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19

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BiaxiaI/Multiaxial Fatigue and FractureAndrea Carpinteri, Manuel de Freitas and Andrea SpagnoIi (Eds.@ Elsevier Science Ltd. and ESIS. AlI rights reserved. 303

INFLUENCE OF DEFECTS ON FATIGUE LIFE OF ALUMINIUM PRESSUREDIECASTINGS

Fernando Jorge LINO1, Rui Jorge NETo2, Alfredo OLIVEIRA2 and Fernando ManuelFernandes de OLIVEIRA I

'Faculdade de Engenharia, Universidade do Porto, Departamento de Engenharia Mecânica eGestão Industrial, Rua Dr. Roberto Frias, 4200-465 Porto, Portugal

2INEGl, Instituto de Engenharia Mecânica e Gestão Industrial, Rua do Barroco, 174-214,4465-591 Leça do Balio, Porto, Portugal

ABSTRACT

Fatigue life of aluminium pressure diecastings is strongly dependent on the microporosity leveIof the parts. Even in a very controlled production process, it is almost impossible to obtainaluminium parts without micropores, which means that a considerable amount of parts arerejected, in accordance to internal companies criteria. Although these criteria are based onstandards, they change from company to company, and depend on the type of the parts and theamount, size and location of the micropores. Many times, parts that could have a good fatiguelife are rejected based on these criteria.The aim of the present work is to study the influence of the microporosity leveI and size on thefatigue life of aluminium pressure diecastings. Two different lots of samples, removed flOroaluminium components (considered unacceptable and acceptable) were tested using thestaircase fatigue testo AlI the fractured parts were analysed macro and microscopically and theimages obtained were digitalized in order to classify the size and amount of the micropores.The results obtained were compared with the fatigue life curves, in order to evaluate theinfluence of the microporosity on the fatigue life of aluminium components.

KEYWORDS

Fatigue life, manufacturing defects, aluminium, staircase fatigue test, diecasting.

INTRODUCTION

One of today's greatest challenges in lhe foundry industry is lhe production of complex andstructurally sound paris. At lhe forefront of this challenge is lhe porosity and inclusions sizeand levels, and how and where they develop. The presence, even in smalllevels, of these typesof defects in pressure diecastings can lead to a significant reduction in lhe tensile strength,ductility, pressure tightness and fatigue life, affecting lhe life and lhe integrity of lhe cast paris[I ].

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RJ UNO ET AL.304

Three factors can lead to the presence of porosity: shrinkage, coupled with a lack ofinterdendritic feeding during mushy zone solidification, evolution of hydrogen gas bubbles dueto a sudden decrease in hydrogen solubility during solidification, and collapsed air [1, 2].

Aluminium diecasting alloys present very interesting properties, namely: goodmachinability, low weight, low transformation cost with the possibility of obtaining complexshapes, and, moreover, they are recyclable. However, they are very prone to present castingdefects. Although the recent developments in pressure diecasting industry (use oflow injectionvelocities, special feeding [2, 3], vacuum and "true isostatic pressure" [1]) and the use ofsimulation processes contributed to the improvement of the aIuminium cast parts quality(possibility of structural parts production), it is almost impossible to avoid the presence ofdefects in the parts that are supplied to the customers [4-6]. Considering this, foundrycompanies follow international standard criteria (for example, ASTM Standard E 505 [7]) andalgo develop internal standards to classify the parts as acceptable or unacceptable. Frequently, alocation or size of one defect is not critical in one part, but is unacceptable in other type ofparts. This is especially important in structural parts, where the loading type during service canconduct to fatigue initiation. Pressure aluminium diecasting aIloys have extremely low ductility(1-3%) [4, 8], which means that once initiated, cracks easily propagate until the failure ofthe

component [9].In the light ofthe above, it is obvious the interest, emphasized by current studies [1, 5, 10],

in evaluating the effect of the presence of defects on fatigue life reduction of pressurediecastings. For example, some authors have been trying to determine the relationship betweencasting conditions and the amount of porosity in a casting. The majority of the models capableof providing a qualitative description of the levei of microporosity fail to give accurate valuesbecause the prediction of microporosity requires a detailed understanding of pore nucleation

and growth in the melt [1].In the aIuminium pressure diecasting industry, the main type of defects susceptible of being

observed are oxidized surfaces, foreign material inclusions (oxide), gas cavities (hydrogen andgas porosity), macroshrinkage (cavities and sponginess), and microshrinkage (feathery, sponge,intercrystalline or interdendritic) [6, 11].

Gas pores, shrinkage pores and gas-shrinkage pores represent the main types of porosity thatare detected in diecastings. In gas pores, liquid aIuminium reacts with water vapour in theatmosphere to produce aIuminium oxide and hydrogen gago Gas porosity arises during thesolidification, due to the difference in solubility ofhydrogen gas in liquid and solid aluminium.If a casting is poorly fed during solidification, shrinkage will cause a hydrostatic stress in theliquid metal. This stress increases until a pore forms with the aid of a nucleus. Gas-shrinkagepores results flOro the fact that gas evolution and shrinkage occur in the same volume of Iiquid

metal atthe same time [1].In this papel, the effect of the presence of porosity on fatigue life reduction of aluminium

pressure diecastings is quantified. Such an effect will then be used in a software, underdevelopment, which will be able to predict fatigue life of high strength castings [12]. One ofthe advantageous of this study is the fact that ali the fatigue tests are conducted in samplesremoved flOro real components or in real components and not in samples pressure diecastedseparately in the metallic moulds. These last samples frequently have a section thickness thatdoes not represent the usual parts thickness obtained in pressure diecasting.

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Influence Df Defects on Fatigue Life Df Aluminium Pressure Diecastings 305

EXPERIMENTAL ANAL YSIS OF DEFECTS

To study the influence of the presence of defects on fatigue life of aluminium pressurediecastings, two lots of 50 parts each, considered acceptable and unacceptable, were suppliedby a foundry company (SONAFI, Porto, Portugal). The selection was made in accordance tothe foundry internal criteria for the part selected, and using adequate quality control techniques(visual control, X-Rays, etc.). Figure 1 presents the component selected, with the fatigue testsample placed in the position from where it was removed.

Fig. I. Brake pedal in an aluminium diecasting alloy AS9U3 (NF A57-703) [8] with thefatigue test sample.

Figure 2 shows an image of the X-Rays control performed in one pedal. As one can see,different defects gizes can be detected in this controlo

Fig. 2. X-Rays contrai in a brake pedal. The central part of the pedal shows pores withdifferent sizes and geometries. The fatigue test sample was removed from region A.

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306 RJ: UNO ET AL.

Ali the parts were pressure diecasted in the AS9U3 (NF A57-703) [8] aluminium alloy. Thetypical microstructure of this alloy consists essentially in IX aluminium dendrites, aluminium-silicon eutectic cells, and intermetallics AbCu, Al7Cu2Fe and AlFeSiMg [6, lI] (see Fig. 3).Table I presentsrhe alloy chemical composition specified by the Standard NF A57-703 and themedium values measured in the components using a spark spectrometer. This table shows thatthere are no significant differences between the two compositions.

Fig.3. Typical microstructure ofthe pressure diecasting AS9U3 alloy (etched with HF 0.5%).This microstructure is composed by.(1 alurniniurn dendrites, alurniniurn-silicon eutectic cells,and intermetallics AbCu, Al7Cu2Fe and AIFeSiMg.

Table Chemical composition (%) afilie alurniniurn alloy AS9U3 (NF A57- 703) [8].

Fe

1.3

Cu

2.5-4.0

Zn

A-I.2

B-I.3

0.81

Mg

0.3

Mo

0.5

Ni

0.5

Pb

0.2

8n

0.2

Ti

0.2NF A 57-703

Si

7.5-10

Measured in

the

components

2.99 0.2 0.23 0.05 0.15 0.04 0.02

rü:78

9.24

Figure 4 presents the cross section of an optical micrograph showing interdendritic (regionA) and gas cavities (region B) regions, and algo a macrograph of a transversal section of anunacceptable pedal, where these defects can algo be observed. As one can see, pressurediecastings present a significant amount of micropores. This fact is responsible for considerableresearch in the foundry area, in order to produce aluminium diecastings with bettercharacteristics [1, 5, 13-15].

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lnftuence of DeJects on Fatigue Life of Aluminium Pressure Diecastings 307

Fig. 4. Porosity in pressure diecastings: a) optical micrograph indicating a region A ofinterdendritic cavities and a region B of gas cavities, and b) macrograph of a polishedtransversal section of an unacceptable pedal showing small and large pores.

Table 2 presents lhe main properties ofthe aluminium alloy AS9U3 (NF A57-702/703) inlhe non heat-treated condition [8].

Table 2. Properties afilie AS9U3 (NF A57- 703) pressure diecasting alloy [8].

Image analysis was performed with software called PAQUI (developed by the Centre ofMateriaIs of University of Porto -CEMUP, Porto, Portugal) in an Olympus opticalmicroscope. The analyses were dane in 10 brake pedaIs (5 acceptable and 5 unacceptable), inthe transversal section of the fatigue test samples region. A routine to perform a specificanalysis was defined in arder to count and measure the defects (considered spherical) in thesamples section. 50 to 80 fields were characterised in each sample, using an optical microscopewith a 5x magnification. Very small defects, with diameter <50 ~, were counted but notmeasured in arder to reduce the amount of data to be treated. The mean reletive defects areawas obtained dividing the total defects area by the total fields area. Figure 5 presents one afiliefields analysed in an unacceptable sample. Figure 6 presents the mean number of defectsdetected in each field, classified in tive diameter (/,J.m) classes. As expected, unacceptable partshave higher amount of defects in alI classes.

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F:J: UNO ET AL.308

Fig. 5. Optical micrograph of one field analysed in an unacceptable sample showing a largeamount of defects and a large pore with a diameter around 5 ~m.

-rJ~Q)o'-o~Q)

~z

.O-50

.50-100

0100-1500150-200.>200

Acceptable Unacceptable

Figo 60 Mean number of defects detected in each tield analysedo The defects are divided in tivearea (~m) classes for acceptable and unacceptable samples.

The mean reletive defects area obtained in acceptable parts was 1.9%, while forunacceptable ones was 2.9%. This is a very small difference between the two lots, which can beexplained by the fact that frequently a single defect is the reason for a part rejection.

FATIGUE TESTS

One fatigue sample was removed from each pedal by EDM and machined for the followingdimensions, 90 mm length, 20 mm width and 3 mm thickness. The geometry of the sample wasdefined according to the ASTM Standard E 466 [16] and is represented in Fig. 7.

300

250

200

150

100

50

n

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309lnfluence of Defects on Fatigue Life of Aluminium Pressure Diecastings

l!li!

t

'atigue

test sample based on the ASTMStandard E466 [16].Fig.7.

Two tensile tests were perfonned iri both seis of samples in order to detennine the mainmechanical properties of the AS9U3 aluminium alloy. The geometry of the sample for thetensile test was modified in accordance with Standard E 8M-89b [17]. A constant cross sectionof 10 mm and 3 mm thickness was adopted. The mechanical properties obtained were verysimilar for acceptable and unacceptable samples. Considering this, the values indicated on Tab.3 represent the medium value obtained from the 4 tensile tests perfonned in both acceptableand unacceptable samples. These values are similar with the ones specified by the Standard(NF A57- 703) [8] (see Tab. 2), which can be the result of the natural defects presence inpressure diecastings. Density values, obtained from three samples of each sei, are algo lowerdue to the presence of micropores in the components and due to the slight difference in thealloy chemical composition. This table algo includes the hardness values, which are equal for

both seis of samples.

rable

3. Measured properties afilie aluminium alloy AS9U3 (NF A57-703).

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EJ UNO ET AL.310

Fatigue tests were performed in a 250 kN Servo-Hydraulic MTS machine (see Fig. 8), andusing the staircase method (DIN EN ISO 9964 [14)). The loading ratio crMinlcrMax selected forthe tests was 0.1, and tests started with 50 % of the aluminium alloy tensile strength. Figure 9presents one pedal and some broken samples.

Fig. 8. Servo-hydraulic MTS machine for the fatigue tests.

Fig.9. Brake pedal and broken fatigue aluminium samples.

To start the staircase fatigue test [16, 18], it was estimated that the fatigue limit was 50% ofthe tensile strength. The number of levels used for each set of 20 samples was 7.

Tables 4 and 5 indicate the values employed in the test and the results obtained, respectively.Surprisingly, the unaccept&ble samples only have a small decrease in the fatigue limit;

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lnfluence of Defects on Fatigue Life of Aluminium Pressure Diecastings 311

however, they present a slightly higher standard deviation. Figures 10 and 11 present theWoehler curves obtained (in accordance with the ASTM Standard E 468 [19]) using thesefatigue limits and the best fit of fatigue tests with three different levels of altemating stress,using 5 samples for each leveI.

Table 5. Fatigue test results.

Curve S-N160

140

120

100

80

60

40

íUDo

~W"C~~Q.E~li)

20

o10000 100000

Number of Cycles--~-

1000000 10000000100 1000

ig. 10. Woehler curve for acceptable samples.

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RJ: UNO ET AL.312

Curve S-N160

140

120

100

80

60

40

20

íiIl.

~QI

"C~~ã.E<InInQI..

+'cn

o10000 100000

Number of Cycles

1000000 10000000100 1000

ig. 11. Woehler curve for unacceptable samples.

As one can see, unacceptable samples have a much broader number of cycles-to-failuredistribution (correlation coefficient R2 equal to 0.25) for the high altemating stress regime,which means that the defects (essentially micropores) have a considerable effect on fatigue lifereduction for high altemating stresses.

AlI the fatigue fracture surfaces were analysed in an Olympus stereograph microscope,connected to a PC, and defects bigger than 50 Ilm classified by manual detection with a DP-80FT software program (version 3.0 from Olympus). Figures 12 and 13 show the fracturesurface of two unacceptable samples. During the defects detection, for counting and areameasurement, it was necessary to frequently compare the image in the computer monitor and inthe microscope, since the image in the computer was not three dimensional, which causeddifficulties in the defects characterisation.

Fig. 12. Macrographof a fracture surface of an unacceptable sample presenting a large pore.

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Influence of Defects on Fatigue Life of Aluminium Pressure Diecastings 313

Fig.

13. Stereographic picture of the fracture surface of an unacceptable sample.

Some of the fracture surfaces were analysed in a SEM microscope. Figures 14 and 15present some of the images obtained characterised by a brittle facture. In fact, Fig. 14 showsvery clearly this type of fracture. However, small regions with some deformation were algOdetected. Figure 14 b) shows a pore interior with a dendrite and small deformation. Figure 15shows other fracture surfaces presenting some regions of small deformation and large fragileintermetallic plates.

Fig. 14. Fracture surface, a) the fracture surface presents regions of small deformation, b)image inside a pore with a dendrite and smal! deformation.

Figure 16 presents, for both the acceptable and unacceptable sets, the frequency of defectsclassified in seven classes of mean pore size diameters. This figure shows the presence ofdefects with diameter higher than 250 flm and higher amounts of large size defects in thefracture surfaces of unacceptable samples, which means that they play an important role in thefatigue life of these parts.

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EJ: UNO ET AL.314

b)a)

Fig.15. Fracture surface, a) the fracture surface presents regions ofsmall deformation, b) somedeformation with large fragile plates between the aluminium.

Figures 17 and 18 present the area percentage of pores detected in the fracture surfacedivided by the total planar fracture surface area (sample reference names are reported along thex axis). As one can see, the pore surface area in the fracture surfaces ofboth sets of samples isvery similar, around 2.7% for the unacceptable samples and approximately 2.2% for acceptableafies. These vaIues are similar to the afies obtained in the cross sections of the pedaIs, whichwere presented previously: 2.9% for unacceptable samples and 1.9% for acceptable samples.

1110

11109

>- 8g 7ao 6=ao 5f 4...3

21O

LL.

o o o ,N !D 10 ,~ ~ ~ ,'" , O O ,

CJ ~"'!D'~ ~ ~laSS:S (J1~)

o~~

o'"'"1\

~g

~o~

g ~ 8 g~ ~ '" '"'" '" '" '"'f '" ., o~ ~ ~ '"

Classes (11m)--

o~1\

a)

Fig. 16. Frequency of defects divided in seven classes of mean pore gizes diameters for; a)acceptable samples, and b) unacceptable samples.

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Influence of Defects on Fatigue Life of Aluminium Pressure Diecastings 315

~~

lU!lUaiU

~~U)

!~-UlU-=J9Ot::lU!lU

!Oao

r-~Q)o~"""~r-~~o"""~o"'r-~Q)~"'~","'r-.oQ)~"':!"'~r-.oQ)o~~~~~~~~~~~~~~~~~~~~88u88888~~o~o~~~BUnacceptable samples ;;';1 ; ~

'--- "':~~!i J~g

Figure 17. Percentage of pore area with respect to planar fracture surface area, and mean valuefor unacceptable samples.

~

~~

~~~Q)u~~li)Q)...~-u~~sot::~~~~o

Q.

"'ONC')NM~\D".""NC')"""""'~Q)~NC')~ N N N U U U U U U U ~ ~ ~ ~ ~ 1: 1: 1: N N N«« UUUUUVVVUUU

Acceptable samples

Figure 18. Percentage of pore area with respect to planar fracture surface area, and mean valuefor acceptable samples.

5,0

4,5

4,Ü

3,5

3,0

2,5

2,0

1,5

1,0

0,5

0,0

5,0

4.5

4,0

3,5

3,0

2,5

2,0

1,5

1,0

0,5

0,0

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316 Rol UNO ET AL.

Figure 19 presents the mean, maximum and minimum defect diameters for the two sets ofaluminium samples. This figure confirms that even though the mean value is very similar forboth sets (around 150-170 Jlm), unacceptable samples have a much broader distribution.

.Maximumvalue

.Meanvalue

~ Minimumvalue

Fig. 19. Mean, maximum and minimum defect diameters for the two sets (acceptable andunacceptable) ofbroken fatigue samples.

The data obtained with the pore area measurements and the fatigue test results can be joinedin a single graph. The result obtained is indicated in Fig. 20, which presents the effect of thestress amplitude (upper curve) on the number of fatigue cycles, N, for alI tested samples. Thegraph also indicates the defects mean diameter (with the standard deviation) of each sample, asa function of the number of cycles to failure. As expected, large pore diameters and largestandard deviations are associated with shorter fatigue lives.

Using the data of this figure and a multiple linear regression analysis, it is possible toestablish an equation (with a correlation coefficient of 0.43) that relates the number of fatiguecycles with the applied stress and the mean defect diameterofthe components:

N = 6217357 -446440- -3109tftm (1)

where, N is the number of cycles to failure, O" is the stress amplitude (MPa), and t/Jm the defectmean diameter (11m). It should be emphasized that although the correlation coefficient obtainedfor this equation is low, it can be considered an acceptable value for a multiple linear

regression.A more suitable equation (with a correlation coefficient ofO.45) can be obtained ifthe mean

diameter is replaced by the maximum defect size (t/Jmáx) detected:

(2)

N

= 6232263 -453140- -825r/Jmãx

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317Influence of Defects on Fatigue Life of Aluminium Pressure Diecastings

This equation represents a good tool for fatigue life prediction of diecastings. In fact, adiecasting company, using a non-destructive test, like the X-Rays control, can detect themaximum defect of one component. Considering the size of the detected defect and theestimated service stress levei of the component, it is possible to estimate the number of thecycles that the component can withstand until breaking.

Fig.20. Effect ofthe stress amplitude (upper curve) and mean pore diameter (lower curve) onthe number of cycles of alI samples. The mean diameter of each sample is indicated with thestandard deviation.

The results achieved represent the first part of a more complete study about the influence ofdefects on the fatigue life of diecasting components. The second part of the work will includefatigue tests in the aluminium rocking arm ofthe Fig. 21. Using the Solid Works software, thedisplacements and the equivalent stress levels will be calculated by the finite element method(FEM). This allows the localization of the regions, which will preferentially suffer fatiguefracture. Using the X-Rays analysis, alllarge size defects present in the parts will be identifiedand the parts separated in different lots, characterized by the maximum defect size and location.The results of the fatigue tests will then be compared with the ones just presented. It isexpected that the conclusions of the study can supply interesting data for the software underdevelopment.

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F:J: UNO ET AL.318

CONCLUSIONS

Fatigue life of aluminium pressure diecastings is influenced by lhe size and amount of defects(essentially pores). The mean leveI ofpores detected in lhe aluminium brake pedais, consideredacceptable and unacceptable, was 1.9% and 2.9%, respectively. The comparison of acceptableand unacceptable lots of parts, have shown similar fatigue limits (91 and 87 MPa), howeverwith a slightly larger standard deviation for lhe unacceptable samples. The amount of pores inlhe fracture surface, 2.2% for acceptable samples and 2.7% for unacceptable ones, was verysimilar to lhe one obtained in lhe cross section of lhe brake pedaIs, 1.9% for acceptable and2.9% for unacceptable ones.

The Woehler curves obtained have shown that for high altemating stresses, defects size havea significant effect on fatigue life reduction. Combining lhe results obtained with lhe imageanalysis and lhe fatigue tests it was possible to develop an equation that relates simultaneouslylhe stress amplitude applied to an aluminium component and lhe maximum defect size detectedin lhe non-destructive controlo The equation developed in this study represent one first roughtool for fatigue life prediction of pressure diecastings. It is expected that more fatigue tests, tobe performed soon in real components, will improve lhe reliability of lhe model presented here.

Fig. 21. Aluminium rocking armo

REFERENCES

2.

Spada, A. T. (1999). Aluminium Casters Discuss Porosity, Melt Quality, Modero Casting.5th International AFS Conference on Molten Aluminium Processing, 58-60.Nguyen, T., and Carrig J. (1986). Water Analogue Studies of Gravity Tilt Casting CopperAlloy Components, AFS Transactions 94, MEM 92, 519-528.Nyamekye, K., An, Y. K., Bain, R., Cunningham, M., Askeland, D., Ramsay, C. (1994).Expert System for Designing Gating System for Permanent Mould Tilt-Pour CastingProcesso AFS Transactions 150,127-131.

3.

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Influence of Defects on Fatigue Life of Aluminium Pressure Diecastings 319

4. ASM INTERNATIONAL (1992). Casting, ASMHandbook, Metais Handbook, FonnerlyNinth Edition, Volume 15, ASM Intemational, Materiais Park, Orno, U.S.A.

5. Tsumagari, N., Brevick, J. R., Mobley, C. E. (1998). Control of Microstructures inAluminium Diecastings, AFS Transactions, 15-20, Milwaukee, Wisconsin, Ohio StateUniversity, Columbus.

6. Backerud, L., Chai, G. and Tamminen, J. (1990). AFS / SKANALUMINIUM: SolidificationCharacteristics of Aluminium Alloys, Volume 2, Foundry Alloys.

7. ASTM (1996). E 505, Reference Radiographs for Inspection of Aluminium andMagnesium Die Castings, Philadelphia, U.S.A.

8. NF (1970). A57- 703, Produits de Fonderie, Piéces Moulées Sous Pression en Aluminiumou en Alliages D' alluminium, 487-505.

9. Hertzberg, R. W. (1989). Deformation and Fracture Mechanics of Engineering Metais,John Wiley & Sons, Inc., USA.

10. Viswanathan, S., Duncan, A. J., Sabau, A. S., Han, Q., Porter, W. D. and Riemer, B. W.(1998). Modeling of Solidification and Porosity in Aluminum Alloy Castings, AFSTransactions, 411-417, ORNL, Oak Ridge Tennessee.

11. Russo, E. (1993). EDIMET: The Atlas of Microstructures of Aluminium Casting Alloys,

Italy.12. Lino, F. J. (2000). Final Report ofthe CRAFT Project Darcast (BRST-CT98-5328, Project

N° BES2-563 7, Coordinated by CIMNE, Barcelona, Spain), INEGI (Institute ofMechanical Engineering and Industrial Management), Porto, Portugal.

13. Kim, S. B., Yeom, K. D., and Hong C. P. (1997). CosI Metais 10.14. Dighe, M. D., Jiang, X. G., Tewari, A., Rahardjo, A. S. B., Gokhale, A. M. (1998).

Quantitative Microstructural Analysis of Microporosity in Cast A356 Aluminium Alloy,AFSTransactions 13,181-190.

15. Klansky, J. (1999). Image Analysis of Aluminum Alloys, Advanced Materiais & Processes7,23-26.

16. ASTM (1982). E 466, Standard Practice for Conducting Constant Amplitude AxialFatigue Tests of Metallic Materiais, 465-469, Philadelphia, USA.

17. ASTM (1989). E 8M-89b, Standard Test Methods for Tension Testing of MetallicMateriais {Metric}, 146-160, Philadelphia, USA.

18. ADHESIVES (1995). DIN EN ISO 9664, The Methods for Fatigue Properties ofStructural Adhesives in Tensile Shear.

19. ASTM (1990). E 468, StandardPracticefor Presentation ofConstantAmplitude FatigueTest Resultsfor Metallic Materiais, 475-480, Philadelphia, USA.

Appendix: NOMENCLATURE

E

N

R2

Young's modulus

Number of cycles

Correlation coefficient

Stress amplitude

Tensile strength

Yield strength

O"

O"r

0"0,2

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O"Min

f/lm

Maximum stress

Minimum stress

Mean defect diameter

Maximum defect diameter