Materials Science Forum Online: 2018-12-26

ISSN: 1662-9752, Vol. 941, pp 1348-1353

doi:10.4028/www.scientific.net/MSF.941.1348
© 2018 Trans Tech Publications Ltd, Switzerland

Evolution of Young’s Modulus of Cold-Deformed Pure Aluminium in a

Tension Test
Isaac Isarn1,a, Jordi Jorba2,b, Antoni Roca3,c,* and Núria Llorca-Isern4,d
1
Department of Mechanical Engineering, Universitat Rovira I Virgili, Av. Països Catalans 26,
43007 Tarragona, Spain
2
Department of Materials Science and Metallurgical Engineering, Universitat Politècnica de
Catalunya, Av. Eduard Maristany 10-14, Edifici A, Planta 8, 08019 Barcelona, Spain
3,4
Department of Materials Science and Physical Chemistry, Universitat de Barcelona, Materials
Science and Engineering, Martí I Franquès 1, 08028 Barcelona, Spain
a
isaac.isarn@urv.cat, bjordi.jorba@upc.edu, croca@ub.edu, dnullorca@ub.edu

Keywords: Young’s modulus. Aluminium. Cold drawing

Abstract. Young’s modulus varies with crystallographic orientation, temperature and alloying, but
also with cold working and heat treatment. In this work, the evolution of Young’s modulus in
polycrystalline pure aluminium (99.5%) with different cold-working levels determined at room
temperature is presented. The deformation process was carried out in a universal tension machine
and measurements were performed by ultrasounds. The Young’s modulus diminished from 70 to
65 GPa for 0-5% of deformation (elongation) and then increased with successive cold-working
(68 GPa for 8.5% of elongation). These values were obtained 8 hours after plastic deformation was
applied. This behaviour is compared with the Young’s modulus determined by extensometry in the
same material. In this case, the modulus decreased from 70 to 63 GPa (3.5% of elongation) and then
increased until 68 GPa for 10% of elongation. Results obtained on pure iron (Armco) deformed in
the same conditions are included for comparative purposes. Values of Young’s modulus measured
during the springback process after plastic deformation at different level are also included. Values
obtained are between 10-15% lower than those measured 8 hours after plastic deformation.

Introduction
It is well known that an increase in temperature weakens the bond between atoms, which generates
a decrease in Young's modulus (E). In monocrystals, and depending on the material, it is possible to
find a very important anisotropy according to the crystallographic direction. For example, Young’s
modulus of lead (FCC) at 25ºC measured in the direction <111> is 27.3 GPa, and in the direction
<100> the value is reduced to 6.9 GPa. Iron (BCC) also presents important differences in Young’s
modulus. On the other hand, tungsten (BCC) has a constant modulus of 393 GPa in any direction. In
polycrystalline aggregates, where there is no macroscopic preferential crystallographic orientation,
intermediate values are found. Although when textures appear, the value of the modulus will change
according to the measured direction [1,2].
The defects in the structure can significantly influence on the elasticity of materials. Plastic
deformation and thermal treatments can lead to changes in Young’s modulus. These changes can be
higher than 10% in some materials. This is not an important factor in material selection processes,
but it has a decisive effect on conformation processes by plastic deformation [3-12] where the
"springback ", the elastic-plastic recovery of the materials just after plastic deformation, is largely
characterized. In this case, changes in Young’s modulus are analysed, to apply in the modeling
calculations of elastic recoveries. Determining and controlling this aspect would result in an
improvement in the quality of the products and an optimization of manufacturing processes.
In the past years, our research group, along with other researchers, has carried out several studies
[9,13-18] to determine changes of Young's modulus with cold deformation and with thermal
treatments in materials such as steels, stainless steel and aluminium. A diminution of E on iron,

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 Materials Science Forum Vol. 941 1349

several steels and pure aluminium measured by tension test were observed. In most cases, E
decreased reaching a minimum value between 2 and 4% of plastic deformation; a subsequent
recovery of modulus was detected when plastic deformation increased.
It seems that the cause of the decrease and its subsequent recovery of Young’s modulus is not due to
the presence of textures, because they significantly appear with high degrees of deformation; and
that was not the case in these works. The authors conclude that dislocations can bow out in their
glide planes, giving an extra elastic strain and consequently a decrease of Young’s modulus. The
decrease in the first level of deformation is due to the increase of the dislocation density. When the
cellular configuration of dislocations is formed (4-6% elongation), there is a decrease in the
dislocation lines capable to bow out and a partial recovery of E values is produced. However, in
aluminium alloys such as 2024 and 7075, Young’s modulus presented a nearly constant modulus
after plastic deformation at different level.
The evolution of Young’s modulus of a polycrystalline sample of pure aluminium (99.5%) with
different cold-working, at room temperature was determined in this work. The deformation process
at different level was carried out in a universal tension machine and measurements of Young’s
modulus were performed by ultrasounds. The observed behaviour is compared with changes
observed in pure iron and in some aluminium alloys.

Materials and Experimental Procedure

The chemical composition of the aluminium sample was determined by emission spectrometry by
inductively coupled plasma (ICP) after chemical attack of the sample. The composition obtained in
ppm was: Fe, 2400; Si, 694; Zn, 220; Ni, 102; Ti, 85.0; V, 74.0; Mn, 48; Cu, 32; Mg, <100 ppm.
The total amount of impurities in aluminium was less than 0.5%.
Previous studies carried out indicated that the best conditions for rolled aluminium annealing would
be 320ºC, 2h (after hot rolled) or 380ºC, 2h (after cold rolled) [19]. A study was carried out by using
temperatures of 365, 380 and 400ºC at different time between 1 h and 2h 30min. The behaviour of
material with thermal treatment was analysed by hardness measurements (Vickers indenter, 100 g).
The different level of cold-working was developed in a MicroTest EM2/20 kN tension machine
using a strain rate of 0.4 mm·min-1. Two electrical extensometers HBM DD1were placed on each
sample.
By means of the electric extensometers used in the tensile tests, together with the applied force data
and the dimensions of the original section of each sample, the graphs of true stress versus true strain
were constructed. The modulus during unloading that was determined is the instantaneous after the
deformation, which is used by many authors when they perform theoretical calculations to predict
the springback of deformed materials. The modulus was calculated using a lineal regression from
the beginning of the diminution of deformation to the force applied by the device until to 20 MPa.
Figure 1 is a typical graph of loading-unloading.
Once the deformation was produced, sections of the samples with a height of 15 mm were cut to
make the measurements by ultrasound. The measurement of elastic constants was made by
ultrasonic transmission-reception method. The wave’s velocity was determined using a Panametrics
5900PR. The density was measured by helium picnometry.

Results and Discussion

Annealing of Aluminium Samples
The temperatures studied were 365, 380 and 400ºC and time between 1 h and 2h 30min. The best
results were obtained at 400ºC at 2h 30min. In these conditions, values of 24.6±0.5 HV0.1 in the
surface of the samples and of 24.4±0.6 HV0.1 inside the samples were measured. All the samples
were subjected to the optimum thermal treatment previously to apply them the deformation by
tensile test.
1350 THERMEC 2018

Figure 1. True stress - true strain graph including the loading-unloading steps of an
AA1050 aluminium sample.

Plastic Deformation of Aluminium by Tensile Test

Table 1 includes the apparent modulus measured during unloading at different deformation level. It
can be observed a decrease of 10-15% of the apparent modulus with respect to the Young modulus
of the original material (69.2±0.8 GPa). This instantaneous modulus after deformation is used in
theoretical calculations for the prediction of the springback of the deformed materials and this
change needs to take into account in simulation processes.
Table 1. Apparent modulus measured during unloading
after plastic deformation at different level.
Deformation [%] Apparent Modulus [GPa] R2
L1 (1.8%) 61.2 0.99908
L5 (3.7%) 59.3 0.99935
L2 (3.8%) 61.7 0.99864
L7 (5.0%) 62.5 0.99848
L3 (6.2%) 60.3 0.99855
L6 (8.4%) 61.5 0.99916

Figures 2 and 3 show the Young’s modulus values measured, respectively, 8 h and 24 h after plastic
deformation. Figures 4 and 5 show the Young’s modulus values measured, respectively, 1 week and
2 weeks after plastic deformation. Figure 6 includes the evolution of Young’s modulus versus time
of the sample deformed at 3.7%. This figure includes the modulus value obtained immediately after
plastic deformation measured during unloading (59.3 GPa).

71 72

70 71

70
69
Young modulus (GPa)

Young modulus (GPa)

69
68
68
67
67
66
66

65 65

64 64
0 2 4 6 8 10 0 2 4 6 8 10
Deformation (%) Deformation (%)

Figure 2. Young’s modulus of aluminium Figure 3. Young’s modulus of aluminium

measured 8 h after plastic deformation. measured 24 h after plastic deformation.
 Materials Science Forum Vol. 941 1351

72 72

71 71

70 70
Young modulus (GPa)

Young modulus (GPa)

69 69

68 68

67 67

66 66

65 65

64 64
0 2 4 6 8 10 0 2 4 6 8 10
Deformation (%) Deformation (%)

Figure 4. Young’s modulus of aluminium Figure 5. Young’s modulus of aluminium

measured 1 week after plastic deformation. measured 2 weeks after plastic deformation.
72
71
70
69
68
Young modulus (GPa)

67
66
65
64
63
62 Determined by tensile test
61
60
59
58
0 50 150 200 250 300 350
Time (h)

Figure 6. Evolution of Young’s modulus versus time (sample deformed at 3.7%).

From Figure 2, it is observed that the Young's modulus reaches a minimum value (5% of cold
deformation) with subsequent recovery of this parameter with successive cold working. The
modulus diminution at the lowest value is 5.5%. The results shown from eight hours after
deformation until two weeks showed little evolution in Young’s modulus values.
The diminution of Young’s modulus (E) with cold working and successive recovery has been well
stablished in previous works. Benito et al [15] observed in iron deformed by tensile test that E
diminished from 210 GPa (original value) to 196 GPa (6% elongation) and then stabilized at 198
GPa in successive cold working. This variation were related to the changes in dislocation density
and specifically, the diminution of E derived from the process in which dislocations can bow out
giving an extra elastic strain. The same behaviour was detected in pure aluminium deformed by
tensile test; in this case deformation was measured by electric extensometry [14]. In cold deformed
and aged aluminium alloys AA7075 and AA2024, the dislocation density increased with cold
working, as expected. However, the dislocation lines interacted with nanometric precipitates, and
the length of the segments between pinned points was very small. Thus, the dislocation can’t bow
out and there is no appreciable extra elastic deformation. For this reason, changes in Young’s
modulus must be minimal, and consequently, E values were similar and nearly independent of
plastic deformation level [17].
Figure 6 shows the evolution of Young’s modulus with time in the sample previously deformed at
3.7% elongation. It can be observed a quick recovery of Young’s modulus from the obtained value
immediately after plastic deformation, from 59.3 GPa to 66.0 GPa, measured 8 h after cold
working; then E recovers up to 67.5-68 GPa and maintains this value in 1 or 2 weeks.
Our research group [20] detected changes in Young’s modulus obtained immediately after plastic
deformation measured during unloading in two steels, UNS G10180 and UNS G10430. This
diminution was up to 20%. Results obtained also indicated that E partially recovers between
unloading at the next cycle of loading. These results are similar to those obtained by Morestin and
1352 THERMEC 2018

Boivin [3] in steels with 0.14 and 0.38%C; but these authors indicated that this behaviour was not
observed in aluminium.

Summary
• The best conditions for annealing of aluminium previously to apply cold working was 400ºC
in 2h 30min. In these conditions, values of 24.6±0.5 HV0.1 in the surface of the samples and
of 24.4±0.6 HV0.1 inside the samples were measured.
• The apparent modulus measured during unloading at different deformation level decreased
(10-15%) with respect to the Young modulus of the original material (69.2±0.8 GPa). This
instantaneous modulus after deformation is used in theoretical calculations for the prediction
of the springback of the deformed materials.
• Young's modulus reaches a minimum value after 5% of cold deformation was applied, with
subsequent recovery of this parameter with successive cold working. The modulus
diminution at the lowest value was 5.5%. The results from eight hours after deformation
until two weeks, showed little evolution in Young’s modulus values.
• In the evolution of Young’s modulus with time (sample deformed at 3.7% elongation), a
quick recovery of this parameter was observed from the obtained value inmediately after
plastic deformation, from 59.3 GPa to 66.0 GPa measured 8 h after cold working; then E
recovers up to 67.5-68 GPa and maintains this value in 1 or 2 weeks.
• Changes of Young’s modulus in aluminium with cold working needs to take into account in
simulation processes as occur with other metallic alloys.

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