九州大学大学院総合理工学府報告第 33 巻 第 1 号 1-6 頁 平成 23 年 6 月

Engineering Sciences Reports, Kyushu University
Vol. 33, No. 1, pp. 1-6, JUN, 2011

Creep behavior in a fine-grained Al-5356 alloy at low stressand intermediate temperature
Junjie SHEN *1,† Ken-ichi IKEDA*2 Satoshi HATA *2
and Hideharu NAKASHIMA*2†

E-mail of corresponding author: nk-j-shen@mms.kyushu-u.ac.jp(Received April 27, 2011)

Creep in an Al-5356 solid solution alloy with an intercept grain size,m was investigated using the helicoid spring specimen technique. The testing temperatures ranged from 423
K to 523 K (0.47 to 0.58 Tm) and the applied stresses from 0.20
to. It was found that
under the above conditions, viscous creep of Bingham type occurs, characterized by a thresholdstress which decreases with increasing temperature. The activation energy is Qc = 44
7 kJ/mol.
No microstructural changes were observed in recrystallized and the as-crept specimens. The measured creep rates were found to be four orders faster than that predicted by Coble creep model.
Key words: Helicoid spring specimen technique, Intermediate temperature, Low-stress creep

1.

Introduction

The creep deformation of materials at low
stressandintermediate
temperature,𝑇m < 𝑇 < 6 𝑇m (Tm: melting temperature)often exhibits the characters: the stress exponent is 𝑛 1, and the activation energy, Qc, isclose to grain boundary diffusional energy1-6）
or dislocation core diffusion energy7-11). The
corresponding viscous creep mechanisms andcreep testing techniques are listed in Table 1.
Those creep mechanisms are dependent on
grain sizes. Harper-Dorn type creep controlled
by dislocation core diffusion motion7,8) occurs
at a large intercept grain size (dg > 120 m),while for a small intercept grain size (dg < 120m) coble type creep controlled by diffusionaltransport of matters via grain boundaries1) or
Singarn-Nix type creep by shearing along slip
band accommodated by diffusion flow12) is activated. However, “H-D creep at intermediate
temperature” is still ambiguous14), and lacks
the support of dislocation substructures. As forcoble creep, there are the discrepancies between theory and experimental data15).
In addition, the creep behavior and mechanism
atintermediateinprecipitate-strengthened fine-grained materials arestill unclear, partly because the creep in thosematerials at intermediate temperature andlow stress will yield to very low strain rate,*1 Department of Molecular and Materials Science,
Graduate student*2 Department of Electrical and Material Scienceε̇ < 1 −10 s−1 . In this range, direct measurement of steady-state creep rates by the traditional uniaxial creep technique is difficult due
to very small magnitudes of strain, and very
long duration of creep tests. As another experimental technique, the helicoid spring
technique has been employed, because thehelicoid spring creep test provides the highest
strain sensitivity in contrast to conventional
compression and tension tests 16). A helicoid
spring sample was used in the creep test for
the first time by Eakin17) and this technique
was then elaborated by Burton and others18-22).
Intensive works on low-strain rate creep using
helicoid spring specimens have been done by
Fiala and Č dek 23, 24). More recently, lots ofstudies on the low-strain rate creep behavior ofvarious materials (heat-resistant steal,Ni-15%Cr solid solution alloy and pure aluminum) have been reported by Kloc etal. 2, 3, 25-27). Those results provided creep datathat are important to analyze creep mechanisms at ultra-low, 𝜀̇, and it was revealed thatextrapolation from power-law creep regime tolow stress conditions can cause serious underestimation of predicted deformation rates.
However, most notably, and in contrast tocompression and tension testing, in spring
testing the stress and strain are not uniform
through the specimen’s cross section. The
stress and strain generally increase from thecenter to the surface, where the values are at a
maximum. Because of that, stress redistribu-

2

Creep behavior in a fine-grained Al-5356 alloy at low stress and intermediate temperaturetion will occur under the condition that creep
behavior is non-viscous. It is possible to findthe correct solution from a series of tests at
various load levels by solving the appropriate
integral equations numerically described by
Kloc et al.. 28)
The purpose of this study is to investigate
the creep behavior and mechanism in precipitate-strengthened Al-5356 Mg solute-solution
alloy with an intercept grain size,
m, at low stress and intermediate temperature ranging from 423 K to 523 K (0.47 
0.58 𝑇m ) using the helicoid spring specimen
technique.
Table 1 Basic mechanisms of creep at low stress and intermediate temperature.
Creep
model

Deformation
process

Ratecontrolling
process

Accommodatingprocess

Coble

Diffusionaltransport ofmatter via
grainboundaries

Grainboundary
diffusionGrainboundary
sliding

Harper-Dorn

Motion oflatticedislocations

Dislocation
core
diffusion

Singarn-Nix

Shearingalong slip
band

The climb
ofdislocations
at grainboundaries

Grainboundary
diffusion

Microstructuralcharacters

Creep ratedependence
on d, or 

Experiment

Testingtechnique

1/d3

[1]

[2-6]

Unaxial [4-6]Multiaxial(helicoidspring creep)[2,3]

Joggedscrew
dislocations

none

[7,8]

[7-11]

Multiaxial(helicoidspring creep)[7-11]

Slip bands

d/4

[12]

[13]

Biaxial(hoop creep)[13]

Electric Furnace withthree adjacent heatersδFig. 1

2

load

𝜏

8𝑃𝐷
π𝑑 3

,

(1)

,

(2)

Reference
TheoryHigh-precision
Optical Micrometer(Receiver)
Helicoid spring specimen

helicoid spring creep tests which has threeadjacent heaters that are independently controlled to obtain uniform temperature distribution in the helicoid sample with an accuracyof 1 K during creep deformation. The pitchesof the helicoids of the sample were measured
using a light-emitting diode with an accuracyof 0.5 m.
The following equations29, 30） have been employed to calculate the mean surface shear
stress, 𝜏, and the surface shear strain, 𝛾, assuming pure torsion of the helicoid spring
specimen:

High-precision
Optical Micrometer(Transmitter)

The scheme of the helicoid-spring creep machine.

Experimental

The experiments were performed on Al-5356
Mg solid-solution alloy in the form of wires
with a diameter, d = 1.6 mm. Its Chemicalcomposition by weight percent is as follows:
4.81 Mg, 0.13 Fe, 0.08 Si, 0.01 Cu, 0.07 Mn,
0.08 Cr, and the balance is Al. Helicoid spring
specimens with a mean coil diameter, D = 18.8mm, were prepared by winding the wires on
threaded stainless steel bolts. The bolts withthe wound wires were heat-treated in air at
723 K for 48 h to fix the helicoid shape andobtain fully recrystallized microstructure. Theintercept grain size ism.
Creep tests were performed at temperature,
T = 423 K, 473 K and 523 K, and applied stress,𝜎≤1, using the helicoid spring technique. Figure 1 illustrates the apparatuse of

𝛾

𝛿𝑑
π𝐷 2

where P is the average load, D is the coil diameters, d is the wire diameters and 𝛿 is theaverage rate of deflection. Since the stress andstrain in the helicoids spring are essentiallyshear ones, they are transformed to the equivalent tensile quantities using the a well known
relations, tension stress 𝜎 √3𝜏 and tensile
strain 𝜀 𝛾⁄√3. In the present study at low
stress, the initial coil pitch spacing is 𝛿
mm. During creep tests, 𝛿 change from 2.5
mm to 3.5 mm. Our earlier investigation31) on
the relation between torsion and normal elastic strains in Sn-Ag helicoid spring analyzed by
the finite element method revealed that one
can neglect the normal elastic strains under
the condition of the coil pitch spacing between
0 to 5 mm. Therefore, the creep deformation in
the present study can be considered as to be
only torsion strains. Though, the normal elastic strain cannot be neglect at high stress, inthis study the creep behavior at high stresshas been also investigated by this technique togive a direct evidence on the creep mechanism
change.
Microstructures in recrystallized andas-crept specimens were observed by transmission electron microscopy (TEM). TEM observation area is middle parts of cross sectionsof the wires. Thin foils for the TEM observation were prepared by mechanical polishingand twin-jet electropolishing using a mixtureof 30% HNO3 and 70% methanol at 243 K. The
TEM observation was conducted with a JEOL
JEM-2000EX/T transmission electron microscope operated at 200 kV of the accelerating
voltage.

九州大学大学院総合理工学報告 第 33 巻 第 1 号

3

where 𝐴
0.771 and 𝐵
0.901 (melting
temperature, 𝑇m
901 K). The figure showsthat the threshold stress decreases with increas of temperature.

3. Results
3.1 Stress dependence of steady state creep
rate
An example of creep curves obtained at 423
K and different stresses is shown in Fig. 2. The
creep curves clearly show that transient creep
rate decreasing with the testing time increasing. After a relatively short period of transient
creep, steadyBC state creep commences.
D

10-6
1.00E-06

1.00E-07

10-7

523 K
473 K
423 K

n = 4.3

1.00E-08
εs / s-1

平成 23 年度

10-8

10-9
1.00E-09

Series1

Series2

n = 1.0

Series3-4
1.5 1015

T = 423 K

10-11
1.00E-11
0.1-4
1 1010ε / 10-5

0.1

1

10

σ – σ1
0 / MPa

10

Fig. 3 Relation between steady-state creep rate and applied stress in double linear coordinates at T = 423, 473

5 10-55

0
0 100
0 0
100

Series4

10-10
1.00E-10

σ = 2.84 MPa

1 105
100

2200
105

0.94

and 523 K.

0.52

0.330

3300
105

4400
105

Measured values
Values after correction

5 105
500

t / 103 s

0.220

σo / 10-2 MPa

Fig. 2 Typical creep curves obtained by helicoid spring
creep technique at test temperature, 423 K.

εs / 10-10 s-1

The applied stress,σ, less than 3 MPa de0.110
pendence of steady-state creep rate, 𝜀̇s , in linear relations is shown in Fig. 3. It is apparent
that the steady-state creep rate is character0 0400
ized by a Bingham viscous behavior, and hence
450
500
550
it is proportional to the difference between the
400
450 T / K 500
550
applied stress and a threshold stress, 𝜏o . In
this case, redistribution of the stress across theFig. 4 Temperature dependence on threshold stress, 𝜎0 . ,coil wire cross-section occurs during creep.
experimental data; , corrected for the stress redistribuThis problem was analysed by Crossland ettion .
32)
al. who showed that the stress redistribution
88.00E-10
is manifested by a slight transient creep com523 K
ponent and that in the steady state it influ473 K
ences only the value of threshold stress
423 K
6.00E-10 6(𝜏ov 3⁄ 𝜏o where 𝜏ov is the threshold stresscorrected for the stress redistribution and 𝜏o is
Series1that of measured values) as obtained by ex- 4.00E-10 4
trapolation of the creep rate-stress relation to
Series2
zero creep rate.
Series3
The threshold stresses are ranging from 0.08 2.00E-10 2
to 0.21 MPa for experimental data and 0.06 to
0.16 MPa for corrected data, and is taken into 0.00E+00 001
23
account in principle. Temperature dependenceof the threshold stress is shown in Fig. 4. It can
0
1 σ / MPa 2
3
be described as:
Fig. 5－Stress, 𝜎 − 𝜎0 , dependence of steady-state creep

𝜎0

𝐴−𝐵

𝑇
𝑇m

(3)

rate in double logarithm coordinates at T = 423, 473
and 523 K respectively.

4

Creep behavior in a fine-grained Al-5356 alloy at low stress and intermediate temperature

A plot of stress, 𝜎 − 𝜎0 , against thesteady-state creep rate, 𝜀̇s, in double logarithm
obtained by the helicoid spring creep tests fordifferent temperatures is shown in Fig. 5. It
is apparent that creep mechanism has changed.
In low stress creep region, a stress exponent isequal to 1, whereas the value is 4.3 at highstress.
3.2 Temperature dependence of steady-state
creep rate
The activation energy, 𝑄c , values were determined by fitting the data to the Arrhenius
equation:𝜀̇s𝑄Aexp (− c )

(4)

𝑅𝑇

where A is a constant depended on materials
and stress, R is the universal gas constant, 𝑇
is the testing temperature. Fig. 6 shows 𝜀̇s inlogarithmic scale plotted against the reciprocal
temperature, 1 ⁄ 𝑇 for low stress creep region(n = 1). The activation energy values of 44 ±7 kJ / mol was obtained. The value is around0.26-0.36 QL (QL is lattice diffusion energy of
Al, and 142 kJ / mol[33]), and slightly less thanthat for grain boundary diffusion (0.33 QL <Qgb < 0.67 QL).

idence for the existence of dislocations is revealed by tilting the specimen. A representative bright-field TEM micrography in thespecimen crept to a steady-state creep stage at𝑇
3 K and 𝜎
is shown in Fig. 7(b). One cannot find the existence of dislocations by tilting this specimen, and apparentchange of microstructures. It should be notedthat there is a possibility that grain growth
may occur during creep, which generally leads
to a change in the stress exponents. However,
the microstructural studies following creep do
not indicate that the occurrence of any suchgrain growth. In addition, if grain growth did
occur during creep, the rates of growth at different test conditions will be different, and it is
not expected that the strain-rate data will follow the linear stress variation as observed inthis study.
(b)

(a)

1 m

1.00E-0810-8
2.84 MPa0.94 MPa0.52 MPa

Qc = 44±7 kJ / mol

1.00E-0910-9

1 mFig. 7 TEM micrographs. (a) In the annealed materials. (b)In the specimen crept to the steady-state stage at 423 K andεs / s-1

0.42 MPa.

3. Discussion

Series1
Series2

1.00E-10

10-10

10-11
1.00E-11
1.8

The stress exponent is n = 1. One of possible mechanisms is that creep controlled by
Coble creep. To clearly establish Coble creep astherate-controllingmechanism,
thesteady-state creep rates obtained at 523 K arecompared to the standard Coble creep model
predications. The Coble creep model is described by the following equation34):

Series3

1.9

2.0

2.1 2.2

2.3 2.4 2.5

0.00180.00190.002
0.00210.0025(1/T)/0.002210-30.0023
K-1 0.0024
Fig. 6 Temperature dependence on the steady-state creep
rate.

3.3 Microstructural observation
TEM was used to study the fine structuraldetails in the recrystallized and as-crept
specimens at low stress. Fig. 7 (a) shows a
representative bright-field TEM micrographyof the recrystallized specimens. That clearly
depicts the equiaxed grain structure present in
the annealed materials and precipitates located in the grain and grain boundary. No ev-

𝜀̇ 𝑘𝑇
𝐷𝑔𝑏 𝐸𝑏𝑏 3 𝜎 1( ) ( )𝑑𝐸(5)where 𝐷 d is the diffusion coefficient along a
grain boundary ( 𝐷 d = 𝐷0 exp[− 𝑄𝑔𝑏 ⁄𝑅𝑇] ,where 𝐷0 is a frequency factor, 𝑄 b is a grainboundary diffusion, b is the magnitude ofBurgers vector, k is Boltzmann’s constant, 1.38

平成 23 年度

九州大学大学院総合理工学報告 第 33 巻 第 1 号

× 10-23 J•K-1, T is the absolute temperature, σis the applied stress and d is an average intercept grain size. In this study, the following
values are set: dg = 5 m, 𝐷0 = 1.70 × 10-4
m2s-1 35), 𝑄 b = 85.2 kJ/mol = 0.6 𝑄L 35), and b= 2.86×10-10 m. A good agreement between theactual strain rates and the Coble creep model
predications would indicate Coble creep as therate-controlling mechanism. Alternatively,
calculating the model prefactor and comparing
it with standard standard prefactor for Coble
creep would serve as a good verification. It wasobserved that Coble constant for the data
points corresponding to 523 K are 1 × 1 4 thatis higher than the theoretical Coble constantvalue, i.e. 22.4 shown in Fig. 8. In that case, itis predicted that creep behavior cannot be described by Coble creep.
Slip band mechanism and “Harper-Dorn
creep controlled by dislocation core diffusion atintermediate temperature” can also be excluded because the microstructural observation did not show the formation of slip band[14]as expected in slip band mechanism and joggedscrew dislocations as expected in “Harper-Dorn
creep at intermediate temperature7, 8)”. In addition, Harper-Dorn creep is generally expected to occur in a relatively larger grain.
The experimental results: stress exponent
equal to 1, creep activation energy ranging
from 0.26 QL to 0.37 QL and no change of microstructure in recrystallized and as-crept
specimens, can not be explained with available
creep theories.
10-11
1.00E-11
10-12
1.00E-12
10-13
1.00E-13
εkT 10-14
1.00E-14
DgbEb -15
10
1.00E-15
1.00E-16
10-16
10-17
1.00E-17
10-18 -6
1.00E-18
10

1.00E-06

Experimental data

Coble creep model

10-5

10-4

1.00E-05

1.00E-04

σ – σwith
0 / Etheoretical Coble
Fig. 8 Correlation of this study
creep model at 423 K.

4.

Summary

Creep tests were carried out on an Al-5356
Mg solid-solution alloy with intercept grain
size,
m in the form of wires byhelicoid spring creep technique at intermedi-

5

ate temperature (0.47 to 0.58 Tm) and low
stress (0.20 to 4.02). The viscous creep ofBingham type occurs, characterized by athreshold stress which decreases with increasing temperature. The activation energy
was 𝑄c
7 kJ / mol that is slightly lessthan that for grain boundary diffusion (0.33 QL< Qgb < 0.67 QL). The measured creep rates
were about four orders faster than expected
Coble creep. No microstructural changes wereobserved in the recrystallized and as-crept
specimens. The creep behavior cannot be explained by the creep models: Coble creep,“Harper-Dorn creep at intermediate temperature” and Slip-band creep mechanism.
Acknowledgments
This work was supported in part by
Grants-in-Aid from the Japan Society for the
Promotion of Science (JSPS) and Grants-in-Aid
from the Ministry of Education, Culture, Science and Technology (MEXT), Japan.
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