Compressive and tensile behaviour of aluminum foams

Materials Science and Engineering A270(1999)113–124

Compressive and tensile behaviour of aluminum foams

E.Andrews,W.Sanders,L.J.Gibson *

Department of Materials Science and Engineering ,Massachusetts Institute of Technology ,Cambridge ,MA 02139,USA

Received 4November 1998

Abstract

The uniaxial compressive and tensile modulus and strength of several aluminum foams are compared with models for cellular solids.The open cell foam is well described by the model.The closed cell foams have moduli and strengths that fall well below the expected values.The reduced values are the result of defects in the cellular microstructure which cause bending rather than stretching of the cell walls.Measurement and modelling of the curvature and corrugations in the cell walls suggests that these two features account for most of the reduction in properties in closed cell foams.?1999Elsevier Science S.A.All rights reserved.

Keywords :Compessive behaviour;Tensile behaviour;Aluminum foams;Cellular microstructure

https://www.wendangku.net/doc/b0687371.html, /locate /msea

1.Introduction

The recent development of a number of cost-effective processes for making metallic foams has increased their potential for application in sandwich panels for lightweight structural components,in energy absorption systems for protection from impacts,in heat sinks for electronic devices and in acoustic insulation.In this study,we report on the compressive and tensile proper-ties of aluminum foams made by a variety of techniques.

Open cell aluminum foams can be made by in?ltrat-ing an open cell foam such as polyurethane with a heat resistant material,removing the polyurethane by heat-ing,casting liquid metal into the resulting form and then removing the heat resistant material [1].Closed cell foams can be made by several techniques.In the Alcan process,gas is injected into a mixture of molten aluminum and ceramic particles (either SiC or Al 2O 3).The volume fraction of ceramic particles is between 5and 15%;the size of the particles is 1–20m m.The injected air causes bubbles to rise to the surface of the melt,forming a liquid foam which is stabilized by the presence of the ceramic particles.The liquid foam is then mechanically conveyed off the surface of the melt

and allowed to cool.Aluminum foams of relative densi-ties ranging from 0.03to 0.15have been produced using this technique [2].Closed cell aluminum foams can also be made by adding titanium hydride powder to either molten or powdered aluminum.The titanium hydride decomposes at 400°C,well below the melting tempera-ture of aluminum (T m =660°C),releasing hydrogen gas to form bubbles in the foam.In the Shinko Wire process,0.2–8wt%calcium and 1–3wt%titanium hydride are added to molten aluminum,which is then mixed with an impeller in a special casting chamber [3].The calcium acts to increase the viscosity of the melt,assisting in stabilization of the foam.The Shinko Wire foam is available at a relative densities of 0.08–0.13.In both the Fraunhofer and Mepura processes,powdered titanium hydride and aluminum are mixed,pressed,and then heated to release the hydrogen gas [4].This pro-cess generally produces foams of higher relative density,between 0.1and 0.25.Additional techniques for pro-ducing metallic foams are reviewed by Davies and Zhen [5]and Shapovalov [6].

The Young’s modulus and compressive strength of each of these foams have been measured in a number of studies [7–15].The results of several of these studies are summarized in Figs.1and 2,which plot the modulus and strength of aluminum foams normalized by those of the solid cell wall material against the foam density normalized by the solid density.Values for the normal-izing parameters are given by Simone and Gibson [14].

*Corresponding author.Tel.:+1-617-253-7107;fax:+1-617-258-6275.

E -mail address :ljgibson@https://www.wendangku.net/doc/b0687371.html, (L.J.Gibson)

0921-5093/99/$-see front matter ?1999Elsevier Science S.A.All rights reserved.PII:S 0921-5093(99)00170-7

E.Andrews et al./Materials Science and Engineering A270(1999)113–124 114

The unloading moduli of the Alporas,Alcan and

Alulight foams are signi?cantly higher than the initial

loading modulus,suggesting that local yielding occurs

almost immediately on loading[10,13,14].The localized

yielding is thought to result from local inhomogeneities

(e.g.variations in density,cell shape,cell orientation,

cell wall curvature).The ERG foam is different:the

unloading modulus is identical with the initial loading

modulus and microcomputed tomography observations

suggest that yielding is widespread throughout the foam

[16].The mechanism of failure depends on the be-

haviour of the cell wall material.The open cell ERG

foam,made from a ductile6101-T6aluminum,fails by

the formation of plastic hinges within the edges[14,16].

The initial yield point of the Alcan foam corresponds to

debonding between the SiC particles and the aluminum

matrix,which is then followed by ductile tearing of the matrix.Once a number of cells have yielded,a defor-mation band forms and subsequent cell collapse is by membrane tearing and the growth of interfacial cracks [11].

Previous comparisons of the tensile and compressive strengths of aluminum foams have yielded different results for different foams.In one of the?rst studies of aluminum foams,Thornton and Magee[17]found that the tensile strengths of their materials was less than the compressive strengths due to different failure mecha-nisms:local fracture in tension and buckling in com-pression.An indirect measurement of the tensile stress–strain curve of Alporas aluminum foam,from extensometer measurements on the tensile and compres-sive faces of a four-point bend specimen,suggested that it was stiffer and stronger in tension than in compres-Fig.2.Plastic collapse strength of aluminum foams normalized by the yield strength of the solid aluminum,|pl*/|ys,plotted against relative density,z*/z s(from Ref.[14]).A?nite element model for te-trakaidecahedral closed cells and the Gibson and Ashby[18]model for open cells are also shown.

sion[13].Von Hagen and Bleck[15]have found the tensile and compressive strengths of Alcan foam to be almost identical over a range of densities.

The mechanical properties of foams can be modelled by considering the mechanisms by which the cells de-form and fail[18].Under uniaxial stress,open cell, elastic–plastic foams deform by bending followed,at suf?ciently large loads,by the formation of plastic hinges within the cell walls.Simple dimensional argu-ments give the Young’s modulus,E*,and plastic col-lapse strength,|pl*as:

E*

E s

=C1

z*

z s

2(1)

|pl*

ys

=C2

z*

s

3/2(2)

where z*,E*and|pl*are the density,Young’s modulus and strength of the foam and z s,E s and|ys are those of the solid cell wall material.C1and C2are constants related to the cell geometry.A more detailed structural mechanics analysis of a low density,open cell,Kelvin foam with tetrakaidecahedral cells and struts with a Plateau border shape gives C1=0.98[19].Comparison with experimental data suggests that C1=1and C2= 0.3for a wide variety of foams.In closed cell foams, bending of the cell edges is accompanied by stretching of the cell faces.The equation for Young’s modulus then has a linear density term,related to face stretch-ing,as well as the squared term,related to edge bend-ing.Similarly,the equation for the plastic collapse strength has an additional linear term in density related to yielding by cell face stretching:

Fig.1.Young’s modulus of aluminum foams normalized by that of the solid aluminum,E*/E s plotted against relative density,z*/z s (from Ref.[14]).The Hashin–Shtrikman upper bound,a?nite ele-ment model for tetrakaidecahedral closed cells and the Gibson and Asbhy[18]model for open cells are also shown.

E.Andrews et al./Materials Science and Engineering A270(1999)113–124115

E* E s =C1 2

z*

z s

2

+C1’(1? )

z*

z s

(3)

|pl*

|ys=C2

z*

z s

3/2

+C2’(1? )

z*

z s

(4)

where is the volume fraction of solid contained in the cell edges.Finite element simulations of a unit te-trakaidecahedral closed cell with?at faces give[20]:

E E s =0.32

z*

z s

2

+0.32

z*

z s

(5)

|pl* ys =0.33

z*

s

2

+0.44

z*

s

(6)

for relative densities less than0.2.For such low relative densities,the second linear density term dominates, implying that cell face stretching is the more signi?cant mechanism of deformation in closed cell foams.Similar simulations,on both tetrakaidecahedral closed cells and Weaire–Phelan closed cells give E*/E s=0.311(z*/z s) [21].

The data for the open cell,ERG aluminum foam are well described by the model(Figs.1and2).The data for both the modulus and strength of most of the closed cell foams lie below the estimates of the model.Mi-crostructural observation of the Alporas and Alcan foams has identi?ed a number of irregularities not accounted for in the models.Many of the cell walls in the Alporas foam have some initial curvature as well as small voids within them[13,14].There are local regions of higher density where the cell walls are thicker at the nodes.The cell walls in the Alcan foam are sometimes corrugated,especially in the lower density materials [11,13,14].The shape and orientation of the cells in the lower density Alcan foams vary throughout the thick-ness of the panel due to processing conditions[14]. There is a density gradient throughout the thickness of the lower density Alcan foams due to drainage of the liquid before solidi?cation[12,14].

The effect cell wall curvature and corrugations on the modulus and yield strength have been modelled using ?nite element simulations of a periodic unit tetrakaidec-ahedral cell[22].The results suggest that the observed cell wall curvature and corrugations may account for up to a70%drop in the modulus and strength of some aluminum foams below the ideal values estimated for planar cell walls.Similar results are found by consider-ing changes in the effective stiffness of individual corru-gated beams and plates[23].The effect of local thickening of the cell walls at the nodes(Plateau bor-ders)on the modulus and strength of a foam has also been modelled using?nite element simulations[20];for typical distributions of solid material,the change in modulus and strength is less than10%.

Here,we examine the compressive and tensile proper-ties of aluminum foams made by?ve manufacturers: Alcan,Shinko Wire(trade name Alporas),Fraunhofer,Mepura(trade name Alulight),and ERG(trade name Duocel).The microstructure of both the cell walls and the cellular structure are characterized,including mea-surements of cell wall curvature and corrugations.The compressive and tensile Young’s moduli and strength are measured and compared with the models.The properties of closed cell aluminum foams are found to fall well below that suggested by models for foams with ideal https://www.wendangku.net/doc/b0687371.html,ing measured values for cell wall curvature and corrugations in the?nite element simula-tions,we?nd that such defects in the cell structure account for most of the reduction below the ideal values for modulus and strength.

Fig.3.Optical photographs of each of the?ve foams studied.(a) Alcan,(b)Alporas,(c)Alulight,(d)Fraunhofer and(e)ERG.

E.Andrews et al./Materials Science and Engineering A270(1999)113–124 116

2.Materials and methods

Aluminum foams were obtained from?ve manufac-

turers:Cymat(Mississauga,Ont.,Canada;using the

Alcan process,nominal density=380kg/m3),Shinko

Wire(Amagasaki,Japan;trade name Alporas,nominal

density=216kg/m3),ERG(Oakland,CA;trade name

Duocel,nominal density=216kg/m3),Mepura(Ran-

shofen,Austria;trade name Alulight,nominal den-

sity=260–470kg/m3)and Fraunhofer Institut Fuer

Angewandte Materialforschung(IFAM,Bremen,Ger-

many;nominal density=375–750kg/m3)(Fig.3).The

Alporas and Alcan foams were obtained in large panels

from which specimens were cut.The Duocel foam was

machined by the manufacturer to the specimen sizes

used in the mechanical tests.The Alulight and Fraun-

hofer foams were available in smaller sections(100mm

cubes and450mm×125mm×40mm panels,respec-

tively),from which test specimens were cut.The Duocel

material is open cell;all of the others are closed cell.

The Alcan,Fraunhofer and Alulight materials all had a

solid skin on the outer surfaces,which was removed

before testing.Specimens were cut using one of three

techniques:band sawing followed by milling of the

surface,diamond sawing,or electric discharge machin-

ing(EDM).The surface preparation technique had little effect on the mechanical test results[24].

The density of individual specimens was calculated by weighing the specimens on a balance and measuring their dimensions using a digital caliper.The cell size of each of the foams was measured using the mean inter-cept length technique.The cell wall composition was determined using wavelength dispersive X-ray analysis (JEOL JXA-733electron probe microanalyzer;JEOL USA Peabody,MA).The volume fraction of each phase was found using NIH image on back-scattered scanning electron micrographs.At least three cell walls were examined for each type of foam.For all the foams except the Alcan,the composition was similar in all the walls examined.Drainage of liquid aluminum during processing decreases the volume fraction of silicon car-bide in the cell walls towards the bottom of the panel in the Alcan material;the composition of the cell walls in the Alcan foam was measured on14walls taken from different depths within the panel.The cell wall density was estimated using a rule of mixtures approach.The yield strength of the cell wall of all of the closed cell foams was measured by indentation.Individual cell walls were cut,mounted in epoxy and polished with a ?nal step of1m m diamond paste.Indentations were made by Nano Instruments(Oak Ridge,TN)using a Berkovich indenter with loads between200and700 mN.Ten indentations were made in each material.The size of the indentations was measured with an optical microscope.The yield stress was taken to be one-third of the hardness value.The thin cell edges in the open Fig.4.Methods used to measure(a)cell wall curvature and(b)cell wall corrugation.

cell ERG made indentation testing more dif?cult;the yield strength of its cell edges was taken to be the handbook value of the yield strength of the6101-T6 aluminum alloy it is made from.

Curvature of the cell walls was measured in the Alcan,Alporas and Alulight foams.Additional curva-ture measurements were also made on previously tested panels of lower density(80and160kg/m3)Alcan foams [14].No cell edge curvature was observed in the open cell ERG foam.The Fraunhofer foams had a variety of major defects including:large cracks spanning more than10cells,large voids spanning a signi?cant fraction of the specimen and sheared cells.In these specimens, the cell wall curvature,although evident,was not thought to be the primary feature responsible for the degradation in mechanical properties.No further char-acterization of its cell microstructure was made. Samples of the Alcan,Alporas and Alulight foams were cut using EDM(Omega Series Electric Discharge Machine;EDM Technology,Central Islip,NY).The contrast of the foam surfaces was improved by spraying them with matte black paint and then grinding the surface to remove paint from the cell walls.The image of the foam surface was digitized using an optical scanner(Apple Color OneScanner600/27;Apple Com-puter,Cupertino,CA)and the contrast improved using NIH Image Version 1.59.Microstructural measure-

E .Andrews et al ./Materials Science and Engineering A 270(1999)113–124117

ments were made using Canvas Version 5.0.The curva-tures of at least 300cell walls were measured for each foam.The curvature of a cell wall was obtained from measurement of the chord length,L ,and the triangular area,A ,shown in Fig.4.The angle,q ,enclosed by the normals at the ends of the cell wall is related to the chord length L and triangular area A (Fig.4)by:q =4tan ?1

4A L 2

(7)

The normalized cell wall curvature,L /2R ,is then:L

2R

=sin

q 2

The Alcan foam properties vary through the thick-ness of the sheet due to density variations resulting

from drainage during processing.Previous microstruc-tural measurements of the cell shape,cell orientation and foam density through the thickness of the panel indicated that there were three approximately homoge-neous sections in the panel [14];curvature measure-ments were made on three corresponding horizontal sections.The Alporas and Alulight materials were found to have roughly equiaxed cells;curvature mea-surements were made on sections cut without reference to panel or block orientation.

Corrugations in the cell walls were previously ob-served on sections cut in the rise direction in the 80and 160kg /m 3Alcan foam [14].They are thought to result from partial cell collapse while the cell walls are solidi-fying during processing.As part of this study,we also measured the length L ,average amplitude h and num-ber of corrugations for each corrugated cell wall for samples from the panels from the previous study,as shown in Fig.4(b).The corrugation data was measured for 44cell walls of the 80kg /m 3foam and 82cell walls for the 160kg /m 3foam.Average and 95th percentile values of the normalized amplitude,h /L ,and normal-ized frequency,L /u ,were calculated for each https://www.wendangku.net/doc/b0687371.html,pression tests were carried out on cubic speci-mens.The size of the specimens varied depending on the available material:the edge lengths of the Alcan,Alporas,ERG,Alulight and Fraunhofer foams were 50,50,25,45and 40mm,respectively.In each case,the edge length was at least seven times the cell size:the results of a separate study indicated that this is the minimum specimen size required to avoid edge effects which reduce the measured values of Young’s modulus and compressive strength [24].Between three and six specimens were tested for each material.The ERG material was loaded both parallel (X 1)and perpendicu-lar (X 2)to the axis of cell elongation;previous data suggests that the ERG material is roughly transversely isotropic [25].The Alcan material was loaded in three perpendicular directions:X 1,in the plane of the sheet of foam,in the direction of the conveyor motion;X 2,in the direction of the thickness of the sheet;and X 3,in the plane of the sheet,perpendicular to the conveyor motion.Although the Alporas cells are equiaxed,the mechanical properties depend on loading direction [14].

Table 1

Solid cell wall properties of aluminum foams Solid density z s Reference yield Foam

Composition

Measured yield Volume fraction

Reference Young’s modulus E s (GPa)(kg /m 3)strength |ys (MPa)strength,|ys (MPa)Al 0.6Mg 0.5Si ERG (6101/T6)2690a –69a –193a Al 0.8192760

93b

Alcan

330

310b SiC

0.152390c

Al matrix only

0.013Al /Si /Mg /Fe Al /Si /Fe 0.0062710Alporas

69Al

120

130d 0.831172c 0.163Al /Ti /Ca Al /Fe 0.006Al

0.6952860Alulight

69250

250d

0.260Al /Si /Fe Al /Ti 0.0250.018Si Ti 0.002Fraunhofer

Al

0.891272069215

173e Al /Si /Fe 0.096250c

0.012Al /Si /Ti Ti 0.002

a

Davies and Zhen [5].b

Alcan data.c

Simone and Gibson [14].d

Sugimura et al.[13].e

Weber et al.[9].

E.Andrews et al./Materials Science and Engineering A270(1999)113–124

118

Table2

Cell size and cell wall curvature for aluminum foams

Average L/2R E/E o95th percentile L/2R

Cell size(mm)|*/|o* Foam

2.5

ERG––––

0.330.52

13.2a0.69

Alcan3%0.15

7.5a

Alcan6%0.280.620.620.34 Alcan14%0.34

3.4a0.660.640.48

0.210.72

4.5a0.56

Alporas0.45

4.2

Alulight0.370.630.740.32

–––

Fraunhofer–

2.6

a Data for cell size of Alcan and Alporas from Simone and Gibson[14].

Table3

Corrugation frequency and amplitude for aluminum foams

Foam Average h/L

Average L/u E/E o95th percentile L/u95th percentile h/L|*/|o*

0.067

Alcan3%0.46

1.67 3.00.050.71

0.0580.65 3.20.19

1.140.22 Alcan6%

The compressive strength of Alporas in three orthogo-nal directions was measured on a separate set of cubes. Compression testing was performed by deforming the specimen between two parallel platens in an Instron model1321(Canton,MA)load frame with a50kN load cell.For the Alporas,Alulight and Fraunhofer foams,up to a strain of approximately10%,displace-ment was measured by two LVDTs(Trans-Tek,Elling-ton,CT)on either side of the specimen;at higher strains the displacement was measured from the Instron crosshead displacement.Up to a strain of approxi-mately10%,the displacement rate was0.01mm/s, while at higher strains,the rate was increased to0.05 mm/s.For the ERG,Alcan and Alporas foams,two extensometers(gauge length32mm)were centrally mounted on the specimen to measure both the applied and transverse strains,from which Poisson’s ratio was calculated.In all of the mechanical testing,load and displacement were recorded using a National Instru-ments SCB-68data acquisition unit,Labview(National Instruments,Austin TX)and a personal computer.The Young’s modulus of the foam was calculated from the slope of the unloading load–de?ection curve taken at approximately75%of the expected plastic collapse stress of the foam,which was found from preliminary tests.The plastic collapse stress was calculated from the initial peak load on the specimen.Densi?cation strain was taken as the strain at which the stress was equal to 1.5times the stress at50%strain:although somewhat arbitrary,this gives a consistent method.

Direct tension tests were performed on the ERG material on dogbone specimens with a waisted region 90mm in length and20mm×20mm in cross-section. Five specimens were tested for loading in each of two directions:parallel and perpendicular to the long axis of the cells.Standard Instron grips with large,custom-made grip faces to accommodate the large foam sam-ples were used.The ends of the specimens were initially potted with epoxy to minimize crushing of the material. Subsequent tests showed that inserting a?ne piece of sandpaper,folded over,between the specimen and the grip faces allowed for suf?cient grip force to avoid slip without excessive clamping force;this technique elimi-nated the need to pot the ends of the specimen with epoxy.The specimens were loaded at a rate of0.01 mm/s.The Young’s modulus was calculated from the slope of the unloading load–de?ection curve.Periodic unloadings and reloadings were performed,both before and after the onset of initial failure in the material.In the?rst set of tests,two extensometers with a gauge length of50.8mm were used to measure axial strain on either side of the https://www.wendangku.net/doc/b0687371.html,parison of the strains on either side of the specimen con?rmed that no bend-ing occurred.In subsequent tests,the second exten-someter,with a gauge length of12.7mm,was used to measure the transverse strain,allowing Poisson’s ratio to be calculated.In all cases,the specimens were loaded until complete tensile failure(separation)occurred. Direct tension tests on dogbone specimens of Alporas and Alcan were performed in a similar manner.The waisted region was nominally125mm in length and25 mm×25mm in cross-section.Four specimens of the Alcan foam and three specimens of the Alporas foam were tested in the X1direction.The dimensions of the Alulight and Fraunhofer materials available were in-suf?cient to produce dogbone specimens for tensile testing.

E.Andrews et al./Materials Science and Engineering A270(1999)113–124119

3.Results

The solid cell wall composition and properties are listed in Table1.The volume fraction of silicon car-bide in the Alcan foams varied from3to48%de-pending on the location of the cell wall:during processing,the liquid aluminum drains to the bottom of the sheet,increasing the concentration of SiC at the top and decreasing it at the bottom.The value of 15.2%represents an average for cell walls taken throughout the sheet.The densities of the cell wall vary only slightly from the value of2700kg/m3for pure aluminum.The Young’s modulus of the cell wall was taken to be the reference value for aluminum(69 GPa)for the ERG,Alporas,Alulight and Fraunhofer foams.The Young’s modulus of the Alcan foam was taken to be93GPa,a reference value given by the manufacturer,which lies close to the lower bound for a composite of SiC particles in an aluminum matrix. The measured values of the yield strength of the cell wall from indentation tests are close to those reported in the literature.

Data for the average cell size,and for the average and95th percentile cell wall curvature are reported in Table2.The orientation of the cells in the Alcan foam was found to vary throughout the thickness of the sheet [14];average cell sizes are reported here.The mean intercept length measurement of cell size was repeated on the Alporas foam and found to be within2%of the previously reported value.The cell size of the Alporas, Alulight and Fraunhofer foams is the same in all direc-tions.The ERG foam is transversely isotropic:the cells are elongated in one direction(2.7mm)and roughly equiaxed in the perpendicular plane(2.4mm).The average cell wall curvature is used to estimate the reduction in Young’s modulus below that for an ideal closed cell foam(Eq.(5)),using the?nite element simulations of Simone and Gibson[22].The95th per-centile cell wall curvature is used to estimate the reduc-tion in the compressive strength below that for an ideal closed cell foam(Eq.(6)),again using the?nite element simulations of Simone and Gibson[22].The corre-sponding values of the modulus and strength reduction are also shown in Table2.

Fig.5.Frequency distribution of cell wall curvature for(a)Alulight,(b)Alporas,(c)3%dense Alcan,(d)6%dense Alcan and(e)14%dense Alcan aluminum foams.

E .Andrews et al ./Materials Science and Engineering A 270(1999)113–124

https://www.wendangku.net/doc/b0687371.html,pressive stress–strain curves for aluminum foams (a)up to strain of 5%and (b)up to densi?cation strain.

Fig.7.Tensile stress–strain curves for aluminum foams.

wall curvature for the Alcan,Alporas and Alulight foams are shown in Fig.5.The histograms for horizon-tal slices taken from the top,middle and bottom of the Alcan panels showed similar distributions,indicating that the distribution of curvature remains roughly con-stant throughout the depth of the panel;Fig.5shows the histogram for the combined data for each density of Alcan foam.

Compressive stress–strain curves for loading up to a strain of 5%and up to the densi?cation strain are shown in Fig.6.All but one unloading slope have been omitted for clarity.The slope of the unloading curve was greater than that for the loading curve except for the ERG foam,for which the two are equal.The peak stress is reached at a strain of between 0.5and 4%.The plateau stress for the ERG and Alporas foams are roughly constant with increasing strain until the densi?-cation occurs.The stress plateau of the Alcan foam is serrated,as is typical of a brittle foam:the serrations correspond to fracture of cell walls.The plateau stress for the Fraunhofer foam gradually increases with strain.Tensile stress–strain curves are shown in Fig.7.The results of the compression and tension tests are summarized in Table 4.The variations in density for each set of test specimens is low except for the Fraun-hofer material,in which the densities ranged from 376to 671kg /m 3;for this material,individual test results are listed.The density of the 14%dense Alcan speci-mens is much less than the nominal value of 380kg /m 3since the specimens were taken from the central region through the thickness of the plate which had a density of about 220kg /m 3.The ERG foam had similar Young’s moduli and strengths in tension and compres-sion for each loading direction.The Young’s modulus and strength in the X 1direction were much higher than those in the X 2direction.The Alcan foam appears to be transversely isotropic from the compressive test results,with much higher moduli and strength in the X 3direc-tion.In tension,it is brittle with a ductility of only 0.17%.Its tensile strength is less than half its compres-sive strength in the X 1direction.The Alporas foam has a slightly lower Young’s modulus in compression than in tension,and slightly higher strength in compression than in tension.The Alporas foam has a lower Young’s modulus in the X 1direction than in the X 2direction.The compressive strengths in the two directions are similar once density differences are accounted for.Pre-vious tests indicated that the Alporas foam is an-isotropic with moduli and strengths of 870and 1.60MPa in one direction and 1210and 1.36MPa in the other [14].The Alulight and Fraunhofer foams were tested without regard for orientation since there was no preferred axis of cell elongation and there was no indication of the orientation of the specimens from the manufacturer.Although these materials were denser than the other foams tested,their mechanical properties were of the same magnitude.

The data for the cell wall corrugations in the low density Alcan foams were treated in a similar manner (Table 3).The average as well as the 95th percentile values of the corrugation frequency and amplitude are reported and used to estimate the reductions in Young’s modulus and compressive strength,respec-tively,below those for an ideal closed cell foam.

Histograms showing the frequency of normalized cell

E .Andrews et al ./Materials Science and Engineering A 270(1999)113–124

121

Table 4

Compressive and tensile test results a Alcan X 1

Alcan X 2

Alcan X 3

Alporas X 1b

Alporas X 2

ERG X 1

Property

ERG X 2

Compression 4

4

4

4

4

4Number of 3

specimens

217(10)212(5)

232(27)

250(4)

220(6)

220(6)

Density (kg /m 3)249(9)

1.18(0.20)Young’s mod- 3.16(1.14)0.634(0.03)

1.00(0.07) 1.14(0.13)0.236(0.05) 1.52(0.33)ulus (GPa) 4.35(0.65) 1.84(0.04) 1.46(0.07)

2.30(0.41) 2.34(0.14)1.39(0.11)2.17(0.12)Strength (MPa)0.65(0.01)

0.63(0.01)0.66(0.02)

0.68(0.02)

–

0.63(0.1)

0.60(0)

Densi?cation strain Tension ––3(*2)4

6Number of 5

specimens

193(9)––244(3)

–190(6)

Density (kg /m 3)217(14)

Young’s mod-–0.502(0.084)

– 1.37(0.03)*–0.184(0.023) 1.33(0.49)ulus (GPa)– 1.44(0.02)–0.93(0.13)1.08(0.18)–Strength (MPa) 1.93(0.29)–

0.012(0.002)

–

0.0120.024(0.005)

–

0.0017(0.001)

Ductility (0.0001)*

Fraunhofer

Property Alulight Fraunhofer c Fraunhofer Fraunhofer Compression 15111Number of specimens

544Density (kg /m 3)274(17)3764295020.82 1.330.691.17(0.47)

0.61Young’s mod-ulus (GPa) 3.01(1.01) 2.50 2.821.88Strength (MPa) 2.300.60

0.60

Densi?cation 0.65(0.01)0.61

0.60

strain

a

ERG:X 1,parallel to elongated cell axis;X 2,perpendicular to elongated cell axis.Alcan:X 1,in plane,along conveyor motion;X 2,along thickness of the plate;X 3,in plane,perpendicular to conveyor motion.Alporas:X 1,perpendicular to the thickness of the plate;X 2,parallel to the thickness of the plate.b

Data from Andrews et al.[24]on prismatic specimens 24mm ×24mm ×48mm.c

Due to the large variation in densities of the Fraunhofer specimens tested,results for individual specimens are reported,rather than the average values.

*No extensometer data for one test.

Fig.8.Relative Young’s modulus plotted against relative density for aluminum foams.The dashed and solid lines represent Eqs.(1)and (5)for ideal open and closed cell foams,respectively.The dash–dot line represents the reduction in the moduli of the ideal closed cell foam resulting from the measured cell wall curvature.

E.Andrews et al./Materials Science and Engineering A270(1999)113–124 122

Fig.9.Relative compressive strength plotted against relative density for aluminum foams.The dashed and solid lines represent Eqs.(2) and(6)for ideal open and closed cell foams,respectively.The dash–dot line represents the reduction in the strength of the ideal closed cell foam resulting from the measured cell wall curvature.Data are shown for the open cell ERG foam as well as the closed cell foams for which the cell wall curvature was the only major defect in the cell structure(14% Alcan,Alporas and Alulight).The solid lines represent the equations for the modulus and strength of ideal closed cell foams(Eqs.(5)and(6)).The dashed lines represent the equations for the modulus and strength of ideal open cell foams(Eqs.(1)and(2)).The dash–dot lines represent the reduction in the modulus and strength below the values for an ideal closed cell foam due to cell wall curvature.The modulus and strength reduction was based on the average of the modulus and strength reduction factors(Table2)for the closed cell foams shown in Figs.8and9.

4.Discussion

The data for the modulus and strength of the ERG foam lie very close to the values given by the model for open cell foams.The data for the modulus and strength of the closed cell foams lies well below the model for an ideal tetrakaidecahedral cell(Eqs.(5)and(6)).Previous ?nite element calculations suggest that cell wall curva-ture can produce signi?cant reductions in modulus and strength below the ideal values for a perfect structure [22].The effect of cell wall curvature on modulus and strength was estimated by assuming that the modulus was related to the average curvature in the cell walls, while the strength was related to the weakest cells with the most cell wall curvature.Since failure can be trig-gered by a small fraction of weak cells[11,26],we selected the95th percentile value of cell wall curvature. The average modulus and strength reductions result-ing from the average and95th percentile values of cell wall curvature for the14%dense Alcan,the Alporas and the Alulight foams were0.67and0.42,respectively. The data for both properties lie slightly below the lines representing the closed cell model corrected for cell wall curvature,suggesting that other imperfections in the cell structure(e.g.cell shape,local density variations) also play a role.

The3and6%dense Alcan foams tested by Simone and Gibson[14]have moduli and strengths one to two orders of magnitude below the model predictions for a

We de?ne Poisson’s ratio as w ij=?m j/m i.Mean

measured values of the elastic Poisson’s ratio were:

ERG(com-w12=0.65,w21=0.25

pression,n=2)

ERG(tension,w12=0.74

n=3)

Alcan(com-w12=0.40,w21=0.23,w13=0.25,

pression,w31=0.38w23=0.13,w32=0.17

n=2)

Alcan(tension,w12=0.35

n=2)

Alporas(com-w=0.37

pression,

n=3)

Alporas(ten-w=0.40

sion,n=2)

We note that the compressive elastic moduli data for

the ERG foam obeys the reciprocal relation E1w21=

E2w12.The data for the Alcan foam do not;the reason

for this is not clear.

Young’s modulus and compressive strength,normal-

ized by the values for the solid cell wall material(Table

1),are plotted against relative density in Figs.8and9.

Table5

Reduction in Young’s modulus and strength of low density Alcan foams due to density variations,curvature and corrugations

3%E(MPa)3%|pl*(MPa)6%E(MPa)6%|pl*(MPa)

945 4.57

Average density17808.55

3.97

1.81

641

Density correction1290

3330.27

+Curvature correction800 1.35

1530.30

+Corrugation correction520

0.19

270.0671090.20 Measured

E.Andrews et al./Materials Science and Engineering A270(1999)113–124123

closed cell foam(Figs.1and2).The discrepancies arise from several sources:density variations within a specimen,cell wall curvature and corrugation,as well as variations in cell shape.The contribution of den-sity variations and cell wall curvature and corruga-tions to the reduction in modulus and strength can be estimated as follows.The density of each of the foams was found to vary through the depth of the specimens;Simone and Gibson report the densities of three horizontal layers of roughly equal thickness through the depth of the specimens.The isostress Young’s modulus was calculated using Eq.(5)and their measurements of layer density.The strength was assumed to be controlled by the lowest density layer; the theoretical strength of the lowest density layer was found using Eq.(6).The modulus and strength reductions corresponding to the average and95th per-centile cell wall curvature and the average and95th percentile corrugation frequency and amplitude(Ta-bles2and3)were then applied.The cumulative ef-fect of density variations,cell wall curvature and cell wall corrugations on the model predictions are given in Table5,along with the measured values of mod-ulus and strength.The cumulative effect of all three imperfections accounts for about80%of the differ-ence between measured E and the ideal closed cell foam model,and about98%of the difference be-tween measured strength and the ideal closed cell foam model.

5.Conclusions

The reduction in the measured values of Young’s modulus and plastic collapse stress of closed cell alu-minum foams below those predicted by models of ideal tetrakaidecahedral cells is associated with imper-fections in the cellular structure,including density variations,cell wall curvature and cell wall corruga-tions.There is potential for substantial improvement in their mechanical properties if such defects could be reduced through improved processing techniques. Acknowledgements

We gratefully acknowledge the?nancial support of ARPA Contract Number N00014-96-1-1028.Toby Freyman made the cell size measurements on the Al-poras,Alulight and Fraunhofer foams.Gael Gioux performed the tension tests on the Alporas foam. Emma Shepherdson performed the compression tests on the Alulight and the Fraunhofer foams.We are grateful to all for their assistance.References

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音响 扬声器材质与尺寸 低档塑料音箱因其箱体单薄、无法克服谐振，无音质可言(也有部分设计好的塑料音箱要远远好于劣质的木质音箱)；木制音箱降低了箱体谐振所造成的音染，音质普遍好于塑料音箱。 通常多媒体音箱都是双单元二分频设计，一个较小的扬声器负责中高音的输出，而另一个较大的扬声器负责中低音的输出。 挑选音箱应考虑这两个喇叭的材质：多媒体有源音箱的高音单元现以软球顶为主(此外还有用于模拟音源的钛膜球顶等)，它与数字音源相配合能减少高频信号的生硬感，给人以温柔、光滑、细腻的感觉。多媒体音箱现以质量较好的丝膜和成本较低的PV膜等软球顶的居多。 低音单元它决定了音箱的声音的特点，选择起来相对重要一些，最常见的有以下几种：纸盆，又有敷胶纸盆、纸基羊毛盆、紧压制盆等几种。 纸盆音色自然、廉价、较好的刚性、材质较轻灵敏度高，缺点是防潮性差、制造时一致性难以控制，但顶级HiFi系统中用纸盆制造的比比皆是，因为声音输出非常平均，还原性好。 防弹布，有较宽的频响与较低的失真，是酷爱强劲低音者之首选，缺点是成本高、制作工艺复杂、灵敏度不高轻音乐效果不甚佳。 羊毛编织盆，质地较软，它对柔和音乐与轻音乐的表现十分优异，但是低音效果不佳，缺乏力度与震撼力。 PP(聚丙烯)盆，它广泛流行于高档音箱中，一致性好失真低，各方面表现都可圈可点。此外还有像纤维类振膜和复合材料振膜等由于价格高昂极少应用于普及型音箱中。 扬声器尺寸自然是越大越好，大口径的低音扬声器能在低频部分有更好的表现，这是在选购之中可以挑选的。用高性能的扬声器制造的音箱意味着有更低的瞬态失真和更好的音质。普通多媒体音箱低音扬声器的喇叭多为3～5英寸之间。用高性能的扬声器制造的音箱也意味着有更低的瞬态失真和更好的音质。 音箱: 有源和无源 有源音箱（ＡｃｔｉｖｅＳｐｅａｋｅｒ）又称为“主动式音箱”。通常是指带有功率放大器的音箱，如多媒体电脑音箱、有源超低音箱，以及一些新型的家庭影院有源音箱等。有源音箱由于内置了功放电路，使用者不必考虑与放大器匹配的问题，同时也便于用较低电平的音频信号直接驱动。

精神分裂症的发病原因是什么

精神分裂症的发病原因是什么 精神分裂症是一种精神病，对于我们的影响是很大的，如果不幸患上就要及时做好治疗，不然后果会很严重，无法进行正常的工作和生活，是一件很尴尬的事情。因此为了避免患上这样的疾病，我们就要做好预防，今天我们就请广州协佳的专家张可斌来介绍一下精神分裂症的发病原因。 精神分裂症是严重影响人们身体健康的一种疾病，这种疾病会让我们整体看起来不正常，会出现胡言乱语的情况，甚至还会出现幻想幻听，可见精神分裂症这种病的危害程度。 (1)精神刺激：人的心理与社会因素密切相关，个人与社会环境不相适应，就产生了精神刺激，精神刺激导致大脑功能紊乱，出现精神障碍。不管是令人愉快的良性刺激，还是使人痛苦的恶性刺激，超过一定的限度都会对人的心理造成影响。 (2)遗传因素：精神病中如精神分裂症、情感性精神障碍，家族中精神病的患病率明显高于一般普通人群，而且血缘关系愈近，发病机会愈高。此外，精神发育迟滞、癫痫性精神障碍的遗传性在发病因素中也占相当的比重。这也是精神病的病因之一。 (3)自身：在同样的环境中，承受同样的精神刺激，那些心理素质差、对精神刺激耐受力低的人易发病。通常情况下，性格内向、心胸狭窄、过分自尊的人，不与人交往、孤僻懒散的人受挫折后容易出现精神异常。 (4)躯体因素：感染、中毒、颅脑外伤、肿瘤、内分泌、代谢及营养障碍等均可导致精神障碍，。但应注意，精神障碍伴有的躯体因素，并不完全与精神症状直接相关，有些是由躯体因素直接引起的，有些则是以躯体因素只作为一种诱因而存在。 孕期感染。如果在怀孕期间，孕妇感染了某种病毒，病毒也传染给了胎儿的话，那么，胎儿出生长大后患上精神分裂症的可能性是极其的大。所以怀孕中的女性朋友要注意卫生，尽量不要接触病毒源。 上述就是关于精神分裂症的发病原因，想必大家都已经知道了吧。患上精神分裂症之后，大家也不必过于伤心，现在我国的医疗水平是足以让大家快速恢复过来的，所以说一定要保持良好的情绪。

基于单片机的自动存包系统设计

基于单片机的自动存包系统设计 摘要 近年来，随着生活水平的提高，人们对于社会消费品的质量和数量的要求也在逐渐增加。为了更好的为广大顾客服务，在一些商场、影院、超市等公共场合通常设置有自动存包柜，本次便是针对这一现象进行设计。 本文详细介绍了国内自动存包控制系统的发展现状，发展中所面临的问题。并详细介绍了本系统采用的AT89S52单片机做控制器，可以同时管理四个存包柜。柜门锁是由继电器控制，当顾客需要存包的时候，可以自行到存包柜前按“开门”键，需要顾客向光学指纹识别系统输入个指纹，然后通过继电器进行开门（用亮灯表示），顾客即可存包，并需将柜门关上。当顾客需要取包时，要将只要将之前输入的指纹放置于指纹识别器前方，指纹识别器采集到指纹信息输出相应的高低电平信号传给单片机，系统比较密码一致后，发出开箱信号至继电器将柜门打开，顾客即可将包取出。它具有功能实用、操作简便、安全可靠、抗干扰性强等特点。 关键词：自动存包柜,单片机,指纹识别器

李少鹏：基于单片机的自动存包系统设计 Based on single chip microcomputer automatic package design Abstract In recent years, with the improvement of living standards, people for social consumer goo ds quality and quantity requirements are to increase gradually. In order to better service for the g eneral customers, in some stores, movie theaters, supermarkets public Settings are to be put auto matically usually bag ark, it is functional practical, simple operation, safe and reliable, anti-jamm ing strong sexual characteristics. Domestic deposit automatic control system are introduced in detail in this paper the development of the status quo, problems faced in the development of. And introduces in detail the system adopts single chip microcomputer controller, can simultaneously manage multiple pack ark. Cupboard door lock controlled by relay, when customers need to save package, will be allowed to save package before the ark according to the "open" button, need customer to the system input fingerprint, and then through the relay to open the door (with lighting), customers can save package, and the cupboard door must be closed. When customers need to pick up package, as long as before the input fingerprint should be placed on the fingerprint recognizer, fingerprint recognizer collecting to the fingerprint information and output the corresponding high and low level signal to the microcontroller, the system is password consistent, signal out of the box to the relay Key words: Automatic Storage Bag, Microcontroller, Fingerprint recognizer。

音响常识

第一部分：音响基础知识 音箱参数 1．阻抗（想知道具体这个物流单位是什么意思，百度的知道一下，下同） 阻抗不是电阻，大家在这里常常犯错误，其实阻抗是电阻和电抗的总和。电阻是指在直流电中，物体对电流的阻碍作用。在交流点中，除了电阻会阻碍电流，电容和电感也会阻碍电流，这就是电抗了。据我查到的资料，阻抗值其实对音质没有关键性影响。但是，如果阻抗过低，造成电流过大，也容易使声音失真，对喜欢听音乐的玩家来说，阻抗就显得相对敏感。音箱常见的值有，4、6、8、16国际推荐值为8○（这个是物流欧姆的符号，找不到……用圈代替） 2.灵敏度 灵敏度，指的是音箱输入1W电功率时，在音箱正面，各个有事情的集合中心1M的距离，测试得来的声压级，单位是DB。换个简单的说法，就是灵敏度关系到音箱的音量大小。在同等音量条件下，灵敏度越高的音箱，声音失真的可能性要小得多。音箱高保真音箱的灵敏度在86db，专业级别的音箱在96db以上，选购音箱时可以参考。 3.功率 额定功率：（RMS）简而言之，称为有效功率，即不失真情况下，音箱长期安全使用的最大功率值。通常情况下，只有一些大型多媒体音箱的厂商才有标出该值，大部分厂商标注的是峰值音乐输出功率。 峰值音乐输出功率（PMPO）：多数厂商标的是这个参数，即不考虑失真的情况下，功放的瞬间最大输出功率。这个值即没有考虑失真，又超过一定范围，那它是否有意义呢？其实也可以通过换算得到我们需要的它与额定功率的比值，具体的我也不清楚，资料显示换算比是1比8. 4.信噪比 指的是音箱回放正常声音信号与无信号时噪声信号的比值，也用DB表示。这个值越高，代表音质越好，但是价格也越高…一般2.0音箱的信噪比达到80db 即可，大一点也可以。至于X.1音箱，只要大于75db就ok！ 5.扬声器口径 有的人认为，扬声器口径是越大越好，其实呢？当然不是。因为扬声器口径增大的同时，纸盆在振动的时候就容易变形、损坏，同样会影响音质。所以，低频扬声器口径一般为20-38cm，当然也有60或72cm的超大口径的大炮。中高音扬声器口径通常在2-6cm之间，偶尔有大于9cm的家伙 6.失真度 就是指没有经过放大器放大前的信号，与经过放大的信号作比较，被放大过的信号与未放大过的信号的差别。单位是百分比。对于多媒体音箱来说，失真无法避免，只要控制在一个合理的范围内就好。比如，2.0音箱必需在1%以下，X.1也要在5%以下2.0音箱必需在1%以下，X.1也要在5%以下。 7.重量 音箱越重，说明用的木材比较好，内部的磁钢比较大，这样可以有效提升音质。所以简而言之，重的好，因为舍得用料。（不排除无良商家塞砖块之类的事情，好像发生过……）

精神分裂症的病因是什么

精神分裂症的病因是什么 精神分裂症是一种精神方面的疾病，青壮年发生的概率高，一般 在16～40岁间，没有正常器官的疾病出现，为一种功能性精神病。 精神分裂症大部分的患者是由于在日常的生活和工作当中受到的压力 过大，而患者没有一个良好的疏导的方式所导致。患者在出现该情况 不仅影响本人的正常社会生活，且对家庭和社会也造成很严重的影响。 精神分裂症常见的致病因素： 1、环境因素：工作环境比如经济水平低低收入人群、无职业的人群中，精神分裂症的患病率明显高于经济水平高的职业人群的患病率。还有实际的生活环境生活中的不如意不开心也会诱发该病。 2、心理因素：生活工作中的不开心不满意，导致情绪上的失控，心里长期受到压抑没有办法和没有正确的途径去发泄，如恋爱失败， 婚姻破裂，学习、工作中不愉快都会成为本病的原因。 3、遗传因素：家族中长辈或者亲属中曾经有过这样的病人，后代会出现精神分裂症的机会比正常人要高。 4、精神影响：人的心里与社会要各个方面都有着不可缺少的联系，对社会环境不适应，自己无法融入到社会中去，自己与社会环境不相

适应，精神和心情就会受到一定的影响，大脑控制着人的精神世界， 有可能促发精神分裂症。 5、身体方面：细菌感染、出现中毒情况、大脑外伤、肿瘤、身体的代谢及营养不良等均可能导致使精神分裂症，身体受到外界环境的 影响受到一定程度的伤害，心里受到打击，无法承受伤害造成的痛苦，可能会出现精神的问题。 对于精神分裂症一定要配合治疗，接受全面正确的治疗，最好的 疗法就是中医疗法加心理疗法。早发现并及时治疗并且科学合理的治疗，不要相信迷信，要去正规的医院接受合理的治疗，接受正确的治 疗按照医生的要求对症下药，配合医生和家人，给病人创造一个良好 的治疗环境，对于该病的康复和痊愈会起到意想不到的效果。

自动存包柜的设计与仿真

自动存包柜的设计与仿真 摘要 本课题是基于单片机的自动存包柜设计。自动存包柜是新一代的存包柜，具有功能实用、操作简单、管理方便、安全可靠等特点，能够更好的服务于不同市场的广大群众，使用者可以根据简明清晰的操作说明自行完成存包取包工作。本系统由MCS-51单片机构成核心控制系统，整个系统由主控部分、键盘显示控制部分、执行部分三部分组成，通过随机密码的产生和核对完成自动存包取包过程。本设计中各元器件便于安装且操作简单，能基本实现存包取包功能。 关键词：自动存包柜；单片机；随机密码

Design and Simulation of Automatic Lockers ABSTRACT This topic is microcontroller-based automatic lockers.Automatic lockers is a new generation of lockers, with a practical, simple operation, easy management, safe and reliable, able to better serve the broad masses of the different markets, users are based on a clear and concise instructions to complete the deposit bags to take the package. The system consists of MCS-51 microcontroller core control system, the entire system from the main section, the keyboard display control part of the implementation of some of the three-part composition, random password generation and check completed automatically save the package to take the package process. Various components of this design is easy to install and easy to operate, can basically save the package to take package function. Key words :Automatic lockers; microcontroller; random password

外阴白色病变的症状表现有哪些

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