Influence of the microstructure on the deformation behaviour of metal

matrix composites

E. Soppaa, S. Schmaudera, G. Fischerb; J. ThesingC, R. RitterC

a Staatliche Materialprüfungsanstalt (MP A) University of Stuttgart, Pfaffenwaldring 32, D­

70569 Stuttgart, Germany

b Dortmunder Initiative zur rechnerintegrierten Fertigung (RIF) e. V., Joseph-von-Fraunhofer­

Straße 20, D-44227 Dortmund, Germany

CInstitut für Meßtechnik und Experimentelle Mechanik, Technische Universität

Braunschweig, Schleinitzstraße 20, Braunschweig, Germany

Abstract

In this contribution, investigations ofthe influence ofthe microstructure on the macro-, meso­

and micro-effects in metal matrix composites are presented by direct combination of

experiment and simulation. The aim of the presented work consists in an improved

understanding of the mechanical behaviour of heterogeneous materials by combining

information of different length scales.

Keywords: metal matrix composites, microstructure, computer simulation, finite elements,

macro-, meso- and micro-Ievel of investigation

1. Introduction

"Tailoring of materials" is still a dream of engineers and scientists because of the unknown

correlation between microstructure and properties of most materials. Real materials are

heterogeneous on different length scales from the nano- up to the macro-Ievel. A special

example are composites, which consist of two or more phases and possess a great variety of

microstructures with different volume fraction, size and shape of the phases, arrangement as

weIl as the grain sizes of the phases. Depending on the length scale of observation/simulation

different details can be investigated. The aim of the present work is an improved

understanding of the deformation behaviour of metal-matrix composites and determination of

microstructure/properties-correlation on different length scales for better prediction of damage

initiation processes and with respect to optimized material design.

2. Materials

Metal-ceramic composites like AI(6061)/SiC (Fig. 1) and AI(6061)/AI203 1 are highly promi­

sing materials because of very interesting mechanical properties. They combine low density

with improved strength, creep and wear resistance, together with sufficient amount of ductility

and stiffness [1, 2].

120 ~m I

Fig.1 Microstructure of AI(6061)/SiC(1 Ovol.%).

3. Methods, results and discussion

In the following chapters the experimental and numerical results obtained on the macro- (3.1),

meso- (3.2) and micro-Ievels (3.3) will be discussed.

3.1 Experimental and numerical investigations of the deformation behaviour of Al/Sie

on the macro-Ievel

The influence of the component2 shape and material properties such as yield stress and work­

hardening on the strain and stress distribution in AI/SiC on the macro-Ievel is studied using an

optical grating method [3, 4] and the finite element method for numerical simulations. The

Al/SiC tensile specimen used in the experiment is represented in Fig. 2a.

I for simplification the description Al/SiC and AI/Alz03 instead of AI(6061)/SiC and AI(6061)/ Alz03 will beused in the further text

2

a) b)

1"'----- ..-----7

I,!! ;.c;;;'/.......----- . , \ "".\-

.,\.'0

"5·

\" \

\\\

image planes

i\ Z

/

//

//

/

j"

c)

grating structure

Fig. 2 a) tensile specimen used in the experiment, b) a stochastic Ti02 grating attached onto

the object surface in the middle part of the component, c) a set-up of a stereographie

arrangement.

2 in this context component means a device element3

A stoehastie Ti02 grating was attaehed onto the objeet surfaee in the middle part of the

speeimen in order to optimize the blaek-white eontrast. Images of the objeet surfaee with the

attaehed grating were reeorded by CCD-eameras and digitaIly proeessed by an area-based

matehing algorithm [3]. A set-up of a stereographie arrangement is shown in Fig. 2e. Und er

external loading, the deformation of the speeimen surfaee is equivalent to the ehange of the

distanee between the attaehed optieal marks. Relating the differenees of the loeation of

neighboring marks to their initial distanee, the average strain in the measured field is obtained.

The result is the whole deformation dataset of the investigated area. On the other hand, one

quarter of the speeimen under symmetry boundary eonditions is simulated, by means of finite

element method in plane strain, using the maeroseopie material properties as input-data. The

3-dimensional FE ea1culations are planed in the next future.

-3.0 -2.0 -1.0 0.0 1.0 2.0 3.0

..... 0.43 %·111·

0.82 %'-r

1.22 %-+..

1.61 %",* ..

201 %....

2.41 %,,,-

2.80%.)C.

3.20%

Fig. 3 Comparison between the measured and simulated deformation fields by uniaxial tensile

loading in Al/SiC(l Ovol.%). The ranges and partitioning of the seala are the same for both

types of results.

Fig. 3 shows a eomparison between the measured and simulated deformation fields in

AI/SiC(lOvol.%). The strain patterns are very similar in both eases. The asymmetrie

distribution of the axial strain with respeet to the symmetry planes in the tensile speeimen

observed in the experiment is probably eaused by an inhomogeneous arrangement of the SiC

partic1es or is due to asymmetriealloading. This faets have not been taken into aeeount in the

numerieal ealeulation, where isotropie and maeroseopie material properties as weIl as a

symmetriealloading were used as an input. This problem eould be probably avoided by using

measured experimental displaeements at the edges of the model as boundary eonditions in the

FE-model.

4

3.2 Investigations on the meso-level

On the mesolevel cut-outs of the microstructure with dimensions of about lOOJ.lmwere

analysed in order to study the influence of different SiC-partic1e arrangements on the stress

and strain development. The stress and strain patterns are calculated for four idealized

microstructures with increasing degree of partic1ealignments (Fig. 4) and for a cut-out of the

real microstructure.

..... - ..........- .• •• •...... - .••••••••• •.... - .•••• a ••••••••••••••••• • •••••••....... - .

••• • ••••••• • ••• ••••• •••• • ••• ••• •••••• • ••• •••••• • ••••• • ••• • ••• • •• •••• • • •• •••••• •• • •••• •• •••

ii

••• ••••••• •••••• .-.•• •••• •••••• ••••••• •• • •••

••••••• •••• •• •••• •• •• •••• •• •• •••••••• ••:. ••• ••

iii

•• •••••••• ••••••••••••••••• •••;-• •• •• •~.• ••• • •• .~••• ••• ••• ••• • •••• ••••• •••••I• ••• • ••

iv

Fig. 4 Idealized microstructures with different degrees of partic1ealignment.

111

11

IV

11.8 %11.010.29.48.67.87.16.35.54.73.93.12.41.60.80.0

Fig. 5a Distribution of effective strains in the idealized mesostructures (i-iv) after a

macroscopic uniaxial horizontal deformation of 2.18%.

5

Fig. 5b Binary picture of the microstructure of an AIIlOvol.%SiC-metal

matrix composite with plastic strain patterns after a macroscopical defor­

mation of 2.76% normal (N) and parallel (P) with respect to the particle

stripes. The arrow represents the loading direction.

21 %

20

1817

15

14

12

11

9

8

6

5

3

2

o

Fig. 5a shows the distribution of effective strains in the idealized mesostructure after a

macroscopic uni axial deformation of 2.18% and Fig. 5b the plastic strain patterns after a

macroscopical deformation of 2.76% normal (N) and parallel (P) with respect to the particle

stripes. A comparison of the strain pattern in the microstructures i-iv shows that the stronger

the tendency in the SiC phase to build up stripes and clusters the higher the strain

concentration, especially in the crossing points ofthe shear bands and near individual particles

in microstructure (iv). Such locations ofhigh strain concentration could be a potentiallocation

of damage initiation [5]. However, particles arranged in the stripes (iv) block the development

of shear bands in a much more effective way than the randomly distributed particles (i) and

the observed strain in the shear bands is much higher than in the microstructure (i) with a

random distribution of the ceramic phase.

The partitioning of the stress in the loading direction between the matrix and the ceramic

particles is shown in Fig. 6a and b. The stress pattern is independent of loading direction für

the random microstructure type (i). The high modulus of elasticity of the SiC-ceramic phase

causes high concentrations of tensile stresses in the particles especially in large particles and

in particle clusters (iv). Experimental results of Wulf [6] have shown that highly stressed SiC

particles with dimensions over lOl-lm can break during externalloading and initiate damage in

this way. Gur calculations support this fact.

6

iP

iv P

iN

ivN

1750

1606

1462

1318

1174

1030

886

742

598454

310

166

22-122

-266

-410

Fig. 6a Stress in loading direction (horizontal) in the microstructures with extremely different

partic1e distributions (i and iv). The partic1es are omitted for a better visualization ofthe stress

patterns.

Fig. 6b Stress in the loading direction (horizontal) in the real

microstructure after a macroscopic deformation of2.76% normal (N)

and parallel (P) to the partic1e stripes.

2350

2200

2050

1900

1750

1600

1440

1300

1140

990

840

690

540

390

240

PN

7

The distribution of the hydrostatic stresses in Fig. 7a and b reflects the distribution of stress in

the loading direction (cf Fig. 6). Hydrostatic stresses represent a very important parameter

providing informations about the potentiallocation of void formation. Especially, regions in

the soft matrix under hydrostatic tensile stress are very prone for void nucleation and

coalescence so that damage may initiate.

The analyses of stresses and strains (Figs. 5-7) in the simulated artificial and real micro­

structures show that the mechanical behaviour of the real material lies between the miificial

microstructures with extremely different particle distributions, random (type i) and strongly

aligned with gaps (type iv), which is evident when we analyse the micrograph of the real

microstructure showing regions with random (analogy to type i) and aligned (with gaps)

arrangement (analogy to type iv) ofthe inclusions.

iP

iv P

iN

ivN

-640

-524

-408

-292

-176

-6056

172288

404

520

636

752

868

984

1100

Fig. 7a Distribution of hydrostatic stress in the microstructures with extremely different

particle distributions (i and iv) due to different loading directions with respect to the particle

stripes. Loading is always in horizontal direction. The particles are omitted for a better

visualization of the stress patterns.

8

N P

Fig. 7b Distribution of hydrostatic stress in the real microstructure

after a horizontal macroscopic deformation of2.76% normal (N) and

parallel (P) with respect to the partic1e stripes.

-380-280

-190

5

100

200

300

390

490

580

680770

870

970

3.3 Investigations on the micro-level

Experimental and numerical estimations of the strain distribution are also performed in micro­

structural regions of a particulate metal-matrix composite All Al203 with an Al203 partic1e size

of about 5-8f!m. Two microstructural areas on the surface of a tensile specimen with a single

Al203 partic1e were selected for experimental and numerical analyses (frames A and B in Fig.

8). Optical marks in the form of dots with distance of 1.5f!m were fixed on the specimen

surface [7, 8](Fig. 8).

t

o

o

Fig. 8 SEM image of AI(6061)/AI20llOvol.%) with optical marks.

9

Area A Area B

1 Binarization 1$///////////1,

'l///I//IIIIII t\j

r . I

I "I matrix

~i ~

1:\ , %

U\\\\\\\~l1l1/////Y mmmf1777~

edge displacementat 3.1 % overall strain

b

Fig. 9 A bitmap of the undeformed structures with experimentally obtained edge displace­

ments used as input for FE-calculation.

Fig. 9 shows a bitmap of the undeformed structure with edge displacements as obtained from

the experiment which were used as input far the FE-calculations in plane strain. The sampie

was strained uniaxially in situ in the SEM (scanning electron microscope) step by step up to a

deformation of 3.1%. The strain development observed in experiment and calculation at three

deformation steps of 0.4, 1.1 and 3.1% is represented in Fig. 10.

As expected, strains are concentrated in shear bands in the soft matrix near the corners and

edges of the ceramic partic1e, which remains plastically undeformed. The general strain

patterns as obtained in the experiment and in the calculation are very similar. The discrepancy

in equivalent strains in partic1es observed in experiment is due to the opening of cracks in the

partic1es (Fig. 11). The interface is assumed to be perfectly bonded in the model and the

presence ofvoids in the Al(6061)-matrix and crack initiation is not inc1uded in the calculation

at present.

10

FE calculation Experiment

\J

a

IOT"rPI

Ü

15 ~mf------1

11111· .•iWlii@i@iiiiI@•••••• _

Eeq, 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 [%]

b

a)

FE calculation Experiment

b

b)

FE calculation Experiment

a

15IJmI---l

c:::=Jc:::=Jr.::::=J __ atiii1i.im, _

Eequ 1 5 9 13 17 21 25 29 33 37 [%]

b

c)

Fig. 10 Strain maps ofmicroregion in an Al/A1203(10vol.%) specimen deformed by tension at

overall strain of a) 0.4%, b) 1.1% and c) 3.1%.

11

Experiment

a

tension

Microstructure at section B

b

15 11m 5 11m

~ I I

~~II;~f»;1.1w;;;illf,f;Wlll'- _

cequ 1 5 9 13 17 21 25 29 33 37 [%]

Fig. 11 Particle cracks in the marked section of astrain map of area B.

4. Conclusions

The presented results show that reasonable agreement between experimental and calculated

results can be expected when realistic informations about microstructure, material properties

and boundary conditions like for instance local displacements were used as input for the

calculation. The observed discrepancies on the micro-Ievel are mostly caused by particle

cracking or particle/matrix debonding in case of Al(6061)/AI203 and materials heterogeneity

in Al/Sie composites.

ACKNOWLEDGEMENTS

This work was performed in frame of the Research Group "Investigation of the deformation

behaviour of heterogeneous materials by direct combination of experiment and computation",

subprojects DFG Rl 339/15-1, DFG FI 686/1-1 and DFG Schm 746/16-1. The authors

gratefully acknowledge the financial support by the Deutsche Forschungsgemeinschaft

(DFG).

References

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12

2. A. Wang and H.J. Rack, Acta metall. Mater. 40 (1992) 2301pp.

3. M. Erbe, K. Galanulis, R. Ritter and E. Steck, Engineering Fracture Mechanics Vol. 48,

No. 1 (1994) 103-118pp.

4. H. Neuhäuser, R. Ritter, E. Steck, J. Thesing, H. Wittich and A. Ziegenbein,

Experimental and numerical investigations of the inelastic behaviour of polycristalline

materials on a microscopic scale,.

5. E. Soppa, S. Schmauder, G. Fischer, Numerical and experimental investigations of the

influence of particle alignment on shear band formation in Al/SiC, Proceedings of the 19th

Ris0 International Symposium on Materials Science: Modelling of Structure and

Mechanics of Materials from Microscale to Product, Ris0 National Laboratory, Roskilde

Denmark (1998) 499-504pp.

6. J. Wulf, Neue Finite-elemente-Methoden zur Simulation des Duktilbruchs in Al/SiC,

Reihe 18, Nr. 173, VDI Verlag, Düsseldorf (1995).

7. Y.-L. Liu and G. Fischer, Scripta Mater., Vol. 36, No. 10 (1997) 1187-1194pp.

8. G. Fischer, E. Soppa, S. Schmauder and Y.-L. Liu, Modelling of strain localization in real

microstructural areas of the particle reinforced metal-matrix composite Al 6061-10%

A1203, Proceedings of the 19th Ris0 International Symposium on Materials Science:

Modelling of Structure and Mechanics of Materials from Microscale to Product, Ris0

National Laboratory, Roskilde Denmark (1998) 26l-266pp.

13