45
*River Water : Qarmat Ali River- Basrah-Iraq
Study the Effect of Cold Rolling of Aluminum-Magnesium (5083) Alloys on the Erosion-Corrosion Test at the Impact Angles (30°, 90°) in River Water*
Safaa A.S. Almtori1, Haider T. Naeem1 and T. A. Selman2
1Materials Engineering Dep., College of Engineering, and
2Physics Dep., College of Science, Basra University - Iraq
Abstract. The present work investigates the effects of cold rolling on the erosion- corrosion rate of (Al-Mg). The alloys specimens which were used for the marine applications were cold rolled at different reductions (2.5, 5, 7.5%), then tested for erosion- corrosion using dynamic rig at different exposure time (0-15 h). to measure the erosion–corrosion rate at impact angles (30º, 90º) . The results showed that the heat treatment of alloys (5083) didn’t improve the erosion- corrosion resistance; this was noticed in the homogenized specimens. Erosion/corrosion resistance at impact angles (30º, 90º) was found good at two impact angles, While erosion/corrosion resistance for (5083) alloys at impact angle 90º was found higher than impact angle 30º, The specimens of the rolled alloys (2.5, 5, 7.5%) reductions showed erosion/corrosion resistance higher than before and after homogenizations process at
both impact angles of (30º & 90º) respectively. The percentage error that obtained from experimental and theoretical at impact angles 30º & 90° were 25 % and 30% respectively.
Keywords: Cold Rolling, Aluminum-Magnesium Alloys, Erosion- Corrosion, Impact Angles.
1. Introduction
The Al-Mg series alloys as important in the marine applications due to its characteristics, strain hardening, excellent corrosion resistance (even in saline water), very high toughness building & construction, automotive, cryogenic and marine applications.
1.1 Cold Rolling
Cold rolling is a metal working process at temperature below its recrystallization temperature, which is associated by the of increase the yield strength, hardness, but the ductility decreases. But ductility can be restored by annealing, the metal could be further rolled without fracture [1].
1.2 Annealing Process
Commercially is important process due to relieve stresses and restores the ductility to a metal that has been severely strain-hardened by different processes.
1.3 Erosion -Corrosion Mechanisms
Erosion- corrosion is the disturbance of the surface film of a material caused by high velocity flow rate. Many models have been suggested to explain that mechanism, but the platelet mechanism is a good way to explain the basic mechanism. The small flow of fluid may cause a small divot in the passive film of the material. But high turbulence flow will damage the protective oxide film, and the velocity at which the divot forms, Erosion-corrosion takes form of grooves, wave gullies and tear dropped shaped pits [2].
Haga et al. [3] had investigated of the ability of the high speed roll casting of 5182 aluminium alloy. Appropriate twin roll caster to cast the 5182 strip was researched. Method used in the present study was an unequal diameter twin roll caster and a vertical type high speed twin roll caster equipped with mild steel rolls without parting material. Their findings are that the vertical type high speed twin roll caster was effective to cast 5182 strip at high speed ,as it is possible to be cast at 10 times higher speed than a conventional twin roll caster for aluminum alloy.
An et al. [4] had carried out preaging treatment of AA6000 alloys be focusing on the alloy development for automotive applications. A heat treatment at 230 to 260 °C for over 60 seconds had been adapted to increase the strength of the material, in particular, the yield strength, significantly.
Ravi et al. [5]: The effect of Fe content (0.2 to 0.6 pct) on the microstructure and mechanical properties of a cast Al-7Si-0.3Mg (LM 25/356) alloy has been investigated. An increase in Fe content increased the volume percentage of Fe-bearing intermetallic compounds (β and π phases), contributing to the lower yield strength (YS), ultimate tensile strength (UTS), percentage elongation, and higher hardness. An addition of 1 pct MM to the alloys containing 0.2 and 0.6 pct Fe was found to refine the microstructure.
Hamed et al. ]6[: The experimental work on turbine blade surface deterioration due to erosion were carried out by the measurements of erosion which was found to increases with impact angle and particle size.
Levin ]7[: While he had suggested a model for solid particle erosion behavior of ductile alloys. He found that erosion parameter shows a good correlation to experimentally measured erosion rates for a variety of industrially important materials.
Tudor [8[: Other studies on erosion – corrosion wear model for the ball valve of crude petroleum extraction pump. He observed that the corrosion rate is variable in time for all materials, and for ceramic composites the corrosives rate has maximum values in time 1440 hr.
Nestorovic et al. ]9[: Studied the results of investigations carried out on cast copper alloy containing 8 wt % Al , and pure copper for the sake of comparison ,were subjected to cold rolling with a final reduction of 30, 50 and 70 %, the cold rolled copper and copper alloy samples were isochronally and isothermally annealed up to the recrystallization temperature. It was concluded, the hardness of the samples during cold rolling increases, the maximum value of hardness was attained at 70%deformation and the strengthening increases with increases degree of prior cold work.
Royset et al. ]10[: The effect of element (Sc) on the recrystallization resistance and hardness of a series of Al-Mn-Mg-Zr alloy was studied. The hardness of the alloys increases with increasing Sc content.
Mazur et al. ]11[:A research work about the improvement of the turbine main stop valves with flow simulation in erosion by solid particle impact CFD(computational fluid dynamic) was carried out. It was found that it was possible to reduce the valve erosion process, due to steam flow and hard particles velocity reduction and due to change of particles and angle of impact.
Malka ]12[: A theoretical study concerned with erosion-corrosion of petroleum steel pipe by saline water containing sand. It was found that the simulation of CFD for the velocity and turbulent intensity greater in the expansion section and hence high corrosion rate were expected. Also for particles (found in the flow) have a higher kinetic energy in the smaller
pipe section, and hence higher erosion rates were expected.
Antonov et al. ]13 [: Were found further studies in the same field on erosion- corrosion of Cr3C2–Ni(chromium carbide based) cermets in salt water at 90° impact angle,were using potentionstatic measurements with a constant size and concentration of the sand as an abrasive medium sea water at 8.2 pH.
Amjad et al. [14]: The corrosion behavior of Al-Si alloy in river, tap, and sea water, had been studied and concluded that corrosion rate in the river water is less than that in the tap and sea water.
Muna [15]: Wear behavior of (Al-12%Si) alloy was studied by using the Pin-On-Disc technique under different conditions at applied loads 5-20 N, at constant sliding speed and at constant time. It was found that the cadmium addition to Al-Si matrix will cause a decrease in the wear rate and improves the wear property for alloys containing -Cd under loads above 10N. It was also found that the alloy Al- 12% Si containing 3% Cd is the best alloy in wear resistance and friction coefficient.
Ahmed et al. ]16[: The erosion-corrosion behavior of (Al-12%Si) alloy as matrix phase and 10% SiC particles as a reinforcing phase with varying impact angles (0, 30, 45, 90º) in slurry solution (1%SiO2 in 3.5% NaCl) had been investigated by some authors. It was found that the erosion –corrosion of composite is lower than that observed on (Al-12%Si) alloy and the erosion –corrosion rate at impact angles 0º is lower than others angles.
2. Theoretical Study 2.1 Equation of Impact Damage
Alternative methods had been suggested by a number of workers, which were based on an impact damage model of the following
form to deduce the equation of impact damage:
) ( F AV
E pn [17]
Where:
E: The erosion rate (g/mm2. hr).
A: Constant depending on the material being eroded and other factors.
Vp: The particle impact velocity (m/s).
n : Material dependent index.
F (α): Material dependent function of the impact angle between 0-1
α : The particle impact angle.
2.2 Mathematical Model
There are many researchers, they used different equation of impact damage formulation, from workers Huser and Kvernvold used impact damage equation in the following form:
) (
F KV mE p pn [17]
Where:
E: The erosion rate (g/mm2. hr)
m p: The mass flow of particles impacting on the exposed area
Vp : The particle impact velocity (m/s) K & n: Constants, values of K, n, F (α) was derived from sand –blasting tests on small material samples.
Figure 1 shows the angle relationship F(α) used by Huser & Kvernvold.The Huser equation of fitting on mass flow can be described as follow[17 [:
[17]
Where:
2 2
D WV ER Sk
ER : The erosion rate (g/mm2. hr).
Sk : Geometry dependent constant.
W : The sand flow rate.
V : Fluid velocity (ft/sec).
D : The pipe diameter (inches).
Fig. 1. The Angle relationship F(α) equation of fitting on mass flow]17 [.
The Salama equation of fitting on fluid velocity can be represented [17].
Using a model which had been utilized with an impact damage of the following form
) (
F V m F FE m s p pn [17]
Fm: Coefficient accounts for the variation in material.
Fs: Coefficient accounts for sand sharpness.
Vp : The particle impact velocity (m/s) m: The mass flow of particles impacting on an area.
However an empirical model had been constructed depending on the impact damage equation and previous workers in the same field of research reached .A best fitting equation was achieved (after testing many equations that leads to best realization to experimental data for alloys which was used in this search).Using Matlap software program then the equation of weight loss deduced with exposure time in the following form:
) /(2
ae
b tW
[17]Where:
W : Weight loss (g/mm2)
a, b: Constant varied with the type of alloys (adjustable parameter).
e
: Exponential function T : Exposure time (hours)
: Small value to avoid divided on zero at t =0The equation of weight loss in the equation of erosion rate which represented erosion rate. So the erosion rate can be calculated from the relationship of the following:
t R DWF
E ( )
. [17]
Where:
D : The value constant in program equal 4 (adjustable parameter) .
W, t,
: The values have been known in the relation above.F (α): The factor of effect as the function for the impact angle for liquid on the samples, known in the above relation and rearranged that can be defined the F (α) through the following relationship:
) 1
( 2.4
e
F [17]
Where:
α : The impact angle
e
: The exponential functionSo for representation of above equations FORTRAN 77 program was adapted to calculate the theoretical erosion/corrosion rate at two impact angles and at different periods.
The comparison between the experimental and theoretical erosion/corrosion rate were carried out in the present study.
3. Experimental Test
Introduction: The cold rolled Aluminum alloys (Al-Mg), heat treated alloys.
Specimens’ preparations erosion/corrosion were tested using the system which has been constructed to perform the test. Aluminum alloys (5083) with composition represented in Table 1 is used, and processing the specimens of the wrought alloys tend to have large crystals of intermetallic compounds distributed randomly through their structure, to effect a more uniform distribution of the soluble constituents and to facilitate fabrication, ingots of these alloys are homogenized by exposure to temperatures near solution heat treatment levels and held there for up 18 hours at 450 °C temperature and then quenched in water at the room temperature. This process was carried out in the electrical furnace. After homogenizing and specimens preparation for rolling process to obtain the desiredreduction percentage (2.5, 5, 7.5%) showed in Table 2, due to improve the mechanical properties and decreasing grain sized by deformation of the
work piece under the rolls pressure. Annealing heat treatment process followed after the cold rolling process at 360 °C for 30 minutes to get rid from the residual stresses ]18[.
3.1 Specimens Preparation
The cutting of process was carried out in laboratory of metallurgy by cut off machine into dimension (2 x 2 x 1) cm, and grinding with water using emery paper of grade (200- 1000 µm), placed on rotary grinding machine, then the specimens were washed with water and acetone then dried by air, finally polished with nap cloth and with solution of alumina powder of particles size (5µm) and the specimens then washed with alcohol and dried by air.
3.2. Erosion/Corrosion System
The erosion/corrosion system was designed and constructed according to the international standards ASTM-G76. The system consists of a rectangular container with dimensions (50 x 50 x 100) cm, made of hot plate of steel of 3mm thickness. The system provided with electric mixer and with speed regulator placed in the center of the container.
The system contains a holder to fix the testing samples by small clipper. The holder fixed on the base containing a protractor to measure the angle with the change of angle measurement is changing the direction of sample of holder at the same time. On the other side of the sample a jet of mechanical nozzle consists of two pipes, directly fixed one pipe connect to air compressor and other pipe placed in the inside of container. The water jet is pumped directly to the sample with a definite small high pressure, which is represented in Fig. 2.
3.3 Erosion/Corrosion Test
The erosion/corrosion was carried out by placing the specimen on the holder with a little clipper which was placed inside the basin with air compressor. At the same time mechanical
nozzle jet was operated according Bernoulli basis, the liquid was pulled from mechanical nozzle jet on the surface specimen for 1.5 hr then after each test the specimen was taken out to clean with (water), then dried by aceton and weighed to determine the weight loss per unit area by dividing the weight loss by the surface area of the specimen. At the same time, the weight loss is divided by the unit area at a given point & time. However, the weight loss relation is shown below.
Where:
E R: The erosion /corrosion rate, T: Exposure time.
3.4. Water Analysis
The river water was analyzed at Oil Southern company. The results were listed in Table 3.
Table 1. The chemical composition of specimens.
Specimens Composition wt %
Si Fe Cu Mn Mg Cr Zn Ti Al
0.4 0.4 0.1 0.4-1 4-4.9 0.25 0.25 0.15 rest
Table 2. The designation suggested for the rolled specimens.
Specimens Suggested designation details
A1 As cast
B1 Heat treated (homogenized)
C1a 2.5% Rolled
C1b 5% Rolled
C1c 7.5% Rolled
Fig. 2. The Scheme of 3D illustration system of the test.
1. Container: It was made from hot plate of steel of cross section (50x50x100) cm placed inside it electric mixer.
2. Electric mixer: The motor (1450 r.p.m)
3. Mechanical nozzle jet: Diameter 1.5cm and consist of two jets and work depend on the Bernoulli basis.
4. Air compressor: It was connected with the mechanical nozzle jet.
5. Clipper holder: It was made from steel of cross-section (10 x 25) cm to carry small clipper which hold test specimens.
6. The specimen of test: It has dimensions (2 x 2 x 1) cm.
7. The regulator: To regulate motor speed for electric mixer.
8. Stand.
E R
Weight loss T
Table 3. The river water analysis.
River water Units
Analysis
7.8 ---
pH
6620 mus/cm
X
4634 mg/l
T.D.S
2000 mg/l
T.H
1200 mg/l
CL ˉ¹
900 mg/l
Ca 2
1000 mg/l
Ca as CaCoз
1100 mg/l
Mg as CaCo3
1284 mg/l
So- 4
0.0 mg/l
P
235 mg/l
M
4.
Results and Discussion4.1. Measuring the Weight loss at two Impact Angles (30°, 90°)
Figure 3 represents the relationship between the weight loss in river water against the exposure time for the specimens (A1, B1, C1a, C1b, C1c) at impact angle 90°. It was noticed that the weight loss in (C1c) specimen was less than (A1) about (63%) and (C1b) about (52.85 %) and (C1a) about (36.85 %) and (B1) about (2.6 %).The weight loss for
(C1c, C1b, C1a) specimens was less than for B1 by about (66.2, 51.57 & 35.13 %) respectively. The weight loss for (C1c & C1b) specimens was less than for (C1a) about (47.9
& 25.3%) respectively. which indicates that the increasing rolling ratios of alloys lead to increasing hardness due to the change in structure of the alloys, and increased the density of defects which is hindered by sliding of dislocations inside the alloys and hindered the establishment of new dislocation and their sliding, these defects can be either point defects (a vacancy on the crystal lattice) or a line defect (an extra half of atoms jammed in a crystal) as defects a accumulated thought deformation, it becomes increasingly more difficult for slip, or the movement of defects, to occur ]19-21[.
Figure (4) represent the relationship between the weight loss in river water against the exposure time for the specimens (A1, B1, C1a, C1b & C1c) at impact angle 30°.
It was noticed that the weight loss in (C1c) specimen was less than for (A1) about (87.15%) and (C1b) about (72.5 %) and (C1a) about (55 %) and (B1) about (6.7 %). The weight loss for (C1c, C1b, C1a) specimens was less than for B1 about (86.22, 70.55 &
52.77 %) respectively. The weight loss fr (C1c
& C1b) specimens was less than for (C1a) about (70.82 & 37.64 %) respectively.
4.2. Erosion/corrosion Rate at Impact Angle 90°
The relationship between the erosion/corrosion rate against exposure time at impact angle 90° is presented in Fig. 5.
It was found that the erosion /corrosion resistance of the specimens (C1c,C1b,C1c) is higher than (A1,B1).due to the increased hardness of rolled specimens (C1c,C1b,C1c) with reduction (2.5, 5, 7.5) % . The high values of the erosion/corrosion resistance for the specimens cold rolled {C1a, C1b and C1c were (4.5, 4, 3.4) g/mm2.hr*106 respectively} and for the specimens {A1,B1 were (9, 8) g/mm2.hr*106 respectively} .All these the values were at impact angle 90°. The decrease of the erosion/corrosion rate for the cold rolled specimens C1a, C1b and C1c compared to in unrolled specimens A1, B1, because of increasing hardness which lead to increasing erosion/corrosion resistance for rolled specimens [22]. We notice in Fig. 5 apparently the period of the incubation is short during the early hours in which the alloy resisted the collision water current impact due to oxide film .Then after that ,we noticed the increasing weight loss rate as a result of the breaking oxide film because of the repeated impacts of the water current, this stage is called (acceleration period), which is resulting
from repeated impact to water current, after this stage ,there was period of (deceleration) in the rate of weight loss when it decreased become the rate become less than as was in the early hours where the oxide film begin to build up. Finally, the steady stage weight loss and the increasing of the time period did not affect the rate of weight loss, which is called (steady period) which is related to the nature of aluminum oxide film and the power of adhesive its with the surface[14,15]. The mechanism of erosion at impact angle 90º is the plastic deformation then strain hardening and after that the steadiness stage begins. The deformations on the specimen surface resulted from probable cracks that make relatively high roughness ]17,18,21] . So erosion /corrosion rate in the impact angle 90°is less than that in impact angle 30º.
4.3 Erosion/Corrosion Rate at Impact Angle 30°
The relationship between the erosion/corrosion rate against the exposure time at impact angle 30°is presented in Fig. 6.
It was found that the erosion /corrosion resistance of the specimens (C1c, C1b, C1c) is higher than (A1,B1) because, the hardness of rolled specimens (C1a, C1b, C1c) in the reduction percentage (2.5, 5, 7.5%) increased by rolling .The high values of the erosion/corrosion rate for the specimens cold rolled {C1a, C1b and C1c were (16, 10, 6) g/mm2.hr x106 respectively} and for the specimens {A1,B1 were (25, 20) g/mm2.hr x106 respectively}.All these values were at impact angle 30°. because the decrease of the erosion/corrosion rate for the cold rolled specimens C1a, C1b and C1c compared the specimens A1, B1, due to obtained increasing of hardness which lead to increasing erosion/corrosion resistance for rolled specimens [23] . We noticed in Fig. 6 the same behavior that the erosion/corrosion appear at impact angle 90º which consist of incubation
period, acceleration period ,deceleration period and steady period. But in this case the mechanism of erosion at impact angle 30° is the processes of cutting that occur to the specimen's surface and it is removed by the cutting in form the micro chips and the deformation is little , the specimen surface will be relatively smooth and have a little roughness erosion/corrosion rate in the impact angle 30° is higher than in impact angle 90°
]4,5,24[.
4.4 Erosion/corrosion Rate at the Impact Angles (30°, 90°)
Figures 7-11 represented the comparison between impact angles and erosion/corrosion rate for(A1, B1, C1a, C1b, C1c) alloys. These the erosion / corrosion rate at impact angle 30° is higher than that observed at impact angle 90°, refer to details about mechanism of erosion for angles. However, resistance erosion/corrosion for alloys at impact angle 90° higher than for at impact angle 30°.It was found from the above figures the erosion/corrosion rates in, (A1) specimen at angle 90° was less than (A1) specimen at angle 30° by about (64%),(B1) specimen at angle 90° was less than (B1) specimen at angle 30°by about (60 %), (C1a) specimen at angle 90° was less than (C1a) specimen at angle 30°by about (71.8 %), (C1b) specimen at angle 90° was less than for (C1b) specimen at angle 30°by about (75 %), (C1c) specimen at angle 90° was less than for (C1c) specimen at angle 30° by about (88.75 %). These results due to the erosion /corrosion resistance at impact angle 90° higher than erosion/corrosion resistance at impact angle 30º [4,5].
4.5. Experimental & Theoretical Erosion/
Corrosion Rate Comparison
From equations in section 2 (Theoretical Study) and FORTRAN 77 program which the following results can be discussed was adapted
to calculate the theoretical erosion/corrosion rate at two impact angles.
Figures 12-16 showed the comparison between the experimental erosion /corrosion rate and theoretical for the alloy (5083) at impact angle 90º.
Figures 17-21 represented the comparison between the experimental erosion /corrosion rate and theoretical for the alloy (5083) at impact angle 30º
From Fig. 21 it is apparent that the convergence measured erosion rate and predicted. We noticed that the difference between measured and predicated curves of international measurement [24], is similar behavior to the error percentage that found between experimental erosion/corrosion rate and theoretical for the first group alloy at impact angles 30º & 90° were 25 % and 30%
respectively, and the error percentage for the second group alloys at the impact angles 30º &
90° were 30% and 20%.
Fig. 3. The Weight Loss &Exposure Time for the specimens (A1, B1, C1a, C1b, C1c) at impact angle 90°.
Fig. 4. The Weight Loss & Exposure Time for the specimens (A1, B1, C1a, C1b, C1c) at impact angle 30°.
Fig. 5. The Erosion/Corrosion rate against Exposure Time for the specimens (A1, B1, C1a, C1b, C1c) at impact angle 90°.
Fig. 6. The Erosion/Corrosion rate against Exposure Time for the specimens (A1, B1, C1a, C1b, C1c) at impact angle 30°.
Fig. 7. The Erosion/Corrosion rate against Exposure Time for the specimens (A1) at impact angle 30°, 90°.
Fig. 8. The Erosion/Corrosion rate against Exposure Time for the specimens (B1) at impact angles 30°, 90°.
Fig. 9. The Erosion/Corrosion rate against Exposure Time for the specimens (C1a) at impact angles 30°, 90°.
Fig. 10. The Erosion/Corrosion rate against Exposure Time for the specimens (C1b) at impact angles 30°, 90°.
Fig. 11. The Erosion/Corrosion rate against Exposure Time for the specimens (C1c) at impact angles 30°, 90°.
Fig. 12. The Comparison between the Experimental Erosion/Corrosion Rate and Theoretical for the alloy (A1) at impact angle 90º.
Fig. 13. The Comparison between the Experimental Erosion/Corrosion Rate and Theoretical for the alloy (B1) at impact angle 90º.
Fig. 14. The Comparison between the Experimental Erosion/Corrosion Rate and Theoretical for the alloy (C1a) at impact angle 90º.
Fig. 15. The Comparison between the Experimental Erosion/Corrosion Rate and Theoretical for the alloy (C1b) at impact angle 90º.
Fig. 16. The Comparison between the Experimental Erosion/Corrosion Rate and Theoretical for the alloy (C1c) at impact angle 90º.
Fig. 17. The Comparison between the Experimental Erosion/Corrosion Rate and Theoretical for the alloy (A1) at impact angle 30º.
Fig. 18. The Comparison between the Experimental Erosion/Corrosion Rate and Theoretical for the alloy (B1) at impact angle 30º.
Fig. 19. The Comparison between the Experimental Erosion/Corrosion Rate and Theoretical for the alloy (C1a) at impact angle 30º.
Fig. 20. The Comparison between the Experimental Erosion/Corrosion Rate and Theoretical for the alloy (C1b) at impact angle 30º.
Fig. 21. The Comparison between the Experimental Erosion/Corrosion Rate and Theoretical for the alloy (C1c) at impact angle 30º.
Fig. 22. The Convergence between the Erosion Rate of Measured and Predicted ]24[.
5. Conclusions
1. The solution heat treatment for alloys (5083) didn’t improve the erosion resistance, this was noticed in the homogenized specimens.
2. Erosion/corrosion resistance for (5083) alloys at impact angle 90º is higher than that observed at angle 30º.
3. The specimens of the rolled alloy (C1a, C1b and C1c) have erosion/corrosion resistance higher than (A1, B1) both at impact angles of (30º, 90º).
4. The percentage error that obtained between experimental erosion/corrosion rate and theoretical at impact angles 30º & 90°
were 25 % and 30% respectively.
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و
1رديح ميعن قيفوت و
1ناملس يبنلا دبع بلاط
2
داوملا ةسدنه
1- ةسدنهلا ةيمك –
ةرصبلا ةعماج
2
و ، ا ةيمك مومعل – ةرصبلا ةعماج -
لا قارع
صمختسملا .
( ةفمتخملا كمسلا ضيفخت بسن دنع درابلا ىمع ةمفردلا ةيممع ريثأت ةسارد ىلإ ثحبلا فدهي 2,3
، 3
، 7,3
٪ ىمع )
ت ةمواقم أ لك - ةيرعت
، للأا كئابسل ىرخلأا ةيكيناكيملا صاوخلا ضعب ىمعو و
موينم - ( ةسماخلا ةمسمسلا مويسينغم 3803
)،
ةمدختسملا
ف ةيرحبلا تاعانصلا ي
، ت ةمواقم سايق مت ثيح أ
لك - ( نمز دنع ةكيبسلا هذهل ةيرعت 8
- 13 ةفمتخم مدص اياوز دنعو ةعاس )
، يهو
08 º و 38 º لكأتلا ةمواقم نسحت مدع جئاتنلا تناك .درابلا ىمع ةمفردملا تانيعمل يرارح ةجلاعملا كئابسمل ةيرعت–
دعبو لبق ا
نتيوازلا لاك دنعو ةمفردلا .
و دجو كلذك أ
لكأتلا ةمواقم ن -
مدص ةيواز دنع ةيرعت 08
º أ ةيواز نم ربك 38
º.
ريخ أ دجو ا أ ةبسن ن
يه ةيرظنلاو ةيممعلا تاباسحلا نيب أطخلا 23
٪ مدص ةيوازل 38
º و 38
٪ مدص ةيوازل 08
º.