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Ahmed Hakem, Youcef Bouafia / International Journal of Engineering Research and
Applications (IJERA) ISSN: 2248-9622 www.ijera.com
Vol. 3, Issue 1, January -February 2013, pp.2077-2081
2077 | P a g e
Elasticity of the 42 000 hypoeutectic alloy in longitudinal
vibration mode
Ahmed Hakem*, Youcef Bouafia*
*Laboratory LaMoMS, Mouloud MAMMERI university of Tizi-Ouzou, 15000 Algeria.
ABSTRACTThe Technical Impulse Excitation (IET)
is one of the recent nondestructive techniques
which makes it possible to identify the frequencies
of resonance principal or fundamental on the one
hand and the frequencies of damping or internalfriction on the other hand of a specimen of
standardized and well defined form. These
frequencies of resonance or damping are closely
related to the chemical composition, the form,
dimensions and the density of the test specimenmachined from one of metals selected and which
governs our study. The fundamental
characteristics of the test specimen for this
purpose are the uniformity of their form and
their dimensions, the precision of their
measurements thus of that of their density andmainly metal studied must be isotropic. Once the
principal frequencies are determined, the
software Resonency Frequency Dumping Analys
(RFDA: Resonance Frequency Damping
Analyzes) calculates the Young’s Modulus, the
shear Modulus and the Poisson's ratio
The Technical Impulse Excitation allowsmeasurements which can be taken with the
ambient temperature or high temperature. The
standardized test piece can be of form
rectangular, cylindrical full or hollow and of a
disc full or pierced with a hole in the center. Liketechnique IET has a great advantage of being
nondestructive, the test piece can be thus used in
several experiments and on real parts
with ambient temperature or low or high
temperature (cryogenic temperature). [3, 4, 5]
Keywords - IET, elastic characteristics,
principal frequencies, vibration, longitudinal.
I. INTRODUCTIONThe study of the elastic properties of solid
materials is of a great importance from the scientific point of view as well as industrial and practical. .
Indeed, in industrial applications, it is required of the builder and the engineer to know in advance andwith precision, the elastic characteristics of materials used to ensure proper operation of their
realizations. This importance is not one of less fromthe scientific point of view, since these properties
also inform us about the nature of the the atomic
bonding, i.e. of the atomic bonding strengths. Thus,we can estimate the energies of atomic interactions.
In order to answer this requirement so much desirednot only by the scientists but also by the
manufacturers, the method of investigationTechnical Excitation, who belongs to the besttechniques used until now, allows to determine in a
simple way and specifies the elastic characteristicsof various solid materials. Moreover, knowing thatthis method is nondestructive, it is very interesting
to follow the evolution of these characteristics
during different heat treatments as well asmechanical operations on the same test piece. [1,
14]
II. PRINCIPE OF THE METHOD The Technical Impulse Excitation (IET), is
one of the recent nondestructive dynamictechniques, which makes it possible to determine theelastic characteristics of various solid materials
to room temperature.The elastic properties are intimately linked
to particular frequencies of resonance, called
primary or fundamental frequency, mechanical
vibration of a specimen. They depend greatly on thechemical composition (intrinsic elastic properties),the mass and geometry of the test specimen. Thus,
the elastic properties of a material can be calculatedif and only if the geometric shape (rectangular,cylindrical ... etc..), The mass and the resonantfrequencies of vibration of a given sample areknown. Using this technique, one can determine thedynamic Young's modulus E and the dynamic shear
modulus G (stiffness modulus) respectively bymeasuring the resonant frequency of vibration in thelongitudinal mode. Then the formula connecting E
and G is used to evaluate the Poisson's ratio.
The Technical Pulse Excitation is of greatimportance because it can also follow the evolution
of the elastic properties of solid materials during thetemperature variation: cryogenic and raisedtemperatures, on condition that making
modifications appropriate to the equipment of measuring equipment in order to compensate for theheating effect. Using this method, to calculate thevalues of the elastic characteristics, one determines
initially the principal frequencies of resonance of thetest piece of a given geometry.
The IET is particularly suitable to
determine the elastic modules of the homogeneous,
isotropic materials and which do not presentexternal defects the such surface cracks, shrinkage
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Ahmed Hakem, Youcef Bouafia / International Journal of Engineering Research and
Applications (IJERA) ISSN: 2248-9622 www.ijera.com
Vol. 3, Issue 1, January -February 2013, pp.2077-2081
2078 | P a g e
pipes and other deformations. Simple method, it hasmany advantages: This dynamic method as well hasseveral advantages by report with the static
techniques of loading as to those of resonance whichrequire a continuous excitation.a- It is nondestructive and can be used for test piece
intended for other tests. b- Unlike other techniques, one uses a tool of impactand very simple supports to excite by impulse thetest piece.
c- This technique is very useful in quality control of the various parts. [3, 4, 5, 6, 12, 13]
III. EQUIPMENT - RFDA - R ESONANT
FREQUENCY AND DAMPENING ANALYZER .
[3, 4]
RFDA SYSTEM 21
RFDA system 21 is used for measurement
of pulse excitation at room temperature. Thesamples are mechanically struck by hand with ahammer small flexible screen. The system RFDA 21is used to measure the resonant frequency and theinternal friction or damping samples al shapes anddetermine the Young's modulus, shear modulus,
Poisson's ratio of rectangular bars, discs, bars ,hollow tubes and disks with a hole in the center.
MOUNTING THE TEST SPECIMEN ON THE
SUPPORT PARTThe test piece is fixed on the support part by means
of special springs.
Window showing the waveform of the longitudinal
vibration (a), the peak of the main frequency (b), the
values of the principal resonance frequency and theattenuation capacity (c), the values of E and E ( d).
IV. EXPERIMENTAL PROCEDURE 4.1 Investigated material
The material used is donated by SNVI .This is the aluminum-based alloy containing 7%silicon in weight percent, an amount of less than 1%magnesium, and some trace impurities. After analysis, the samples sand cast metal shell and
gravitation have the following chemicalcomposition:
Chemical elements Si Mg Fe
% Depending analysis 6,85 0,35 0,15
Results of chemical analysis of controlsamples after casting sand and shell
4.2 Development of the alloy studied
4.2.1. Casting The melting of the metal takes place in a
gas oven production is tiltable front to rear,
comprising a graphite crucible capacity 350Kg
whose load is made approximately 40% of ingotsin new AlSi7Mg standard dimensions, compositionand specified characteristics., supplied by theFrench company Pechiney and a mixture of casting
jets 60% return (appendices supply, evacuation,regulation, defective parts and scrap ).
4.2.2 Molding This alloy is prepared by two different
methods: sand casting and die casting considering
for three states; crude of casting noted: F,soaked designated: T, aging noted: T46
4.3 Form of the test specimenTo determine the Young's modulus, weused the longitudinal vibration mode.
a b
c
d
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Ahmed Hakem, Youcef Bouafia / International Journal of Engineering Research and
Applications (IJERA) ISSN: 2248-9622 www.ijera.com
Vol. 3, Issue 1, January -February 2013, pp.2077-2081
2079 | P a g e
The measurements were performed on rectangular specimens (Fig. 1) for the previous mode at roomtemperature. For obtaining reliable and accurate
results and to carry out our measurements, virtuallyall precautions have been taken into account.Among them we can mention the most important
- The measuring accuracy of the coasts of the test piece is largely higher than 0.1 mm.- The value of the dimension thickness must beuniform along the length and of the width of the test
piece.Before placing the test piece on the door
sample, we carried out the following operations:
- Calculation of the median values of its dimensions by taking a certain number of measurements (in preference to less 05) in various places of thesample (it is recommended that the step of
measurement either identical and the taking away or carried out along dimension considered).
- To carry out the weighing of the sample (at least03 measurements) to determine its average mass. [3,4]
4.4 Measurements in longitudinal mode
Fig. 1 - Form of the specimen for testing Impulse
Excitation Technique dynamic
Fig. 2 - Installation diagram of the fastening deviceof the test piece (1) and excitation of a mechanical or acoustic vibration mode longitudinal.1 - sample,
2 - Drive, 3 - sensor signal, 4 - system son and special springs for fixing the specimen (sampleholder), 5 - support (tablet).
After taking measurements and dimensionsof the weighing of the sample (1), placing itvertically suspended in the sample holder (5) with
the aid of special son (4) attached to the springs,fixed at their turn to the base (5). Another system isdesigned for adjusting the tension of the son. The
whole rests on a system of shock. This automaticallyeliminates all external vibration that significantlydisrupt the measurements
After this operation of measurements, one
actuates the software of device RFDA measurement by choosing window external first of all then Set
external measurement information into which oneintroduces the data of mass and dimensions. Of thewhole of the frequency spectrum of resonance posted, only the principal frequencies, those whose
amplitude of signal FFT (Fast Fourier Transformations) is maximum, will be taken intoaccount. [3, 4, 5, 6]
V. EQUATIONS OF THE ELASTIC
CHARACTERISTICS IN MODE OF
LONGITUDINAL VIBRATION.The dynamic Young’s modulus E of the
test piece having a principal frequency of resonanceof vibration in longitudinal mode F is given by the
equation below (ref. ASTM E 1876-97):
2 2
9
4. . ..
10
L f E K
with
22 2
2
. .1
i K
L
L f
i
- length of the bar in (mm) ;- principal frequency of resonance inlongitudinal mode of vibration in (Hz);- density of the test piece in (g/cm
3 );
-12
l i , l – width of the bar in (mm)
and4
d i , d – diameter of the bar in
(mm)
VI. EXPERIMENTAL RESULTS The objective consists in following the
evolution of the elastic characteristics of the alloy
hypoeutectic AlSi7Mg for three states: crude of casting noted: F, soaked designated: T, aging noted:T46
AlSi7Mg is an alloy of foundry with heattreatment having a good flow and a good behavior
1
3
4
2
5
l
Lt
Li Li
I.
e
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Ahmed Hakem, Youcef Bouafia / International Journal of Engineering Research and
Applications (IJERA) ISSN: 2248-9622 www.ijera.com
Vol. 3, Issue 1, January -February 2013, pp.2077-2081
2080 | P a g e
with corrosion.The test piece crude of casting undergo thefollowing specific heat treatments of
T46 designation: - heating and setting in solutionwith homogenization at a well determinedtemperature and time, - follow-up immediately of a
quenching water with room temperature (20 to 25°C), - ageing natural with environment or maturation and followed immediately – of anartificial ageing or income at a temperature for quite
selected lengths of time.First of all, we determined the Young's
modulus corresponding to the various states
considered of our alloy by the mode of longitudinalvibration.Dimensions and the masses of the test piece used, of parallelepipedic form, are given to the tableau.1.
These values represent the averages of 05 measurestaken on each dimension of the specimen.
With an aim of obtaining very approximate valuesof the elastic characteristics, measurements weretaken with a very high degree of accuracy largelyexceeding those required for the calculation of E.
Moreover, all the recommendations were respected:- uniformity of dimensions of the sample.- the length of the sample is largely higher than 2.5
times the dimension thickness.In our case, the material considered has a polycrystalline structure. It can be then regarded ashomogeneous and isotropic. [1, 2, 7, 8, 9, 10, 11,14]
Table 1 - Mean dimensions geometric of the test
pieces of the alloy hypoeutectic AlSi7Mg
State F
(a) f L (Hz) E (GPa) E (GPa)
1 53451 75,52 1,18
2 53450 75,51 1,18
3 53449 75,51 1,18
4 54449 75,52 1,18
5 53451 75,52 1,18
Average 53650 75,52 1,18
State T
(b) f L (Hz) E (GPa) E (GPa)
1 52760 73,25 1,50
2 52762 73,25 1,50
3 52760 73,25 1,50
4 52760 73,25 1,50
5 52758 73,24 1,50
Average 52760 73,25 1,50
State T46
(c) f L (Hz) E (GPa) E (GPa)
1 52341 70,46 2,08
2 52345 70,47 2,08
3 52342 70,46 2,08
4 52343 70,46 2,085 52344 70,47 2,08
Average 52343 70,46 2,08
values of 05 measurements of the elasticCharacteristics of AlSi7Mg measured longitudinal
vibration mode: fL - resonance frequency,
E - Young's modulus, E - absolute uncertainty
< fL > ( Hz) < E > (GPa) E (GPa)
F 53650 75,52 1,18
T 52760 73,25 1,50
T46 52343 70,46 2,08
Table 2 - Average values of 05 measurements of
the elastic Characteristics of AlSi7Mg measured inmode of longitudinal vibration:< fL > – frequency of average resonance,
< E > – average Young’s modulus, E - absoluteuncertainty of E.
Length(mm)
Width (mm) Thickness(mm)
F 50,12 ± 0,01 9,98 ± 0,02 4,99 ± 0,06
T 50,04± 0,05 10,04 ± 0,05 4,98 ± 0,06
T46 49,97 ± 0,04 9,92 ± 0,09 5,05 ± 0,09
Mass (gramme) Density (g/cm3)
F 6,557 ± 0,001 2,629 ± 0,001
T 6,571 ± 0,001 2,625 ± 0,001
T46 6,448 ± 0,001 2,573 ± 0,001
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Ahmed Hakem, Youcef Bouafia / International Journal of Engineering Research and
Applications (IJERA) ISSN: 2248-9622 www.ijera.com
Vol. 3, Issue 1, January -February 2013, pp.2077-2081
2081 | P a g e
graph, histogram and sector average Young’smodulus of 03 states considered
VII. CONCLUSION
Throughout homogenization, the atoms of the aqueous solution probably migrate towards thegrain boundaries which constitute the seatsfavorable for the reception of any kind of specific
defects. This diffusion is accentuated of advantageduring aging This phenomenon of displacement of the atoms towards the grain boundaries causes an
impoverishment of the element of aqueous solutioninside the grains. In addition, the dynamic Young'smodulus E and the dynamic shear modulus G
(stiffness modulus) are closely related to the energyof interaction created by the whole of the atomic bonding strengths. This report, the reduction in the
content of So inside the grains involves a fall of theenergy of interaction. Consequently the elasticcharacteristics decrease of the rough state crude of casting in a soaked state and aging. [1, 14]
Bibliographical references1. Ahmed HAKEM, memory of magister,
Microstructure and Mechanical propertiesof the Hypoeutectique Alloy AlSi7Mg,2005, Department Genius - Mechanics,
Faculty of the Genius of Construction,University Mouloud MAMMERI of Tizi – Ouzou Algeria.
2. Spinner and W. E. Tefft, A Method for determining Mechanical ResonanceFrequencies and for Calculating Elastic
Moduli from These Frequencies,Proceedings, ASTM, 1961, pp. 1212 – 1238.
3. G. Roebben, B. Bollen, A. Brebels, J. VanHumbeek, O. Van Der Biest, "Impulseexcitation apparatus to measure resonant
frequencies, elastic moduli and internalfriction at room and high temperature",Review of Scientific Instruments, Vol. 68, pp. 4511-4515 (1997).
4. G. Roebben, O. Van Der Biest, "Dampingand elastic properties by impulse excitationtechnique for Quality Control", presented
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5. G. Roebben, O. Van Der Biest, Elastic and
anelastic properties of silicon nitride athigh temperatures by non-destructive
impulse excitation", Materials ScienceForum, 325-326, 167-172, (2000).
6. G. Roebben, R.G. Duan, D. Sciti, O. Vander Biest, "Assessment of the high
temperature elastic and damping propertiesof silicon nitrides and carbides with theimpulse excitation technique (IET)", J.
Europ. Ceram. Soc., 2002.7. J. Lemaître, J. - L. Chaboche, Mechanics of
solid materials, Dunod-Bordered, 2ndedition, Paris (1988) p. 544.
8. Jean-Paul Baïllon, Jean-Marie Dorlot, Of Materials, Ed. polytechnic School National,
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11. D. Altenpohl, a glance inside aluminium,
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excitation tests to determine the high
temperature elastic and damping propertiesof si3n4 and other ceramics".
13. G. Roebben, O. Van der Biest,"Recentadvances in the use of the impulse
excitation technique for the characterisationof stiffness and damping of ceramics,ceramic coatings and ceramic laminates at
elevated temperature".14. Ahmed HAKEM, Y. Bouafia, S. Naïli, A.
Bouhaci, industrial Development of aluminium alloys of AlSi7Mg
foundry, AlSi10Mg and AlSi13,International symposium - Characterizationand Modeling of Materials and Structures
November 16th, 17th and 18th, 2008 -
University Mr. Mammeri de Tizi-Ouzou,Algeria.