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Materials Science and Engineering A 397 (2005) 195–203

Application of ANOVA method to precipitation behaviour studies

Z. Cvijovic a,∗, G. Radenkovic b, V. Maksimovic c, B. Dimcic c

a Department of Metallurgical Engineering, Faculty of Technology and Metallurgy, University of Belgrade, 11120 Belgrade,

Karnegijeva 4, Serbia and Montenegrob Faculty of Mechanical Engineering, University of Niˇ s, 18000 Niˇ s, A. Medvedeva 14, Serbia and Montenegro

c Department of Materials Science, Institute of Nuclear Sciences “Vinˇ ca”, 11001 Belgrade, Serbia and Montenegro

Received 23 August 2004; received in revised form 4 February 2005; accepted 11 February 2005

Abstract

The Analysis of variance (ANOVA) method has been used to illustrate the implementation of adaptive numerical (AN) techniques for

the prediction of the precipitation behaviour of commercial materials. Case studies involving the analysis of -phase precipitation kinetics

in duplex stainless steel (DSS) produced by sand casting and age hardening of 2219 aluminium alloy microalloyed with Ge and/or Si are

presented. For each alloy, complex datasets comprised the results obtained from heat treatment trials on a range of commercial processing

conditions, so that a single and combined effect of various parameters can be determined. This enabled an estimate of the most influential

parameters to be made, providing an effective means of commercial alloy development and process optimisation.

© 2005 Elsevier B.V. All rights reserved.

Keywords: Duplex stainless steel; Modified 2219 alloy; Precipitation behaviour; -Phase; Si–Ge particle; ANOVA method

1. Introduction

The precipitation behaviour of metallic alloys is known to

depend on many process variables, including composition,

cooling rate, temperature, time, etc. Due to the complexity

of the relationships between these variables and precipitation

kinetics, the optimisation and accurate prediction of the pre-

cipitation process and, therefore, the properties are difficult.

In order to obtain the desired properties, it is necessary to

determine a single and combined effect of various parame-

ters, which would allow the correct choice of the processing

parameters. If there are not enough data, a large number of

expensive and time-consuming experiments need to be car-ried out. To solve this problem, the calculation and modelling

of the precipitation kinetics would be applied.

In the last few years, there has been a constantly increas-

ing interest in adaptive numeric (AN) modelling in different

fields of materials science [1–3]. The physically based ap-

proach is only possible in a limited number of cases where a

∗ Corresponding author. Tel.: +381 11 3370 469; fax: +381 11 3370 387.

E-mail address: [email protected] (Z. Cvijovic).

physical understanding of the processes and model parame-ters/physical constants are accurately known. For more com-

plex situations, with many interrelated variables and where

the mathematical relationships between model inputs and the

output parameter are not clear, an AN approach to modelling

mayprovide a variety of complex (usually non-linear) mathe-

matical relationships which equally well predict the observed

data distributions, although the underlying mechanisms are

not easily visualised from these relationships. In addition, the

use of various AN modelling techniques enables a successful

interpretation of available datasets of different sizes, so that

this approach to modelling may have to be performed even

with data that are limited, or badly distributed, or both.The examples presented in this paper illustrate how the

Analysis of variance (ANOVA) technique can be successful

in analysing selected aspects of precipitation behaviour of

alloys for different composition/processing combinations. In

one case, we consider the dataset on the amount of -phase

for duplex stainless steel (DSS) in various microstructural

states achieved by different heat treatment regimes, with the

objective to predict the kinetics of secondary phases (SP)

precipitation in one of the most commonly used DSSs. The

0921-5093/$ – see front matter © 2005 Elsevier B.V. All rights reserved.

doi:10.1016/j.msea.2005.02.021



196 Z. Cvijovi´ c et al. / Materials Science and Engineering A 397 (2005) 195–203

modelling was motivated by the desire to provide a more

complete understanding of the variations in pitting corrosion

resistance under particular microstructural states, which is

regarded to be of crucial importance in DSSs applications.

Since the severity of corrosion attack depends on the nature

and amount of SP precipitates, a thorough knowledge of the

kinetics of precipitate formation is important in determiningthe heat treatment and cooling rates required during produc-

tion to ensure precipitate-free parts.

In another case, we will present results on the predic-

tion of age-hardening response of the commercial 2219 alu-

minium alloy microalloyed with small additions of Ge and/or

Si, using data on the hardness obtained for each alloy vari-

ant and different aging treatments. Recent studies of exper-

imental Al–Si–Ge–Cu alloys designed in such a way as to

enhance the artificial age-hardening characteristics [4] have

shown that the precipitation of Si–Ge particles can be used to

improve the strengthening potential of 2xxx alloys. But, al-

though there are several reports on theprecipitation processes

in quaternary Al–Cu–Si–Ge alloy [5,6], further improvementof the mechanical properties of commercial alloys as well as

process optimisation require a broad integrated experimen-

tal and modelling investigation. Thus, the present work aims

at obtaining new knowledge on the precipitation-hardening

behaviour of the commercial Al–Cu-based alloys modified

by Si–Ge additions and applying the ANOVA approach to

identify the most influential parameters.

2. ANOVA method

A novel way to determine the influence of any given inputparameter on the precipitation process from a series of exper-

imental results is to employ the design of experiment (DoE)

approach. The decisions, concerning which parameters affect

the response of investigated process are made with assistance

of various analytical techniques. Analysis of variance will be

the predominant statistical method used to interpret experi-

mental data, since this method is most objective [7,8]. It is

designed to represent a concept that any high dimensional

function may be broken down into a subset of terms from the

expansion:

f (x) = f o +n

i=1

f i(xi)+n

i=1

n

j=i+1

f i,j(xi, xj)+ . . .

+f 1,2,...,n(x) (1)

where n represents the number of inputs, f o is a constant (bias

term) and the other terms on the right hand side represent the

univariate, bivariate, trivariate, etc., functional combinations

of the input parameters.

Analysis of variance (V ), namely, is a mathematical tech-

nique, which partitions the total variation into its appropriate

components. Thus, the total variation of the system, defined

by the total sum of squares term:

SST =

y2

i , for i = 1, 2, . . . , n, (2)

can be given as:

SST = SSm + SSe (3)

where SSm = nM 2 and SSe = ( yi− M )2 are the mean sum

of squares and the error sum of squares, respectively, with

M = 1/ n yi(i = 1,2, . . ., n). In the case of two-way ANOVA,

when the interaction effect of main factors affects the out-

put values, the total variation may be decomposed into more

components:

SST = SSA + SSB + SSAB + SSe (4)

where SSA = ( A1 − A2) and SSB = ( B1 − B2) are varia-

tions due to the factors A and B, respectively, while

SSAB = ( AB)i2 / nABi for i = 1, 2, . . ., k is variation due to

the interaction of factors A and B, where k represents the

number of possible combinations of interacting factors andnABi is the number of data points under this condition.

However, for complete ANOVA calculations, degrees of

freedom (d.f.) should also be considered together with each

sum of squares. As ANOVA studies are in fact experimen-

tal studies with certain test error (Err), the determination of

error variance is an essential step in such studies. Similarly,

the sample variance within the factor levels should be calcu-

lated since the sample size establishes the confidence level

of the results derived from the analysis. These data are sub-

sequently used to estimate the value F of the Fisher test (F -

test). The portion of total variation observed in an experi-

ment attributed to each significant factor and/or interactionis reflected in the percent contribution (P), which indicates

the relative power of a factor and/or interaction to reduce

variation, i.e. factors and interactions with substantial per-

cent contribution are the most important. A more detailed

description of the ANOVA method is given in the literature

[7,8].

3. Analysing precipitation behaviours of selected

alloys

3.1. Case 1: -phase precipitation in DSS

DSSs composed of -ferrite and -austenite offer a great

combination of properties, so that they are suitable for

many industrial applications [9,10]. During inappropriate

heat treatment or prolonged exposure at elevated tempera-

ture, the precipitation of various secondary phases, like sec-

ondary austenite (2), chromium carbides, nitrides, -phase

and other intermetallic phases [11–14] can take place, caus-

ing the time-dependent degradation of the material and par-

ticularly its pitting corrosion resistance [15–17]. Of the SP

mentioned above, -phase has the most deleterious effect

because of its large volume fraction. Since the tendency



Z. Cvijovi´ c et al. / Materials Science and Engineering A 397 (2005) 195–203 197

toward -phase formation, as well as its precipitation ki-

netics, mechanism and stability range may vary consider-

ably depending on the exact composition and microstruc-

tural state of steel [12,17–20], it is necessary to clarify

the behaviour of -phase precipitation in highly alloyed

DSSs.

3.1.1. Material and experimental procedure

The steel with main composition in mass% 27Cr–6.7Ni–

2.1Mo–2.8Cu–0.12N–0.085C–bal Fe was supplied by the

manufacturer in the form of a 20 kg sand cast (SC) Y-block.

To reveal microstructure, metallographic samples taken from

the central region of SC block were prepared for light opti-

cal microscopy (LOM) by grinding and polishing, using dia-

mond pastes of 3, 1 and 0.25 m. The polished sections were

then electrolytically etched at 1–3 V for 15 s in 10% NaOH

aqueous solution that etches-ferrite blue-light brown, while

-austenite remains virtually uncoloured.

The initial microstructure of the as-received SC block is

presented in Fig. 1a. It consists of the large and elongated -platelets inhomogeneously distributed in the -ferrite matrix,

although some globular or rod-like particles of intragranular

austenite (i) are also visible. Additionally, the etchant used,

which tints precipitates brownish-red, revealed the presence

of SP particles. The rows of these fine particles nucleated

along the slightly curved / -interfaces and thin films of

secondary austenite (2) immediately adjacent to them are

consistent with a proposed model for the cooperative precip-

itation of Cr-rich M23C6 carbide and 2 [21–24]. The low

cooling rate of the order 10−1 to 101 K/s, related to conven-

tional casting process [25], and a C content higher than that

of most duplex grades makes investigated steel more feasiblefor carbide to precipitate.

Thetotal amount of precipitates was determined by means

of image analysis. The volume fraction of phases present,

V V, was measured by line-intercept method using the Kon-

tron semi-automatic systemattachedto a Reichert MeF3 light

microscope. A confidence interval of 95% was used for mea-

surementstakenat a magnificationof 500times. Theobtained

data show that after casting the microstructure of investi-

gated steel consists of a -ferrite matrix with 33.5 vol.% ,

2.1 vol.% (M23C6 +2) mixed structure and small amounts

of non-metallic inclusions.

In order to eliminate the SP precipitation and produce a

duplex (+) microstructure, the base SC material was so-

lution treated (ST) at 1150 ◦C for 60 min, followed by water

quenching. After this heat treatment, the only phases present,

except non-metallic inclusions, are and . At the same

time, the → transformation occurred, so that a ratio of

:= 70.5:29.5 was obtained.

Subsequently, this steel in both as-cast and as-cast with

1-h long solution-treatment states was subjected to isother-

mally annealing at 800, 850, 900 and 950 ◦C for 15 and

60 min, followed by water quenching. The microstructural

changes that occur on annealing are determined using image

analysis.

Fig. 1. Micrographs of sand cast block before (a) and after 60 min of an-

nealing at 800 ◦C (b) and 950 ◦C (c), showing the presence of austenite ()

platelets, intragranular austenite (i), -phase and mixed constituent (M) of

M23C6 carbide and secondary austenite (2) in the matrix of -ferrite.




Table 1

The results of image analysis

Microstructural state Volume fraction of -phase (vol.%)

800 ◦C 850 ◦C 900 ◦C 950 ◦C

15 min 60 min 15 min 60 min 15 min 60 min 15 min 60 min

As-cast 0.14 24.34 1.61 33.16 1.19 21.47 0.31 1.29

ST 0.25 16.72 1.52 30.96 0.82 11.66 – 0.97

3.1.2. Microstructural data

During annealing the2, M23C6 carbide and-phase were

formed (Fig. 1b and c). The precipitation proceeds exten-

sively causing a drastic decrease in the volume fraction of re-

tained -ferrite. At each temperature, the first transformation

product is M23C6. This was particularly evident in the ST ma-

terial. At later stages, the -phase formation was observed to

occur. Although the nucleation of carbide is more favourable

and faster than the nucleation of -phase, the vast major-

ity of particles precipitated on the curved / -boundariesas the highly preferred sites for nucleation [26] are found

to be -phase. The -phase formation mechanism changes

with annealing temperature [11,18,24,27]. At temperatures

up to 900 ◦C, the -phase forms by the eutectoid reaction

→+2 (Fig. 1b), while at higher temperatures by an in

situ transformation (Fig. 1c). This observation is supported

by the fact that the composition of -phase varies over a wide

range of concentrations of its component elements [28], so

that at 950 ◦C, the shorter the time needed for the -phase to

achieve equilibrium of the chemical composition. As a con-

sequence, an in situ transformation of the - to -phase is

favoured.

The extent and kinetics of -phase precipitation vary sig-nificantly with annealing condition and with the initial mi-

crostructural state of DSS. The volume fractions of -phase

after annealing treatments (V V ), measured for 16 microstruc-

tural state-annealing treatment combinations, are presented

in Table 1. The most influential parameter is determined by

applying the AN modelling approach. Namely, the datasets

on the volume fraction of -phase contained up to 32 data

lines were further analysed using the ANOVA method.

3.1.3. ANOVA analysis

The ANOVA analyses were done with software package

“Design of experiment” V1.0 CIM College. The univariate

terms shown in Fig.2 reflect relations between annealing tem-

perature, annealing time and initial microstructural state of

the steel on the one hand and -phase fraction on the other.

It may be seen that for a given set of inputs (microstruc-

tural state whose levels are as-cast and solution treated, four

levels for temperature, namely from 800 to 950 ◦C in steps

of 50

◦

C, and two levels of time, namely 15 and 60 min), theconstructed model selected theannealing time as the main pa-

rameter influencing -phase precipitation behaviour, whilst

to a much lesser extent the annealing temperature can play a

role.

However,the influence of the annealingtemperature varies

with different levels. On the other hand, the process kinetics

are only slightly affected by variations in matrix homogene-

ity. Namely, the influence of single parameter is stronger as

the slope of the targed line is larger.The results of the analysis

of variance presented in Table 2 show that a bivariate term

combining annealing temperature and time, along with an

univariate term for temperature had a statistically significant

influence in the final fraction of -phase. It should be notedthat the P-value obtained for annealing time is almost twice

that for the annealing temperature or the combination of an-

nealing temperature and time. A combined effect of anneal-

ing temperature and time on -phase fraction is presented

in Fig. 3. As can be seen, the -phase fraction was unaf-

fected by the annealing time increase up to 15 min, due to

the sluggish kinetics of the reaction at all temperatures in the

investigated range. When the annealing time was increased to

Fig. 2. Univariate subfunctions, showing the influence of (a) annealing temperature, (b) annealing time and (c) initial microstructural state of steel on the

-phase fraction.




Table 2

Summary of the results obtained by the ANOVA analysis used for the -phase precipitation investigated

Source SS d.f. V F P

Temperature 1061.56 3 353.85 −316782.60 24.16

Time 2269.02 1 2269.02 −2031317.00 51.64

State 53.10 1 53.10 −47533.30 1.21

Temperature× time 904.02 3 301.34 −269771.20 20.57

Temperature× state 29.74 3 9.91 −8874.14 0.68Time× state 46.51 1 46.51 −41639.75 1.06

Temperature× time× state 30.14 3 10.05 −8995.39 0.69

Err −0.02 16 0.00 0.00

Total 4394.10 31 100.0

Fig. 3. Bivariate subfunction, showing a combined influence of annealing

temperature and time on the -phase fraction.

60 min, the temperature is much more important. It is further

noted that this model can be applied to predict the maximum

volume fraction of -phase, which is reached after 60 min of

annealing as-cast DSS in the temperature range from 850 to

880 ◦C.

3.2. Case 2: age-hardening of modified 2219 Al-alloy

The Al–Cu alloys of the 2xxx series have been widely

studied due to their excellent mechanical properties devel-

oped by age-hardening. Upon aging, the 2219 alloy displays

the well-known precipitation sequence [29]:

Supersaturated solid solution

→ GP zones → θ → θ → θ(Al2Cu).

Si, Mn, Be, Sn, Ag and Cd additions are known to influence

metastable phase formation and can, therefore, have a large

effect on the precipitation kinetics and mechanical properties

[30–33].

Renewed interest in this system was stimulated by stud-

ies of the rapid hardening that occurs in base Al–Si–Ge

alloys and the observation that this effect is enhanced by

Cu additions. Recently, it has been shown that the resul-

tant Al–Cu–Si–Ge alloys show very fast aging response, high

peak hardness and better microstructural stability after pro-

longed aging [4,6]. This was attributed to the formation of

Si–Ge precipitates which act as heterogeneous sites for nu-

cleation of phase. Mitlin et al. [4] identified precipitates

by high-resolution electron microscopy (HREM) in contact

with multiply twinned Si–Ge particles after aging for 3 h at

190 ◦C. Si–Ge particles nucleate quickly and they were de-

tected after as little as 30 min at 190 ◦C [6]. The comparison

of the hardening curves for the two laboratory Al–Cu–Si–Ge

alloys aged at 190 ◦C with that of the commercial alloy 2219

or of the alloy 2014 in their T6 peak-aged condition showedthat both Al–Cu–Si–Ge alloys with different Cu level and

(Si + Ge) content on equiatomic proportions possess signifi-

cantly higher peak hardness [4]. Additionally, they achieved

maximum hardness at a shorter aging time (for example, after

3 h instead of the 8 h required for 2219 alloy), while overaged

at a rate similar to 2219 alloy. In contrast, alloy 2014 which

is not known to display high-temperature stability overaged

relatively quickly. These observations indicate that microal-

loying with Si and Ge may be used to produce higher precip-

itation hardening than that which occurs in the commercial

2xxx alloys, andit is importantto investigate theeffect of vari-

ous parameters on the precipitation behaviour of these alloys.

3.2.1. Selection of alloys and experimental details

For this purpose, two laboratory alloys were prepared by

adding small amounts of Ge and/or Si to the 2219 commer-

Table 3

Chemical compositions of modified 2219 alloys used in the present study

Alloy designation Element (mass%)

Cu Ge Si Fe Mn Mg Zn Ti Zr V Cr

2219S 5.91 – 0.51 0.24 0.28 0.01 0.05 0.08 0.12 0.09 0.007

2219SG 5.90 0.69 0.28 0.26 0.29 0.01 0.06 0.08 0.13 0.09 0.007




Fig. 4. Hardness–time curves for the 2219S and 2219SG alloys aged at

190 ◦C.

cial base alloy produced by Kaiser Aluminium Company, i.e.one alloy (designated as 2219S) with about 0.5 at.% Si and

another alloy with 0.27 at.% Si and 0.26 at.% Ge (designated

as 2219SG). The equiatomic proportions of Si and Ge were

chosen because the Si and Ge solute atoms have misfits of

opposite sign in Al, thus, contributing significantly to the re-

duction of the elastic strains produced in the matrix and the

precipitate [34]. The chemical compositions of the investi-

gated alloys are given in Table 3.

Thealloys were hot-rolled from 27 to 2 mm in thicknessaf-

ter homogenisation for 48 h at 500 ◦C and subsequently sub-

jected to annealing for 24 h at 500 ◦C, water quenching and

holding at room temperature for 9 days. Two different artifi-cial aging treatments followed after the natural aging: (1) the

samples were aged at 190 ◦C for times ranging from 10 min

to 200 h; (2) the samples were kept at 50, 75 and 100 ◦C for

30 min, 1 and 2 h after which they were aged at 190 ◦C for

times ranging from 15 min to 256 h. Aging at 190◦C was

chosen as the main temperature of investigation due to its

relevance to commercial applications. The age-hardening re-

sponse of the alloys was evaluated by Vickers hardness mea-

surements using a load of 98.1 N load.

The microstructures of the samples in the underaged, peak

hardness and overaged conditions were examined with JEOL

200CX and PHILIPS CM200-FEG analytical electron mi-

croscopies operated at 200 kV. Transmission electron mi-

croscopy (TEM) samples were prepared by grinding slices

to a thickness between 125 and 150m, then by twin-jet

electropolishing using a 25% nitric acid–methanol solution

at temperature of −25 ◦C. In order to estimate the chemical

composition of precipitates, the EDS microchemical analyses

were done in a CM200-FEG microscope.

3.2.2. Characterisation of alloys aged at 190 ◦C

Fig. 4 shows the variation in hardness of each alloy as a

function of the aging time at 190 ◦C. Note that the hardness

of both alloys initially decreased to a minimum, which may

Fig. 5. TEM bright-field image of microstructure (a) and corresponding

SAED pattern recorded near the [0 0 1]Al zone axis (b) of 2219SG alloy

aged for 3 h at 190◦C.

be ascribed to reversion and then increased until a peak hard-

ness followed by overaging. However, the hardness values of

the 2219S alloy are smaller at all times monitored, whereas

the stage of hardening involved a gradual rise to peak hard-

ness. Thus, a 2219SG alloy displays a maximum hardness

of 100 HV after 8 h of aging, whereas the Si-containing alloy

peaks at 80 HVafter 24 h of aging, which is three times longer

than for 2219 alloy modified by Si and Ge. After the max-

imum, the hardness of 2219S alloy significantly decreases

with prolonged aging, approaching the level of about 73 HV.

This is in contrast to the case of the 2219SG alloy, where

the overaged samples show an initial period of constant hard-

ness from the peak hardness condition before reaching a final

hardness of 90 HV after 200 h of aging. These results indi-

cate that the artificial aging response of the 2219SG alloy is

nearly the same as that in the quaternary Al–Cu–Si–Ge alloy.

This means that there is the beneficial age-hardening effect

due to the early onset of Si–Ge particles precipitation.




Fig. 6. TEM micrograph of Si–Ge particles in microstructure of overaged 2219SG alloy with the typical EDS spectrum obtained from them.

Fig. 5a and b shows a representative TEM bright-field

(BF) image and a [1 0 0] selected-area electron diffraction

(SAED) pattern obtained from the 2219SG alloy aged for

3 h at 190 ◦C. As can be seen in Fig. 5a, the equiaxed Si–Ge

particles with diameters less than 100 nm are present in rel-

atively large amounts. The EDS analysis of such particles(Fig. 6), which are observed to be in the majority even in

the grossly overaged samples, confirmed that they contain

both Si and Ge. Since the diffraction pattern, as provided in

Fig. 5b, exhibits streaking from the face-on precipitates,

it seems reasonable that these precipitates act as nucleation

sites for Si–Ge particles.

The BF image shown in Fig. 7a demonstrates that after

8 h of aging, the main contributor to the hardness increase

is the precipitates. The early onset of precipitation in

the peak-aged 2219SG alloy is indicated by the very faint

reflections detected in the SAED pattern shown in Fig. 7b.

Since a mixture of and precipitates is present at the

maximum hardness of 2219SG alloy, it is obvious that the

addition of Ge in a commercial 2219 alloy promotes faster

aging kinetics than in alloy without Ge. Namely, thin edge-on plates appear in the matrix of 2219S alloy after 24 h of

aging (peak-aged condition).

Fig. 7c illustrates the presence of these precipitates in the

2219SGalloyafter150 h of aging.The BF image shows edge-

on platestogether with equiaxed Si–Ge particles. The spots

from the edge-on precipitates can be discerned in the corre-

sponding SAED pattern, as can be seen in Fig. 7d. The pre-

cipitates are found to be associated with the Si–Ge particle/ -

Al interfaces arrowed in Fig. 7c, owing to the positive volume

Fig. 7. TEM bright-field images of microstructure (a, c) and corresponding SAED patterns recorded near the [0 0 1]Al zone axis (b, d) of 2219SG alloy aged

at 190 ◦C for 8 h (a, b) and 150 h (c, d).




Table 4

Summary of the results obtained by the ANOVA analysis used for the modified 2219 alloys hardening response investigated

Source SS d.f. V F P

Composition 147.00 1 147.00 26.55 4.47

Temperature (t 1) 72.93 2 36.46 6.59 1.95

Time (τ 1) 2.90 2 1.45 0.26 0

Time (τ 2) 2592.10 2 1296.05 234.12 81.48

Composition× t 1 30.93 2 15.47 2.79 0.63Composition× τ 1 22.19 2 11.10 2.00 0.35

Composition× τ 2 27.92 2 13.96 2.52 0.53

Err 276.79 50 5.54 10.59

Total 3167.64 63 100.00

misfit between the Si–Ge precipitate and Al matrix. This may

also be correlated with the average thickness and diameter of

the precipitates [35].

3.2.3. Response to two-step aging

When the naturally aged 2219S and 2219SG alloys are

subjected to two-step artificial aging, a variety of microstruc-tures develop. Assessment of hardness for each variation in

the temperature and time of first stage aging and second stage

aging time provides a complex dataset, leading to precipita-

tion process optimisation that can generally be obtained by

Fig. 8. Bivariate subfunctions, showing a combined influence of (a) alloy

composition and second stage aging time,and (b) alloy composition and first

stage aging temperature on the hardening response of modified 2219 alloys.

any AN modelling technique. The present dataset contains a

total of 54 alloy-aging treatment combinations and the fol-

lowing input parameters: two levels of alloy composition,

three levels for first stage aging temperature (t 1), three levels

of first stage aging time (τ 1), and three levels of second stage

aging time (τ 2), namely, 15 min, 16 and 256 h, was analysed

using the ANOVA approach which handles smaller datasets

more consistently.

The results obtained from a statistical analysis of these

data are summarised in Table 4. They reveal the second stage

aging time (τ 2) and the (Si + Ge) addition as the main param-

eter influencing precipitation hardening of these alloys. The

P-values clearly show that the duration of second stage aging

is the most influential parameter, in agreement with known

physical behaviour. As is further illustrated in Fig. 8a, the

composition x versus τ 2 dependency shows that the 2219SG

alloy displays faster hardening response and a higher peak

hardness than the other alloy. This result supports the earlier

observation, indicating that the precipitation of fine Si–Ge

particles enhances the aging kinetics in 2219SG alloy. Onthe other hand, the hardening response of both alloys is al-

most unaffected by the first stage aging conditions as shown

in Fig. 8b. Hence, two-step aging treatment of commercial

2219 alloys modified by (Si + Ge) additions is not econom-

ically viable. Instead, by control of the duration of aging at

190 ◦C, the optimum hardening effect can be easily obtained.

4. Conclusions

The precipitate formation in a cast DSS and commercial

2219 aluminium alloy modified with Ge and/or Si has been

analysed by combining the microscopical methods for qual-

itative and quantitative characterisation of structure with the

experimental design approach adapted for prediction of the

precipitation behaviour of selected alloys which display var-

ious structures over a wide range of heating temperature and

time. The intention was not to describe solely the structural

characteristics of heated alloys, but rather to verify the capa-

bility of the ANOVA method to predict the effect of chosen

variables and theirinteraction affectingthe precipitating char-

acteristics of thesealloys.The obtained results clearly showed

that databases of different sizes can all be analysed success-




fully providinga means for process optimisationand alloy de-

velopment. Furthermore, the physical-based microstructural

parameter used together with empirical capability of the ap-

plied modelling technique can be used to control the amount

of deleterious SP precipitates, enabling a useful balance of

properties to be attained.

Acknowledgments

This work is supported by the Ministry of Science and

Environmental Protection, Republic of Serbia through the

Project No. 1261. All TEM experiments were performed

at the National Center for Electron Microscopy, Lawrence

Berkeley National Laboratory, University of California. The

authors are grateful to Dr. V. Radmilovic for very useful dis-

cussions, and to Dr. A.J. Tolley for carrying out the TEM

experiments.

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