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The application of advances in quench factor analysis property prediction to the heat treatment of 7010 aluminium alloy
Journal of Materials Processing Technology 153–154 (2004) 674–680
The application of advances in quench factor analysis property prediction to the heat treatment of 7010 aluminium alloy Robert J. Flynn a,∗ , J.S. Robinson b b
a Materials Ireland Research Centre, University of Limerick, Limerick, Ireland Department of Materials Science and Technology, University of Limerick, Limerick, Ireland
Abstract 7010 is an Al–Zn–Mg–Cu forging and plate alloy, primarily used in the aerospace industry for the production of key structural components. These alloys develop their strength through the development of a precipitation-hardened microstructure produced by ageing of a quenched super-saturated solid solution. For over 30 years Evancho and Staley developed quench factor analysis model has been applied successfully to the prediction of post-quenched physical properties, in aged aluminium alloys. In recent years improvements have been made to the initial model incorporating the effect of remaining solute on nucleation rate as a function of temperature. This extends the usefulness of the quench factor approach to beyond the 15% loss in properties, allowing the prediction of properties in both fast-quenched and slow-cooled conditions such as in annealing. Tensile time–temperature–property (TTP) or ‘C’ curves produced by an interrupted quench technique are presented for 7010-T76 including quench factor analysis and subsequent modifications based on an improved non-isokinetic model. © 2004 Elsevier B.V. All rights reserved. Keywords: Aluminium alloys; Quench factor analysis; 7010; Heat treatment
1. Introduction Quench factor analysis (QFA) was originally developed by Evancho and Staley [1] in an attempt to predict the effect of continuous cooling quench rates on the corrosion resistance and yield strength of aluminium alloys. To date it has been shown to be very successful as a property prediction technique in the post-quenched properties of both cast and wrought aluminium alloys [2–6] where the maximum property loss did not exceed 10–15%. Recent developments [7,8] have shown that it is now possible to successfully predict properties beyond this limit using modifications to the original quench factor model. 1.1. 7000 series alloys and 7010 The 7000 series Al–Zn–Mg–Cu alloys are used by the aerospace and automotive industries for structural applications due to a combination of high strength-to-weight ratio and low specific gravity. 7010 (DTD5636) [9], a
∗ Corresponding author. E-mail addresses: [email protected] (R.J. Flynn), [email protected] (J.S. Robinson).
0924-0136/$ – see front matter © 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.jmatprotec.2004.04.133
zirconium-containing Al–Zn–Mg–Cu was originally developed by HDA Forgings (now Mettis Aerospace) and Alcan International Ltd. in order to improve upon the stress corrosion cracking resistance, fracture toughness and strength available in alloys such as 7075-T651 and 7079-T6 [10]. The elemental composition of 7010 and a selection of other high-strength 7000 series alloys are shown in Table 1. 1.2. Precipitation kinetics 7000 series alloys attain their strength by rapid quenching from above the solvus to form a metastable supersaturated solid solution which can then be precipitation-hardened to produce the required mechanical properties. These properties are dependant upon the quench-cooling rate from the solution heat treatment temperature as this determines the amount of solute available for the precipitation of the strengthening precipitates. Any loss in mechanical properties that does occur is primarily attributable to heterogeneously nucleated precipitates, which reduce the supersaturation of the matrix and the resultant hardening of the alloy during ageing [1]. The quenching process is especially important in the commercial production of aluminium components as slower cooling rates are often used as rapid quenches may introduce undesirable residual stresses.
R.J. Flynn, J.S. Robinson / Journal of Materials Processing Technology 153–154 (2004) 674–680
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Table 1 Elemental composition (wt.%) for 7010, 7050, and 7075 Alloy
Si
Fe
Cu
Mn
Mg
Cr
Zn
Ti
Zr
7010 7050 7075
0.12 max 0.12 max 0.40 max
0.15 max 0.15 max 0.50 max
1.5–2.0 2.0–2.6 1.2–2.0
0.10 max 0.10 max 0.30 max
2.1–2.6 1.9–2.6 2.1–2.9
0.05 max 0.10 max 0.18–0.28
5.7–6.7 5.7–6.7 5.1–6.1
0.06 max 0.06 max 0.20 max
0.10–0.16 0.08–0.15 0.05 max
Precipitation in 7010 series alloys proceeds through a succession of phases [11]. After solution treatment and quenching the alloy is subjected to a dual ageing process. The first stage heat treatment involves the formation of GP zones. This GP formation occurs due to the presence of quenched in vacancies, which accelerate diffusion that is slow at these temperatures. During the second-stage heat treatment the GP zones grow and are replaced by precipitates which form on the dissolving GP zones. is usually associated with producing the maximum strength T6 condition. In the T76 condition which is the temper used in this study, phase is replaced by the equilibrium (MgZn2 ) phase. The T76 temper is primarily used to prevent exfoliation and improve stress corrosion cracking resistance. 1.3. Property prediction and quench factor analysis In order to relate the quenching rate with the final alloy strength, Fink and Willey [12] developed a technique to determine the temperature range over which the quench rate has the most critical influence over the mechanical properties after ageing. This was achieved by construction of time–temperature–property (TTP) or ‘C’ curves using an interrupted quench technique which defines the time required to precipitate sufficient solute to reduce the strength by a specified amount but this method proved unsuitable where variations in the quench rate through the critical range occurred. This led to the subsequent development of quench factor analysis by Evancho and Staley [1]. The critical time Ct (T) function which mathematically describes the C-curve was defined by Evancho and Staley as the reciprocal of the classic nucleation equation and is shown in Eq. (1): k3 k42 k5 Ct (T) = −k1 k2 exp exp (1) RT RT(k4 − T)2 where Ct (T) is the critical time required to precipitate a constant amount of solute (s), k1 the constant that equals the natural log of the fraction untransformed during quenching, k2 the constant related to the reciprocal of the number of nucleation sites (s), k3 the constant related to the energy required to form a nucleus (J mol−1 K−1 ), k4 the constant related to the solvus temperature (K), k5 the constant related to the activation energy for diffusion (J mol−1 ), R the universal gas constant (J mol−1 K−1 ), and T the absolute temperature (K).
The C-curve is the loci of the critical times and identifies the time required to attain some fraction of the required property for a set transformation temperature. QFA is based on the principle of using isothermal transformation kinetics to predict transformations under non-isothermal conditions at temperatures below the solvus, such as those that occur during continuous cooling. The kinetics for isothermal reactions is assumed to follow an Avrami-type transformation as shown in Eq. (2): X = 1 − exp(−kt)n
(2)
where X is the volume fraction transformed, n the constant (Avrami exponent), t the time (s), and k the temperature-dependant constant. The value of n, the Avrami exponent, depends on the rate of nucleation and the morphology of the precipitates and has been shown [13] to have a value of 1 for needle- and plate-type precipitates observed in aluminium alloys. The value of k depends on the degree of supersaturation and the rate of diffusion. For continuous cooling in aluminium alloys this equation is redefined as ζ = 1 − exp(k1 τ)
(3)
where ζ is the fraction untransformed, k1 the constant, and τ the measure of the amount transformed (quench factor). Cahn’s analyses of transformation kinetics during continuous cooling [14] showed that reactions at different temperatures are additive whenever the nucleation rate is proportional to the growth rate (i.e. isokinetic). For these reactions he demonstrated that the fraction transformed under non-isothermal conditions is given by tf dt τ= (4) t0 Ct (T) where t0 is the quench start time (s), tf the quench finish time (s), and Ct (T) the critical time as a function of temperature (s); when τ = 1 the fraction transformed equals the fraction represented by the C-curve. 1.4. Property prediction By assuming that the kinetics of transformation follows the Johnson–Mehl–Avrami–Kolmomogorov equation (JMAK) where the Avrami exponent n = 1, an approximation for growth in the early stages of the reaction can be assumed [15]; therefore the required property of the alloy can be predicted from Eq. (5) [16]:
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σx − σmin = exp(k1 τ)n σmax − σmin
(5)
where τ is the quench factor, σ x the Rp0.2 after ageing to the T76 condition (MPa), σ min the minimum T76 Rp0.2 (constant or temperature-dependant) (MPa), σ max the maximum T76 Rp0.2 after an infinitely fast quench (MPa), and k1 the natural log of the fraction untransformed during quenching. Evancho and Staley [1] in their original model set σmin = 0 in order to utilise Cahn’s model of predicting the extent of transformation under non-isothermal conditions. For many industrial applications this provides adequate results when the loss in properties is less than 10%. Based on that assumption σx = σmax exp(k1 τ)n
(6)
The quench factor describes the severity of the quench with low quench factors associated with rapid quench rates, low precipitation and higher strengths after ageing; conversely, high quench factors correspond to higher rates of precipitation and lower strengths.
2. Experimental The 6 mm diameter tensile test pieces were machined from the LT direction of a cold-compressed (2.25 ± 0.5%) AA7010-W52 rectilinear open die forging manufactured by HDA Forging Ltd., Redditch, UK (Fig. 1). 2.1. C-curve determination A test matrix of temperatures versus isothermal hold times based on a previously determined 7010-T6 C-curve [17] was constructed using temperatures ranging from 210 to 440 ± 2 ◦ C and at isothermal holding periods from 2 to 15 000 s. Samples were solution heat-treated (2 h at 475 ± 2 ◦ C) using a Carbolite re-circulating fan oven followed by rapid
quenching (<3 s) into a salt bath containing an AG 140 Degussa specification sodium nitrite/potassium nitrate eutectic mixture. This was followed by a coldwater quench (∼22 ◦ C) and artificial ageing to the T76 condition (10 h at 120 ± 2 ◦ C and 8 h at 172 ± 2 ◦ C). Tensile properties were determined using a Dartec 500 kN servo hydraulic universal testing machine in accordance with BS4A4 and an Epsilon Corp. extensometer was used to measure extension. Cooling curves were determined using an embedded K-type thermocouple centrally located within a representative sample and a high-speed data acquisition system. Previous authors [5] have shown that time intervals above 0.4 s may cause significant variation in the resulting quench factors; therefore time–temperature data was recorded at a frequency of 10 Hz for the duration of the run and the subsequent cooling curves constructed. The cumulative quench factor (τ) is determined from the combination of a cooling curve and C-curve where τ is defined as the sum of the incremental quench factors as shown in Eq. (7): τ= q (7) where q is defined as the ratio of the time step length divided by its corresponding Ct value and can be expressed by Eq. (8): q=
t Ct (T)
(8)
where q is the incremental quench factor, t the time step (s).
3. Results and discussion 3.1. Method 1: curve fitting method The isothermal hold time (t) required to attain 95% of the maximum Rp0.2 at each isothermal hold temperature was plotted producing an experimental C-curve. Using multiple linear regression analysis, coefficients k2 –k5 in Eq. (1) were determined as shown in Table 2. These coefficients were then used for the construction of C-curves for 90, 95 and 99.5% of the maximum Rp0.2 (σ max ) as shown in Fig. 2. Using the cooling curves and the constructed C-curves for 99.5% of Rp0.2 quench factors (σ) were determined, allowing the prediction of Rp0.2 using Eq. (6).
Table 2 k2 –k5 coefficients for 7010-T76 C-curve
Fig. 1. Tensile specimen geometry.
k2 k3 k4 k5
(s) (J mol−1 ) (K) (J mol−1 )
5.6E−20 5.78E+3 8.97E+2 1.90E+5
R.J. Flynn, J.S. Robinson / Journal of Materials Processing Technology 153–154 (2004) 674–680
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Table 3 k2 –k5 coefficients determined using quench factor analysis k2 k3 k4 k5
(s) (J mol−1 K−1 ) (K) (J mol−1 )
5.8E−20 7.37E+3 8.99E+2 1.81E+5
Table 4 Predicted Rp0.2 from methods 1 and 2 % of actual σ max Measured (MPa) Method 1 (MPa) Method 2 (MPa)
Fig. 2. C-curves predicted from experimental interrupted quench data of 0.995 of Rp0.2 σ max .
3.2. Method 2: quench factor analysis In order to improve the correlation between the measured and the predicted Rp0.2 , the measured Rp0.2 values were plotted against predicted values. Using Microsoft Excel® solver the estimated standard deviation (ESD) [7] was minimised for various values of k2 –k5 using the initial multiple regression results as candidate values. The ESD is defined as j=n 2 j=1 (σmj − σxj ) (9) N −6
98 86 92
514 508 480
517 506 496
516 509 486
nose of the curve, the times required for precipitation again increases due to the low rate of solid-state diffusion. In order to extend the use of QFA beyond the 10% loss in properties several modifications to the Evancho and Staley model have been investigated by various authors [7,8,15]. 3.3. New models
where σ mj is the measured Rp0.2 (MPa), σ xj the predicted Rp0.2 (MPa), and N the total number of samples. The resultant 99.5% C-curve and the determined k2 –k5 coefficients using this technique are shown in Fig. 3 and Table 3, respectively. Rp0.2 predicted values using this technique and method 1 are shown in Table 4. At temperatures above the nose of the curve but below the solvus temperature, long isothermal times are necessary to nucleate and grow the precipitates due to the low driving force available for transformation. As the temperature approaches the nose of the curve, the amount of supersaturation of the matrix and the driving force available for precipitation increases due to the increased undercooling reducing the time required for precipitation. Below the
In order to use Cahn’s model for isokinetic transformations the value of σ min was assumed to be 0. This has the result of QFA predicting the properties of alloys, cooled very slowly at temperatures in the upper portion of the curve, approaching zero as σ x /σ max or the fraction of the maximum property values decreases. A solution proposed by Ives et al. [7] assumed that σ min was a non-temperature-dependant constant σ 0 , which could be used with the EXCEL solver method and k2 –k5 to minimise the ESD. In this case σ 0 was assigned the value of 128 MPa, the annealed Rp0.2 for 7010. A comparison of the C-curves for σmin = 0 versus σmin = constant are shown in Fig. 4 and the k2 –k5 coefficients for σmin = constant are shown in Table 5. Several authors [18] in their studies of transformations that involve both coupled nucleation and growth of precipitates by diffusion realised that Cahn’s additive model was not suitable for all quench paths in aluminium alloys. This
Fig. 3. 99.5% of maximum Rp0.2 C-curve determined using methods 1 and 2.
Fig. 4. C-curves for 99.5% Rp0.2 σmin = 0 vs. σmin = constant.
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Table 5 Re-evaluated k2 –k5 coefficients for Ives et al. model where σmin = constant k2 k3 k4 k5
(s) (J mol−1 K−1 ) (K) (J mol−1 )
5.58E−20 4.77E+03 8.50E+02 1.92E+05
is because the precipitation rate at a particular temperature is related to the amount of solute remaining in the matrix and subsequently the amount of precipitation that can occur at that temperature. The use of the Cahn model requires that the rate of precipitation is just a function of the temperature and the amount transformed. A non-isokinetic model has been suggested to overcome this limitation and is based on a solution where σ min is related to the slope of the solvus curve and hence the solute content. Based on this approach Staley and Tiryakoglu [8] have developed a model which allows property prediction from very rapid quench conditions, to beyond the 15% loss in properties and to very slow cooling conditions such as those which may occur at the centre of large forgings or during annealing. 3.4. Non-isokinetic model In order to use Cahn’s model for isokinetic transformations the value of σ min was assumed to be equal to 0, which has the consequence of QFA predicting the properties of alloys, cooled very slowly at temperatures in the upper portion of the C-curve, approaching zero, as the fraction of the maximum property value decreases. To overcome this limitation, a non-isokinetic model was developed [8] where σ min is related to the slope of the solvus. In order to retain the maximum amount of solute available for precipitation hardening the alloy is quenched at as close to an infinite rate as possible from the solution heat treatment temperature. If an alloy is quenched to a temperature below the solution heat treatment temperature, held isothermally until equilibrium is achieved and subsequently quenched to room temperature, a quantifiable amount of solute will be lost from the alloy. The solute remaining is proportional to the maximum achievable Rp0.2 at that temperature (σ max(T ) ) and is equivalent to the strength that would be obtained if the alloy was solution heat-treated at that temperature. Therefore an increasing amount of solute is lost as the isothermal hold temperature decreases, until equilibrium is reached which implies a lower σ min . It follows that the relationship between min and the isothermal hold temperature should follow the same trend as the solvus curve from the equilibrium phase diagram. This model is based on the assumption that strength and solute content follow a linear relationship and that the alloy loses an incremental amount of the capability to develop the property over each individual time interval, thus:
tj σj = (σj−1 − σmin(Tj ) ) 1 − exp − (10) Ct(T)
where σ j is the loss of incremental amount of strengthening capability (MPa), tj the time interval (s), Ct (T) the critical time (s) and σ min (Tj ) the minimum Rp0.2 (MPa), and n=j−1 σj−1 = σmax(Tj ) = σmax − n=1 σn (MPa). The Rp0.2 after quenching is thus defined σ max —the sum of the incremental losses as shown in Eq. (11): σ = σmax −
j=n
σj
(11)
j=1
If we assume that the Rp0.2 and solute content show a linear relationship, the Rp0.2 of the alloy will be equivalent to the intrinsic annealed Rp0.2 of the alloy plus a strength factor related to the solute content, s, thus: σ = σint + As
(12)
where s is the solute content, σ int the annealed Rp0.2 (MPa), σ min (T) the minimum Rp0.2 at temperature (T) after T76 ageing (MPa), and A the constant related to the solute content. If we assume that there exists a temperature Tint below which the driving force is insufficient for precipitation and we represent the solute content at this temperature as sint , then σmin = σint + A(s − sint )
(13)
The change in solubility with temperature can be described by the following equation: S H0 exp (14) s = exp − RT R where H0 is the standard enthalpy (J mol−1 ), S the standard entropy (J mol−1 K−1 ), R the universal gas constant (J mol−1 K−1 ), and T the temperature (K). Combining with Eq. (13): H0 H0 (15) − exp σmin = σint + A exp − RT RTint which can be rewritten as k7 k7 − exp − σmin = σint + k6 exp − T Tint
(16)
where k6 and k7 are the constants. Applying this model to 7010-T76, tensile test specimens were solution heat-treated (2 h at 475±2 ◦ C) followed by furnace cooling at 0.2 ◦ C/min to temperatures ranging from 440 to 70 ± 2 ◦ C in a Carbolite air circulation furnace followed by isothermal holds to ensure the alloy had reached equilibrium. This was followed by cold water quenching, ageing to the T76 condition and determination of Rp0.2 . These values represent the minimum Rp0.2 (σ min ) obtainable at these temperatures. A plot of σ min versus temperature is shown in Fig. 5 with the slope of the curve following the same trend as the equilibrium phase diagram. From this data, values for coefficients k6 and k7 and temperature Tint were determined for 7010-T76 (see Table 6). This allows the determination of σ min at each incremental time step tj .
R.J. Flynn, J.S. Robinson / Journal of Materials Processing Technology 153–154 (2004) 674–680
Fig. 7. 0.995 C-curves for 7010-T76 obtained using QFA where σmin = 0 and σmin = constant, and non-isokinetic C-curves for 0.995 and 0.50 of Rp 0.2 σ max .
Fig. 5. Variation of σ min with temperature.
Table 7 Comparison of isokinetic and non-isokinetic models
Table 6 Values for k6 , k7 , σ int and Tint k6 (MPa) k7 (J mol−1 ) Tint (◦ C) σ int (MPa)
679
8.13E+5 5.63E+3 156 128
When σ min is applied as a function of temperature, the k1 term is removed from the critical time Ct (T) equation (see Eq. (1)) as the C-curve no longer represents points of equal strength. The C-curve that is obtained can be used to obtain iso-strength curves for various fractions of σ max as shown in Fig. 6. Fig. 7 shows a comparison of the C-curves obtained by the variation of σ min and the non-isokinetic C-curves. If we compare fractions of σ max obtained with the non-isokinetic model and compare them with those obtained using the classic isokinetic QFA model (see Table 7) we can see that there is only a minor difference in the Rp0.2 obtained at values approaching σ max . At fractions of σ max where the solute content is low, the difference obtained between the two models is significant.
Fig. 6. 7010 C-curves based on non-isokinetic behaviour for fractions of σ max .
% of σ max
Measured (MPa)
Isokinetic model (MPa)
Non-isokinetic model (MPa)
96.7 93.0 72.3 61.0 32.6
507 482 379 320 171
517 488 396 332 141
509 483 379 318 163
4. Conclusions The Ives et al. approach of defining σ min as constant can extend quench factor analysis to 15% loss of the maximum property for alloy 7010-T76. The non-isokinetic model shows substantial improvement over the original Evancho and Staley model and demonstrates that the non-isokinetic approach to property prediction for 7010-T76 alloys is valid and extends the prediction to up to 70% loss of property. References [1] J.W. Evancho, J.T. Staley, Metall. Trans. 5 (1974) 43–48. [2] C.E. Bates, T. Landig, G. Seintanakis, Heat Treat. 17 (12) (1985) 13–17. [3] P. Archambault, J. Bouvaist, J.C. Chevrier, G. Beck, Mater. Sci. Eng. 43 (1980) 1–6. [4] P. Archambault, J.C. Chevrier, G. Beck, J. Bouvaist, Heat Treatment’76, Book 181, The Metals Society, 1976, pp. 105–109. [5] C.E. Bates, G.E. Totten, Heat Treat. Met. 4 (1988) 89–97. [6] J.D. Bernardin, I. Mudawar, Int. J. Heat Mass Transfer 38 (5) (1995) 863–873. [7] L.K. Ives, J. Swartzendruber, W.J. Boettinger, M. Rosen, S.D. Ridder, F. Biancaniello, R.C. Reno, D.B. Ballard, R. Mehrabian, NBSIR (1983) 83–2669. [8] J.T. Staley, M. Tiryakoglu, The use of TTP curves and quench factor analysis for property prediction in aluminium alloys, in: Proceedings of the Materials Solution Conference of ASM International, 2001, pp. 6–14. [9] Aerospace Material Specification, DTD5636, Materials Department, RAE, Farnborough, Procurement Executive, Ministry of Defence, UK, July 1989. [10] M.A. Reynolds, et al., Presentation of properties of a new high-strength aluminium alloy designated 7010, in: Proceedings of
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the Symposium on Aluminium Alloys in the Aircraft Industry, 1976, pp. 115–124. [11] H.P. Degischer, W. Lacom, A. Zahra, C.Y. Zahra, Z. Metallk. 71 (1980) 231. [12] W.L. Fink, L.A. Willey, Trans. Am. Inst. Mining Met. Eng. 175 (1947) 414–427. [13] J.W. Christian, The Theory of Transformations in Metals and Alloys, 2nd ed., Pergamon Press, Oxford, 1975.
[14] J.W. Cahn, Acta Metall. 4 (1956) 572–575. [15] P.A. Rometsch, M.J. Strarink, P.J. Gregson, Mater. Sci. Eng. A 339 (2003) 255–264. [16] J.T. Staley, Mater. Sci. Technol. 3 (1987) 923–935. [17] J.S. Robinson, R.L. Cudd, D.A. Tanner, G.P. Dolan, J. Mater. Process. Technol. 119 (2001) 261–267. [18] Ø. Grong, O.R. Myhr, Acta Mater. 48 (2000) 445–452.
The application of advances in quench factor analysis property prediction to the heat treatment of 7010 aluminium alloy Robert J. Flynn a,∗ , J.S. Robinson b b
a Materials Ireland Research Centre, University of Limerick, Limerick, Ireland Department of Materials Science and Technology, University of Limerick, Limerick, Ireland
Abstract 7010 is an Al–Zn–Mg–Cu forging and plate alloy, primarily used in the aerospace industry for the production of key structural components. These alloys develop their strength through the development of a precipitation-hardened microstructure produced by ageing of a quenched super-saturated solid solution. For over 30 years Evancho and Staley developed quench factor analysis model has been applied successfully to the prediction of post-quenched physical properties, in aged aluminium alloys. In recent years improvements have been made to the initial model incorporating the effect of remaining solute on nucleation rate as a function of temperature. This extends the usefulness of the quench factor approach to beyond the 15% loss in properties, allowing the prediction of properties in both fast-quenched and slow-cooled conditions such as in annealing. Tensile time–temperature–property (TTP) or ‘C’ curves produced by an interrupted quench technique are presented for 7010-T76 including quench factor analysis and subsequent modifications based on an improved non-isokinetic model. © 2004 Elsevier B.V. All rights reserved. Keywords: Aluminium alloys; Quench factor analysis; 7010; Heat treatment
1. Introduction Quench factor analysis (QFA) was originally developed by Evancho and Staley [1] in an attempt to predict the effect of continuous cooling quench rates on the corrosion resistance and yield strength of aluminium alloys. To date it has been shown to be very successful as a property prediction technique in the post-quenched properties of both cast and wrought aluminium alloys [2–6] where the maximum property loss did not exceed 10–15%. Recent developments [7,8] have shown that it is now possible to successfully predict properties beyond this limit using modifications to the original quench factor model. 1.1. 7000 series alloys and 7010 The 7000 series Al–Zn–Mg–Cu alloys are used by the aerospace and automotive industries for structural applications due to a combination of high strength-to-weight ratio and low specific gravity. 7010 (DTD5636) [9], a
∗ Corresponding author. E-mail addresses: [email protected] (R.J. Flynn), [email protected] (J.S. Robinson).
0924-0136/$ – see front matter © 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.jmatprotec.2004.04.133
zirconium-containing Al–Zn–Mg–Cu was originally developed by HDA Forgings (now Mettis Aerospace) and Alcan International Ltd. in order to improve upon the stress corrosion cracking resistance, fracture toughness and strength available in alloys such as 7075-T651 and 7079-T6 [10]. The elemental composition of 7010 and a selection of other high-strength 7000 series alloys are shown in Table 1. 1.2. Precipitation kinetics 7000 series alloys attain their strength by rapid quenching from above the solvus to form a metastable supersaturated solid solution which can then be precipitation-hardened to produce the required mechanical properties. These properties are dependant upon the quench-cooling rate from the solution heat treatment temperature as this determines the amount of solute available for the precipitation of the strengthening precipitates. Any loss in mechanical properties that does occur is primarily attributable to heterogeneously nucleated precipitates, which reduce the supersaturation of the matrix and the resultant hardening of the alloy during ageing [1]. The quenching process is especially important in the commercial production of aluminium components as slower cooling rates are often used as rapid quenches may introduce undesirable residual stresses.
R.J. Flynn, J.S. Robinson / Journal of Materials Processing Technology 153–154 (2004) 674–680
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Table 1 Elemental composition (wt.%) for 7010, 7050, and 7075 Alloy
Si
Fe
Cu
Mn
Mg
Cr
Zn
Ti
Zr
7010 7050 7075
0.12 max 0.12 max 0.40 max
0.15 max 0.15 max 0.50 max
1.5–2.0 2.0–2.6 1.2–2.0
0.10 max 0.10 max 0.30 max
2.1–2.6 1.9–2.6 2.1–2.9
0.05 max 0.10 max 0.18–0.28
5.7–6.7 5.7–6.7 5.1–6.1
0.06 max 0.06 max 0.20 max
0.10–0.16 0.08–0.15 0.05 max
Precipitation in 7010 series alloys proceeds through a succession of phases [11]. After solution treatment and quenching the alloy is subjected to a dual ageing process. The first stage heat treatment involves the formation of GP zones. This GP formation occurs due to the presence of quenched in vacancies, which accelerate diffusion that is slow at these temperatures. During the second-stage heat treatment the GP zones grow and are replaced by precipitates which form on the dissolving GP zones. is usually associated with producing the maximum strength T6 condition. In the T76 condition which is the temper used in this study, phase is replaced by the equilibrium (MgZn2 ) phase. The T76 temper is primarily used to prevent exfoliation and improve stress corrosion cracking resistance. 1.3. Property prediction and quench factor analysis In order to relate the quenching rate with the final alloy strength, Fink and Willey [12] developed a technique to determine the temperature range over which the quench rate has the most critical influence over the mechanical properties after ageing. This was achieved by construction of time–temperature–property (TTP) or ‘C’ curves using an interrupted quench technique which defines the time required to precipitate sufficient solute to reduce the strength by a specified amount but this method proved unsuitable where variations in the quench rate through the critical range occurred. This led to the subsequent development of quench factor analysis by Evancho and Staley [1]. The critical time Ct (T) function which mathematically describes the C-curve was defined by Evancho and Staley as the reciprocal of the classic nucleation equation and is shown in Eq. (1): k3 k42 k5 Ct (T) = −k1 k2 exp exp (1) RT RT(k4 − T)2 where Ct (T) is the critical time required to precipitate a constant amount of solute (s), k1 the constant that equals the natural log of the fraction untransformed during quenching, k2 the constant related to the reciprocal of the number of nucleation sites (s), k3 the constant related to the energy required to form a nucleus (J mol−1 K−1 ), k4 the constant related to the solvus temperature (K), k5 the constant related to the activation energy for diffusion (J mol−1 ), R the universal gas constant (J mol−1 K−1 ), and T the absolute temperature (K).
The C-curve is the loci of the critical times and identifies the time required to attain some fraction of the required property for a set transformation temperature. QFA is based on the principle of using isothermal transformation kinetics to predict transformations under non-isothermal conditions at temperatures below the solvus, such as those that occur during continuous cooling. The kinetics for isothermal reactions is assumed to follow an Avrami-type transformation as shown in Eq. (2): X = 1 − exp(−kt)n
(2)
where X is the volume fraction transformed, n the constant (Avrami exponent), t the time (s), and k the temperature-dependant constant. The value of n, the Avrami exponent, depends on the rate of nucleation and the morphology of the precipitates and has been shown [13] to have a value of 1 for needle- and plate-type precipitates observed in aluminium alloys. The value of k depends on the degree of supersaturation and the rate of diffusion. For continuous cooling in aluminium alloys this equation is redefined as ζ = 1 − exp(k1 τ)
(3)
where ζ is the fraction untransformed, k1 the constant, and τ the measure of the amount transformed (quench factor). Cahn’s analyses of transformation kinetics during continuous cooling [14] showed that reactions at different temperatures are additive whenever the nucleation rate is proportional to the growth rate (i.e. isokinetic). For these reactions he demonstrated that the fraction transformed under non-isothermal conditions is given by tf dt τ= (4) t0 Ct (T) where t0 is the quench start time (s), tf the quench finish time (s), and Ct (T) the critical time as a function of temperature (s); when τ = 1 the fraction transformed equals the fraction represented by the C-curve. 1.4. Property prediction By assuming that the kinetics of transformation follows the Johnson–Mehl–Avrami–Kolmomogorov equation (JMAK) where the Avrami exponent n = 1, an approximation for growth in the early stages of the reaction can be assumed [15]; therefore the required property of the alloy can be predicted from Eq. (5) [16]:
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σx − σmin = exp(k1 τ)n σmax − σmin
(5)
where τ is the quench factor, σ x the Rp0.2 after ageing to the T76 condition (MPa), σ min the minimum T76 Rp0.2 (constant or temperature-dependant) (MPa), σ max the maximum T76 Rp0.2 after an infinitely fast quench (MPa), and k1 the natural log of the fraction untransformed during quenching. Evancho and Staley [1] in their original model set σmin = 0 in order to utilise Cahn’s model of predicting the extent of transformation under non-isothermal conditions. For many industrial applications this provides adequate results when the loss in properties is less than 10%. Based on that assumption σx = σmax exp(k1 τ)n
(6)
The quench factor describes the severity of the quench with low quench factors associated with rapid quench rates, low precipitation and higher strengths after ageing; conversely, high quench factors correspond to higher rates of precipitation and lower strengths.
2. Experimental The 6 mm diameter tensile test pieces were machined from the LT direction of a cold-compressed (2.25 ± 0.5%) AA7010-W52 rectilinear open die forging manufactured by HDA Forging Ltd., Redditch, UK (Fig. 1). 2.1. C-curve determination A test matrix of temperatures versus isothermal hold times based on a previously determined 7010-T6 C-curve [17] was constructed using temperatures ranging from 210 to 440 ± 2 ◦ C and at isothermal holding periods from 2 to 15 000 s. Samples were solution heat-treated (2 h at 475 ± 2 ◦ C) using a Carbolite re-circulating fan oven followed by rapid
quenching (<3 s) into a salt bath containing an AG 140 Degussa specification sodium nitrite/potassium nitrate eutectic mixture. This was followed by a coldwater quench (∼22 ◦ C) and artificial ageing to the T76 condition (10 h at 120 ± 2 ◦ C and 8 h at 172 ± 2 ◦ C). Tensile properties were determined using a Dartec 500 kN servo hydraulic universal testing machine in accordance with BS4A4 and an Epsilon Corp. extensometer was used to measure extension. Cooling curves were determined using an embedded K-type thermocouple centrally located within a representative sample and a high-speed data acquisition system. Previous authors [5] have shown that time intervals above 0.4 s may cause significant variation in the resulting quench factors; therefore time–temperature data was recorded at a frequency of 10 Hz for the duration of the run and the subsequent cooling curves constructed. The cumulative quench factor (τ) is determined from the combination of a cooling curve and C-curve where τ is defined as the sum of the incremental quench factors as shown in Eq. (7): τ= q (7) where q is defined as the ratio of the time step length divided by its corresponding Ct value and can be expressed by Eq. (8): q=
t Ct (T)
(8)
where q is the incremental quench factor, t the time step (s).
3. Results and discussion 3.1. Method 1: curve fitting method The isothermal hold time (t) required to attain 95% of the maximum Rp0.2 at each isothermal hold temperature was plotted producing an experimental C-curve. Using multiple linear regression analysis, coefficients k2 –k5 in Eq. (1) were determined as shown in Table 2. These coefficients were then used for the construction of C-curves for 90, 95 and 99.5% of the maximum Rp0.2 (σ max ) as shown in Fig. 2. Using the cooling curves and the constructed C-curves for 99.5% of Rp0.2 quench factors (σ) were determined, allowing the prediction of Rp0.2 using Eq. (6).
Table 2 k2 –k5 coefficients for 7010-T76 C-curve
Fig. 1. Tensile specimen geometry.
k2 k3 k4 k5
(s) (J mol−1 ) (K) (J mol−1 )
5.6E−20 5.78E+3 8.97E+2 1.90E+5
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Table 3 k2 –k5 coefficients determined using quench factor analysis k2 k3 k4 k5
(s) (J mol−1 K−1 ) (K) (J mol−1 )
5.8E−20 7.37E+3 8.99E+2 1.81E+5
Table 4 Predicted Rp0.2 from methods 1 and 2 % of actual σ max Measured (MPa) Method 1 (MPa) Method 2 (MPa)
Fig. 2. C-curves predicted from experimental interrupted quench data of 0.995 of Rp0.2 σ max .
3.2. Method 2: quench factor analysis In order to improve the correlation between the measured and the predicted Rp0.2 , the measured Rp0.2 values were plotted against predicted values. Using Microsoft Excel® solver the estimated standard deviation (ESD) [7] was minimised for various values of k2 –k5 using the initial multiple regression results as candidate values. The ESD is defined as j=n 2 j=1 (σmj − σxj ) (9) N −6
98 86 92
514 508 480
517 506 496
516 509 486
nose of the curve, the times required for precipitation again increases due to the low rate of solid-state diffusion. In order to extend the use of QFA beyond the 10% loss in properties several modifications to the Evancho and Staley model have been investigated by various authors [7,8,15]. 3.3. New models
where σ mj is the measured Rp0.2 (MPa), σ xj the predicted Rp0.2 (MPa), and N the total number of samples. The resultant 99.5% C-curve and the determined k2 –k5 coefficients using this technique are shown in Fig. 3 and Table 3, respectively. Rp0.2 predicted values using this technique and method 1 are shown in Table 4. At temperatures above the nose of the curve but below the solvus temperature, long isothermal times are necessary to nucleate and grow the precipitates due to the low driving force available for transformation. As the temperature approaches the nose of the curve, the amount of supersaturation of the matrix and the driving force available for precipitation increases due to the increased undercooling reducing the time required for precipitation. Below the
In order to use Cahn’s model for isokinetic transformations the value of σ min was assumed to be 0. This has the result of QFA predicting the properties of alloys, cooled very slowly at temperatures in the upper portion of the curve, approaching zero as σ x /σ max or the fraction of the maximum property values decreases. A solution proposed by Ives et al. [7] assumed that σ min was a non-temperature-dependant constant σ 0 , which could be used with the EXCEL solver method and k2 –k5 to minimise the ESD. In this case σ 0 was assigned the value of 128 MPa, the annealed Rp0.2 for 7010. A comparison of the C-curves for σmin = 0 versus σmin = constant are shown in Fig. 4 and the k2 –k5 coefficients for σmin = constant are shown in Table 5. Several authors [18] in their studies of transformations that involve both coupled nucleation and growth of precipitates by diffusion realised that Cahn’s additive model was not suitable for all quench paths in aluminium alloys. This
Fig. 3. 99.5% of maximum Rp0.2 C-curve determined using methods 1 and 2.
Fig. 4. C-curves for 99.5% Rp0.2 σmin = 0 vs. σmin = constant.
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Table 5 Re-evaluated k2 –k5 coefficients for Ives et al. model where σmin = constant k2 k3 k4 k5
(s) (J mol−1 K−1 ) (K) (J mol−1 )
5.58E−20 4.77E+03 8.50E+02 1.92E+05
is because the precipitation rate at a particular temperature is related to the amount of solute remaining in the matrix and subsequently the amount of precipitation that can occur at that temperature. The use of the Cahn model requires that the rate of precipitation is just a function of the temperature and the amount transformed. A non-isokinetic model has been suggested to overcome this limitation and is based on a solution where σ min is related to the slope of the solvus curve and hence the solute content. Based on this approach Staley and Tiryakoglu [8] have developed a model which allows property prediction from very rapid quench conditions, to beyond the 15% loss in properties and to very slow cooling conditions such as those which may occur at the centre of large forgings or during annealing. 3.4. Non-isokinetic model In order to use Cahn’s model for isokinetic transformations the value of σ min was assumed to be equal to 0, which has the consequence of QFA predicting the properties of alloys, cooled very slowly at temperatures in the upper portion of the C-curve, approaching zero, as the fraction of the maximum property value decreases. To overcome this limitation, a non-isokinetic model was developed [8] where σ min is related to the slope of the solvus. In order to retain the maximum amount of solute available for precipitation hardening the alloy is quenched at as close to an infinite rate as possible from the solution heat treatment temperature. If an alloy is quenched to a temperature below the solution heat treatment temperature, held isothermally until equilibrium is achieved and subsequently quenched to room temperature, a quantifiable amount of solute will be lost from the alloy. The solute remaining is proportional to the maximum achievable Rp0.2 at that temperature (σ max(T ) ) and is equivalent to the strength that would be obtained if the alloy was solution heat-treated at that temperature. Therefore an increasing amount of solute is lost as the isothermal hold temperature decreases, until equilibrium is reached which implies a lower σ min . It follows that the relationship between min and the isothermal hold temperature should follow the same trend as the solvus curve from the equilibrium phase diagram. This model is based on the assumption that strength and solute content follow a linear relationship and that the alloy loses an incremental amount of the capability to develop the property over each individual time interval, thus:
tj σj = (σj−1 − σmin(Tj ) ) 1 − exp − (10) Ct(T)
where σ j is the loss of incremental amount of strengthening capability (MPa), tj the time interval (s), Ct (T) the critical time (s) and σ min (Tj ) the minimum Rp0.2 (MPa), and n=j−1 σj−1 = σmax(Tj ) = σmax − n=1 σn (MPa). The Rp0.2 after quenching is thus defined σ max —the sum of the incremental losses as shown in Eq. (11): σ = σmax −
j=n
σj
(11)
j=1
If we assume that the Rp0.2 and solute content show a linear relationship, the Rp0.2 of the alloy will be equivalent to the intrinsic annealed Rp0.2 of the alloy plus a strength factor related to the solute content, s, thus: σ = σint + As
(12)
where s is the solute content, σ int the annealed Rp0.2 (MPa), σ min (T) the minimum Rp0.2 at temperature (T) after T76 ageing (MPa), and A the constant related to the solute content. If we assume that there exists a temperature Tint below which the driving force is insufficient for precipitation and we represent the solute content at this temperature as sint , then σmin = σint + A(s − sint )
(13)
The change in solubility with temperature can be described by the following equation: S H0 exp (14) s = exp − RT R where H0 is the standard enthalpy (J mol−1 ), S the standard entropy (J mol−1 K−1 ), R the universal gas constant (J mol−1 K−1 ), and T the temperature (K). Combining with Eq. (13): H0 H0 (15) − exp σmin = σint + A exp − RT RTint which can be rewritten as k7 k7 − exp − σmin = σint + k6 exp − T Tint
(16)
where k6 and k7 are the constants. Applying this model to 7010-T76, tensile test specimens were solution heat-treated (2 h at 475±2 ◦ C) followed by furnace cooling at 0.2 ◦ C/min to temperatures ranging from 440 to 70 ± 2 ◦ C in a Carbolite air circulation furnace followed by isothermal holds to ensure the alloy had reached equilibrium. This was followed by cold water quenching, ageing to the T76 condition and determination of Rp0.2 . These values represent the minimum Rp0.2 (σ min ) obtainable at these temperatures. A plot of σ min versus temperature is shown in Fig. 5 with the slope of the curve following the same trend as the equilibrium phase diagram. From this data, values for coefficients k6 and k7 and temperature Tint were determined for 7010-T76 (see Table 6). This allows the determination of σ min at each incremental time step tj .
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Fig. 7. 0.995 C-curves for 7010-T76 obtained using QFA where σmin = 0 and σmin = constant, and non-isokinetic C-curves for 0.995 and 0.50 of Rp 0.2 σ max .
Fig. 5. Variation of σ min with temperature.
Table 7 Comparison of isokinetic and non-isokinetic models
Table 6 Values for k6 , k7 , σ int and Tint k6 (MPa) k7 (J mol−1 ) Tint (◦ C) σ int (MPa)
679
8.13E+5 5.63E+3 156 128
When σ min is applied as a function of temperature, the k1 term is removed from the critical time Ct (T) equation (see Eq. (1)) as the C-curve no longer represents points of equal strength. The C-curve that is obtained can be used to obtain iso-strength curves for various fractions of σ max as shown in Fig. 6. Fig. 7 shows a comparison of the C-curves obtained by the variation of σ min and the non-isokinetic C-curves. If we compare fractions of σ max obtained with the non-isokinetic model and compare them with those obtained using the classic isokinetic QFA model (see Table 7) we can see that there is only a minor difference in the Rp0.2 obtained at values approaching σ max . At fractions of σ max where the solute content is low, the difference obtained between the two models is significant.
Fig. 6. 7010 C-curves based on non-isokinetic behaviour for fractions of σ max .
% of σ max
Measured (MPa)
Isokinetic model (MPa)
Non-isokinetic model (MPa)
96.7 93.0 72.3 61.0 32.6
507 482 379 320 171
517 488 396 332 141
509 483 379 318 163
4. Conclusions The Ives et al. approach of defining σ min as constant can extend quench factor analysis to 15% loss of the maximum property for alloy 7010-T76. The non-isokinetic model shows substantial improvement over the original Evancho and Staley model and demonstrates that the non-isokinetic approach to property prediction for 7010-T76 alloys is valid and extends the prediction to up to 70% loss of property. References [1] J.W. Evancho, J.T. Staley, Metall. Trans. 5 (1974) 43–48. [2] C.E. Bates, T. Landig, G. Seintanakis, Heat Treat. 17 (12) (1985) 13–17. [3] P. Archambault, J. Bouvaist, J.C. Chevrier, G. Beck, Mater. Sci. Eng. 43 (1980) 1–6. [4] P. Archambault, J.C. Chevrier, G. Beck, J. Bouvaist, Heat Treatment’76, Book 181, The Metals Society, 1976, pp. 105–109. [5] C.E. Bates, G.E. Totten, Heat Treat. Met. 4 (1988) 89–97. [6] J.D. Bernardin, I. Mudawar, Int. J. Heat Mass Transfer 38 (5) (1995) 863–873. [7] L.K. Ives, J. Swartzendruber, W.J. Boettinger, M. Rosen, S.D. Ridder, F. Biancaniello, R.C. Reno, D.B. Ballard, R. Mehrabian, NBSIR (1983) 83–2669. [8] J.T. Staley, M. Tiryakoglu, The use of TTP curves and quench factor analysis for property prediction in aluminium alloys, in: Proceedings of the Materials Solution Conference of ASM International, 2001, pp. 6–14. [9] Aerospace Material Specification, DTD5636, Materials Department, RAE, Farnborough, Procurement Executive, Ministry of Defence, UK, July 1989. [10] M.A. Reynolds, et al., Presentation of properties of a new high-strength aluminium alloy designated 7010, in: Proceedings of
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the Symposium on Aluminium Alloys in the Aircraft Industry, 1976, pp. 115–124. [11] H.P. Degischer, W. Lacom, A. Zahra, C.Y. Zahra, Z. Metallk. 71 (1980) 231. [12] W.L. Fink, L.A. Willey, Trans. Am. Inst. Mining Met. Eng. 175 (1947) 414–427. [13] J.W. Christian, The Theory of Transformations in Metals and Alloys, 2nd ed., Pergamon Press, Oxford, 1975.
[14] J.W. Cahn, Acta Metall. 4 (1956) 572–575. [15] P.A. Rometsch, M.J. Strarink, P.J. Gregson, Mater. Sci. Eng. A 339 (2003) 255–264. [16] J.T. Staley, Mater. Sci. Technol. 3 (1987) 923–935. [17] J.S. Robinson, R.L. Cudd, D.A. Tanner, G.P. Dolan, J. Mater. Process. Technol. 119 (2001) 261–267. [18] Ø. Grong, O.R. Myhr, Acta Mater. 48 (2000) 445–452.