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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J. Murken et al. / Materials Science and Engineering A363 (2003) 159–170
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),
r̄3 − r̄03 =
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
J. Murken et al. / Materials Science and Engineering A363 (2003) 159–170
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-
161
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 = πd̄ 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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J. Murken et al. / Materials Science and Engineering A363 (2003) 159–170
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.
J. Murken et al. / Materials Science and Engineering A363 (2003) 159–170
163
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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J. Murken et al. / Materials Science and Engineering A363 (2003) 159–170
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.
J. Murken et al. / Materials Science and Engineering A363 (2003) 159–170
165
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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J. Murken et al. / Materials Science and Engineering A363 (2003) 159–170
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, r̄3 − r̄03 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).
J. Murken et al. / Materials Science and Engineering A363 (2003) 159–170
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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J. Murken et al. / Materials Science and Engineering A363 (2003) 159–170
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, c̄␣ , is
still significantly higher than the Gibbs-Thomson solubility,
c␣ (r̄), and the precipitate volume fraction is still increasing
[46]. c̄␣ is initially the alloy content and c␣ (r̄) is the solute
concentration corresponding to the average particle radius,
r̄. The process is pure coarsening only if c̄␣ ≈ c␣ (r̄), 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 r̄ → ∞:
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␣ (r̄)
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.
J. Murken et al. / Materials Science and Engineering A363 (2003) 159–170
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.
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