Low Cycle Fatigue (LCF) Behavior of AA6063 Aluminium Alloy at ...

International Journal of Emerging Technology and Advanced Engineering

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100

Low Cycle Fatigue (LCF) Behavior of AA6063 Aluminium

Alloy at Room Temperature Mazin Mahmood Yahya

1, Nilanjan Mallik

2, I Chakrabarty

3

1Research Scholar,

2Senior Assistant Professor, Mechanical Engineering Dept., IIT (BHU), Varanasi -221005, India

3Associate Professor, Metallurgical Engineering Dept., IIT (BHU), Varanasi-221005, India

Abstract— Low cycle fatigue (LCF) behavior of as received

aluminum alloy AA 6063 was investigated at room

temperature condition. The influence of strain amplitude and

strain rate on the LCF behavior of AA6063 in the normalized

condition is reported. The tests were conducted at a constant

strain rate of 2*10-3 s-1 and various strain amplitudes (0.4%,

0.5%, 0.6%, 0.7%, 0.8% and 1%). Fatigue life was found to

decrease with increase of strain amplitude and decreasing

frequency. Microstructural features and failure mechanisms

studied through scanning electron microscopy (SEM)

confirmed low cycle fatigue failure nature. The high

amplitudes of testing was marked by extensive crack

branching and the formation of secondary cracks.

Keywords— Aluminum alloy, low cycle fatigue, Coffin–

Manson relationship, cyclic hardening, hysteresis loop,

simply supported fatigue testing

I. INTRODUCTION

Al–Mg–Si (6xxx) alloys containing magnesium and

silicon as major elements have been studied extensively

due to their technological importance and their exceptional

increase in strength as a result of precipitation hardening.

These alloys are mostly used in extruded products, as well

as for construction and automotive purposes. The ease with

which these alloys can be shaped, their low density, their

very good corrosion resistance and surface properties and

good weldability are factors that together with a low price

make them commercially very attractive alloy.

Fatigue is the progressive, localized, and permanent

structural change that occurs in a material subjected to

repeated or fluctuating strains at nominal stresses that have

maximum values less than (and often much less than) the

static yield strength of the material. Fatigue damage is

caused by the simultaneous action of cyclic stress, tensile

stress, and plastic strain [1]. When the load levels are low,

stresses and strains are linearly related, at high load levels

in the low cycle fatigue (LCF) regime the cyclic stress-

strain response and the material behavior are best modeled

under strain-controlled conditions [2]. The strain-based

approach for fatigue problems is widely used at present,

especially in the low-cycle fatigue (LCF) loading of

machine parts and structures.

Srivatsan, T. S. [3] studied the cyclic stress- and strain-

amplitude-control fatigue response of aluminum alloy

7055. Under total strain-amplitude control, the alloy

showed evidence of softening to failure, the degree of

cyclic softening increased with increasing temperature. For

both stress and strain amplitude control fatigue, the

macroscopic fracture mode was essentially identical, cyclic

fatigue fracture on a microscopic scale revealed features

reminiscent of locally ductile and brittle mechanisms.

Borrego, L. P., et al. [4] performed low cycle fatigue tests

in two Al-Mg-Si aluminium alloys with different chemical

composition, viz. 6082-T6 and 6060-T6 alloys. The tests

were undertaken in strain control with a strain ratio

( ). The geometry of the hysteresis loops and the

occurrence of Masing behavior are also analyzed. The

observed behavior is discussed in terms of the chemical

composition of the alloys with Mg2Si hardening particles

and Mn dispersoid content and fracture mechanisms. Alloy

6060-T6 exhibits nearly ideal Masing behavior, while alloy

6082-T6 presents significant deviations from the Masing

model. The type of cyclic deformation behavior in Al-Mg-

Si alloys seems to be influenced by the dispersoid phase.

The present paper deals with low cycle fatigue behavior

of as received AA 6063-T6 aluminum alloy at room

temperature. The strain controlled fatigue response of the

alloy to cyclically softening and hardening is also

discussed. The effects of strain rate and strain amplitude on

LCF behavior are also investigated. Fatigued samples are

examined using scanning electron microscopy in order to

understand the failure mechanism (SEM).

II. METHODOLOGY

A. Theory

Of late, low cycle fatigue analysis of AA 6063

aluminum alloy is being performed by strain based

approach [5-6]. The total strain amplitude is resolved into

elastic and plastic strain components based on data from

the steady-state hysteresis loops. The strain-life fatigue

curves or low-cycle fatigue curves, are plotted on log–log

scales.



101

Furthermore, Basquin [7] observed that strain-life data

could be linearized on log–log scale and can be represented

by

Where, is true strain amplitude, is reversals to

failure, is fatigue strength coefficient, and b is fatigue

strength exponent. Coffin and Manson also observed that

the plastic strain-life data could also be linearized on log–

log scale. This line can be expressed as

Where, is plastic strain amplitude, is fatigue

ductility coefficient, and c is fatigue ductility exponent.

The total strain amplitude can then be considered as the

summation of elastic and plastic amplitudes and the

resulting strain-life curve can be expressed as:

Where, is the total strain amplitude which consists

of elastic and plastic parts viz. and , E is the

modulus of elasticity, is the fatigue strength coefficient,

b is the fatigue strength exponent, is the fatigue ductility

coefficient and c is the fatigue ductility exponent. The life

at which elastic and plastic components of strain are equal

is called the transition fatigue life (2Nt). For lives shorter

than 2Nt the deformation is mainly plastic, whereas for

lives longer than 2Nt the deformation is mainly elastic.

Since fatigue damage is assessed directly in terms of

local strain, this approach is also called the ‘‘local strain

approach”. A reasonable expected fatigue life (number of

stress cycles Ni), based on the nucleation or formation of

small macro cracks, can then be determined iteratively

using Coffin–Manson equation [9-10, 14-17]. Other

material parameters regarding to the low-cycle fatigue (the

cyclic strength coefficient, K’, and the cyclic strain

hardening exponent, n’) can be estimated from the low-

cycle fatigue parameters as follows [14-17]:

B. Experiments

The material used in this paper is the as received

aluminum alloy AA 6063 from Hindalco Company.

Monotonic tension and constant amplitude fully reversed

fatigue tests for the alloys tested in this study were

performed using test methods specified by ASTM

Standards E8 and E606, respectively [11]. Tensile tests

were carried out with cylindrical Hounsfield tensile

specimens of gauge length, 15.4 mm and gauge diameter,

4.5 mm as shown in Fig. 1 at a nominal strain rate of 1.2 *

10–4

s–1

using Instron 4206 machine having loading

capacity of 100KN.

Fig. 1 Tensile test sample

The simply supported samples for low cycle fatigue test

are prepared in Machine shop and CISF Shops as shown in

Fig. 2. A digital closed-loop servo-hydraulic computer

controlled (Model No.: 810 MTS) 50 kN axial load frame

fatigue testing machine as shown in Fig. 3 is used for low

cycle fatigue tests.

Fig. 2 Simply supported fatigue test specimen

(All dimensions are in mm)

Polishing of the surfaces of the samples is initially done

by emery paper made of silicon carbide with different

grades viz. P400, P600, P800, P1000 and P1500. The

polishing was done with emery papers starting from coarse

i. e. P400 and ending with fine i. e. P1500. Next, liquid

alumina polishing is done with alumina solution and cloth

obtained from Chennai Metco Pvt Ltd in Machine shop.



102

Fig. 3 Fatigue testing setup

III. RESULTS AND DISCUSSION

Chemical composition results of AA 6063 as received by

chemical analysis method and EDAX method are shown in

Table 1. It may be seen that while concentration of most of

the elements is almost comparable in the two analysis, that

of Si and Mg is relatively higher. Chemical composition

analysis by two methods provides good agreement.

Table 1

Chemical composition of as received AA 6063 alloy

Element

Weight%

Chemical

Analysis

EDAX

Analysis

Al (Balance) 99.17 88.60

Si 0.612 1.38

Mg 0.0798 0.82

Fe 0.0280 0.98

Cu 0.0374 0.64

Zn 0.0019 0.63

Mn 0.0132 0.51

Ti 0.0024 0.49

Cl -- 0.36

Ga 0.0197 --

S 0.0193 --

Ho 0.0070 --

Pb 0.0019 --

O -- 5.60

Error 0.83 0.26

The SEM-EDAX system used is FEG Quanta -200. The

EDAX spectra collected from polished cross-sections of

AA 6063 surface is elaborated in a previous publication by

the authors [18]. The results are not repeated here. The

spectra confirm the alloy to be of aluminium.

The result of the tensile test is provided in Table 2. The

XRD spectra of the sample clearly shows the major 2θ

peaks of Al. Table 3 shows diameters of the crystallize size

and intensity of Bragg peaks at different 2θ angles as

obtained from XRD test and compared with that available

in JCPDF (Joint Committee for Powder Diffraction

Standards) File No. 851327 for aluminium Cubic system.

The crystal structure in the sample is investigated

through XRD analysis, the crystal structure is predicted

from the intensities and the angular position of the Bragg

peaks in the diffraction pattern as shown in Fig. 4. The total

broadening is due to instrumental broadening and

broadening due to average domain size and the lattice

micro strains.

Vickers micro hardness (HV) is measured on the plane

surface with different loads. Prior to each hardness

measurement, the surfaces of the specimen are polished

mechanically using emery paper and alumina liquid to

remove the surface reactions. An average of at least three

readings on the surface of the specimen is taken to obtain a

micro hardness value.

Table 2

Tensile properties of as received Aluminum alloy AA 6063-T6 at

room temperature

Value Symbol Parameter

169.67 MPa σYS Yield stress

214.8 MPa σULT. Max. tensile stress

54.2 MPa σf Fracture strength

0.002457 εYD Yield strain

68 GPa E Young’s modulus

0.242 εf % Strain at failure

J/3

7 4 14 7 Kc Toughness

16651 σULT. / σYS

Micro hardness test is carried out using HMV-2

shimadzu micro hardness tester to evaluate the strength and

ductility of the AA 6063 alloy subjected to the different

applied load.



103

Strain control was used in all low cycle fatigue tests,

which were conducted in load control mode. For these

tests, strain control was used initially to determine the

stabilized load. Then load control was used for the

remainder of the test. For the strain-controlled tests, the

applied frequencies ranged (0.1%, 0.8%, 0.7%, 0.6%, 0.5%

and 0.4%), depending on the applied strain amplitude. All

tests were conducted using a triangular waveform. Test

data were automatically recorded at regular intervals

throughout each test, and stable stress and strain amplitude

data at about midlife were used to generate the fatigue

properties. In low cycle fatigue it is plastic strain, which

dominates, it is the principal cause of hysteresis loops. The

area enclosed by a loop is proportional to the energy

irreversibly by the material during one load cycle.

Table 3

Intensity and crystallite diameter

S.

N

o.

Miller

indice

s

d(A) Intensity

JCPD

F XRD

JCPD

F XRD

1 1 1 1 2.3379 2.3428

6 999

716.4

1

2 2 0 0 2.0247 2.0286

8 455

509.4

4

3 2 2 0 1.4316 1.4337

1 233

111.7

3

4 3 1 1 1.2209 1.2225

1 228

211.5

8

5 2 2 2 1.689 1.1702

7 63

50.27

Stress response is known to depend on the ratio of

monotonic ultimate stress and monotonic yield stress (σYS).

Metals with σUTS/σYS <1.2 undergo softening while those

with σUTS/σYS > 1.4 exhibit cyclic hardening. The ratio of

σUTS/σYS for the present alloy is presented in Table 2. The

term fatigue hardening is used when the stresses increase

with the number of cycles at a given constant plastic strain

amplitude, on the other hand, if the plastic strain amplitude

decreases with the number of cycles at constant stress

amplitude, cyclic hardening occurs, which is in accordance

with the customary terminology (irrespective of tests under

the constant plastic strain or stress amplitude constant) [14-

17]. Cyclic hysteresis loop stress-strain curves plotted at

different strain amplitude 0.4%, 0.5%, 0.6%, 0.7%, 0.8%

and 1% and are shown in Fig. 5. It can be observed that

when the strain amplitude increases the hysteresis loop area

increases.

20 40 60 80 100

0

1000

2000

3000

4000

5000

[5]: d=1.1703(2),

2-theta=82.33(2)

[4]: d=1.22251(8), 2-theta=78.112(6)

[3]: d=1.4337(17), 2-theta=64.995(9)

[2]: d=2.0287(2), 2-theta=44.630(5)

Inte

nsi

ty (

cps)

2- Theta (Deg.)

X-RD Meaasurement- as recevied

[1]: d=2.3429(2), 2-theta=38.389(4)

Fig. 4 XRD pattern for AA 6063 alloy

The cyclic stress response of the alloy at different strain

amplitude conditions is presented in Fig. 6. This is plot of

tensile stress (peak stress) with the number of cycles to

failure Nf, illustrates that stress response decreases with

increase in strain amplitudes.

-0.3 -0.2 -0.1 0.0 0.1 0.2 0.3

-12

-10

-8

-6

-4

-2

0

2

4

6

8

10

12

Stre

ss A

rray

(kN

/mm

²)

Strain Array (mm/mm)

0.4%

0.5%

0.6%

0.7%

0.8%

1%

Fig. 5 Cyclic hysteresis loop stress-strain curves plotted at different

cycles numbers at different strain amplitude.

The extent of initial hardening also decreased with

increasing strain amplitudes. Cyclic stress–strain curves

plotted with cyclic stress and strain corresponding to half-

lives are important means of characterizing stress response

of the material under cyclic loading. Figure 7 illustrates

average stress vs number of cycles of failure.

Figure 8 show that when the frequency

increases the

number of cycles to failure also increases. The total

average stress amplitude decreases with number of cycles

of failure as illustrated in Fig. 9.



104

Figure 10 demonstrates that with the increase in

frequency, the strain amplitude decreases. The plastic strain

amplitude increase with the number of cycles to failure as

shown in Fig. 11.

10 100 1000

160

180

200

220

240

260

280

Ten

sile

Str

ess

Am

plit

ud

e ,

MP

a

Numbers of Cycles

1 %

0.8 %

0.7 %

0.6 %

0.5 %

0.4 %

Fig. 6 Variation of stress amplitude with number of cycles for

different strain amplitudes

Figures 12 to 17 show cyclic stress-strain curves at

0.4%, 0.5%, 0.6%, 0.7%, 0.8% and 1.0% strain amplitudes,

respectively, for different cycles. By looking at the

movement of the cycles cyclic stress-strain behavior is

concluded.

It is found that only 0.5% and 0.6% strain amplitude

cases show cyclic hardening while all other cases show

cyclic softening behavior. Though behavior can be roughly

predicted from σUTS/σYS ratio, it is heavily dependent on

strain amplitudes.

Optical and electron microscopes are used in the study

of fracture microstructure, in microfractography. Plastic or

ductile fracture is preceded by macroscopic plastic strain

due to deformation in the slip planes as a result of higher

fracture resistance in the cleavage planes and at grain

boundaries. Plastic fracture is also called fibrous fracture

because of its appearance or shear fracture because of the

crack propagation mechanism.

The optical micrograph has been taken with different

magnification as shown in Fig. 18. The Samples for optical

metallography were etched with a solution containing by

volume 5% HNO3, 10% HF and 85% H2O at room

temperature and the microstructures were examined under

Metallux-3 optical microscope. At 50X magnification there

is no visible crack in the micrograph before test.

Dimples as a rule arise from microvoids, which exist in

the material and grow during loading until they combine

under plastic strain and plastic fracture. There were mainly

two dimple populations: the first one was related to Si &

Mg particles, the second population consisted of very small

dimples located in the space between the reinforcement

particles associated with the intermetallic particles.

Table 5

Variation of number of reversals to failure (2Nf) with different components of strain amplitude at RT for the alloy AA6063 at fracture point of each

sample

Strai

n

Amp

.

(%)

Strai

n

Rate

(*10 -

3)

Freq.

(Hz)

Time

(hr

:min)

Stress

peak

(kN/

mm2)

at

fractur

e

Stress

Valley

(kN/

mm2)

at

fractur

e

Stress

Amp.

(GPa),

Δσ/2

at

fractur

e

Reversal

s

to

failure

(2Nf) at

fracture

Strain

Max.

(mm/

mm)

at

fractur

e

Strain

Min.

(mm/

mm)

at

fractur

e

Strain

Amp.

Δε/2

at

fractur

e

1

2

0.050

0

1:18 0.1584 0.2021 0.1802

5

236 0.0069 0.0069 1

0.8 0.062

5

1:57 0.2192 0.2291 0.2241

5

440 0.0043 0.0041 0.0042

0.7 0.071

4

2:15 0.2017 0.2338 0.2177

5

580 0.0037 0.0033 0.0035

0.6 0.083

3

3:40 0.1659 0.2039 0.1849 1100 0.0037 0.0031 0.0034

0.5 0.100

0

4.59 0.1599 0.2090 0.1844

5

1724 0.002 0.0018 0.0019

0.4 0.125

0

6:18 0.0040 0.0040 0.001 2834 0.0005 0.0007 0.0006



105

10 100 1000 10000

120

150

180

210

240

270

300

Ave

rag

e S

tre

ss ,

MP

a

Number of Cycles to Failure, Nf

Average Stress at Strain Amplitude 1 %

Average Stress at Strain Amplitude 0.8 %





Fig. 7 Variation of Average cyclic stresses with number of cycles for

as received AA 6063 alloy

0 500 1000 1500 2000 2500 3000

0.045

0.060

0.075

0.090

0.105

0.120

0.135

Fre

qu

en

cy H

z

Reversals to Failure (2Nf)

Frequency Vs Reversals to Failure (2Nf)

Fig. 8 Frequency with the reversal to failure

0 500 1000 1500 2000 2500 3000

170

180

190

200

210

220

230

Tota

l Ave

rage

Str

ess

Am

plit

ud

e (

MP

a)

Number of Cycles to Failure , Nf

Total Average Stress Amplitude

Fig. 9 Total Average stress amplitude with number of cycles to failure

0.04 0.06 0.08 0.10 0.12 0.14

0.4

0.6

0.8

1.0

1.2

Stra

in A

mp

litu

de

%

Frequency Hz

Strain Amplitude Vs Frequency

Fig. 10 Variation of strain amplitude with

Frequency

0 500 1000 1500 2000 2500 3000

0.4

0.5

0.6

0.7

0.8

0.9

1St

rain

Am

plit

ud

e %

Reversals to failure (2Nf)

Strain Amplitude %

Fig. 11 Variation of strain amplitude with reversal to failure

-0.004 -0.002 0.000 0.002 0.004

-0.21

-0.14

-0.07

0.00

0.07

0.14

0.21 Hystersis Loops at 0.4% Strain Amplitude

and 2*10-3

Strain Rate

Stre

ss A

rray

(K

N/m

m2

)


Cycle No. 2829

Cycle No. 2000

Cycle No. 800

Cycle No. 50

Fig. 12 Cyclic Stress-Strain Response at 0.4 % Strain Amplitude and

2*10-3 Strain (cyclic softening)



106

-0.006 -0.004 -0.002 0.000 0.002 0.004 0.006

-0.25

-0.20

-0.15

-0.10

-0.05

0.00

0.05

0.10

0.15

0.20

0.25 Hysteresis Loops at 0.5 % Strain Amplitude

and 2*10-3

Strain Rate

Stre

ss A

rray

(K

N/m

m2 )


Cycle No. 50

Cycle No. 500

Cycle No. 1000


2*10-3 strain rate (cyclic

hardening)

-0.006 -0.004 -0.002 0.000 0.002 0.004 0.006

-0.25

-0.20

-0.15

-0.10

-0.05

0.00

0.05

0.10

0.15

0.20

0.25 Hysteresis Loops at 0.6 % Strain Amplitude

and 2*10-3

Strain Rate

Stre

ss A

rray

(K

N/m

m2 )


Cycle No. 10

Cycle No. 50

Cycle No. 100

Cycle No. 500

Cycle No. 1000


2*10-3 strain rate (cyclic hardening)

-0.008 -0.006 -0.004 -0.002 0.000 0.002 0.004 0.006 0.008

-0.3

-0.2

-0.1

0.0

0.1

0.2

0.3 Hysteresis Loops at 0.7% Strain Amplitude

and 2*10-3

Strain Rate

Stre

ss A

rray

(K

N/m

m2 )


Cycle No. 5

Cycle No. 80

Cycle No. 200

Cycle No. 500

Cycle No. 575

Fig. 15 Cyclic stress-strain response at 0.7 % strain amplitude and

2*10-3 strain rate (cyclic hardening)

-0.010 -0.005 0.000 0.005 0.010

-0.3

-0.2

-0.1

0.0

0.1

0.2

0.3 Hysteresis Loops at 0.8% Strain Amplitude

and 2*10-3

Strain Rate

Stre

ss A

rray

(K

N/m

m2 )


Cycle No. 430

Cycle No. 200

Cycle No. 20

Cycle No. 5

Fig. 16 Cyclic stress-strain response at 0.8 % strain amplitude and

2*10-3 strain rate (cyclic softening)

-0.010 -0.005 0.000 0.005 0.010

-0.3

-0.2

-0.1

0.0

0.1

0.2

0.3

Hystersis Loop at 1% Strain Amplitude

and 2*10-3

Strain Rate

Stre

ss A

rray

(K

N/m

m2

)


Cycle No. 1

Cycle No. 10

Cycle No. 100

Cycle No. 190

Cycle No. 225

Fig. 17 Cyclic stress-strain response at 1% strain amplitude and 2*10-

3 strain rate (cyclic softening)

(a) (b)

Fig. 18 Optical micrograph for as received AA6063 samples before the

test at: (a) 50x magnification, (b) 100x magnification



107

(a) (b)

Fig. 19 SEM picture before the test at:

(a) 40000x magnification , (b) 80000x magnification

Fig. 19 illustrates scanning electron micrographic

pictures before the test at high magnification. The location

c has a relatively coarse grain structure. A cross-sectional

view of this fatigue failure shows that the piece is domed

with the smallest radius near the outer edge. Also of

interest is the shape of the overload zone. The fact that it is

elongated indicates some plane bending loads were present,

as demonstrated in Fig. 20 [19]. Micro cracks (initiating

fracture) began almost simultaneously on parts of the

circumference of the specimen. Here we can see the

overload zone, or fast fracture zone, where the final

catastrophic failure occurs.

The pictures of Fig 21 look like a river on physical map,

showing the direction of progression of the fatigue crack.

And show up most frequently in the relatively fast-growing

sections of the fatigue zone, and, other than indicating the

direction of the crack growth [19].

(a) (b)

(c) (d)

(e) (f)

Fig. 20 SEM over view pictures for LCF simply supported samples at:

(a) 1% strain amplitude, (b) 0.8% strain amplitude

(c) 0.7% strain amplitude, (d) 0.6% strain amplitude

(e) 0.5% strain amplitude, (f) 0.4% strain amplitude

This zone is usually macroscopically brittle, although in

a small percentage ductility is present, and indicates the

magnitude of the load when the final fracture occurs, that

is, a large overload zone indicates the part was heavily

stressed at the time of final fracture. The arrows as shown

in Fig. 21(e) and Fig. 21(f) indicate the direction of the

principal fatigue crack propagation.

Striations are the trace of a crack advancing in each

cycle. They are perpendicular, or almost so, to the direction

of crack propagation, although various exceptions have

been noted. Striations may be continuous and regular, as in

aluminum alloys, with the separation between them varying

with the stress and the crack growth rate. They may also be

discontinuous and irregular as illustrated in Fig. 21. In

same time at high magnification we can see the Progression

Marks (beach marks), and these marks tell us exactly how

the crack face has progressed across the test piece. Figure

21(e) and 21(f) show coarse and fine ductile dimples on the

fracture surface of AA 6063 material (strain amplitude =

0.5% and 0.4% R=-1, triangular wave).

(a) (b)



108

(c) (d)

(e) (f)

Figure 21 Striations arrays on the surface of a fatigue fracture of

AA6063-T6 of simply supported samples

(a) 1% strain amplitude with 100µm,

(b) 0.8% strain amplitude with 200µm

(c) 0.7% strain amplitude with 100µm,

(d) 0.6% strain amplitude with 50µm

(e) 0.5% strain amplitude with 50µm,

(f) 0.4% strain amplitude with 100µm

IV. CONCLUSIONS

In the present paper, low cycle fatigue behavior of as

received AA 6063-T6 alloy at room temperature is

investigated using strain controlled Simply Supported beam

test. Microstructural observation are done using both

optical microscopy and scanning electron microscopy.

Effect of variation of Strain Amplitude on fatigue life is

presented. Cyclic softening was observed at three cases of

strain amplitudes and cyclic hardening was observed at

other three cases of strain amplitudes. The increase in the

degree and the rate of softening at higher strain amplitudes

is associated with increase in the number and more

complete shearing of the ordered Si and Mg precipitates,

from increase in the number of slip bands and glide

dislocations. The increase in the number of glide

dislocations in each cycle, with increase in strain amplitude

occurs from increase in the effective strain rate to maintain

the cyclic frequency at constant level.

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