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On the effect of macroporosity on the tensile properties of the Al-7%Si-0.4%Mg casting alloy
SuiptahIdall~caet~alia.
Pergamon
Vol. 32, No. 11. pp. 18514856.1995 ~~O~~~~~~scienct~ 0956-716x/9 T@-$9.50 + .oo
0956-716x(9!Fpoo31-3
ON THE EFFECT OF MACROPOROSITY ON THE TENSILE PROPERTIES OF THE Al-7%Si-0.4%Mg CASTING ALLOY C.H. Circeres Cooperative Research Centre for Alloy and Solidification Technology (CAST) Department of Mining and Metallurgical F@ineering The University of Queensland, Queensland 4072 (Australia) (Received November 29,1994) (Revised January 10,1995)
Jntrot&tion
~~~dparosityonthetensileprapertiesofacastinghas,beentlaematterofseverslstudies,n~~~ and Smith(l), Henera and Kondic(2) aud Surappa et aL(3). Eady and Smith(l) studied tbe effect oflarge average volume&&ions of-, up to 7%, cQthe mechanicalbehaviour ofAL7%Si with Mg levels of 0.1-0.47%. They foundthatcntytfielowcr~low-yieldskssvarietiesofthe alloy (l~thauO.25%Mg) cantoleratepomsilylevels in excess of 1%. Hen-era and KondiN2) and Surappa et aL(3) studied the e&ct oflow levels of porosity (4.4%) onA1-Si~oys.~studiesshowedthatthe~~intensile~Qesnot~~to~averagevolulne ~~~ofporosity.Instead,abettacorrelat~wasobtainedwiththel~)orthearea(3)oftheporesinthe ~surface.~Batfistudiesalsosuggestedthattherelativedecreaseintensilesbrengthislargerthanpredictedby the~intheloadbearingareasurappaetalalsoobseavedthat~piasticactivityoccursaroundthe pcaeS~acaswnritantiorreaseinthelocaldamageby~ofeutecticSipamclesandtheyshowedthatthe tensile~decreclsed~~withthe~oftheporesinthe~smface.Naneofthase~however, pnzsenkdamodeltoexplaintheobse~~ede&cts. The pqx~~ of the present note is to put forward a simple model which predicts the effect of porosity on the tensile behaviour of the Al-7%Si-O.4%Mg alloy in the T-6 condition_ In order to validate the calculations, the predictions of the model are contrasted against the experimental results of Surappa et aL(3) for the same material (see Table I).
1851
1852
MACROPOROSlTY IN A Al-7?“i-O.4?hMg CASTlNG ALLOY
Vol. 32, No. 11
A Model for the Effect of Porosity on the Tensile Behaviour Fracture Mechanisms
in the AlSiMe A&g
Plastic deformati~ results in the cmcking of a sign&u& fiactim of eut&ic Si particles(4-6) in this alloy. The craclcingafSiparticlesoccursgraduallywithstrain,~~the~cniginof~e.Crackedparticles giveplacetovoidsthatgrowandlinkf~gcracksintheAlmatrixwhicheventually~unstable,causing fracture. The rate of generation of damage is deknnkd by the relative coarseness of the microshucture (i.e., dendrite~~sizeandSiparticlesizeand~)andinprinciple,,~v~microstructureischaracterisedbya particular fracture strain(6). assumethatporousregionsyieldfirstdue Whenparosityispresentinatensilesample,itseemsreasonableto concentratonofthestraincau(mly tothereducedloadbeariug~~thestrainnearthevoids.The accelerate the production of damage in the porous regim causing pxwnatue ii-a&ne.Therateofstrain ~~~becalculated~~thestrainhardeningabilityofthematerialanda~lemodelforthis process is presented below. The Effect of Porn&v on the Lucalisation of Strain
For the present analysis we follow the work of Ghosh(ll), with the exception that strain rate eilkcts are neglected. ThegeomelryfarthemodelisdepictedinFig. 1.Forsimplicity,onlyasinglevoidisassumedinthe gaugelengthofanotherwkp&xtspecimen,whichisp&xk@reali&inthecaseofamacnqxe inathinwakd ~Intlaevoid~~regiontheinitial~sectionofthesampleA,islessthantherestofthesampleby af?actionf, suchthattheaxialloadequilibGmismaintainedif ot (1 -
f) A,,e-’ - oh Aoeweh
(1)
o=KE”
(2)
~a~e~~truestressandtrueplasticstrain,respectve~,,KK372 audn=O.lOlarethesugge&d material~fcrthisalloyin~T~condit~(l3).Asimple~shows(12,14)thatthemrurimumload intbeengioeering~straincurve~toe=nin~(2).Thepublished~~~curveby Surappa et aL(3) reaches the maximum loadatkrauelongationofabout11%,whichis conkkntwithasirain harden&expoxntn::0.1.Substitutionofequation(2)into(1)leadsto: (l-f)
e4
e: - e*’ e;
Equatian(3)crmnOWbesolV~numericayIandthestrainEiplottedasafuncti~ofE,ThisisQneinFig.2 t5rn=O.landarangeofarealiMionsoflxscsiQf Iheameforf=OrepresentsasoundsamplewhicheventuaUy
(3)
Vol. 32, No. 11
1853
MACROPGROSITY IN A Al-7%si-0.4?@& CASTING ALLOY
willdevelopa“~~~cneckforstrains~~O.l.Itcanbeseenthat,atincreasing strainconcentratesrapidlyinthevoidregion
vahles off; the
The data in Fig. L can be used to predict the tensile ductility by plotting the maximum homogeneous strain ei,* when E i attains a specified fia~ture strain a i*. In order to compare with Surappa et al’s data (Table I) note that the elongation to ii-actureoftheir most ductile sample is s E.14.6%. Thus, the model assumes that fracture occurs when the strain in the void region approaches si*= 0.14. Fig. 3 compares the calculated values with those of Surappa et al., converted to natural strains as E = ln( l+s), where s is the fracture strain listed in Table I. It should be noted, regarding Fig. 3, that the m points represent elongation to f?acture while the calculated curve refers to the true strain in the uniform region and, as such, it has a maximum value of Q*= n = 0.1. For small values off, Surappa et al’s samples necked to some extent, the post-uniform &formation amounting to about 0.04 in strain. The calculated values were thus expected to underestimate the fracture strain by the same amount. At large values off the length of the neck is likely to be constrained by the thickness in the tensile direction of the cavitated section, reducing its contribution to the total elongation. A better agreement was therefore expected for large porosity, which is what is observed in Fig. 3.
The maximum in the load deflection curve of a sound sample is reached when( 12,14) eb = n in equation (2). The true tensile shength is then o*= IW. Thus, if porosity f causes premature fracture at a strain Ed*,the true stress at fracture, a r*, is such that
. [I I
;. 0’
2 n
(4)
Fig. 4 shows the calculated a*,/ o* for n = 0.1 and E,,*values ti-om Fig. 3, together with the data from Surappa et aL(3). The latter were calculated as( 14) a = TS( l+ln( I+@), where TS and s are listed in Table I, and normal&d to the true tensile strength of the most ductile sample. It can be seen, once again that the calculated curve predicts very well the general trend of the experimental data. JGscussioq
The main assumption in the present analysis is that the tensile ductility is controlled by the local level of porosity, and this seems to be well supported by the experimental data. Thus, it is apparent that the average volume fraction of porosity is not a sensible parameter to quantify the porosity content, as pointed out correctly by Herrera and Kondic(2) and Surappa et al(3). TABLE1 Experimental Values for Figs. 3 and 4 (taken from Surappaet aL(3)). The Area Fractionof Porosity in the Fracture Surface is Representedby f, s is the Elongation to Fractureand TS the FractureStress. f(%)
0.38
0.46
0.60
0.78
1.13
1.20
1.90
3.39
3.73
4.65
s (%)
14.6
13.0
11.6
13.6
9.1
7.9
5.6
2.2
3.2
1.9
315
315.5
319
309
315
317.5
301.5
302
295
275
TS(MPa)
1854
MACROPOROSITY IN A Al-7%!!&0.4%Mg CASTING ALLOY
VoL 32, No. 11
The model indicates that even a small amount of localised porosity has a significant effect on the tensile ductility,in agreenxentwith the experiments. The same con&&n applies to the effect on the tensile strength; even a small level of porosity produces a measurable loss in tensile strength. These are actually general conclusions regarding the effect of geometrical defects on tensile ductility(7,ll). The relative effect is enhanced for materials with very limited strain hardening capacity, as in the present case. It would seem, therefore, that increasing the strain hardening coefficient, for instance by altering the heat treatment, should result in a more porosity-tolerant material. Herreraand~2)notedthata~ti~inthescatteroftheexperimentaldataresulted~thectuctility wasccaelatedwithtbe~~~ratherthanwiththe~jjectedareaofthevoid Similar@,Surappaetal.(3) sugg&edthattbeenvelopeofthevoid,defined asacircle withdiamekrequaltothelargestdinxmsionofthevoid, ccnelatesbetterwiththeductilitythautheprojectedama. Thisindicatesthattheshapeofthevoidshouldbetaken intoaccounfandis~anaspecttoexpl~e~~yYmo~&~.In~ti~e~with artificial (drilled) holes in wrought ahlminium alloys show that different airofvoids, at constam local volume fraction result in ditkent ductilities(15). Thus, the degree of clustaing when several voids coexist in a ~~Bthe~~mayneedtobe~~aswe~.Themodelalsoignoresany~ectsofthegradual~tion of damage on the flow behaviour. It has been shown that cavitation damage may decrease the local strain hardening rate, rendering the deformation process more unstable(7). Thus, it is clear that the model sutkrs from a number of limitations and more work is needed, which should include systematic studies of the elk& of void shape and distribution, as well as the efkct of varying the strain harderringcapability of the material. Nevertheless, the good agmement between theory and experiments suggests that most of the simplifyingassumptionsofthe model are justified. Summarv and Conclusion
On~~~thatlocalisedpccosityinatensile~leconcentratesthestrain~tothereducedloadbearing area, the rate of strain concentration can be described using existing models fop the growth of plastic instabilities. Byassumingthat~~occuIsintheregionofmaximumstrainatagivenvalueofthelocalstrain,theoverall straiu to tku%urecan be calculated for ditkent levels of porosity. The pro&ure can be applied to calculate the eflbct of porosity on the Cactllre stress. The calculations indicate that even low levels of local&d porosity may have a signiscant eEect on both the tensile ductility and the tensile stmngth ofthe mat&al These predictions are in good agmement with published results for the casting alloy Al-7Si-O.4MgT-6.
References 1. 2. 3. 4. 5. 6. 7. 8.
IA Fdy ad D.M. Smaq M&aids Faum, 9.217 (1986). AHerren,andV.Koodic,Proc.Ld~~o~Q1SOlidificBtimaodCastMetals;lheMetalsSodety,,~p460(19n). MK. fbapp, E. Bladcd J.C. Jaqud, Saiptametall, 24 1281(19w A~~aodJ.GurlaorZTrannMetSoc.Aeue;239,269(1%7) S.F. Fredmidcad W.A Bailey, Tram h4ehU Sot. AME, 242,2063 (1%8). C.H.ChqC.D.Da~audJ.RGrifGbhqsubnrittedtoMater.Sci.Eog. (1994). J.J. Jonasmd~lhdele&AdameCalt,25,43(19n). E. Dummbe, ht. J. Med~ Sci, 14,325 (1972).
Vol. 32, No. 11
9. 10. 11. 12. 13. 14. 15.
MACROPOROSITY IN A Al-7?/&0.4%Mg CASTING ALLOY
E Duoaab, Int J.SolidsStruck,141445 (1974) E.W. Harf Actametall,15,351(1%7). AK Ghosb,Adametd., 25.1413(1977). F.A Nichols,Adad, 28,663(1980). Z Wang ad R Zbng, Mdl. Tms, 22A, 1585(1991). G.E. Dieter,Me&mid Mehlhqy, (3”‘ed), McGraw-Hi&New York (1980, cl+= EM. DubmskydD.A Kosa,h&all. Tms., ISA, 1887(1987)
8.
1855
Vol. 32, No. 11
MACROPGROSITY IN A Al-7%Si-O.4%MgCASTING ALLDY
1856
0.16 FI-1’
t F
Co.14 _
f (%I=
6 5 4
3
1
2
-I
-
.E 0.12 *h
uh
A0
% p, 0.10 : 2 0.08 ” 0.06 .c 2 t; 0.04 0.02 -
0.00
4F Figure 1. A sckmatic view of the geometry assumed for the model.
?! J
0.02
0.04
0.06
0.08
0.10
strain outside the void region, E,,
Figure2.?beshaine,inthevoidregionasafunctionofthe strain eh outside the void region, for porosity f between 0 and 6% Values computed using equation (3) for n=O.1.
A 0.10 -
ij E ; 0.08 -
.r ; 0.06 0.04 r 0.02 -
F 0.00
10.00
0.01
0.02
0.03
0.04
0.05
0.06
area fraction of porosity, f
Figure3.?behduresbain~,asafinxihofaftbeanzalia&m ofporc&y,,toeq . ~lvaluesihxnTableI, convertedtotmezhius(seetext).Tbe-line~ tbesbiae,cbidethevoidxegioaiuFig2forasbaiunearlhe void e;= 0.14.
0.55 0
no
calculated
0.01
0.02
0.03
0.04
area fraction of porosity, f F~4.‘ihet11~taaiie~(solidlirre)mamalisedtothet~e ~ite~aftheaouxtnxibiaLasalix@hofthearea -ofpansay,=P@edusingequation(4).TbeexJPpl poitlts~hmTableI,conWedtoimestreps(seetext~
0.05
Pergamon
Vol. 32, No. 11. pp. 18514856.1995 ~~O~~~~~~scienct~ 0956-716x/9 T@-$9.50 + .oo
0956-716x(9!Fpoo31-3
ON THE EFFECT OF MACROPOROSITY ON THE TENSILE PROPERTIES OF THE Al-7%Si-0.4%Mg CASTING ALLOY C.H. Circeres Cooperative Research Centre for Alloy and Solidification Technology (CAST) Department of Mining and Metallurgical F@ineering The University of Queensland, Queensland 4072 (Australia) (Received November 29,1994) (Revised January 10,1995)
Jntrot&tion
~~~dparosityonthetensileprapertiesofacastinghas,beentlaematterofseverslstudies,n~~~ and Smith(l), Henera and Kondic(2) aud Surappa et aL(3). Eady and Smith(l) studied tbe effect oflarge average volume&&ions of-, up to 7%, cQthe mechanicalbehaviour ofAL7%Si with Mg levels of 0.1-0.47%. They foundthatcntytfielowcr~low-yieldskssvarietiesofthe alloy (l~thauO.25%Mg) cantoleratepomsilylevels in excess of 1%. Hen-era and KondiN2) and Surappa et aL(3) studied the e&ct oflow levels of porosity (4.4%) onA1-Si~oys.~studiesshowedthatthe~~intensile~Qesnot~~to~averagevolulne ~~~ofporosity.Instead,abettacorrelat~wasobtainedwiththel~)orthearea(3)oftheporesinthe ~surface.~Batfistudiesalsosuggestedthattherelativedecreaseintensilesbrengthislargerthanpredictedby the~intheloadbearingareasurappaetalalsoobseavedthat~piasticactivityoccursaroundthe pcaeS~acaswnritantiorreaseinthelocaldamageby~ofeutecticSipamclesandtheyshowedthatthe tensile~decreclsed~~withthe~oftheporesinthe~smface.Naneofthase~however, pnzsenkdamodeltoexplaintheobse~~ede&cts. The pqx~~ of the present note is to put forward a simple model which predicts the effect of porosity on the tensile behaviour of the Al-7%Si-O.4%Mg alloy in the T-6 condition_ In order to validate the calculations, the predictions of the model are contrasted against the experimental results of Surappa et aL(3) for the same material (see Table I).
1851
1852
MACROPOROSlTY IN A Al-7?“i-O.4?hMg CASTlNG ALLOY
Vol. 32, No. 11
A Model for the Effect of Porosity on the Tensile Behaviour Fracture Mechanisms
in the AlSiMe A&g
Plastic deformati~ results in the cmcking of a sign&u& fiactim of eut&ic Si particles(4-6) in this alloy. The craclcingafSiparticlesoccursgraduallywithstrain,~~the~cniginof~e.Crackedparticles giveplacetovoidsthatgrowandlinkf~gcracksintheAlmatrixwhicheventually~unstable,causing fracture. The rate of generation of damage is deknnkd by the relative coarseness of the microshucture (i.e., dendrite~~sizeandSiparticlesizeand~)andinprinciple,,~v~microstructureischaracterisedbya particular fracture strain(6). assumethatporousregionsyieldfirstdue Whenparosityispresentinatensilesample,itseemsreasonableto concentratonofthestraincau(mly tothereducedloadbeariug~~thestrainnearthevoids.The accelerate the production of damage in the porous regim causing pxwnatue ii-a&ne.Therateofstrain ~~~becalculated~~thestrainhardeningabilityofthematerialanda~lemodelforthis process is presented below. The Effect of Porn&v on the Lucalisation of Strain
For the present analysis we follow the work of Ghosh(ll), with the exception that strain rate eilkcts are neglected. ThegeomelryfarthemodelisdepictedinFig. 1.Forsimplicity,onlyasinglevoidisassumedinthe gaugelengthofanotherwkp&xtspecimen,whichisp&xk@reali&inthecaseofamacnqxe inathinwakd ~Intlaevoid~~regiontheinitial~sectionofthesampleA,islessthantherestofthesampleby af?actionf, suchthattheaxialloadequilibGmismaintainedif ot (1 -
f) A,,e-’ - oh Aoeweh
(1)
o=KE”
(2)
~a~e~~truestressandtrueplasticstrain,respectve~,,KK372 audn=O.lOlarethesugge&d material~fcrthisalloyin~T~condit~(l3).Asimple~shows(12,14)thatthemrurimumload intbeengioeering~straincurve~toe=nin~(2).Thepublished~~~curveby Surappa et aL(3) reaches the maximum loadatkrauelongationofabout11%,whichis conkkntwithasirain harden&expoxntn::0.1.Substitutionofequation(2)into(1)leadsto: (l-f)
e4
e: - e*’ e;
Equatian(3)crmnOWbesolV~numericayIandthestrainEiplottedasafuncti~ofE,ThisisQneinFig.2 t5rn=O.landarangeofarealiMionsoflxscsiQf Iheameforf=OrepresentsasoundsamplewhicheventuaUy
(3)
Vol. 32, No. 11
1853
MACROPGROSITY IN A Al-7%si-0.4?@& CASTING ALLOY
willdevelopa“~~~cneckforstrains~~O.l.Itcanbeseenthat,atincreasing strainconcentratesrapidlyinthevoidregion
vahles off; the
The data in Fig. L can be used to predict the tensile ductility by plotting the maximum homogeneous strain ei,* when E i attains a specified fia~ture strain a i*. In order to compare with Surappa et al’s data (Table I) note that the elongation to ii-actureoftheir most ductile sample is s E.14.6%. Thus, the model assumes that fracture occurs when the strain in the void region approaches si*= 0.14. Fig. 3 compares the calculated values with those of Surappa et al., converted to natural strains as E = ln( l+s), where s is the fracture strain listed in Table I. It should be noted, regarding Fig. 3, that the m points represent elongation to f?acture while the calculated curve refers to the true strain in the uniform region and, as such, it has a maximum value of Q*= n = 0.1. For small values off, Surappa et al’s samples necked to some extent, the post-uniform &formation amounting to about 0.04 in strain. The calculated values were thus expected to underestimate the fracture strain by the same amount. At large values off the length of the neck is likely to be constrained by the thickness in the tensile direction of the cavitated section, reducing its contribution to the total elongation. A better agreement was therefore expected for large porosity, which is what is observed in Fig. 3.
The maximum in the load deflection curve of a sound sample is reached when( 12,14) eb = n in equation (2). The true tensile shength is then o*= IW. Thus, if porosity f causes premature fracture at a strain Ed*,the true stress at fracture, a r*, is such that
. [I I
;. 0’
2 n
(4)
Fig. 4 shows the calculated a*,/ o* for n = 0.1 and E,,*values ti-om Fig. 3, together with the data from Surappa et aL(3). The latter were calculated as( 14) a = TS( l+ln( I+@), where TS and s are listed in Table I, and normal&d to the true tensile strength of the most ductile sample. It can be seen, once again that the calculated curve predicts very well the general trend of the experimental data. JGscussioq
The main assumption in the present analysis is that the tensile ductility is controlled by the local level of porosity, and this seems to be well supported by the experimental data. Thus, it is apparent that the average volume fraction of porosity is not a sensible parameter to quantify the porosity content, as pointed out correctly by Herrera and Kondic(2) and Surappa et al(3). TABLE1 Experimental Values for Figs. 3 and 4 (taken from Surappaet aL(3)). The Area Fractionof Porosity in the Fracture Surface is Representedby f, s is the Elongation to Fractureand TS the FractureStress. f(%)
0.38
0.46
0.60
0.78
1.13
1.20
1.90
3.39
3.73
4.65
s (%)
14.6
13.0
11.6
13.6
9.1
7.9
5.6
2.2
3.2
1.9
315
315.5
319
309
315
317.5
301.5
302
295
275
TS(MPa)
1854
MACROPOROSITY IN A Al-7%!!&0.4%Mg CASTING ALLOY
VoL 32, No. 11
The model indicates that even a small amount of localised porosity has a significant effect on the tensile ductility,in agreenxentwith the experiments. The same con&&n applies to the effect on the tensile strength; even a small level of porosity produces a measurable loss in tensile strength. These are actually general conclusions regarding the effect of geometrical defects on tensile ductility(7,ll). The relative effect is enhanced for materials with very limited strain hardening capacity, as in the present case. It would seem, therefore, that increasing the strain hardening coefficient, for instance by altering the heat treatment, should result in a more porosity-tolerant material. Herreraand~2)notedthata~ti~inthescatteroftheexperimentaldataresulted~thectuctility wasccaelatedwithtbe~~~ratherthanwiththe~jjectedareaofthevoid Similar@,Surappaetal.(3) sugg&edthattbeenvelopeofthevoid,defined asacircle withdiamekrequaltothelargestdinxmsionofthevoid, ccnelatesbetterwiththeductilitythautheprojectedama. Thisindicatesthattheshapeofthevoidshouldbetaken intoaccounfandis~anaspecttoexpl~e~~yYmo~&~.In~ti~e~with artificial (drilled) holes in wrought ahlminium alloys show that different airofvoids, at constam local volume fraction result in ditkent ductilities(15). Thus, the degree of clustaing when several voids coexist in a ~~Bthe~~mayneedtobe~~aswe~.Themodelalsoignoresany~ectsofthegradual~tion of damage on the flow behaviour. It has been shown that cavitation damage may decrease the local strain hardening rate, rendering the deformation process more unstable(7). Thus, it is clear that the model sutkrs from a number of limitations and more work is needed, which should include systematic studies of the elk& of void shape and distribution, as well as the efkct of varying the strain harderringcapability of the material. Nevertheless, the good agmement between theory and experiments suggests that most of the simplifyingassumptionsofthe model are justified. Summarv and Conclusion
On~~~thatlocalisedpccosityinatensile~leconcentratesthestrain~tothereducedloadbearing area, the rate of strain concentration can be described using existing models fop the growth of plastic instabilities. Byassumingthat~~occuIsintheregionofmaximumstrainatagivenvalueofthelocalstrain,theoverall straiu to tku%urecan be calculated for ditkent levels of porosity. The pro&ure can be applied to calculate the eflbct of porosity on the Cactllre stress. The calculations indicate that even low levels of local&d porosity may have a signiscant eEect on both the tensile ductility and the tensile stmngth ofthe mat&al These predictions are in good agmement with published results for the casting alloy Al-7Si-O.4MgT-6.
References 1. 2. 3. 4. 5. 6. 7. 8.
IA Fdy ad D.M. Smaq M&aids Faum, 9.217 (1986). AHerren,andV.Koodic,Proc.Ld~~o~Q1SOlidificBtimaodCastMetals;lheMetalsSodety,,~p460(19n). MK. fbapp, E. Bladcd J.C. Jaqud, Saiptametall, 24 1281(19w A~~aodJ.GurlaorZTrannMetSoc.Aeue;239,269(1%7) S.F. Fredmidcad W.A Bailey, Tram h4ehU Sot. AME, 242,2063 (1%8). C.H.ChqC.D.Da~audJ.RGrifGbhqsubnrittedtoMater.Sci.Eog. (1994). J.J. Jonasmd~lhdele&AdameCalt,25,43(19n). E. Dummbe, ht. J. Med~ Sci, 14,325 (1972).
Vol. 32, No. 11
9. 10. 11. 12. 13. 14. 15.
MACROPOROSITY IN A Al-7?/&0.4%Mg CASTING ALLOY
E Duoaab, Int J.SolidsStruck,141445 (1974) E.W. Harf Actametall,15,351(1%7). AK Ghosb,Adametd., 25.1413(1977). F.A Nichols,Adad, 28,663(1980). Z Wang ad R Zbng, Mdl. Tms, 22A, 1585(1991). G.E. Dieter,Me&mid Mehlhqy, (3”‘ed), McGraw-Hi&New York (1980, cl+= EM. DubmskydD.A Kosa,h&all. Tms., ISA, 1887(1987)
8.
1855
Vol. 32, No. 11
MACROPGROSITY IN A Al-7%Si-O.4%MgCASTING ALLDY
1856
0.16 FI-1’
t F
Co.14 _
f (%I=
6 5 4
3
1
2
-I
-
.E 0.12 *h
uh
A0
% p, 0.10 : 2 0.08 ” 0.06 .c 2 t; 0.04 0.02 -
0.00
4F Figure 1. A sckmatic view of the geometry assumed for the model.
?! J
0.02
0.04
0.06
0.08
0.10
strain outside the void region, E,,
Figure2.?beshaine,inthevoidregionasafunctionofthe strain eh outside the void region, for porosity f between 0 and 6% Values computed using equation (3) for n=O.1.
A 0.10 -
ij E ; 0.08 -
.r ; 0.06 0.04 r 0.02 -
F 0.00
10.00
0.01
0.02
0.03
0.04
0.05
0.06
area fraction of porosity, f
Figure3.?behduresbain~,asafinxihofaftbeanzalia&m ofporc&y,,toeq . ~lvaluesihxnTableI, convertedtotmezhius(seetext).Tbe-line~ tbesbiae,cbidethevoidxegioaiuFig2forasbaiunearlhe void e;= 0.14.
0.55 0
no
calculated
0.01
0.02
0.03
0.04
area fraction of porosity, f F~4.‘ihet11~taaiie~(solidlirre)mamalisedtothet~e ~ite~aftheaouxtnxibiaLasalix@hofthearea -ofpansay,=P@edusingequation(4).TbeexJPpl poitlts~hmTableI,conWedtoimestreps(seetext~
0.05