Download pdf - Lj 3120772081

7/29/2019 Lj 3120772081

http://slidepdf.com/reader/full/lj-3120772081 1/5

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

7/29/2019 Lj 3120772081





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

7/29/2019 Lj 3120772081





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

7/29/2019 Lj 3120772081





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

7/29/2019 Lj 3120772081





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

at the Intl. Sympos. On Ceramic Materialsand Components for Engines, Arita, Japan,oct 97).

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,

3rd edition, Montreal (2000), p. 729.9. Jean Baralis, Gérard Maeder, Precis of

Metallurgy: (Development, structure- properties, standardisation), p.232,1ereédition, AFNOR-Nathan, Paris (1997).

10. M. Colombié and Coll, Materials: Metallicmaterials, p.867, Dunod, Paris (2000).

11. D. Altenpohl, a glance inside aluminium,

p.272, eldmeilen, Switzerland (1976).12. G. Roebben, O. Van der Biest, "impulse

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.