Proceedings of the 12th International Conference on
Aluminium Alloys, September 5-9, 2010, Yokohama, Japan
©2010
2010 The Japan Institute of Light Metals
pp. 1065-1070

1065

Effect of Amount of Pre-strain on Bake-hardening Responseof an Al-Mg-Si Alloy
Tetsuya Masuda1,2, Yasuo Takaki2 and Shoichi Hirosawa3
1

Graduate student, Department of mechanical engineering and materials science,
Yokohama National University, 79-5 Tokiwadai, Hodogaya, Yokohama, Kanagawa 240-8501, JAPAN2
Material & process research section, Aluminum sheets and coils research department, Kobe steel,Ltd.,
15 Kinugaoka, Moka, Tochigi 321-4367, JAPAN
3Department of mechanical engineering and materials science, Yokohama National University,
79-5 Tokiwadai, Hodogaya, Yokohama, Kanagawa 240-8501, JAPANThe effect of amount of pre-strain on the bake-hardening response of an Al-0.6mass%Mg-1.0
mass%Si alloy was investigated by means of Vickers hardness test and transmission electron
microscopy (TEM). The bake-hardening response at 443K was improved by pre-straining to 3%, but
reduced with increasing amount of pre-strain larger than 5%. TEM observation confirmed that theevolution of bake-hardening response with pre-straining is related to the number density of fineprecipitates in the matrix. This suggests that the improvement and degradation of bake-hardenability
can be explained by the contradicting effects of dislocations induced by pre-straining.
Keywords: Al-Mg-Si alloy, pre-strain, bake-hardening response, β” phase, dislocation

1. Introduction
Heat treatable Al-Mg-Si alloys are mainly used for automotive body panels because of their good
formability, corrosion resistance, surface quality and precipitation strengthening after paint-baketreatment at 443-453K (i.e. bake-hardening response) during car manufacturing processes. It is wellknown that the β” phase greatly contributes to the bake-hardening response and the alloys containing
excess of Si over Al-Mg2Si quasi-binary composition exhibit more pronounced bake-hardenability[1].
Pre-straining has a substantial effect on precipitation kinetics and processes for Al-Mg-Si alloys. A
large amount of pre-strain lowers the bake-hardenability due to the unfavorable heterogeneous
precipitation on dislocations induced by pre-straining[2]. On the other hand, the authors recently
reported that a small amount of pre-strain below 3%, combined with pre-aging process, enhances thebake-hardening response due to the accelerated precipitation of the β” phase in the matrix[3].
However, the mechanism of such effects of pre-strain on the bake-hardening response has not been
fully clarified.
In this work, the effect of amount of pre-strain by 0.5 to 30% on bake-hardening behavior of an
Al-0.6mass%Mg-1.0mass%Si alloy was investigated in attempts to clarify the mechanism ofenhancement or degradation of bake-hardenability by pre-straining.
2. Experimental
The chemical composition of the alloy utilized in this work is listed in Table 1. The alloy ingot washomogenized and hot- and cold-rolled through the standard manufacturing processes to a plate withfinal thickness of 1.0mm. The specimens were solution heat-treated at 823K for 60s, and then waterquenched. Shortly after water quenched, pre-strain was introduced with a tensile testing machine (by0.5, 3, 5 and 8%) or with a cold-rolling mill (by 10 and 30%). The corresponding equivalent strain bywhich the two different deformation modes can be compared is 5.0x10-3, 3.0x10-2, 4.9x10-2, 7.7x10-2,1.2x10-1 or 4.1x10-1, respectively. Some specimens were processed without pre-straining forcomparison. The hardness was measured by a Vickers hardness tester with 19.6N load and dwell time1066of 15s to evaluate the bake-hardening response during final aging at 443K. The specimens were heldat room temperature for approximately 300s between solution heat treatment and final aging. For thespecimens final aged at 443K for 3.6ks, transmission electron microscopy (TEM) observation wasperformed under accelerating voltage of 200kV.
Table 1 Chemical composition of the alloy utilized in this work [in mass%].
SiFeMnMg

Al

1.02

0.17

0.07

0.57

Bal.

3. Results
3.1 Bake-hardening response
The hardness evolution during final aging at 443K is shown in Fig.1(a) for the specimens withdifferent amounts of pre-strain. The hardness before final aging; HVBefore, is increased with increasing
amount of pre-strain from HV46(0% pre-strain) to HV78(30% pre-strain). The time to peak hardnessbecomes shorter with increasing amount of pre-strain. To compare the bake-hardening response, theincrement in hardness by final aging up to 3.6ks (indicated by broken line in Fig.1(a)); ∆HV(=HV-HVBefore), is plotted in Fig.1(b). ∆HV increases with 0.5% pre-strain, and then decreases withincreasing amount of pre-strain. Namely, it was found that the bake-hardening response of the alloy isenhanced by <3% pre-strain, but reduced by >5% pre-strain.
(a)

(b)
70
Increment in hardness ,∆HVHardness ,HV

13012011010030%
10%8%5%3%
0.5%0%

9080
70605040Before
100final aging

Final aged at 443K for 3.6ks
605040301000
10000
Aging time ,t /s

1000000510Amount of pre-strain ,ε /%3015Fig.1 (a)Hardness evolution during final aging at 443K and (b)increment in hardness; ∆HV,
after final aged for 3.6ks of the specimens with 0 to 30% pre-strain.
3.2 TEM microstructure
Fig.2 shows TEM bright- and dark-field images together with selected area diffraction patterns(SADPs) of the specimens without pre-strain, with 3 and 30% pre-strain, subjected to final aging at
443K for 3.6ks. It is found from bright-field images that the dislocation density becomes higher withincreasing amount of pre-strain. In dark-field images, the β” precipitates in the matrix, which giverise to streaks along [010]Al and [100]Al in SADPs, decrease in number density with increasing
amount of pre-strain due to the formation of large precipitates along dislocation lines. The
corresponding size distribution of precipitates is shown in Fig.3. It is revealed that while large
precipitates than 10nm in maximum length monotonically increase in number density with increasing
amount of pre-strain (Fig.3(a)), the number density of fine precipitates with <10nm once increases
with 3% pre-strain, then decreases with larger amount of pre-strain than 5% (Fig.3(b)).

1067

Dark-field image

30% pre-strain

3% pre-strain

Without pre-strain

Bright-field image

100nm

100nm

Fig.2 TEM bright- and dark-field images and selected area diffraction patterns of the specimens
without pre-strain, with 3 and 30% pre-strain, subjected to final aging at 443K for 3.6ks.
(a)(b)Number density, N /μm

3

Number density of the precipitateswith<10nm in maximun size, N /μm3

10000

1000
Without
pre-strain
100With 3%
pre-strain
With 30%
pre-strain

1000-555-10
10-15
1015Size, d /nm

1520

8000

7000

6000

5000

4000
Without
3%
10%
30%
Amount of pre-strain, ε /%Fig.3 (a)Size distribution of all the observed precipitates and (b)number density of smaller
precipitates than 10nm in maximum length for the specimens without pre-strain, with 3 to 30%
pre-strain, subjected to final aging at 443K for 3.6ks.

10684. Discussion
4.1 Evolution of bake-hardening response with amount of pre-strain
As shown in Figs.1, 2 and 3, the effect of pre-straining on the bake-hardening response strongly
depends on amount of pre-strain. Fig.4 shows the relationship between the number density of smaller
precipitates than 10nm; N (Fig.3(b)) and the increment in hardness; ∆HV (Fig.1(b)) in the specimens
with different amounts of pre-strain. It is suggested that bake-hardening response at 443K is mainly
determined by the number density of fine precipitates, since ∆HV well agrees with N irrespective ofamount of pre-strain. Pre-strain by 3% increases the number density of smaller precipitates than 10nm,and enhances the bake-hardening response. The authors previously reported that smaller amount ofpre-straining than 3% suppresses the age-hardenability of the present Al-Mg-Si alloy at lower
temperatures below 373K, but improves the bake-hardening response at 443K[3]. This can beexplained by the decreased concentration of quenched-in excess vacancies with pre-straining,resulting in the suppressed clustering of solute atoms in the matrix. On the other hand, pre-strain
larger than 5% decreases the number density of smaller precipitates than 10nm, and lowers thebake-hardening response due to the preferential heterogeneous formation of larger precipitates on
dislocation lines. Softening of the alloy specimen by recrystallization and grain growth is thought tobe negligible at 443K, since recrystallization is expected to occur only above 573K when 20%
pre-strain is applied to this alloy[4].
Increment in hardness ,∆HV70
Final aged at 443K for 3.6ks6050

Without
pre-strain

3%10%4030%
305000
6000
7000
8000
-3
Number density of precipitates ,N /µm

Fig.4 Relationship between number density of precipitates with <10nm N and increment
in hardness ∆HV for the specimens with different amounts of pre-strain.
4.2 Modeling of precipitation in the matrix
According to the classical nucleation theory[5], nucleation rate J is given by ∆G 
J = N s ⋅ β ⋅ Z ⋅ exp − ,
 kT (1)where Ns is the number of potential nucleation sites, β = A ⋅ D ⋅ c is frequency factor, Z is Zeldovich
non-equilibrium factor, ∆G is activation energy for nucleation, k is Bolzman constant, T is aging
temperature, A is a constant, D is diffusivity and c is solute concentration in the matrix, respectively.
Since it is believed that the site saturation does not occur in the early stages of phase decomposition,
the number density of precipitates in the matrix Np is thought to be related to J.
In this work, to clarify the effect of amount of pre-strain, the ratio of number densities ofprecipitates in the matrix for the specimens with and without pre-strain Np/Np’ was defined as theproduct of c/c’ and Ns/Ns’; i.e1069

Np'=Jc N= ' ⋅ s' ,'Jc Ns

Np
where Np’, J’, c’, Ns’ are the values for the specimen without pre-strain.

(2)(a) Solute concentration in the matrix cAssuming that dislocations induced by pre-straining act as sink sites for quenched-in excess
vacancies, the estimated lifetime τ of quenched-in excess vacancies to annihilation at dislocations
pronouncedly decreases with amount of pre-strain as shown in Fig.5[3]. Since it is thought that soluteconcentration in the matrix c increases with decreasing τ due to the suppressed formation of clusters
during natural aging, c can be defined asc = c0 − (c0 − c' ) ⋅τ
,
τ'(3)

10000

Estimated lifetime of excess
vacancies, τ /s1

where c0 is the initial solute concentration and τ’ is lifetime of quenched-in excess vacancies for thespecimen without pre-straining. In this work, c0 and c’ were adapted as 1.58at% and 1.34at% by
taking into account concentrations of Si and Mg in the alloy. Broken lines in Fig.6 show pre-strain
dependence of the estimated ratio of solute concentrations c/c’. It is noted that c/c’ increases withsmall amount of pre-strain and saturates at ~1.18 above 0.5% pre-strain.

Without pre-strain
1000

100

10

102468Amount of pre-strain ,ε /%10Fig.5 Pre-strain dependence of estimated lifetime τ of quenched-in excess vacancies[3].
(b) Number of potential nucleation sites Ns
In general, precipitates are expected to form preferentially on dislocation lines due to thedecreased activation energies for nucleation and growth. It is considered that potential nucleationsites in the matrix decreases with increasing amount of precipitation on dislocations as a result ofsolute atoms consumption. The potential nucleation sites in the matrix Ns can be therefore assumed as
N s ∝ 1 − πr 2 ρ ,(4)where r is the radius of cylindrical zones affected by precipitation on dislocation lines and ρ=Xεn/Y isthe dislocation density calculated from reported values X=0.185nΩm, n=0.648 (for an Al-0.47
mass%Mg alloy[6]), Y=3x10-25Ωm3 (for high-purity aluminum[7]) and true strain ε. In this work, r
was assumed to be 20nm from TEM observation, and dislocation densities of the specimens without
pre-strain, with 3, 10 and 30% pre-strain were estimated as 1x1011[8], 6x1013, 1x1014 and 3x1014m/m3,respectively. Dotted lines in Fig.6 show pre-strain dependence of the estimated ratio of potential

1070

nucleation sites in the matrix Ns/Ns’. It is noted that Ns/Ns’ monotonously decreases with increasing
amount of pre-strain.

4.3 Number density of precipitates in the matrix Np/Np’
The evolution of Np/Np’ estimated through Eq.(2) is shown by straight lines in Fig.6. The trend ofNp/Np’ change is similar to the change of number densities of smaller precipitates than 10nm inFig.3(b). Therefore, the evolution of bake-hardening response with pre-straining in Fig.1(b) can beexplained by the contradicting effects of dislocations induced by pre-straining; i.e. the enhanced
precipitation in the matrix due to the highly supersaturated solute concentrations (<3% pre-strain) andthe suppressed precipitation in the matrix due to the preferential formation of large precipitates on
dislocation lines (>5% pre-strain).
(a)
(b)
1.2

1.2c/c'1.1
N p /N p '1.0
Fig.6(b)0.9

N s /N s 'c/c' , Ns/Ns' or Np/Np'c/c' , Ns/Ns' or Np/Np'

c/c'

0.8
Without0
pre-strain

1.1
N p /N p '1.0
N s /N s '

0.9

0.8
2468
Amount of pre-strain ,ε /%10Without0
pre-strain

12
Amount of pre-strain ,ε /%3Fig.6 Pre-strain dependence of number densities of precipitates in the matrix Np/Np’, soluteconcentrations in the matrix c/c’ and numbers of potential nucleation sites Ns/Ns’.

5. Conclusions
The effect of pre-strain on the bake-hardening response of an Al-0.6mass%Mg -1.0mass%Si alloy
was investigated. The bake-hardening response strongly depends on amount of pre-strain. Smaller
amount of pre-straining below 3% accelerated bake-hardenability during final aging at 443K,
whereas larger amount of pre-straining reduced the bake-hardening response. This can be explainedby the contradicting effects of dislocations induced by pre-straining; i.e. the enhanced precipitation offine β” in the matrix due to the highly supersaturated solute concentrations and the suppressed
precipitation in the matrix due to the preferential formation of large precipitates on dislocation lines.

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