca addition are recorded to be 70.3 lm and 58.2 lm respectively. The aspect ratios of dendritic arms of 7178 alloy with and without Ca additions are noted to be 2.8 ± 0.5 and 1.6 ± 0.3 respectively. It is thus observed that the microstructure of 7178 alloys get refined significantly due to addition of 1 wt.% Ca.
Fig. 2. (a) Microstructure of 7178 Al alloy, (b) microstructure of Ca added 7178 Al alloy, (c) higher magnification microstructure of 7178 alloy, (d) higher magnification microstructure of Ca added 7178 Al alloy, and (e) microstructure of Ca added 7178 Al alloy showing submicron precipitates.
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3.2. Compressive deformation The true stress–true strain curves of the investigated material when tested at different strain rates are shown in Fig. 3. From these true stress–true strain plots, the yield stress and flow stress at different strains are determined using standard methodology. It may be noted that the curves do not show any sharp yield point. It is observed that when strain rate is increased from 0.01/s to 1/s, stress increases while when strain rate is further increased to 10/s, true stress decreases marginally. As a whole, it is found that stress varies in a narrow range with change in strain rate. The compressive stress–strain curve also demonstrates that due to the addition of 1 wt.% Ca, the yield stress and flow stress of 7178 alloy is increased by around 35–50 MPa at a strain rate of 0.01/s and 7178 alloy without Ca failed at lower strain value. The flow stress at different strain and strain rate recorded from the true stress–strain curves are shown in Table 1. The stress–strain curve of a material could be defined by the following equation:
rf ¼ re þ K p enp
ð1Þ
where re is the elastic limit stress, Kp is the plastic strength coefficient, ep is the plastic strain and n is the strain-hardening exponent. Eq. (1) can be written in two parts as follows:
rf ¼ re ¼ Eee
ð2Þ
rf ¼ K p enp
ð3Þ
where E is the modulus of elasticity and ee is the elastic limit strain. The value of re, Kp and n are calculated using methodology described elsewhere [21] considering Eqs. (2) and (3). 3.3. Strain-hardening exponent, Plastic Strength coefficient and Elastic limit stress Strain-hardening exponent is calculated from ln (r) and ln (e) plots, which were made from the recorded true stress and true strain values. A typical plot of ln (r) vs. ln (e) is shown in Fig. 4. This plot shows two regimes, one for elastic (lower) and other for plastic (upper) flow. From these curves, ‘n’, ‘Kp’ and re are calculated using the methodology described elsewhere [21] and are reported in
Table 1 Flow stress at different strain and strain rate recorded from the true stress–strain curves. Alloy
Al Ca
7178 Al Alloy
Strain rate
Flow stress rf (MPa) 0.03
0.05
0.07
0.09
0.11
0.13
0.01/s 0.1/s 1/s 10/s 0.01/s 1/s
288 308 336 303 240 290
364 373 390 362 319 345
417 418 439 416 385 395
461 462 476 460 428 429
495 496 511 491 456 478
527 528 534 524 498 488
Fracture strain 0.152 0.148 0.141 0.133 0.156 0.148
Table 2. The variation of ln (re) as a function of ln (e ) is shown in Fig. 5a. It is noted that the elastic limit stress is varying with strain rate within a narrow range. The overall change in strain rate from 0.01/s to 10/s results in the variation of elastic limit stress of 23 MPa, which is less than 10% of the elastic limit, stress of the material. However, the elastic limit stress of 7178 alloy without Ca is noted to be considerably less (248 MPa). The variation of Kp vs. ln (e ) is shown in Fig. 5b. It can be observed from this figure that Kp decreases with strain rate when strain rate is increased from 0.01/s to 1/s. But further increase in strain rate to 10/s increases Kp. The variation of n vs. ln (e ) also follow the similar trend to that of Fig. 5b as shown in Fig. 5c. It may be noted from Table 2 that the values of both Kp and n in 7178 alloy without Ca are significantly less than that of the alloy with Ca addition. Marginal variation of elastic limit stress with strain rate (except at strain rate of 0.01/s) signifies that the re of the material is almost invariant to the strain rate, whereas the variation of Kp and n with strain rate signifies that the plastic deformation is influenced by the strain rate. If examined more carefully, it will be observed that except in slower strain rate of 0.01/s, the Kp and n both are varying in a narrow range signifying that these two parameters are almost invariant to the strain rate especially at relatively higher strain rate. 4. Discussion 4.1. Effect of Ca addition on microstructures Addition of Ca in 7178 alloy suppresses the formation of eutectic phase along the inter-dendritic region and also helps in
Fig. 3. Variation of true stress vs. true strain at different strain rate.
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Fig. 4. Variation of ln(stress) vs. ln(strain) at varying strain rate.
Table 2 The strain-hardening exponent, the plastic strength and elastic limit of the investigated material at different strain rate. Material
Strain rate (s1)
n
re (MPa)
Kp (MPa)
7178 Alloy
0.01 1 0.01 0.1 1 10
0.43 0.365 0.465 0.366 0.339 0.385
248 255.81 287.16 295.84 294.81 310.63
1236.45 1021.5 1417.99 1116.55 1081.39 1165.61
7178 alloy with Ca
formation of submicron precipitates within the dendritic arms. This is attributed to the fact that (i) addition of Ca results in the formation of Al4Ca and mixed inter-metallic phases which might be shifting the eutectic point of the alloy system [14] and (ii) fine Al2Ca precipitate or calcium oxide particles (due to oxidation of Ca) [14] within the melt acts as nucleating agent for solidification making the solidification rate faster and thus suppressing the formation of eutectic phase to some extent. Because of the higher solidification rate, the secondary arm spacing in the Ca added alloy becomes finer. Additionally the higher rate of nucleation, presence of fibrous Al4Ca precipitates and mixed inter-metallic precipitates (Mg2Ca, Mg, Zn, Ca) also results in lower aspect ratio of the dendritic arms. The fibrous precipitates formed around the dendritic arms resist the growth of the dendritic arm and thus finer and comparatively equiaxed dendritic arms are formed in Ca added alloy. As per the composition of the alloy, Al2Ca precipitate will not form in the liquid melt. But, in the present case Ca is added in the form of granules in the liquid melt through mechanical stirring prior to pouring into the die. As s result, there is a possibility of non uniform distribution of Ca in the melt. In some of the localized regions, there is a possibility of higher Ca content and these Ca might be in solid particles which react with aluminium to form Al2Ca within the melt. Al2Ca has significantly higher melting point (1079 °C) [14] than the melt temperature. Because of the same reason, there would have the possibility of formation of Mg2Ca also [14]. X-ray diffraction pattern of this alloy confirms the presence of Al2Ca, Al4Ca, Mg2Ca, MgAl2 and solid solution of aluminium Fig. 9. The natures of precipitates are further confirmed by EDX analysis. The EDX pattern of rod like precipitates at inter-dendritic region is shown in Fig. 10a demonstrating that the precipitate consists of Al and Ca. The larger precipitates within the dendrites (Fig. 10b) also show the presence of Al and Ca only. But the concentration of Ca in these cases is much higher than that in Fig. 10a.
This demonstrates that the larger precipitates within the dendritic arms would be Al2Ca and the precipitates in the interdentric region are of Al4Ca. The precipitation of Al2Ca starts at higher temperature and subsequently these particles act as nucleating agent during solidification. A fraction of Ca also makes a solution with Mg at higher temperature because of inhomogeneous mixing of Ca in the melt. At temperature below 500 °C this solution transforms into Mg-solid solution and Al2Ca [14]. At still lower temperature (475– 500 °C) Mg-solid solution get transformed into Mg2Ca and Mg. During solidification, at temperatures lower than 613 °C, Al4Ca precipitate formed from the liquid melt left at that temperature. As a result it is expected that fine fibrous type Al4Ca precipitates around the dendritic arms and fine precipitates of Al2CA, Mg2Ca, and MgAl2 (XRD pattern in Fig. 9) precipitates within the dendritic arms (Fig. 2). These submicron precipitates within the dendritic arms and the needle like precipitates along the dendrite arms spacing are responsible for higher ‘n’, ‘Kp’ and ‘re’ in Ca added 7178 alloys. 4.2. Effect of Ca addition on compressive deformation It is observed from Fig. 3 and Table 2 that the yield stress and/or flow stress of 7178 alloy increases by 50 MPa due to addition of 1 wt.% Ca. This is attributed to the microstructural refinement and modification due to Ca addition as discussed earlier. It may be noted that very fine precipitates are formed within the dendritic arms of the Ca added alloy (Fig. 2e). Higher strength, Kp and n in Ca added alloy is due to refinement of the structure and the presence of submicron precipitates within the dendritic arms. As the eutectic phase constituent gets reduced in Ca added alloy, it provides higher fracture strain as compared to the 7178 alloy. 4.3. Effect of strain rate In earlier studies by the present authors [21] it was observed that the compressive deformation behaviour of 2014-SiC composites and 2014 alloy is almost invariant to the strain rate. The strain rate sensitivity ‘m’, is very low at room temperature. In the present study, it is observed that the value of ‘m’ for the Ca added alloy is very low signifying that the overall compressive deformation behaviour of this alloy at room temperature is almost invariant to the strain rate under the selected range of strain rate. The value of Kp and ‘n’ are noted to be relatively higher at a strain rate of 0.01/s. This is attributed to the fact that at lower strain rate the movement of dislocation vis-a-vis plastic flow of material is very slow
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Fig. 5. Variation of: (a) ln (elastic limit stress), (b) plastic strength coefficient and (c) strain-hardening exponent with ln (strain rate).
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Al Ca 6.3
6.2
Ln (Stress)
6.1 6 5.9 5.8
-5
-4
-3
-2
-1
5.7
0
1
2
3
Ln (Strain Rate)
Strain rate sensitivity (m)
Fig. 6. Variation of ln(stress) vs. ln(strain rate) at different strain rate of Ca added 7178 alloy.
Flow strain Fig. 7. Variation of strain rate sensitivity with flow strain.
and thus there is a greater possibility of higher degree of interaction of dislocation with the precipitates and possibility of generation of more dislocations during deformation. This finally leads to higher plastic strengthening coefficient and n value (Fig. 5b and c). The flow stress increases with increase in strain as observed in Fig. 6. The value of ‘m’ is also noted to decrease with strain. This is attributed to greater strain hardening at higher strain value and the material becoming harder and harder with the progress of deformation and thus becoming more and more insensitive to strain rate. 4.3.1. Strain rate sensitivity The stress of a material in terms of strain rate could be written as follows:
rf ¼ K s em
ð4Þ
where rf is the flow stress, Ks is the flow stress at a strain rate of 1/s m is the strain rate sensitivity and e is the strain rate. Thus the flow behaviour could be expressed as follows:
rf ¼ re þ K s em
ð5Þ
The strain rate sensitivity (m) and Ks was calculated from the slope of linear fit between ln (rf) and ln (e ) as shown in Fig. 6, where rf is flow stress and e is strain rate. The value of m is found to be varying in the range of 0.0013–0.0036. Very low value of m signifies that the compressive deformation behaviour of Ca–added alloy at room temperature is almost invariant to the strain rate. The variation of m as a function of strain is shown in Fig. 7. It may also be noted that m decreases with increase in strain, signifying that at higher strain, the variation of flow stress with strain rate would be reduced. The variation of Ks with strain in Fig. 8 shows that Ks increases with increase in flow strain.
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550
Strength Coefficeint K
500
450
400
350
300
250
200
0
0.03
0.06
0.09
0.12
0.15
Flow strain Fig. 8. Variation of strength coefficient as a function of strain.
.
.
Al 4Ca, Δ Al 2Ca, ◊ Mg2Ca, ο Mg Al 2,
.
Al
Fig. 9. X Ray diffraction pattern of 7178 Alloy with calcium addition.
The flow curves of a material can also be defined using the following relations:
rf ¼ K se eme ðwhen stress is limited to elastic stressÞ
ð6Þ
where Kse is the elastic strength coefficient at strain rate of 1, ‘me’ is the strain rate sensitivity on elastic stress.
rf ¼ K sp emp ðwhen stress is beyond the elastic limit stressÞ
ð7Þ
where Ksp is the flow strength coefficient at strain rate of 1/s, ‘mp’ is the strain rate sensitivity on flow stress. 4.3.2. Correlation of flow stress with strain rate and strain Flow stress of a material could be defined using Eqs. (1)–(6). It can be noted from the best fitted curve of Fig. 5a that elastic limit
stress of the Ca added alloy follows the following relation with strain rate:
re ¼ e0:001ln ðe Þ2þ0:0012ðln e Þþ5:699 ðup to elastic limitÞ
ð8Þ
The plastic strengthening coefficient Kp can be expressed in the following form as a function of strain rate (from Fig. 5b).
K p ¼ 11:25ðln e Þ2 2:005ðln e Þ3 þ 21:28ðln e ÞÞ þ 1081
ð9Þ
The strain-hardening exponent ‘n’ follows the relation with strain rate as mentioned below:
n ¼ 0:006ðln e Þ2 þ 0:004ðln e Þ þ 0:339
ð10Þ
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D.P. Mondal et al. / Materials and Design 32 (2011) 2803–2812 Table 3 Flow stress calculated theoretically from Eqs. (12) and (15). Material
7178 alloy with Ca
Strain rate
Flow strain
rf (MPa)
0.01
0.03
288
0.05
364
0.07
417
0.09
461
0.11
495
0.13
527
0.03
308
0.05
373
0.07
418
0.09
462
0.11
496
0.13
528
0.03
336
0.05
390
0.07
439
0.09
476
0.11
511
0.13
534
0.03
303
0.05
362
0.07
416
0.09
460
0.11
491
0.13
524
0.03
240
0.05
319
0.07
385
0.09
428
0.11
456
0.13
498
0.03
290
0.05
345
0.07
395
0.09
429
0.11
478
0.13
488
0.1
1
10
Fig. 10. EDX pattern of: (a) particles within the dendrites and (b) needle shape particles in the inter-dendritic region.
By putting the values of re, Kp and n in Eq. (1), the flow stress can be correlated with strain and strain rate in terms of the following relation:
7178 alloy
0.01
re ¼ e0:001ln ðe Þ2þ0:0012ðln e Þþ5:699
when stress is limited to elastic limit stress:
ð11Þ
Flow stress beyond elastic limit can be related in terms of following relation:
rf ¼ ½11:25ðln e Þ2 2:005ðln e Þ3 þ 21:28ðln e Þ þ 1081 e0:006ðln e Þ2þ0:004ðln e Þþ0:339
ð12Þ
The flow stress can be correlated with strain and strain rate empirically using the following approach also using Eqs. (6) and (7). The elastic limit stress can be correlated with strain rate as shown in Eq. (6). The flow stress as a function of strain and strain rate can be correlated through the following relation by putting the value of Ksp and mp as a function of e (as observed from the best fitting curves in Figs. 7 and 8) in Eq. (7):
K sp ¼ 148:28ln ðeÞ þ 825
ð13Þ
1
exp
rf (MPa) calculated Eq. (11)
Eq. (14)
294.78 (2.3) 370.56 (1.8) 430.82 (3.2) 482.14 (4.4) 527.47 (6.2) 568.45 (7.3) 308.52 (0.2) 372.07 (0.2) 420.93 (0.7) 461.57 (0.09) 496.82 (0.2) 528.20 (0.03) 329.28 (2.03) 391.54 (0.4) 438.84 (0.03) 477.87 (0.4) 511.51 (0.1) 541.31(1.4)
291.28 (1.12) 366.58 (0.7) 416.68 (0.07) 454.648 (1.4) 485.52 (1.9) 511.76 (2.9) 296.28 (3.9) 371.58 (0.4) 421.68 (0.8) 459.64 (0.5) 490.52 (1.1) 516.76 (2.2) 301.36 (11.5) 376.66 (3.5) 426.76 (2.8) 464.73 (2.4) 495.61 (3.1) 521.84 (2.3) 306.53 (1.2) 381.83 (5.2) 431.92 (3.6) 469.89 (2.1) 500.76 (1.9) 527.01 (0.6) 261.54 (8.2) 333.21 (4.26) 380.89 (1.07) 417.00 (2.63) 446.35 (2.15) 471.29 (5.66) 271.62 (6.7) 343.29 (0.49) 390.96 (1.03) 427.08 (0.44) 456.43 (4.72) 481.37 (1.37)
307.37 (1.4) 373.22 (3.0) 424.13 (1.9) 466.63 (1.4) 503.61 (2.5) 536.62 (2.4) 273.74 (12.3) 340.98 (6.44) 394.06 (2.3) 439.03 (2.51) 478.60 (4.72) 514.24 (3.15) 283.90 (2.14) 342.09 (0.84) 386.80 (2.11) 423.95 (1.18) 456.17 (4.78) 484.8 (0.64)
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m ¼ 0:0463ðeÞ 0:4688ðeÞ2 þ 0:0025
ð14Þ
By putting the values of Ksp and mp in Eq. (7), the flow stress is calculated from the equation given below:
rf ð148:28ln ðeÞ þ 825Þ eð0:0463ðeÞ0:4688ðeÞ2þ0:0025Þ
ð15Þ
The values of rf calculated from the Eqs. (12) and (15) at different strain rate and strain are compared with the flow stress measured experimentally at different strain and strain rate in Table 3. Values in the parenthesis in Table 3 indicate the percentage deviation from the experimental values. The table shows that the flow stress measured through the experimental curves is in good agreement with the values measured through the above empirical relations. Maximum deviation is noted to be 7.3%. The equation so developed for 7178 alloy with Ca addition have been employed to the 7178 alloy for predicting their flow behaviour. It has been observed that with minor alteration of the coefficients of Eq. (13), the predicted values of flow stress are in good agreement with the experimental values (Table 3). It is noted that the Eq. (13) for 7178 alloy could be as follows:
K sp ¼ 145:25ln ðeÞ þ 775
ð16Þ
This signifies that the strain rate effect on 7178 alloy without Ca addition is almost similar to that of 7178 alloy with Ca addition. 5. Conclusions Following conclusions could be drawn from the present study: (1) The microstructure of 7178 alloy can be modified and refined through Ca addition. Addition of Ca suppress eutectic reaction and different types of inter-metallic precipitates are formed in the microstructures. Fibrous type Al4Ca precipitates were present along the grain boundary while submicron precipitates are formed within the dendritic arms. (2) The microstructural modification and refinement causes increase in elastic limit stress and flow stress of 7178 alloy due to Ca addition. (3) Plastic strengthening coefficient and strain-hardening exponent of the Ca added alloy varies with strain rate. These values for this alloy are considerably higher than for 7178 alloy without Ca addition. (4) The compressive deformation behaviour of Ca added 7178 alloy as a whole varies marginally with strain rate. The strain rate sensitivity of the alloy at ambient temperature is noted to be very low.
(5) The flow curves or the flow stress can be correlated empirically with strain rate and strain quite accurately for the alloy. The proposed relation once achieved can be used for prediction of flow curves for the alloy at any strain rate and strain under the used domain of strain rate.
References [1] Miller WS, Heinz A, Haszler A, Keidel C, Moldenhauer S, Benedictus R. Recent development in aluminium alloys for aerospace applications. Mater Sci Eng A 2000;280:102–7. [2] Strake EA, Staley JT. Applications of modern aluminium alloys to aircraft. Progress Aerospace Sci 1999;32:131–72. [3] Froes FH. Advanced metals for aerospace and automotive use. Mater Sci Eng A 1994;184:119–33. [4] Starke EA. Aluminum: alloying. Encyclopedia Mater Sci Technol 2008:101–8. [5] Zhongxia Liu, Zijiong Li, Mingxing Wang, Yonggang Weng. Effect of complex alloying of Sc, Zr and Ti on the microstructure and mechanical properties of Al– 5Mg alloys. Mater Sci Eng A 2008;483 484:120–2. [6] Thompson DS, Zinkham RE. The effect of alloying and processing on the fracture characteristic of aluminium sheets. Eng Fract Mech 1975;7:389–92. [7] Heusler Leonhard, Schneider Wolfgang. Influence of alloying elements on the thermal analysis of Al–Si cast alloys. J Light Metals 2002;2:17–26. [8] Manas Dash, Makhlouf Makhlouf. Effect of key alloying elements on the feeding characteristics of aluminium silicon casting alloys. J Light Metals 2001;1:251–65. [9] Immarigeom JP, Holt RT, Koul AK, Zhao L, Wallace W, Beddoes JC. Lightweight materials for aircraft applications. Mater Charact 1995;35:41–67. [10] Williams james C, Strake Edgar A. Progress in structural materials for aerospace systems. Acta Mater 2003;51:5775–99. [11] Chandrashekar T, Muralidhara MK, Kashyap KT, Raghothama Rao P. Effect of growth restricting factor on grain refinement of aluminium alloys. Int J Adv Manuf Technol 2009;40:234–41. [12] Pekguleryuz Mihriban O, Eric Baril. Creep resistant magnesium die casting alloys based on alkaline earth elements. Mater Trans JIM 2001;42:1258–67. [13] Ninomiya R, Ojtro T, Kubpte K. Improved heat resistance of Mg–Al alloys by the Ca addition. Acta Metall Mater 2005;43:669–74. [14] Rokhlin LL, Dobatkina TV, Nikitina NI, Tarytina IE. Calcium alloyed magnesium alloys. Metal Sci Heat Treat 2009;51:164–9. [15] Lyakishdev NP, editor. Phase diagrams of metallic systems. reference manual in 3 volumes, Mashinostroenic, Moscow; 1996–2000 [in Russian]. [16] Drits ME, Sviderskaya ZA, Rokhlin LL. Effect of alloying and treatment conditions on damping of ultrasonic vibrations in magnesium alloys. Lzv Akad Nauk SSSR Metally 1996;6:114–20. [17] Yue Wu, William A Cassada, Lavernia EJ. Microstructure and mechanical properties of spray deposited Al–17Si–4. 5Cu–0.6Mg wrought alloys. Metall Mater Trans 2005;26 A:1235–47. [18] Loper CR, Cho JI. Influence of trace amounts of calcium in aluminium casting alloys – review of literature. Trans Am Foundrymen’s Soc 2000;108:585–92. [19] Sreeja Kumari SS, Pillai RM, Pai BC. Role of calcium in aluminium based alloys and composites. Int Mater Rev 2005;50:216–38. [20] Knuutinen A, Nogita K, McDonald SD, Dhale AK. Modification of Al Si alloys with Ba, Ca, Y and Yb. J Light Metals 2001;1:229–40. [21] Mondal DP, Ganesh NV, Muneshwar VS, Das S, Ramakrishnan N. Effect of SiC concentration and strain rate on the compressive deformation behaviour of 2014Al–SiCp composite. Mater Sci Eng A 2006;433:18–31.
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Materials and Design journal homepage: www.elsevier.com/locate/matdes
Effect of calcium addition on the microstructure and compressive deformation behaviour of 7178 aluminium alloy D.P. Mondal a,⇑, Nidhi Jha a, Anshul Badkul a, S. Das a, M.S. Yadav a, Prabhash Jain b a b
Advanced Materials and Processes Research Institute (CSIR LAB), Bhopal 462 064, India University Institute of Technology, Barkatullah University, Bhopal 462 026, India
a r t i c l e
i n f o
Article history: Received 6 August 2010 Accepted 31 December 2010 Available online 8 January 2011 Keywords: A. Non-ferros metals and alloys E. Mechanical F. Microstructure
a b s t r a c t Aluminium 7178 alloys containing 1% calcium are used to study the effect of calcium addition on their microstructure and compressive deformation behaviour. The compressive deformation behaviour of aluminium alloy containing 1% calcium is studied at varying strain rates (102–10/s). The material is prepared using stir casting technique. The yield stress, flow stress and elastic limit are measured from the true stress–strain graph. The strain rate sensitivity and strain-hardening exponent was also determined for each material at different strain rates. Its microstructural characterization reveals that Ca particles act as grain refiners for primary base alloy and helps in improving the strength of the virgin alloy. An empirical relationship has been proposed to predict the flow curve of the alloys as a function of strain and strain rate. Ó 2011 Elsevier Ltd. All rights reserved.
1. Introduction Aluminium and its alloys have potential applications in aerospace and automotive industry because of its higher specific strength and stiffness [1–3]. Pure aluminium is relatively a soft material. For applications requiring greater mechanical strength, it is generally alloyed with other elements such as copper, magnesium, manganese, iron, silicon and zinc. Strake [4] reviewed in detail the effect of different alloying elements on the microstructure and mechanical behaviour of aluminium and its alloys. Zhongxia et al. [5] reported that addition of rare earth metals like Sc, Zr and Ti, in small quantities refined the microstructure and thus improved the strength of Al–5Mg alloy significantly. Thompson and Zinkham [6] also examined that addition of alloying elements like Zr, Cr and Fe in a 7075 Aluminium alloy results in different kinds of inter-metallic phases of various size ranges which results in microstructural refinement and influences in age hardening characteristics as well as recrystallisation and grain growth. The inter-metallic precipitates also causes for higher strength and fatigue crack growth resistance. Heusler and Schneider [7] examined that addition of Mg, Na and Sr in small quantities influenced the eutectic transformation of Al–Si cast alloys and modified silicon morphologies to a great extent and thus improve its strength and toughness. It is further reported by Dash and Makhlouf [8] that the castability of Al–Si alloys improved, hydrogen absorption decreased and microstructure got refined and modified due to addition of Mg, ⇑ Corresponding author. Tel.: +91 755 2418952. E-mail address: [email protected] (D.P. Mondal). 0261-3069/$ - see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.matdes.2010.12.056
Mn, Cu, Sr and Ti. All these factors lead to higher strength and ductility. The 7178 series alloys based on Al–Zn–Mg system have unique combination of desirable characteristics including low density, high strength and fracture toughness [9]. Increased strength of these alloys was achieved through the formation of finer inter-metallic precipitates with increasing Zn, Mg and Cu concentration [10]. However, improved mechanical properties require a strict control on alloy preparation and processing aiming to achieve refined and modified microstructure along with generation of fine coherent precipitates. Elements like Ti [8], Cr [6], Zr [6] and Sc [5], and component like TiB2 [11] are used for obtaining refined microstructure. Calcium has been used by Mihriban and Pekguleryuz as an important alloying element in magnesium alloys to improve their high temperature strength vis-a-vis creep resistance [12]. It was examined by these investigators that Ca offers a thermally stable second phase Mg2Ca and thus significantly improved the elevated temperature strength and creep property. Ca added Mg–Al alloy becomes a promising low cost magnesium alloy for improved heat resistant and elevated temperature creep resistant automobile engine component applications [13]. It was reported that the addition of small amount of Ca into Mg–Al alloys can result in refinement of grain-structure and thus increasing their mechanical properties [14,15]. It was also examined by Drits et al. [16] that addition of Ca in Mg-alloys not only refined the microstructure and improved its creep resistance but also improved its high temperature oxidation resistance. In this context, it is suspicious that calcium can also be used as grain refiner for Al–Zn–Mg alloy. But this aspect, to the best of our knowledge had been overlooked so far.
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Silicon when added to aluminium alloys to increase the mechanical properties led to coarse microstructures containing coarse Si needle which in due course caused inherent brittleness and poor workability [17]. Calcium has been used as a modifier of the silicon eutectic phase in Al–Si cast alloys [18]. It was reported that the addition of Ca in Al–Si alloys modified the needle shaped silicon to fibrous type of silicon or fine silicon particles [19], which finally led to the improvement in strength and toughness [20]. It is noted from Al–Ca phase diagram (as shown in Fig. 1) that it has high eutectic temperature (613 °C). This makes it suitable for higher temperature applications with increased strength. In this context, it is interesting to understand the effect of calcium addition on the microstructure and compressive deformation behaviour of 7178 alloys under varying strain rates. Attempts have been made for empirical prediction of flow curves as a function of strain rate and strain for Ca added 7178 alloys. 2. Experimental 2.1. Material synthesis and microstructure 7178 alloy is prepared through stir casting technique. This technique involves melting of 7178 aluminium alloy ingot in an electrical resistance furnace.7178 alloy normally contains Si 0.4 wt.%, Fe 0.5 wt.%, Cu 1.75 wt.%, Mn 0.3 wt.%, Mg 2.5 wt.%, Cr 0.2 wt.%, Zn 6.3 wt.% and remaining Al. After maintaining the temperature between 750 and 800 °C, a vortex was created using a mechanical stirrer. Calcium granular is added to the melt with continued stirring. Stirring was continued for about 10 min after addition of calcium particles for uniform distribution in the melt. The melt temperature was then maintained at 800 °C for half an hour, so that Ca particles
got dissolved into the melt. Castings were prepared by pouring the melt into preheated cast iron moulds of cylindrical shapes. From these castings, samples of 10 mm diameter and 15 mm length were prepared for microstructural examination. For microstructural characterization, the samples were polished using standard metallographic technique and etched with Keller’s reagent. Before examination under SEM, samples were sputtered with gold. 2.2. Compressive deformation Compression tests were performed on a Universal Testing Machine (BISS, Bangalore India make of 50 KN capacity) at room temperature and at varying strain rates (0.01/s, 0.1/s,1/s and 10/s). For the compression test samples of 10 mm diameter and 15 mm length were prepared form the castings. The surfaces of the specimens were polished mechanically prior to testing and were lubricated with thin molybdenum sulphide coating so as to reduce the friction between the specimen surface and the compression test plates. The density of all the samples was determined and it was noted that the average density of Ca added samples was 2.7 ± 0.02 g/cc and that of 7178 alloy was 2.83 g/cc. The true stress–true strain graph was plotted during the testing using the built in software. Different data related to compressive deformation have been determined from the analysis of true stress–strain curves. 3. Results 3.1. Material and microstructure Fig. 2a shows the microstructure of 7178 alloy exhibiting the dendrites of aluminium. The dendrites are highly elongated. The
Fig. 1. Phase diagram of Al–Ca system.
D.P. Mondal et al. / Materials and Design 32 (2011) 2803–2812
addition of 1 wt.% calcium in the alloy also provides dendritic structures, but less elongated and relatively finer (Fig. 2b). Additionally, Fig. 2b shows the presence of Al4Ca inter-metallic precipitates (marked arrow) along the grain boundary. Higher magnification micrograph of 7178 alloy without Ca addition (Fig. 2c) shows the presence of eutectic phase in the inter-dendritic region (marked arrow). This signifies that addition of Ca suppresses the formation of eutectic phase along the inter-dendritic region. Fig. 2d reveals that there are two different types of shapes of the particles (precipitates): fibrous and particulates. Generally fibrous types of precipitates (marked arrow) are present along the interdendritic region and particulate type precipitates (marked P) are present within the arms of dendrite. Particulate type precipitates
2805
are generally Al2Ca which have significantly higher melting point and they act as a nucleating agent of dendrites, where as fibrous type (generally Al4Ca, Mg2Ca) opposes the growth of dendrites. The microstructure of 7178 alloy with Ca addition also reveals that a large amount of submicron precipitates are formed within the dendritic arms (Fig. 2e), but no such precipitates are observed in 7178 alloy without Ca addition. The average dendritic spacing in 7178 alloy with and without Ca addition are recorded to be 70.3 lm and 58.2 lm respectively. The aspect ratios of dendritic arms of 7178 alloy with and without Ca additions are noted to be 2.8 ± 0.5 and 1.6 ± 0.3 respectively. It is thus observed that the microstructure of 7178 alloys get refined significantly due to addition of 1 wt.% Ca.
Fig. 2. (a) Microstructure of 7178 Al alloy, (b) microstructure of Ca added 7178 Al alloy, (c) higher magnification microstructure of 7178 alloy, (d) higher magnification microstructure of Ca added 7178 Al alloy, and (e) microstructure of Ca added 7178 Al alloy showing submicron precipitates.
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3.2. Compressive deformation The true stress–true strain curves of the investigated material when tested at different strain rates are shown in Fig. 3. From these true stress–true strain plots, the yield stress and flow stress at different strains are determined using standard methodology. It may be noted that the curves do not show any sharp yield point. It is observed that when strain rate is increased from 0.01/s to 1/s, stress increases while when strain rate is further increased to 10/s, true stress decreases marginally. As a whole, it is found that stress varies in a narrow range with change in strain rate. The compressive stress–strain curve also demonstrates that due to the addition of 1 wt.% Ca, the yield stress and flow stress of 7178 alloy is increased by around 35–50 MPa at a strain rate of 0.01/s and 7178 alloy without Ca failed at lower strain value. The flow stress at different strain and strain rate recorded from the true stress–strain curves are shown in Table 1. The stress–strain curve of a material could be defined by the following equation:
rf ¼ re þ K p enp
ð1Þ
where re is the elastic limit stress, Kp is the plastic strength coefficient, ep is the plastic strain and n is the strain-hardening exponent. Eq. (1) can be written in two parts as follows:
rf ¼ re ¼ Eee
ð2Þ
rf ¼ K p enp
ð3Þ
where E is the modulus of elasticity and ee is the elastic limit strain. The value of re, Kp and n are calculated using methodology described elsewhere [21] considering Eqs. (2) and (3). 3.3. Strain-hardening exponent, Plastic Strength coefficient and Elastic limit stress Strain-hardening exponent is calculated from ln (r) and ln (e) plots, which were made from the recorded true stress and true strain values. A typical plot of ln (r) vs. ln (e) is shown in Fig. 4. This plot shows two regimes, one for elastic (lower) and other for plastic (upper) flow. From these curves, ‘n’, ‘Kp’ and re are calculated using the methodology described elsewhere [21] and are reported in
Table 1 Flow stress at different strain and strain rate recorded from the true stress–strain curves. Alloy
Al Ca
7178 Al Alloy
Strain rate
Flow stress rf (MPa) 0.03
0.05
0.07
0.09
0.11
0.13
0.01/s 0.1/s 1/s 10/s 0.01/s 1/s
288 308 336 303 240 290
364 373 390 362 319 345
417 418 439 416 385 395
461 462 476 460 428 429
495 496 511 491 456 478
527 528 534 524 498 488
Fracture strain 0.152 0.148 0.141 0.133 0.156 0.148
Table 2. The variation of ln (re) as a function of ln (e ) is shown in Fig. 5a. It is noted that the elastic limit stress is varying with strain rate within a narrow range. The overall change in strain rate from 0.01/s to 10/s results in the variation of elastic limit stress of 23 MPa, which is less than 10% of the elastic limit, stress of the material. However, the elastic limit stress of 7178 alloy without Ca is noted to be considerably less (248 MPa). The variation of Kp vs. ln (e ) is shown in Fig. 5b. It can be observed from this figure that Kp decreases with strain rate when strain rate is increased from 0.01/s to 1/s. But further increase in strain rate to 10/s increases Kp. The variation of n vs. ln (e ) also follow the similar trend to that of Fig. 5b as shown in Fig. 5c. It may be noted from Table 2 that the values of both Kp and n in 7178 alloy without Ca are significantly less than that of the alloy with Ca addition. Marginal variation of elastic limit stress with strain rate (except at strain rate of 0.01/s) signifies that the re of the material is almost invariant to the strain rate, whereas the variation of Kp and n with strain rate signifies that the plastic deformation is influenced by the strain rate. If examined more carefully, it will be observed that except in slower strain rate of 0.01/s, the Kp and n both are varying in a narrow range signifying that these two parameters are almost invariant to the strain rate especially at relatively higher strain rate. 4. Discussion 4.1. Effect of Ca addition on microstructures Addition of Ca in 7178 alloy suppresses the formation of eutectic phase along the inter-dendritic region and also helps in
Fig. 3. Variation of true stress vs. true strain at different strain rate.
D.P. Mondal et al. / Materials and Design 32 (2011) 2803–2812
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Fig. 4. Variation of ln(stress) vs. ln(strain) at varying strain rate.
Table 2 The strain-hardening exponent, the plastic strength and elastic limit of the investigated material at different strain rate. Material
Strain rate (s1)
n
re (MPa)
Kp (MPa)
7178 Alloy
0.01 1 0.01 0.1 1 10
0.43 0.365 0.465 0.366 0.339 0.385
248 255.81 287.16 295.84 294.81 310.63
1236.45 1021.5 1417.99 1116.55 1081.39 1165.61
7178 alloy with Ca
formation of submicron precipitates within the dendritic arms. This is attributed to the fact that (i) addition of Ca results in the formation of Al4Ca and mixed inter-metallic phases which might be shifting the eutectic point of the alloy system [14] and (ii) fine Al2Ca precipitate or calcium oxide particles (due to oxidation of Ca) [14] within the melt acts as nucleating agent for solidification making the solidification rate faster and thus suppressing the formation of eutectic phase to some extent. Because of the higher solidification rate, the secondary arm spacing in the Ca added alloy becomes finer. Additionally the higher rate of nucleation, presence of fibrous Al4Ca precipitates and mixed inter-metallic precipitates (Mg2Ca, Mg, Zn, Ca) also results in lower aspect ratio of the dendritic arms. The fibrous precipitates formed around the dendritic arms resist the growth of the dendritic arm and thus finer and comparatively equiaxed dendritic arms are formed in Ca added alloy. As per the composition of the alloy, Al2Ca precipitate will not form in the liquid melt. But, in the present case Ca is added in the form of granules in the liquid melt through mechanical stirring prior to pouring into the die. As s result, there is a possibility of non uniform distribution of Ca in the melt. In some of the localized regions, there is a possibility of higher Ca content and these Ca might be in solid particles which react with aluminium to form Al2Ca within the melt. Al2Ca has significantly higher melting point (1079 °C) [14] than the melt temperature. Because of the same reason, there would have the possibility of formation of Mg2Ca also [14]. X-ray diffraction pattern of this alloy confirms the presence of Al2Ca, Al4Ca, Mg2Ca, MgAl2 and solid solution of aluminium Fig. 9. The natures of precipitates are further confirmed by EDX analysis. The EDX pattern of rod like precipitates at inter-dendritic region is shown in Fig. 10a demonstrating that the precipitate consists of Al and Ca. The larger precipitates within the dendrites (Fig. 10b) also show the presence of Al and Ca only. But the concentration of Ca in these cases is much higher than that in Fig. 10a.
This demonstrates that the larger precipitates within the dendritic arms would be Al2Ca and the precipitates in the interdentric region are of Al4Ca. The precipitation of Al2Ca starts at higher temperature and subsequently these particles act as nucleating agent during solidification. A fraction of Ca also makes a solution with Mg at higher temperature because of inhomogeneous mixing of Ca in the melt. At temperature below 500 °C this solution transforms into Mg-solid solution and Al2Ca [14]. At still lower temperature (475– 500 °C) Mg-solid solution get transformed into Mg2Ca and Mg. During solidification, at temperatures lower than 613 °C, Al4Ca precipitate formed from the liquid melt left at that temperature. As a result it is expected that fine fibrous type Al4Ca precipitates around the dendritic arms and fine precipitates of Al2CA, Mg2Ca, and MgAl2 (XRD pattern in Fig. 9) precipitates within the dendritic arms (Fig. 2). These submicron precipitates within the dendritic arms and the needle like precipitates along the dendrite arms spacing are responsible for higher ‘n’, ‘Kp’ and ‘re’ in Ca added 7178 alloys. 4.2. Effect of Ca addition on compressive deformation It is observed from Fig. 3 and Table 2 that the yield stress and/or flow stress of 7178 alloy increases by 50 MPa due to addition of 1 wt.% Ca. This is attributed to the microstructural refinement and modification due to Ca addition as discussed earlier. It may be noted that very fine precipitates are formed within the dendritic arms of the Ca added alloy (Fig. 2e). Higher strength, Kp and n in Ca added alloy is due to refinement of the structure and the presence of submicron precipitates within the dendritic arms. As the eutectic phase constituent gets reduced in Ca added alloy, it provides higher fracture strain as compared to the 7178 alloy. 4.3. Effect of strain rate In earlier studies by the present authors [21] it was observed that the compressive deformation behaviour of 2014-SiC composites and 2014 alloy is almost invariant to the strain rate. The strain rate sensitivity ‘m’, is very low at room temperature. In the present study, it is observed that the value of ‘m’ for the Ca added alloy is very low signifying that the overall compressive deformation behaviour of this alloy at room temperature is almost invariant to the strain rate under the selected range of strain rate. The value of Kp and ‘n’ are noted to be relatively higher at a strain rate of 0.01/s. This is attributed to the fact that at lower strain rate the movement of dislocation vis-a-vis plastic flow of material is very slow
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Fig. 5. Variation of: (a) ln (elastic limit stress), (b) plastic strength coefficient and (c) strain-hardening exponent with ln (strain rate).
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Al Ca 6.3
6.2
Ln (Stress)
6.1 6 5.9 5.8
-5
-4
-3
-2
-1
5.7
0
1
2
3
Ln (Strain Rate)
Strain rate sensitivity (m)
Fig. 6. Variation of ln(stress) vs. ln(strain rate) at different strain rate of Ca added 7178 alloy.
Flow strain Fig. 7. Variation of strain rate sensitivity with flow strain.
and thus there is a greater possibility of higher degree of interaction of dislocation with the precipitates and possibility of generation of more dislocations during deformation. This finally leads to higher plastic strengthening coefficient and n value (Fig. 5b and c). The flow stress increases with increase in strain as observed in Fig. 6. The value of ‘m’ is also noted to decrease with strain. This is attributed to greater strain hardening at higher strain value and the material becoming harder and harder with the progress of deformation and thus becoming more and more insensitive to strain rate. 4.3.1. Strain rate sensitivity The stress of a material in terms of strain rate could be written as follows:
rf ¼ K s em
ð4Þ
where rf is the flow stress, Ks is the flow stress at a strain rate of 1/s m is the strain rate sensitivity and e is the strain rate. Thus the flow behaviour could be expressed as follows:
rf ¼ re þ K s em
ð5Þ
The strain rate sensitivity (m) and Ks was calculated from the slope of linear fit between ln (rf) and ln (e ) as shown in Fig. 6, where rf is flow stress and e is strain rate. The value of m is found to be varying in the range of 0.0013–0.0036. Very low value of m signifies that the compressive deformation behaviour of Ca–added alloy at room temperature is almost invariant to the strain rate. The variation of m as a function of strain is shown in Fig. 7. It may also be noted that m decreases with increase in strain, signifying that at higher strain, the variation of flow stress with strain rate would be reduced. The variation of Ks with strain in Fig. 8 shows that Ks increases with increase in flow strain.
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550
Strength Coefficeint K
500
450
400
350
300
250
200
0
0.03
0.06
0.09
0.12
0.15
Flow strain Fig. 8. Variation of strength coefficient as a function of strain.
.
.
Al 4Ca, Δ Al 2Ca, ◊ Mg2Ca, ο Mg Al 2,
.
Al
Fig. 9. X Ray diffraction pattern of 7178 Alloy with calcium addition.
The flow curves of a material can also be defined using the following relations:
rf ¼ K se eme ðwhen stress is limited to elastic stressÞ
ð6Þ
where Kse is the elastic strength coefficient at strain rate of 1, ‘me’ is the strain rate sensitivity on elastic stress.
rf ¼ K sp emp ðwhen stress is beyond the elastic limit stressÞ
ð7Þ
where Ksp is the flow strength coefficient at strain rate of 1/s, ‘mp’ is the strain rate sensitivity on flow stress. 4.3.2. Correlation of flow stress with strain rate and strain Flow stress of a material could be defined using Eqs. (1)–(6). It can be noted from the best fitted curve of Fig. 5a that elastic limit
stress of the Ca added alloy follows the following relation with strain rate:
re ¼ e0:001ln ðe Þ2þ0:0012ðln e Þþ5:699 ðup to elastic limitÞ
ð8Þ
The plastic strengthening coefficient Kp can be expressed in the following form as a function of strain rate (from Fig. 5b).
K p ¼ 11:25ðln e Þ2 2:005ðln e Þ3 þ 21:28ðln e ÞÞ þ 1081
ð9Þ
The strain-hardening exponent ‘n’ follows the relation with strain rate as mentioned below:
n ¼ 0:006ðln e Þ2 þ 0:004ðln e Þ þ 0:339
ð10Þ
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D.P. Mondal et al. / Materials and Design 32 (2011) 2803–2812 Table 3 Flow stress calculated theoretically from Eqs. (12) and (15). Material
7178 alloy with Ca
Strain rate
Flow strain
rf (MPa)
0.01
0.03
288
0.05
364
0.07
417
0.09
461
0.11
495
0.13
527
0.03
308
0.05
373
0.07
418
0.09
462
0.11
496
0.13
528
0.03
336
0.05
390
0.07
439
0.09
476
0.11
511
0.13
534
0.03
303
0.05
362
0.07
416
0.09
460
0.11
491
0.13
524
0.03
240
0.05
319
0.07
385
0.09
428
0.11
456
0.13
498
0.03
290
0.05
345
0.07
395
0.09
429
0.11
478
0.13
488
0.1
1
10
Fig. 10. EDX pattern of: (a) particles within the dendrites and (b) needle shape particles in the inter-dendritic region.
By putting the values of re, Kp and n in Eq. (1), the flow stress can be correlated with strain and strain rate in terms of the following relation:
7178 alloy
0.01
re ¼ e0:001ln ðe Þ2þ0:0012ðln e Þþ5:699
when stress is limited to elastic limit stress:
ð11Þ
Flow stress beyond elastic limit can be related in terms of following relation:
rf ¼ ½11:25ðln e Þ2 2:005ðln e Þ3 þ 21:28ðln e Þ þ 1081 e0:006ðln e Þ2þ0:004ðln e Þþ0:339
ð12Þ
The flow stress can be correlated with strain and strain rate empirically using the following approach also using Eqs. (6) and (7). The elastic limit stress can be correlated with strain rate as shown in Eq. (6). The flow stress as a function of strain and strain rate can be correlated through the following relation by putting the value of Ksp and mp as a function of e (as observed from the best fitting curves in Figs. 7 and 8) in Eq. (7):
K sp ¼ 148:28ln ðeÞ þ 825
ð13Þ
1
exp
rf (MPa) calculated Eq. (11)
Eq. (14)
294.78 (2.3) 370.56 (1.8) 430.82 (3.2) 482.14 (4.4) 527.47 (6.2) 568.45 (7.3) 308.52 (0.2) 372.07 (0.2) 420.93 (0.7) 461.57 (0.09) 496.82 (0.2) 528.20 (0.03) 329.28 (2.03) 391.54 (0.4) 438.84 (0.03) 477.87 (0.4) 511.51 (0.1) 541.31(1.4)
291.28 (1.12) 366.58 (0.7) 416.68 (0.07) 454.648 (1.4) 485.52 (1.9) 511.76 (2.9) 296.28 (3.9) 371.58 (0.4) 421.68 (0.8) 459.64 (0.5) 490.52 (1.1) 516.76 (2.2) 301.36 (11.5) 376.66 (3.5) 426.76 (2.8) 464.73 (2.4) 495.61 (3.1) 521.84 (2.3) 306.53 (1.2) 381.83 (5.2) 431.92 (3.6) 469.89 (2.1) 500.76 (1.9) 527.01 (0.6) 261.54 (8.2) 333.21 (4.26) 380.89 (1.07) 417.00 (2.63) 446.35 (2.15) 471.29 (5.66) 271.62 (6.7) 343.29 (0.49) 390.96 (1.03) 427.08 (0.44) 456.43 (4.72) 481.37 (1.37)
307.37 (1.4) 373.22 (3.0) 424.13 (1.9) 466.63 (1.4) 503.61 (2.5) 536.62 (2.4) 273.74 (12.3) 340.98 (6.44) 394.06 (2.3) 439.03 (2.51) 478.60 (4.72) 514.24 (3.15) 283.90 (2.14) 342.09 (0.84) 386.80 (2.11) 423.95 (1.18) 456.17 (4.78) 484.8 (0.64)
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m ¼ 0:0463ðeÞ 0:4688ðeÞ2 þ 0:0025
ð14Þ
By putting the values of Ksp and mp in Eq. (7), the flow stress is calculated from the equation given below:
rf ð148:28ln ðeÞ þ 825Þ eð0:0463ðeÞ0:4688ðeÞ2þ0:0025Þ
ð15Þ
The values of rf calculated from the Eqs. (12) and (15) at different strain rate and strain are compared with the flow stress measured experimentally at different strain and strain rate in Table 3. Values in the parenthesis in Table 3 indicate the percentage deviation from the experimental values. The table shows that the flow stress measured through the experimental curves is in good agreement with the values measured through the above empirical relations. Maximum deviation is noted to be 7.3%. The equation so developed for 7178 alloy with Ca addition have been employed to the 7178 alloy for predicting their flow behaviour. It has been observed that with minor alteration of the coefficients of Eq. (13), the predicted values of flow stress are in good agreement with the experimental values (Table 3). It is noted that the Eq. (13) for 7178 alloy could be as follows:
K sp ¼ 145:25ln ðeÞ þ 775
ð16Þ
This signifies that the strain rate effect on 7178 alloy without Ca addition is almost similar to that of 7178 alloy with Ca addition. 5. Conclusions Following conclusions could be drawn from the present study: (1) The microstructure of 7178 alloy can be modified and refined through Ca addition. Addition of Ca suppress eutectic reaction and different types of inter-metallic precipitates are formed in the microstructures. Fibrous type Al4Ca precipitates were present along the grain boundary while submicron precipitates are formed within the dendritic arms. (2) The microstructural modification and refinement causes increase in elastic limit stress and flow stress of 7178 alloy due to Ca addition. (3) Plastic strengthening coefficient and strain-hardening exponent of the Ca added alloy varies with strain rate. These values for this alloy are considerably higher than for 7178 alloy without Ca addition. (4) The compressive deformation behaviour of Ca added 7178 alloy as a whole varies marginally with strain rate. The strain rate sensitivity of the alloy at ambient temperature is noted to be very low.
(5) The flow curves or the flow stress can be correlated empirically with strain rate and strain quite accurately for the alloy. The proposed relation once achieved can be used for prediction of flow curves for the alloy at any strain rate and strain under the used domain of strain rate.
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