Strain path dependence of the precipitate size evolution of an Al–Mg–Li alloy under combined thermal and mechanical loading

Materials Science and Engineering A363 (2003) 159–170

Strain path dependence of the precipitate size evolution of an Al–Mg–Li alloy under combined thermal and mechanical loading J. Murken1 , R. Höhner, B. Skrotzki∗ Ruhr-University Bochum, Department of Mechanical Engineering, Institute for Materials, 44780 Bochum, Germany Received 29 November 2002; received in revised form 14 July 2003

Abstract The microstructural evolution during combined thermal and mechanical loading of an Al–Mg–Li alloy was studied. Hot tensile tests that followed or were preceded by annealing experiments without any applied stress, along with interrupted creep tests, were carried out. The ␦ - and S1 - precipitate structure was characterized by TEM. The results show that in the microstructural evolution, the path to reach a fixed strain plays an important role; for a high creep stress, the ␦ -phase coarsens somewhat faster than under either combined thermal and mechanical loading or when isothermally aged without stress for the same time. The applied stress during creep affects the solute equilibrium concentration at the ␦ /Al-matrix interface and modifies the local growth rate. The S1 -phase is formed earlier in deformed microstructures due to heterogeneous nucleation at dislocations. © 2003 Elsevier B.V. All rights reserved. Keywords: Al–Mg–Li alloy; Creep; Aging; Precipitate growth; Precipitate coarsening; Phase stability

1. Introduction High strength aluminum alloys are hardened by finely dispersed second-phase particles, which are usually coherent or semi-coherent to the Al-matrix, and they are generally metastable. At elevated temperatures, these particles not only begin to grow and coarsen, but moreover can transform into their thermodynamically stable forms if the temperature is sufficiently high and enough time is given. A number of technical applications of Al-alloys require an increased improvement of thermal stability at elevated temperatures (up to 250 ◦ C for Al-alloys). Furthermore, components are usually exposed to mechanical loads as well (creep). This is often the case in aviation and space technology applications. Under creep conditions, the effect of stress and strain has to be considered as an additional parameter affecting growth and coarsening. Thermodynamic calculations have shown that coherency strains of misfitting precipitates sta∗ Corresponding author. Present address: Federal Institute for Materials Research and Testing, 12200 Berlin, Germany. Tel.: +49-30-8104-1520; fax: +49-30-8104-1527. E-mail address: [email protected] (B. Skrotzki). 1 SMS Demag AG, Wiesenstr. 30, 57271 Hilchenbach-Dahlbruch, Germany.

0921-5093/$ – see front matter © 2003 Elsevier B.V. All rights reserved. doi:10.1016/S0921-5093(03)00596-3

bilize a single-phase field, i.e. they shift the solvus line into the equilibrium two-phase field [1,2]. Externally imposed strains may change the stability of a phase and may move the solvus line either into the single-phase or two-phase region. Consequently, externally applied stresses and internal stresses associated with second-phase particles can affect nucleation, growth and coarsening of precipitates [1,2]. Only a few investigations have been reported on the growth and coarsening of precipitates under creep conditions of commercially viable precipitation hardened Al-alloys [3–5]. Single-phase model materials such as Al–11 wt.% Zn and Al–5 at.% Mg were extensively studied with respect to their macroscopic creep deformation behavior and the accompanying evolution of the microstructure [6–10]. These results, however, are only applicable to a small extent to technical Al-alloys. Recent studies on creep of precipitation hardened Al-alloys have placed greater emphasis on the measurement of mechanical creep data rather than directly evaluating the microstructural development of the precipitate structure [11–14]. We have therefore carried out a systematic study on the effect of stress on nucleation, growth, and coarsening of precipitates on different Al-alloys [15–21]. The main results of this study were that in the nucleation stage, precipitates are preferentially oriented on those crystallographic planes parallel to an external tensile stress

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when aging binary Al–Cu and quaternary Al–Cu–Mg–Ag alloys in the solution heat-treated condition [15]. There is a threshold stress which must be exceeded in order to orient precipitates on certain habit planes. The effect of an external stress on growth and coarsening of precipitates depends on the specific alloys and precipitates, respectively. Growth and coarsening of precipitates present in an Al–Cu–Mg–Ag and an Al–Si–Ge alloy were not affected by the creep parameters used in this study [16,18–21]. However, fresh nucleation of GeSi precipitates was observed under all creep conditions. In contrast, ␦ -precipitates present in an Al–Mg–Li alloy grew somewhat faster with an external stress applied than under stress free conditions [17,19,21]. Particle coarsening (Ostwald ripening) represents a softening process, which needs to be well understood in order to safely utilize components at high temperature. It is driven by the reduction of interfacial free energy, γ, stored in the particle-matrix interface, and follows a time law [22,23]. The coarsening rate is controlled by the concentration of solute atoms, c0 , and their transfer within the matrix governed by the diffusion coefficient of the solute in the matrix, Dm , if lattice diffusion is the rate controlling process. For the evolution of the particle radius, r, during coarsening, a quantitative description was presented by Lifshitz and Slyozov [22], and Wagner [23] (LSW), r¯ 3 − r¯03 =

9γc0 Dm Vm (t − t0 ) = k(t − t0 ) 8RT

(1)

with Vm being the molar volume, R the universal gas constant, T the temperature and (t − t0 ) the exposure time. Under creep conditions, stress and strain may affect parameters of Eq. (1): it is well known that there is a stress dependence of mass transport phenomena in metals. Generally, the diffusion coefficient also depends on hydrostatic pressure [24]. Eshelby developed a model, which described the elastic deformation of an inhomogeneity surrounded by a homogeneous elastic solid of infinite size due to an external elastic stress [25,26]. He calculated analytically how the inhomogeneity (with a higher stiffness than the matrix) affects the surrounding matrix. This model can be used as a first approach to analyze the stress field around spherical precipitates in an aluminum matrix. Hydrostatic tensile and compression stresses are developed around particles due to an applied external stress, and may change the interfacial equilibrium concentration and solubility around particles [27]. This can be illustrated with Eshelby’s model: if an external stress is applied to a system with a hard precipitate embedded in a soft matrix, then the matrix and the particle want to deform differently because their elastic constants are not the same. Consequently, hydrostatic tensile and compression stresses may arise at the interface. In addition, these stresses may result in an increased diffusion flux from areas under compression to those that are under tension which is analogous to Nabarro–Herring creep. Furthermore, supplementary vacancies for the diffusion flux are provided by grain boundaries and pores under

creep conditions [28]. Deformation processes are generally associated with an increase of the density of sessile and mobile dislocations and these may well provide diffusion paths which accelerate mass transport [29]. Thus, in a microstructure with particles in close contact with a constant number of dislocations, coarsening might take place by a combined process of volume and pipe diffusion [30]. These factors seem to be effective in increasing the coarsening rate. Other authors, however, claim that creep stress and strain have negligible effects on particle coarsening [31,32]. Nevertheless, several experimental studies on precipitation hardened Al-alloys have shown that particle coarsening and/or transformation of metastable precipitates into more thermodynamically stable forms can be accelerated if an external stress is applied during aging, i.e. under creep conditions [19,33–35]. Path dependence is also a potential contributor to overall precipitate growth behavior. Path-dependent behavior would dictate that observable differences in coarsening behavior will occur based upon differences in mechanical loading conditions with respect to aging treatments. Two examples of different loading circumstances would be conditions whereby (i) thermal and mechanical loading are simultaneously applied to a component, and (ii) mechanical loading is applied and accompanying strain is fully accumulated prior to the aging treatment of the component. The present paper addresses these specific treatments and investigates the associated path-dependent effects of combined thermal and mechanical loading on the microstructural evolution of an age-hardenable Al–Mg–Li alloy. The Al–Mg–Li alloy serves only as a model material providing metastable coherent precipitates possessing a small misfit and is not considered for applications at elevated temperature. Three relevant phases are formed in the ternary Al–Mg–Li system: (i) the metastable, spherical ␦ -phase Al3 Li (fully coherent, small misfit, L12 crystal structure), (ii) the equilibrium phases ␦-AlLi (cubic B32), and (iii) the equilibrium phase S1 -Al2 MgLi (incoherent, cubic). Compared to ␦ , precipitation of S1 takes place at higher temperatures or at much longer aging times [36]. Small amounts of Zr and Sc inhibit recrystallization during homogenization. These elements form the ␤-Al3 (Sc, Zr)-phase. In the present study, we focus on the ␦ and on the S1 -phase because in the chosen alloy, ␦ is the major strengthening phase in this alloy system. The formation of the Li-rich Al2 MgLi phase contributes to the detrimental effect to alloy ductility, fracture toughness, and corrosion resistance [37].

2. Experimental The nominal composition of the alloy used in this investigation is Al–5.8 wt.% Mg–1.5 wt.% Li–0.5 wt.% Zn–0.08 wt.% Sc–0.1 wt.% Zr. The material was hot rolled to a 4 mm thickness and solution heat-treated for 1 h at 480 ◦ C followed by a three-step aging representing the as-received

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Fig. 1. Schematic representation of different strain-time paths: nos. 1 and 5, hot tensile test followed by isothermal aging; nos. 2 and 6, creep test; no. 3, isothermal aging followed by hot tensile test; nos. 4 and 7, isothermal aging; no. 8, hot tensile test.

condition (three-step aging at 85, 120, and 100 ◦ C). In the present study, we address the question of path dependence by comparing material states which have achieved a certain degree of strain after a certain time in different ways. For the lower stress loading, three paths are considered, which are schematically shown in Fig. 1. The first one consists of a hot tensile test followed by stress free annealing (no. 1). In the second case, the specimen reaches the same strain in a normal creep test (no. 2). Finally, a third situation is considered, where a period of stress free annealing is followed by a hot tensile test (no. 3). The first two steps are also conducted for the high stress level (nos. 5 and 6). On one sample, a hot tensile test was carried out with no preceding or following aging treatment (no. 8). Further details are given in Table 1. Creep and tensile samples had a total length of 100 mm, a gauge length of 30 mm, a width of 3 mm, and a thickness corresponding to the sheet thickness. Further details with respect to creep testing are given in [21]. The creep tests (tension) were conducted at 120 ◦ C at constant load and stress levels of 220 and 280 MPa (rep-

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resenting 66 and 84% of the room temperature yield stress, or 75 and 95% of the yield stress at 120 ◦ C) and were interrupted after 3 and 4% total strain, respectively, by cooling down under load. The stress levels of the creep tests were chosen to allow comparison to previous studies on the effect of creep on nucleation and growth of precipitates in different Al alloys [15,16,20]. The hot tensile tests were carried out at 120 ◦ C at a constant deformation rate of 0.1 mm/min. The time to reach the fixed strains was 9 min and 12 min, respectively. The tests were stopped at the chosen strain levels, unloaded and quickly cooled to room temperature. The thermally and/or mechanically treated specimens were compared to samples, which were isothermally aged at 120 ◦ C without applied stress (nos. 4 and 7). The microstructure was characterized using a 200 kV Philips CM 20 transmission electron microscope (TEM). The foils were taken from the center of the tensile and creep specimens parallel to the stress direction. TEM images were taken from the precipitates in the bright field and dark field mode using a superlattice reflection. The ␦ -precipitates were characterized by their diameter, d, and the particle density, NV , which were obtained independently from TEM images. This was accomplished by transferring the TEM images onto a transparency and digitizing, followed by a quantitative image analysis. The particle density was estimated from the number of particles, Nt , found in the examined volume, V: Nt NV = (2) V The volume fraction, f, was calculated from the particle density and the average precipitate volume: 1 f = πd¯ 3 NV (3) 6 The density, ρ, of free (a/2) 1 1 0 dislocations in the Al-matrix is given by [38]: 2N ∗ ρ= (4) Lt

Table 1 Experimental data (average value and their standard deviation) characterizing the as-received and the deformed microstructures: mean ␦ -precipitate diameter, d, (linearization of the upper and lower bars lead to different distances to the median value), precipitate density, NV , precipitate volume fraction, fp , and dislocation density, ρ No.

σ (MPa)

Condition ε (%)

t (h)

a.r.

–

–

–

1

–

3

332

2

220

3

332

3

–

3

332

4

–

–

332

5

–

4

67

6

280

4

67

7

–

–

67

8

–

4

–

NV (103 ␮m−3 )

fp (%)

ρ (1013 m−2 )

54.8 ± 20.3

1.5 ± 0.6

1.6 ± 1.3

25.0 ± 3.0

4.9 ± 0.6

31.9 ± 4.7

22.4 ± 8.3

4.3 ± 1.6

16.0 ± 4.1

26.3 ± 4.6

5.1 ± 1.0

36.3 ± 4.1

24.7 ± 5.5

5.1 ± 1.6

23.2 ± 3.8

1.3 ± 0.2

28.1 ± 7.1

20.4 ± 6.2

1.4 ± 0.4

24.9 ± 2.4

33.0 ± 10.4

1.7 ± 0.5

d (nm) 8.1+1.4 −1.2

15.7+3.0 −2.2

15.3+2.8 −2.2

15.3+3.6 −2.8 15.3+3.3 −2.5 10.1+2.3 −1.9 +2.6 11.2−2.1 +2.3 10.4−1.7 –

–

–

–

– 42.1 ± 6.4

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N∗ is the number of intersections with dislocations made by random lines of length, L, in an area and t is the foil thickness. Images of dislocations were taken with g = {1 1 1} and g = {2 0 0} applying the weak beam technique. Naturally, not all variants of the (a/2) 1 1 0 dislocations are visible under two-beam conditions. Therefore, the dislocation density, ρ, was corrected [38] assuming a homogeneous distribution of dislocations and a mean value was calculated from both image conditions. The foil thickness was evaluated using convergent beam electron diffraction (CBED) techniques. The accuracy of this technique is ±2% [39]. In addition to the TEM observations, the changes in the microstructure were followed by electrical conductivity (applying the standard four-point potential method) and Vickers hardness measurements. X-ray diffraction studies were carried out with a Philips X’pert-MRD System using a copper target (λCu K␣ = 0.15405 nm) at 40 kV and 40 mA from which the lattice parameter of the Al-matrix is calculated using a modified Cohen’s method [40].

3. Results 3.1. Creep tests The creep curves for applied stresses of 220 and 280 MPa are represented as plastic strain versus exposure time in Fig. 2(a). The material behaves in a ductile manner and the strain rate versus strain curves in Fig. 2(b) exhibit a short primary regime characterized by a continuous decrease in creep rate until a regime with minimum strain rate is reached. At the higher stress level of 280 MPa, this minimum creep rate is about one order of magnitude higher than at 220 MPa. This results in a much shorter creep time of 67 h to reach the 4% fixed strain compared to 332 h to reach the 3% strain at 220 MPa. With increasing strain the creep rate rises again. 3.2. Microstructure of the as-received condition Optical microscopy (Fig. 3) revealed that the microstructure in the as-received condition is unrecrystallized with

Fig. 2. (a) Plastic creep strain vs. time and (b) strain rate vs. strain curves of the creep tests conducted at T = 120 ◦ C.

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Fig. 3. Optical micrograph of the as-received microstructure shows an unrecrystallized pancake structure.

pancake shaped grains due to the inhibition effect of Al3 (Zr, Sc). Fig. 4(a) shows a TEM micrograph of the homogeneously distributed spherical ␦ -precipitates within a subgrain of the as-received (a.r.) condition with an average diameter of 8.1 nm. Composite particles containing a spherical core of Al3 (Zr, Sc) enveloped by ␦ are also observed and some are marked by arrows. Fig. 4(b) reveals that the diameter of the ␦ -particles increases during creep. Coarsening of ␦ -precipitates takes place after isothermal aging with and without stress. Oriented coarsening under stress was neither observed (Fig. 4(b)) nor expected due to the spherical shape and the small misfit of ␦ . The S1 -phase is rarely seen in the as-received condition. It is noteworthy that these rare S1 -precipitates nucleate on smaller spherical particles with a diameter in the range of 20–50 nm as shown in Fig. 5(a) at lower magnifications and in Fig. 5(e) at higher magnifications. The S1 -precipitates nucleate heterogeneously during three-step aging on coarse, stable ␤-Al3 (Sc, Zr) particles formed during solidification (Fig. 5(e)) [41. Both the metastable ␤ -phase (L12 superlattice) and the stable ␤-phase (D023 lattice) may form in this system. The coherent ␤ -phase forms uniformly within the grains. Fig. 5(b) shows a dark field image of the incoherent ␤ particles, which are nonuniformly distributed due to the heterogeneous nucleation on dislocations and grain boundaries. EDS analysis of the spherical particles in Fig. 5(a) and (b) revealed that they are rich in Al, Sc, and Zr, which supports the conclusion that they are Al3 (Scx Zr1−x ). Fig. 5(c) shows a selected area diffraction (SAD) pattern of Fig. 5(b), while Fig. 5(d) shows the corresponding calculated diffraction pattern. In addition to the bright reflections of the Al-matrix, superlattice reflections are visible caused by the ␦ and ␤ phases. As both ␦ and ␤ have a L12 ordered crystal structure and the lattice parameters are almost identical, their reflections

Fig. 4. TEM dark field images show spherical ␦ -precipitates in (a) the as-received condition and (b) after creep (σ = 220 MPa, ε = 3%, t = 332 h).

cannot be separated. Furthermore, there are spots which can be attributed neither to Al nor to ␦ or ␤ (some marked by arrows in Fig. 5(c)). They were used for dark field imaging in Fig. 5(b) and therefore it can be concluded that they are most likely caused by the ␤-Al3 (Sc, Zr) particles. The hardening effect of the ␤ and ␤ phase is negligible and their number is very small. Therefore, their evolution was not studied. 3.3. Evolution of δ -precipitates The results of the quantitative image analysis are presented as a cumulative frequency distribution of the logarithm of the ␦ -precipitate diameter plotted in a probability net in Fig. 6(a). A straight line was fitted through the data points, which means that the logarithm of the diameters is approximately a Gaussian normal distribution. The average diameter (median) is given at Σ = 50%, the standard deviation lies in the range of 16–84%. Precipitate diameters and

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Fig. 5. The S1 -phase nucleates on ␤-Al3 (Sc, Zr) particles (marked by arrows): (a) bright field and (b) dark field TEM image, (c) shows the corresponding diffraction pattern, (d) the calculated diffraction pattern and (e) Bright field image at higher magnification.

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Fig. 6. (a) Evolution of the ␦ -precipitate size as cumulative frequency distribution, Σ, vs. logarithmic diameter, d, after isothermal stress free aging at T = 120 ◦ C. (b) Change of lattice parameter, a0 , electrical conductivity, κ, and Vickers hardness, HV vs. aging time during isothermal aging.

number densities as well as ␦ volume fractions are summarized for all conditions in Table 1. In the initial state (a.r.), the ␦ -particles are characterized by the smallest mean particle size (d = 8.1 nm) as expected. Subsequent isothermal stress free aging results in larger particle sizes (d = 10.4 nm after 67 h, d = 15.3 nm after 332 h, see Fig. 6(a) and Table 1). The volume fraction of ␦ increases from 1.5% in the a.r. condition to 5.1% after 332 h of aging at 120 ◦ C. Fig. 6(b) shows that concurrently, the lattice parameter of the Al-matrix decreases while both the hardness and the electrical conductivity increase. This implies that in the as-received condition (after three-step aging) there still exists a supersaturation of solute in the matrix and further precipitation of ␦ and/or S1 can take place. All values reach nearly a plateau after 500 h of aging. Fig. 7(a) summarizes the data obtained for the ␦ -precipitate size evolution after aging with and without stress. Table 1 and Fig. 7(a) reveal that (within the experimental scatter) nearly the same average diameter of 15 nm results

for all deformation paths when aged for 332 h (nos. 1–4). Compared to the as-received condition, the ␦ -precipitate diameter is nearly doubled after exposure. Table 1 also shows that during coarsening, the particle density falls from about 5.5 × 104 ␮m−3 in the as-received condition to about 2.5 × 104 ␮m−3 after 332 h exposure. At the same time, the ␦ -precipitate volume fraction rises from 1.5% in the initial state to about 5% in all aged and/or deformed conditions, which is in agreement with experimental data reported for binary Al–Li alloys [42]. The decreasing particle density agrees well with the classical Ostwald ripening theory; however, it assumes a constant volume fraction of particles. For the lower stress level, there is no additional effect of stress and strain as compared to stress-free aging. Table 1 also shows that hot deformation changes the dislocation density, ρ. Creep deformation at 220 MPa and 120 ◦ C to a creep strain of 3% (no. 2) raises ρ from 1.6 × 1013 m−2 in the as-received state to 1.6 × 1014 m−2 , i.e. by one order of magnitude. Fig. 8 shows a weak beam dark field image

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Fig. 7. (a) Evolution of the ␦ -precipitate diameter, d, after isothermal aging at T = 120 ◦ C with and without external stress applied. (b) ␦ -precipitate radii, r¯ 3 − r¯03 vs. aging time with (σ = 280 MPa) and without stress. Coarsening is somewhat faster under stress.

of dislocations of this deformed state (no. 2). The dislocations are homogeneously distributed within the subgrains. Although, the precipitates are not visible under these imaging conditions, it can be concluded from the wavy shape of

some dislocations (marked “b”) that they are in close proximity to precipitates. The arrow marked with “a” shows an Orowan loop which remains around a S1 -particle. Hot tensile tests following aging (no. 3) result in a much higher dislocation density of 3.63 × 1014 m−2 . However, aging following the hot tensile tests (no. 1) might cause some recovery and ρ is somewhat lower (3.19 × 1014 m−2 ). Compared to isothermally aged samples without stress (no. 4), neither crept (no. 2) nor deformed conditions followed (no. 1) or preceded (no. 3) by aging exhibit an accelerated coarsening after identical aging times. Results of the quantitative image analysis of samples crept at a higher stress are summarized in Fig. 7(a) and Table 1 as well. These data are again being compared to the as-received condition and to the thermally and/or mechanically treated conditions. The aging time was only 67 h, i.e. much shorter than in the case of the lower applied stress. Fig. 7(a) shows that creep (no. 6 in Table 1) results in slightly higher ␦ -precipitate diameters as compared to pure isothermal aging (no. 7) or 4% hot deformation followed by aging (no. 5). Compared to the as-received state, the volume fraction of precipitates does not rise significantly, as shown in Table 1. In Fig. 7(b), the cube of the average radii of the ␦ -precipitates is plotted vsersus aging and creep time according to the LSW relation, Eq. (1). The straight lines represent a fit. Different exponents varying between two and five were used to plot (r n − r0n ) versus time, but n = 3 yielded the best fit. Fig. 7(b) illustrates that coarsening with stress (σ = 280 MPa) is somewhat faster than under stress free conditions. This result confirms our observations made in a previous study, which had also shown that aging under stress accelerates coarsening of ␦ [17,19]. This small effect was only observed at the higher stress level and therefore suggests that there might exist a critical external

Fig. 8. Weak beam dark field image of dislocations in the Al-matrix after creep (σ = 220 MPa, ε = 3%, t = 332 h). g = (0 0 2).

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stress, which must be exceeded in order to accelerate the coarsening rate noticeably at a given temperature. 3.4. Evolution of the S1 -phase In the as-received condition, the S1 -phase was observed within the subgrains and rarely at subgrain boundaries. The number of S1 -precipitates is small and their distribution varies from grain to grain (Fig. 5(a)). A remarkable change of the morphology of S1 was not observed for stress free isothermal aging, neither after 67 h nor after 332 h exposure. Fig. 9(b) illustrates the S1 -microstructure after creep at σ = 220 MPa/120 ◦ C for 332 h. The microstructure of the crept

167

specimen (Fig. 9(b)) exhibits a considerably higher number of coarse precipitates when compared to specimens aged for the same time without stress (Fig. 9(a)). These predominately rod shaped precipitates extend mainly parallel to the 1 1 0 Al directions. They were observed within the grains as well as at grain boundaries and they are more uniformly distributed within the subgrains than those observed in the as-received condition (cf. Fig. 5(a)). The occurrence of the S1 -phase in the as-received condition was explained by heterogeneous nucleation at ␤-precipitates (see above). It is reasonable to assume that additional nucleation and growth of rod shaped particles within the subgrains observed after prolonged creep is caused by heterogeneous nucleation at

Fig. 9. TEM micrographs showing the evolution of the S1 -precipitates: (a) after stress free aging for 332 h at 120 ◦ C ([1 1 0]Al -zone axis, g = (1 1 1)); (b) aging with stress (σ = 220 MPa/ε = 3%/t = 332 h/120 ◦ C) results in a higher number of rod shaped S1 particles extending mainly parallel to 1 1 0 Al ([1 1 0]Al -zone axis, g = (2 2 0)).

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dislocations. The density of free dislocations increases by one order of magnitude, and therefore they provide a sufficient number of uniformly distributed nucleation sites. A similar observation was made for the hot tensile test followed by isothermal aging for 332 h (path no. 1). Here again a high number of S1 is present which nucleates at dislocations that are present in a higher density after deformation. After loading path no. 5, S1 was only found on subgrain boundaries. The aging time (67 h) was probably too short to form precipitates homogeneously within the subgrains. Aging during creep (σ = 280 MPa, 67 h; no. 6) results in a noticeable formation of equiaxed S1 -particles at grain boundaries (not shown).

4. Discussion Before discussing the ␦ -precipitate coarsening, we will address the perhaps somewhat surprising fact that the ␦ volume fraction changes considerably during aging. Particle coarsening, or Ostwald ripening, means that, driven by the release of excess interfacial free energy, larger precipitates grow at the expense of smaller ones, which dissolve. At the same time, the precipitate size distribution changes and the number density decreases. To describe coarsening by applying the Lifshitz-Slyozov-Wagner (LSW) equation given in Eq. (1), a number of assumption are made: (1) the volume fraction of precipitates is small (fp ≈ 0), (2) fp ≈ const. (i.e. the supersaturation c ≈ 0), and (3) the linearized form of the Gibbs-Thomson equation may be used. For finite particle volume fractions, the growth rate of an individual precipitate depends on its local environment. Computer simulations have shown that regardless of fp , the cube of the particle diameter coarsens linearly with time, but the constant k in (1) depends on the particle volume fraction [43–45]. In addition, the precipitate size distribution becomes flatter and broader at larger fp . It is clear from Table 1 that for longer aging times, the volume fraction of ␦ is not a constant. The lattice parameter, the electrical conductivity, and the hardness change considerably as compared to the as received condition (Fig. 6b). This is due to ␦ coarsening and to the formation of S1 . The lattice parameter decreases if the supersaturation of the Al-matrix is reduced by the formation of precipitates. At the same time, the electrical conductivity increases. The higher volume fraction of ␦ (and the precipitation of S1 ) further strengthen the Al-alloy and result in an increase of the Vickers hardness. It is a common assumption that coarsening starts after the precipitation reaction is completed. However, several authors have pointed out that nucleation, growth and coarsening must be seen as competing and overlapping processes [43,46]. The number density decreases already during the precipitate reaction, i.e. Ostwald ripening can start even while the average solute content (in at.%) in the matrix, c¯ ␣ , is still significantly higher than the Gibbs-Thomson solubility, c␣ (¯r ), and the precipitate volume fraction is still increasing

[46]. c¯ ␣ is initially the alloy content and c␣ (¯r ) is the solute concentration corresponding to the average particle radius, r¯ . The process is pure coarsening only if c¯ ␣ ≈ c␣ (¯r ), but the volume fraction of precipitates will still increase due to the change of the Gibbs–Thomson solubility. Martin et al. [46] have pointed out that the solubility increases significantly for very finely dispersed systems as the mean particle radius grows. The equilibrium volume fraction of precipitates, fe , according to the lever rule will not be achieved until r¯ → ∞: fe =

c0 − c␣ c␤ − c ␣

(5)

where c0 is the solute content of the alloy, and c␣ and c␤ are the equilibrium solubility of the ␣-matrix and the ␤-precipitate, respectively [46]. The particle volume fraction develops with time as follows: fp (t) =

c0 − c␣ (¯r ) c␤ − c ␣

(6)

From Table 1 we see that the number density of ␦ decreases for all aging paths. This implies that coarsening (and not growth) of ␦ takes place, although the volume fraction still changes. The results of the present study have shown that a somewhat accelerated coarsening of ␦ -precipitates is only observed during creep and only if a high enough stress is applied (effect only noticeable for path no. 6). The particles do not coarsen faster after a hot tensile test followed by isothermal aging (no. 1 and 5), although the mean particle distance (λp = d/f 1/2 = 66 nm) of the as-received condition is in the same order of magnitude as the mean dislocation distance after conducting a hot tensile test (λd = 1/ρ1/2 = 56 nm for path no. 1 and 60 nm for path no. 5). This means that the probability is high that precipitates are in close contact with dislocations and Fig. 8 shows that this is the case. This implies that the higher dislocation density does not accelerate coarsening after deformation, i.e. by pipe diffusion. Lattice diffusion seems to be the rate controlling process for coarsening which can be attributed to the relatively high aging temperature (120 ◦ C is a commonly used aging temperature for this alloy). Pipe diffusion, however, is known to be especially contributing at low temperatures. We therefore conclude (1) that the applied stress is responsible for the higher coarsening rate during creep and (2) that it does indeed depend on the path to reach the fixed strain. A minimum stress is required (220 MPa is not sufficient) and this stress has to assist aging.The local diffusion flux in a solid is influenced by chemical inhomogeneities. Internal and external stresses can affect diffusion as well. Generally, a hydrostatic pressure affects the mobility of atoms in a solid and the relation between stress and diffusion is well known [24]. If pressure is increased, the material loses vacancies to relieve the pressure increase, which in turn decreases the diffusion coefficient. This, however, cannot explain the accelerated coarsening observed in this investigation.

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On the other hand, the applied stress affects the diffusion potential, MBA , which is the difference in the chemical potential of the components, µi [48]: MBA (T, σij , xB ) = µB (T, xB ) − µA (T, 1 − xB ) − 13 (ΩB − ΩA )σkk

(7)

where T is the temperature, xB the mole fraction of the component B, Ωi the atomic volume of the components, σ ij the stress tensor, and σ kk the trace of the stress tensor. Recent theoretical approaches conclude that the elastic strain energy resulting from internal and external stresses is part of the chemical potential as well [49]. A system with a precipitate, which grows into a supersaturated matrix is not in thermodynamic equilibrium. This is due to gradients in chemical or diffusion potential that give rise to mass diffusion and alter the size of precipitates. Applying an external stress changes the local values of the diffusion potential within each of the phases and at the interface. Johnson [27] has shown by conducting thermodynamic calculations that the equilibrium concentration at the interface of a coherent precipitate in a matrix is a function of position along the interface in the presence of an applied stress. The external stress field modifies the local growth rate (and may even result in a shape change of the precipitate, e.g. rafting of ␥ in Ni-base superalloys). In addition, the external stress field changes the relative stability of the precipitate and of the parent phase and, consequently, the precipitate has a tendency to either grow or dissolve. So far, we have only discussed the coarsening behavior of the ␦ phase. However, under certain conditions, rod shaped S1 -precipitates form parallel to 1 1 0 Al , that is during creep (path nos. 2 and 6) or on isothermal aging following a tensile test (nos. 1 and 5). The narrow zones free of ␦ around the S1 particles (not shown) indicate that S1 is formed at the expense of ␦ . Under these conditions, i.e. if a higher dislocation density is present in the material, S1 is formed after shorter aging times and more homogeneously than after comparable isothermal stress free aging. This is due to the higher dislocation density, which provides heterogeneous nucleation sites for S1 and thus reduces the required activation energy. This process is well known and intentionally used in a number of commercial age-hardenable aluminum alloys (e.g. stretching of sheets) to produce particles in a finer dispersion than in unstretched products. However, in the material studied here, the formation of S1 should be avoided because it results in a degradation of the mechanical properties [47], although this aspect was not studied in further detail in the present work.

quantitative image analysis. The microstructure of samples aged (σ = 0) prior to or after conducting hot tensile tests, and aged during a creep test, respectively, were compared to conditions after isothermal stress free aging. The results demonstrate the following: (i) The ␦ phase coarsens somewhat faster under creep conditions than under combined thermal and mechanical loading or under comparable stress free isothermal aging. This effect was only observed for the higher stress load. (ii) The accelerated coarsening of ␦ is attributed to the applied stress during creep, which affects the solute equilibrium concentration at the interface and modifies the local growth rate. (iii) A higher dislocation density caused by plastic deformation developed during creep or hot tensile tests results in the early precipitation of the S1 -phase as compared to unstrained aging. This can be ascribed to the dislocations serving as heterogeneous nucleation sites. (iv) The experimental data show that the path to reach a fixed strain does indeed play an important role in the microstructural evolution. Although no mechanical characterization has been carried out for the different aging treatments, it is expected that the resulting data will differ.

Acknowledgements The authors gratefully acknowledge funding by the “Deutsche Forschungsgemeinschaft” (DFG Sk 47/1-1 and 47/1-2). We wish to thank Prof. G. Eggeler for providing the motivation for this work. We thank EADS Deutschland GmbH, Ottobrunn, for supplying the Al–Mg–Li material. References [1] [2] [3] [4] [5] [6]

[7] [8] [9] [10] [11]

5. Summary and conclusions The microstructural evolution during combined thermal and mechanical loading of an Al–Mg–Li alloy was studied by means of transmission electron microscopy and by

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