镁 气孔-英文

E?ect of microporosity on the tensile properties of AZ91

magnesium alloy

Choong Do Lee

a,*

,Kwang Seon Shin

b

a

Technical Development Division,GM Daewoo Auto &Technology (GMDAT),199-1Cheongcheon-dong,Bupyong-gu,Incheon 403-714,Republic of Korea b

Magnesium Technology Innovation Center,Department of Materials Science and Engineering,Seoul National University,San 56-1,Shillim-dong,

Gwanac-gu,Seoul 151-744,Republic of Korea

Received 19July 2006;received in revised form 23March 2007;accepted 26March 2007

Available online 25May 2007

Abstract

The e?ect of microporosity on the tensile deformation of as-cast AZ91magnesium alloy was investigated through systematic exper-imental approaches and theoretical predictions of a constitutive model for tension instability.The strain rate sensitivity was measured at room temperature by the incremental strain rate change test,and the microporosity was quantitatively obtained by fractography analysis on fractured surfaces.The tensile strength and elongation of as-cast AZ91alloy have a strong inverse parabolic dependence on micro-porosity variation.The constitutive model can exactly predict the tensile deformation of AZ91alloy through a practical estimation of strain-related terms and load carrying capacity by quantitative fractography.The overall plastic deformation of AZ91alloy depends fun-damentally upon not only the variation of load carrying capacity,but also on the strain hardening exponent and strain rate sensitivity.The contribution of strain rate sensitivity to plastic deformation becomes increasingly signi?cant with a decreased strain hardening abil-ity.As the strain rate sensitivity of the conventional material is very low but not zero,the constitutive model for the exact prediction of plastic deformation should take the strain rate sensitivity term into account.ó2007Acta Materialia Inc.Published by Elsevier Ltd.All rights reserved.

Keywords:Magnesium alloy;Plastic deformation;Microporosity

1.Introduction

From the viewpoint of load carrying capacity,the tensile properties of castings are very sensitively dependent on the existence of internal casting defects such as micro-voids and shrinkage holes,which are unavoidable in the conven-tional casting process [1–3].Due to widespread weight reduction trends in the transportation industry,these inter-nal discontinuities have been recognized as a decisive factor for the mechanical properties of structural components such as thin-walled or small integrated castings.Therefore,many experimental studies have focused on the mechanical properties of typical light alloys such as aluminum [4–10]

and magnesium alloys [11,12]and on creating theoretical predictions for a constitutive model [5,6,11].

As is well known,the accuracy of the description of the distribution of stresses around internal discontinuities is intrinsically decided by the exact estimation of load carry-ing capacity [8,11–16].Herrera and Kondic [8]suggested that the microporosity measured from the projected area of micro-voids on fractured surfaces could re?ect the vari-ation of load carrying capacity more exactly than measure-ments based on bulk density [13–15].Surappa et al.[4]and Ca

′ceres [5,6]reported that the plastic deformation of Al–7%Si–0.4%Mg alloy is practically related to the variation of load carrying capacity by a shape factor and the distri-bution of micro-voids.Also,Gokhale and Patel [16–18]emphasized the e?ectiveness of fractography analyses on fractured surfaces in providing exact descriptions of load carrying capacity.In particular,they con?rmed the signif-icance of fractography analyses through comparisons

1359-6454/$30.00ó2007Acta Materialia Inc.Published by Elsevier Ltd.All rights reserved.doi:10.1016/j.actamat.2007.03.026

*

Corresponding author.

E-mail address:choongdo.lee@https://www.360docs.net/doc/267334284.html, (C.D.Lee).

https://www.360docs.net/doc/267334284.html,/locate/actamat

Acta Materialia 55(2007)

4293–4303

between the projected area of micro-voids and bulk poros-ity of AZ91and AM50alloys[16,18].

On the other hand,the tensile instability of material containing internal discontinuities has been investigated in depth by Ghosh[2]and Ghosh’s constitutive model has been experimentally veri?ed by Ca′ceres[5].They reported that the constitutive prediction based upon Ghosh’s model agreed relatively well with the experimental results,even though the strain rate sensitivity(SRS)term was not considered.However,most metallic materials have a very low SRS-value at room temperature[1].This sug-gests that SRS makes a practical contribution to plastic deformation,even though overall plastic deformation depends preferentially upon strain hardening ability and load carrying capacity.Ghosh proved that the stress distri-bution neighboring internal discontinuities depends more sensitively upon the variation of SRS with decreasing strain hardening ability and load carrying capacity.Therefore, the constitutive model should take into account SRS,the strain hardening exponent(SHE)and load carrying capac-ity in order to exactly estimate plastic deformation behavior.

Numerous studies have been performed on the e?ects of microporosity on the mechanical properties of magnesium alloy[11,16,18–21].Even though several studies described the obvious dependence of tensile properties on micropo-rosity variation,the practical contribution of SRS and strain hardening related terms to tensile deformation is still unclear and not yet thoroughly understood.The present study aims to investigate the e?ect of internal micro-voids on the tensile property of as-cast magnesium alloy and to clarify the practical contribution of SRS and strain harden-ing ability to plastic deformation behavior through a veri-?cation of the experimental results using a constitutive model.

2.Theoretical background and experimental procedures 2.1.Constitutive model of tension instability

Except for the thermal contribution,the constitutive equation of a simple power relationship between true stress and strain is primarily concerned with the strain and strain related terms,and can be expressed as follows[1]:

r?K e n_e me1Twhere r and e are true stress and true strain and_e is the true strain rate,i.e.,(o e/o t)in numerical form.In Eq.(1),n and m represent SHE and SRS,which are numerically de?ned in Eqs.(2a)and(2b),respectively:

n?eo ln r=o ln eT

_e;T

e2aT

m?eo ln r=o ln_eT

e;T

e2bTUnder the assumption that the material containing internal discontinuities experiences a tensile load under axial local equilibrium,the conventional equation for stress distribu-tion can be expressed in terms of load carrying area as the following equation[1,2,6,11]:

r ie1àfTA0eàe i?r h A0eàe he3Twhere r i,e i and r h,e h are true stress and strain within the void region and outside the void region,respectively,and A0is the initial cross-sectional area with a microporosity f.

Combining Eqs.(1)and(3),the stress distribution equa-tion can be simply expressed as the following equation [1,2]:

e1àfTeàe i e n

i

_e m

i

?eàe h e n

h

_e m

h

e4TDi?erentiating Eq.(4)over time leads to a general formula which is fundamentally time independent[2]:

e1àfT1=m eàe i=m e n=m

i

d e i?eàe h=m e n=m

h

d e he5TThe relative increase of e i and e h can be calculated by the Newton–Raphson iteration on Eq.(5)and it can also be obtained by various methods as a form of strain pro?le, which consists of the relative increase of D e i and D e h for gi-ven values of m,n and f.

The well-known basic formula of the Newton–Raphson equation is simply given by

x it1?x ià?fex iT=f0ex iT e6TSince the relative increase D e i is the di?erence of strain be-tween the(i+1)th and(i)th steps,(e i+1àe i),the relative increase D e i is obtained according to Eqs.(7a)and(7b), by substituting Eq.(5)into the basic formula of the New-ton–Raphson equation:

D e i?e1àfT1=m eàe i=m e n=m

i

D e iàeàe h=m e n=m

h

D e h

h i

.

e1àfT1=me1=mTeàe i=m D e i n e n=mà1

i

àe n=m

i

h i

e7aT

e1àfT1=me1=mTeàe i=m D e2

i

n e n=mà1

i

àe n=m

i

àe1àfT1=m eàe i=m e n=m

i

D e i

?eàe h=m e n=m

h

D e he7bTRearranging Eq.(7b),the?nal formula for the relative in-crease of D e h can be written as:

D e h?e1àfT1=m eàe i=m D e ieD e i=mTe n=m

i

h

àeD e i=mTn e n=mà1

i

àe n=m

i

i.

eàe h=m e n=m

h

h i

e8TAdditionally,since the true uniform strain of sound mate-rial is equivalent to SHE under maximum loading condi-

tions,the tensile stress,r?

f

,with a microporosity f can be expressed as the following equation from the simple power curve relationship[5,6,11]:

r?

f

=r??ee?

i

=e hTn?ee?=i nTne9T

where e?

i

is the premature true strain which has a micropo-rosity f,and r*and e h are the maximum true stress(ulti-mate tensile strength,UTS)and maximum strain to fracture(elongation)of sound material,respectively.From

4294 C.D.Lee,K.S.Shin/Acta Materialia55(2007)4293–4303

the viewpoint of tension instability,the numerical form for the calculation of UTS is divided into two alternatives for the relative magnitude between SHE and true uniform strain e h,as in the following equations:

r?f =r??ee?

i

=e hTnee h6nTe10aT

r?f =r??ee?

i

=nTnee h P nTe10bT

2.2.Materials and specimen preparation

The raw material used in the present study was commer-cial grade AZ91D alloy(Norsk Hydro Co.),the chemical composition of which is listed in Table1.The test specimen was prepared by a gravity-casting process under an argon atmosphere using a metallic cylindrical mold(inner diame-ter50mm and125mm,respectively)and a cone type mold (height,125mm;upper diameter,75mm;lower diameter, 10mm)preheated to$100°C.The pouring temperature of the melt was controlled from690to750°C along with inoculation treatment(C2Cl6).

After casting,roughly machined test specimens were grouped into several porosity levels by measuring the bulk density using the Archimedes method.The test specimens were prepared up to an extremely high porosity level, which in practice is di?cult to achieve in a conventional casting process,in order to avoid narrowness of porosity range restricting understanding of the dependence of ten-sile properties on microporosity variation.The tensile spec-imen was then fabricated as a rectangular shape with a gauge length of20mm and a width of4mm.2.3.Tension test and measurement of microporosity

The tension test was performed at room temperature with an extensometer at a strain rate of4.2·10à4sà1. The SRS of AZ91alloy was measured through the incre-mental strain rate change method at room temperature [1].In the strain rate change test,the initial strain rate was 4.2·10à4sà1and the second strain rate was 4.2·10à3sà1at engineering strains of0.5%, 1.0%and 2.4%.The SHE was measured by linear?tting to the slope between true stress and strain on log–log scale[1]and the nominal value of SHE was expressed as an average value for the entire specimen.

The projected area of micro-voids on the fractured sur-faces was measured through quantitative fractography by scanning electron microscope(SEM)observation for entire specimens.The microporosity was de?ned as the ratio of micro-void area to the initial cross-sectional area of the test

Table1

Chemical composition of AZ91alloys

Alloy Element

Al(wt.%)Zn(wt.%)Mn(wt.%)Si(wt.%)Fe(ppm)Cu(ppm)Ni(ppm)Be(ppm)Mg(ppm)

AZ91D8.90.740.180.009332195

Balance

Fig.1.Optical micrograph of micro-voids in as-cast AZ91

alloy.

Fig. 2.Typical morphologies of interdendritic micro-voids(a)and

clustered micro-voids(b)by SEM observation of the fractured surface.

C.D.Lee,K.S.Shin/Acta Materialia55(2007)4293–43034295

specimen.Also,the observation by optical microscopy was conducted on the longitudinal section of tensile deformed specimens in order to describe the fracture path and mech-anism,with a microstructural observation.

3.Experimental results and theoretical predictions

3.1.Morphology of micro-voids and fractography

Fig.1shows an optical micrograph for a cluster of micro-voids which were formed along the grain boundary and at the grain corner of as-cast alloy.As shown,the over-all contours of interdendritic shrinkage voids are very sim-ilar to the morphology of Mg17Al12precipitate.These voids are formed by the de?ciency of the interdendritic feeding of the liquid phase on solidi?cation[7,8,22].Typical SEM images of the fractured surface of as-cast AZ91alloy are presented in Fig.2.Fig.2a shows that the fracture surface of as-cast AZ91alloy is composed of a facet surface by frac-ture of Mg17Al12precipitate with a small-deformed area of a-Mg matrix.Also,it shows that the interdendritic shrink-age voids are widely distributed over the entire fractured surface.Moreover,Fig.2b shows typical morphology for some clusters of interdendritic micro-voids in tensile frac-ture surfaces which have extremely high porosity levels. From comparison between Figs.1and2,it is noted that the volumetric porosity measured by microstructural obser-vation cannot but present very limited and inexact informa-tion on the description of the load carrying capacity by the distribution aspect and shape of micro-voids[4].This is par-ticularly true in the case where micro-voids are locally clus-tered or have a high aspect ratio[4,16].

3.2.Tensile properties of as-cast magnesium alloy and theoretical prediction

Fig.3demonstrates the dependence of yield strength on microporosity variation.As shown,the yield strength of as-cast AZ91alloy has a linear dependence on the micropo-rosity and this dependence is similar to the level predicted by the variation of load carrying capacity[9,10,21].

The SRS of as-cast AZ91alloy at room temperature is listed in Table2.The nominal SRS value of as-cast AZ91 alloy is very low,0.002–0.004under the several engineering strains in this experiment.The nominal SHE and strength coe?cients of as-cast AZ91alloy are0.27and530MPa, respectively.These values are relatively higher value than those of Al–7%Si–0.4%Mg alloy(n=0.101and K=372MPa)[4,5].

Fig.4exhibits experimental results for the dependence of elongation(a)and UTS(b)on microporosity variation, with constitutive predictions for n=0.27and m=0.005. The maximum values of UTS and elongation used in the constitutive prediction were obtained from regression anal-yses based on the experimental results,i.e.,240MPa and 6.0%,respectively.As shown in Fig.4,the elongation and UTS of as-cast AZ91alloy have an inverse parabolic dependence on the microporosity variation.The theoretical prediction is in relatively good agreement with the experi-mental results,even though there is a slight divergence between the experimental results and the constitutive pre-dictions as the microporosity increases,especially in the case of UTS.

4.Discussion

4.1.Strain rate sensitivity and strain hardening ability

On the assumption that the material containing internal discontinuities undergoes tensile loading under local

axial

Fig.3.Dependence of yield strength on microporosity variation.

Table2

Strain rate sensitivity of as-cast AZ91alloy for several engineering strains

Engineering strain(%)0.5 1.0 2.4

Strain rate sensitivity0.002±0.0010.004±0.0010.004±0.001 4296 C.D.Lee,K.S.Shin/Acta Materialia55(2007)4293–4303

equilibrium,the individual contributions of SRS and SHE on overall plastic deformation can be described schemati-cally as the strain pro?les shown in Fig.5.In Fig.5,the iso-strain line implies the strain pro?le of a defect-free sound material,i.e.,there is no di?erence between strain within the void region and strain outside the void region (e h =e i ).Fig.5a explains the e?ect of SRS on the overall contour of the strain pro?le for given values of n and f .As shown,the strain pro?le abruptly deviates from the iso-strain line (e h =e i )as the SRS decreases to lower values,even at lower strain levels outside the void region e h .This means that the local plastic strain adjacent to the internal void can be increased to the utmost limit,even though the nominal true strain is very low.

The contribution of SHE to the overall contour of the strain pro?le is revealed in Fig.5b.The strain pro?le for given m and f values gets closer to the iso-strain line (e h =e i )as the strain hardening exponent increases.In con-trast,the in?ection point of the strain pro?le that deviates

from the iso-strain line (e h =e i )is drastically decreased as SHE decreases.

For simplicity,however,the constitutive equation can be expressed as Eq.(11),except for the SRS term [5]

e1àf Te àe i e n i _e m i ?e

àe h e n h _e m

h e4Te1àf Te àe i e n i ?e

àe h e n

h e11T

Although Eq.(11)can easily o?er a numerical solution for theoretical prediction [5],it can only suggest a stationary strain pro?le,which is decided by SHE at a given micropo-rosity.This dependence of strain pro?le on the variation of SRS is schematically described in Fig.6.

As shown in Fig.6,the constitutive model with di?erent SRS values [(a)m =0.005,(b)m =0.1]shows an obvious divergence among strain pro?les with regard to the varia-tion of SHE and microporosity.The constitutive model that does not take SRS into account,however,can only produce a ?xed strain pro?le.This is because the SHE alone domi-nates the stress distribution neighboring micro-voids at

a

https://www.360docs.net/doc/267334284.html,parison between the experimental results and calculated values of elongation (a)and UTS (b)on microporosity for n =0.27and m =0.005.

C.D.Lee,K.S.Shin /Acta Materialia 55(2007)4293–43034297

given microporosity.Since the SRS of conventional metallic material is very low but not zero,the practical contribution to the strain pro?le is less sensitive than that based upon the assumption that SRS is zero,i.e.,without considering SRS

in the constitutive model (_e m h or i ?1,for m =0).

Furthermore,regarding the e?ect of SRS on tensile deformation,Mabuchi et al.[23]reported that the ?ne-grained AZ91alloy exhibits super-plasticity by grain boundary sliding with increasing SRS up to 0.4–0.5and ele-vated temperature.This super-plasticity is described as a typical feature of a strain pro?le whereby the strain within the void region steadily increases along the iso-strain line (e h =e i )with increasing SRS,as shown in Fig.6b.4.2.Quanti?cation of load carrying capacity

As shown in Figs.1and 2,the morphology of interden-dritic shrinkage voids in as-cast AZ91alloy has a high aspect ratio compared to that of trapped gas holes.The overall porosity level of as-cast magnesium alloy is a?ected

by the existence of interdendritic shrinkage voids.Gokhale and his colleagues [16,18]reported that the bulk porosities of 3%and 1.36%in AM50and AZ91alloys corresponded to the fractional areas of the fractured surface of 11%and 9%,respectively.

The e?ect of the morphology of micro-voids on tensile deformation can be simply estimated by introducing the aspect ratio (A.R.).The A.R.of an ellipsoid is de?ned as the ratio of the length of the long axis,l long-axis ,to that of the short axis,l short-axis ,as in the following equation:A :R :?l long-axis =l short-axis

e12T

With the assumption that the sphere (A.R.=1,r x =r y =r z )and ellipsoid (A.R.>1,r x =r y ?r z )have the same volume,the area ratio between the ellipsoid and sphere increases according to the third power of the A.R.,i.e.,

A ellipsoid =A sphere ?eA :R :T1=3

e13

T

Fig.5.Deviation of strain pro?le from the iso-strain line on variation of strain rate sensitivity (a)and strain hardening exponent (b).

4298 C.D.Lee,K.S.Shin /Acta Materialia 55(2007)4293–4303

The ?uctuation of load carrying capacity based on the A.R.can in?uence the overall contour of the strain pro?le.Fig.7a indicates that the strain pro?le is considerably a?ected by the variation of A.R.,even at the same level of microporosity.Fig.7b also exhibits the dependence of fracture strain on the variation of the A.R.of micro-voids.As shown,the di?erence of the fracture strain between the sphere and ellipsoid increases more and more remarkably,even at the same level of microporosity as the A.R.of ellip-soidal micro-void increases to 30.In particular,as shown in Fig.7c,the increase of the A.R.induces an obvious di?er-ence in the normalized strain of ellipsoidal micro-voids compared to those of spheres.Thus,the complicated mor-phology of the micro-voids may lead to error in the estima-tion of load carrying capacity and may eventually lead to misunderstanding and controversy concerning the practical role of micro-voids as typical stress concentration factors on mechanical properties.Therefore,quantitative fractog-raphy,including SEM observation,can be recommended as an e?ective methodology for the exact measurement of load carrying capacity [16–18].

4.3.Mg 17Al 12precipitate on plastic deformation

Fig.8shows a typical microstructure on a longitudinal section of a tensile deformed specimen.This image shows a fracture aspect where the crack initiation of the Mg 17Al 12precipitate occurs in the direction normal to the loading axis with severe deformation of the a -Mg matrix.This fracture mode of as-cast magnesium alloy is very similar to the frac-ture mechanism of Al–Si alloys [24–26].With the increased stress level under axial tensile loading,the accumulation of plastic deformation in the a -Mg matrix preferentially in-duces premature fracture of Mg 17Al 12precipitate.Addition-ally,the premature crack formed in the Mg 17Al 12precipitate propagates along the crystallographic planes of the a -Mg matrix by the accumulation of local plastic deformation.Finally,macroscopic fracture is accomplished through the agglomeration of the adjacent growing cracks [20,27].

Even though micro-voids play a signi?cant role as a major stress concentration source in overall tensile defor-mation,crack initiation in the Mg 17Al 12precipitate may introduce an additional decrease in load carrying

capacity.

Fig.6.Dependence of strain pro?les on the variation of the strain rate sensitivity term in the constitutive model:(a)m =0.005;(b)m =0.1.

C.D.Lee,K.S.Shin /Acta Materialia 55(2007)4293–43034299

Unfortunately,it is very di?cult to estimate exactly the additional decrease in load carrying capacity caused by crack initiation at the Mg 17Al 12precipitate.This additional decrease in load carrying capacity will be a source of diver-

gence between the constitutive prediction and experimental results,as shown in Fig.4.

In order to exclude the concomitant e?ect by crack ini-tiation at the Mg 17Al 12precipitate,the tensile property

of

Fig.7.Deviation of strain pro?les from (a)the iso-strain line (e h =e i ),(b)strain to fracture and (c)normalized strain with the variation of aspect ratio.

4300 C.D.Lee,K.S.Shin /Acta Materialia 55(2007)4293–4303

fully solution-treated alloy was also estimated by measur-ing SRS and SHE.For AZ91alloy on solution treat-ment,the nominal SRS value,m ,is 0.004±0.001and

the nominal SHE value,n ,is 0.4±0.02.The maximum values of UTS and elongation obtained from regression analyses of experimental results are 260MPa and 9.5%,respectively.For the given values of n =0.4and m =0.005,Fig.9shows that there is a strong correspon-dence between the experimental results and the constitu-tive prediction.This could con?rm the additional decrease of load carrying capacity caused by premature fracture of Mg 17Al 12precipitate and its practical contri-bution to overall plastic deformation.

4.4.Constitutive prediction for the defect-free condition In strain pro?les,the strain outside the void region in practice means the observed strain,i.e.,the fractured strain on tensile deformation.The localized strain within the void region,e ?i ,which corresponds to the fractured strain,can be obtained from the constitutive equation for each microporosity.Fig.10shows the modi?ed strain pro?le between localized strain within the void region and fractured strain for several experimental data

shown

Fig.8.Morphology of cracks formed at the Mg 17Al 12precipitate as seen in a longitudinal section of a tensile deformed

specimen.

https://www.360docs.net/doc/267334284.html,parison between the experimental results and calculated values of (a)elongation and (b)UTS with microporosity for the projected area of n =0.4and m =0.005.

C.D.Lee,K.S.Shin /Acta Materialia 55(2007)4293–43034301

in Fig.4.As shown,there is an intersection point between the iso-strain line (e h =e i )and linear-?tted aver-age values among localized strains for each strain pro?le.This means that the fractured strain of sound material does not have any internal discontinuity.This approach can obtain an average predicted strain of 6.8%as a max-imum value for defect-free AZ91alloy.Likewise,the maximum UTS of defect-free AZ91alloy can be esti-mated by substitution of the maximum strain into the strain term of Eq.(10).For a maximum strain of 6.8%,the UTS of defect-free AZ91alloy can be up to 255MPa,and the experimental results are higher than that of regression at $15MPa.5.Summary

The UTS and elongation of as-cast AZ91alloy have nonlinear and inverse parabolic dependence upon micro-porosity variation,even though the yield strength depends linearly on the load carrying capacity.The con-stitutive prediction of tensile deformation of AZ91alloy agrees relatively well with the experimental results.The premature fracture of Mg 17Al 12precipitate results in a slight deviation between the constitutive prediction and experimental results due to the in?uence of load carrying capacity on plastic deformation.However,the constitu-tive prediction can predict the overall plastic deformation of solution-treated AZ91alloy very successfully.

The practical errors in the estimation of load carrying capacity may originate from the complex morphology of micro-voids and the additional increase of discontinuity by crack initiation at the Mg 17Al 12precipitate.However,exact estimation of the load carrying capacity can be achieved by quantitative fractography through SEM obser-vation of the fractured surface.

The in?uence of micro-voids and cracks on the load carrying capacity plays a more signi?cant role on overall

plastic deformation as the SHE and SRS simultaneously decrease to lower levels.Given that the SRS of conven-tional metallic material is very low but not zero,the consti-tutive model with the SRS term is less sensitive than the simple constitutive model where the SRS is not taken into consideration.Therefore,the constitutive equation should take the SRS into account in order to accurately predict the tensile properties of conventional metallic materials at room temperature.References

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