Materials Science and Engineering, A 185 (1994) L9-L12 L9

Letter

Elastic behaviour of an aluminium matrix composite reinforced with new alumina platelets

V. Massardier, R. Fougeres and P. Merle

Groupe d'Etudes de MOtallurgie Physique et de Physique des Materiaux, Unit~ de Recherche associ~e au CNRS 341, lnstitut National des Sciences AppliquOes, Bhtiment 502, 69021 Villeurbanne ('~dex (France)

(Received January 19, 1994; in revised form February 29, 1994)

Abstract

Young's modulus for an aluminium-based metal matrix composite reinforced with a-alumina platelets was investigated from an experimental and a theoretical point of view by varying the following parameters: the nature of the matrix, the morphology and the volume fraction of the platelets. An iterative Eshelby method, taking into account different families of inclusions, was used to perform the theoretical calculations. Good agreement between theory and experiment was observed.

Finally, to assess the effectiveness of the platelets as reinforc- ing phases, a comparison with the values of Young's moduli obtained theoretically with other shapes of reinforcement (spheres or short fibres) was carried out.

volume fraction can vary between 15 and 35%. The size of the platelets, defined by two parameters the diameter d and the thickness t, may vary, depending on the synthesis conditions, as can be seen in Table 1. However, whatever the size of the platelets, their aspect ratio t /d ranges from 1/20 to 1/10. By varying the adjustable parameters of the reinforcement and the matrix materials (either a pure aluminium matrix (99.99% A1) or an aluminium alloy 6061 matrix (1Al-lwt.%Mg-0.6wt.%Si)), different types of com- posite material were obtained by squeeze casting. The aluminium alloy 6061 matrix composites were sub- mitted to a T6 thermal heat treatment.

2.2. Experimental procedure Young's moduli were essentially measured by exten-

sometry during tensile tests. They were determined from the slope of the initial elastic domain. A few dynamic measurements obtained from the mechanical resonance frequency of a parallelepipedic composite bar were performed additionally, to ascertain the

1. Introduction

Aluminium-based metal matrix composites (MMCs) reinforced with new pre-forms of a-alumina platelets produced by Elf-Atochem were fabricated. We estab- lished a correlation between the experimental values of the Young's moduli and the theoretical evolutions predicted by a model based on an iterative Eshelby method developed by Hamann et aL [1]. It must be pointed out that the platelets studied allow one to obtain a higher modulus than other alumina reinforce- ments for identical volume fractions. For example, the moduli of an aluminium alloy 6061 matrix composite reinforced with 20% of platelets, short fibres [2] or spheres [3] are 104 GPa, 92 GPa and 86 GPa respec- tively.

2. Materials and experimental procedure

2.1. Materials The pre-forms consist of randomly oriented hexag-

onal and monocrystalline platelets (Fig. 1). Their

Fig. 1. Pre-forms of hexagonal a-alumina platelets (scanning electron microscopy).

TABLE I. Definition of the different types of platelet

Type of Diameter Thickness Mean aspect platelet d (/~m) t (/~m) ratio (t/d)

T I 5-10 0.5 1/15 T2 10-15 1.0 1/12.5 T~ 15-25 1.2 1/16.5

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L 10 V. Massardier et al. / Elastic behaviour ofA l-platelet-reinforced A l matrix composite

evolutions observed. In this paper, we shall refer to the values of the static moduli. Indeed, the two types of measurement led us to the same conclusions, although the values of the dynamic moduli were slightly higher than the values of the static moduli (less than 5%).

3. The iterative Eshelby method

The iterative Eshelby method used to perform the theoretical study differs from most other models based on the Eshelby analysis in that the reinforcement of the composite can be represented by several families of inclusions, which is necessary in the case studied. Each family is characterized by a representative inclusion defined by its thermoelastic constants, its shape (aspect ratio) and its orientation in fixed axes related to the composite and its volume fraction. The principle of the calculation of Young's modulus with this method is detailed elsewhere [1 ]. The results obtained are satisfy- ing up to a volume fraction of reinforcement of 30%.

In the case of the composite studied, the theoretical calculations of Young's modulus were performed under the following conditions.

(1) The platelets were simulated by oblate spher- oids characterized by the same elastic constants, the same aspect ratio a3/a l = t/d (Fig. 2) but by different orientations.

(2) No distribution of aspect ratios was taken into account in the calculations. This is supported by the fact that the aspect ratio distribution of the platelets around their mean aspect ratio is narrow. Moreover, it has been shown that a distribution of aspect ratios is equivalent to a single mean aspect ratio for the evalua- tion of Young's modulus for a composite material [1].

(3) The orientation of the representative inclusions in fixed axes linked to the composite (defined by two angles ¢ and a, as shown in Fig. 3) was chosen to allow the simulation of a random orientation of the platelets in the composite. To account for such a configuration, nine families of oblate spheroids having different orientations were considered.

(4) The volume fraction fl attributed to each family was f~ = F/N, where F is the total volume fraction of the platelets in the composite and N is the number of families.

(5) The platelets used in this study are single crys- tals of a-alumina, the structure of which is trigonal. As a result, they present a certain degree of elastic aniso- tropy [4]. However, Young's modulus for a single crystal of alumina varies by + 10% according to the crystallographic direction. As this variation is rather low, the platelets were assumed to be elastically iso- tropic. They were thus defined by two parameters:

Platelet Oblate sph6ro'fd

Fig. 2. Simulation of the morphology of the platelets by oblate spheroids.

0 I t L v

Fig. 3. Definition of the angles ¢ and a.

O

TABLE 2. Typical values of the parameters

Parameter Typical value

Young's modulus for the matrix ~ E,~ = 69 GPa Poisson's ratio ---" v m = 0.33 Aspect ratio a3/aj of the reinforcement 1 / 15 Volume fraction of the reinforcement 20%

Young's modulus Er and Poisson's ratio Yr. The choice of these two parameters will be discussed below.

4. Results

4.1. Correlation between theoretical and experimental results

In the experimental and theoretical parametric study performed, a single parameter to be focused on was used as a variable, whereas the remaining parameters were set equal to their typical values shown in Table 2.

4.1.1. Preliminary study." choice of the elastic constants of the reinforcement Our experimental results showed us that the nature

of the matrix had an influence on Young's modulus for the composite. It can only be attributed to a difference between Young's moduli for the two matrices, the other

v. Massardier et al. / Elastic behaviour of Al-platelet-reinforced AI matrix composite L 11

parameters being the same. The data in the literature [5], confirmed by our own experimental results, led us to a modulus of 69 GPa for the aluminium alloy 6061 and of 62 GPa for pure aluminium. We used the experi- mental data on the modulus of the composites fabri- cated with the two matrices to determine the elastic constant values, which have to be taken, in the theore- tical calculations of Young's moduli, for the alumina platelets. Their Poisson's ratio was set equal to 0.25, a value commonly attributed to a dense isotropic polycrystalline alumina ceramic body. Moreover, Young's modulus for the platelets was chosen in such a way that the calculated Young's moduli for these two types of composite fitted the experimental values. To this end, we plotted in Fig. 4 the evolution of Young's modulus for an aluminium alloy 6061 or a pure alumi- nium matrix composite as a function of Young's modulus of the alumina particles (in the range of pos- sible values for a single crystal of alumina). It appears that Young's modulus of 380 GPa leads to identical experimental and calculated values in the case of the A1-A1203 composite. With the AI alloy 6061/A1203 composite, good agreement is also observed, as shown in Table 3.

Referring to the data in the literature relative to an isotropic polycrystalline alumina reinforcement [6], a value of 380 GPa appears to be quite acceptable.

4.1.2. Effect of the aspect ratio of the reinforcement Figure 5 is a representation of the theoretical evolu-

tion of Young's modulus E¢ of the composite as a func- tion of the aspect ratio of the platelets. E~ decreases with increasing aspect ratio of the platelets, particularly when it does not exceed 1/5. Above this value, the influence of this parameter is almost negligible.

The platelets used (whatever their size) have a mean aspect ratio which varies roughly between 1/20 and 1 / 10. In this range of values, the aspect ratio has a great effect on the modulus. We have thus measured Young's

moduli for composites reinforced with the same volume fraction of platelets of different types (see Table 1 ). The experimental values are plotted in Fig. 5. We observe good agreement between the experiment and the theory with the platelets denoted T~ and T,. The discrepancy observed in the case of the largest platelets T3 could be attributed to a less homogeneous distribution of these platelets in the composite. It is supported by the fact that pile-ups of platelets have been observed in this particular case. If we assume, in a first approach, that the piled-up platelets remain joined side by side during the tensile loading in the elastic domain and that they are perfectly bonded, then the real aspect ratio of the platelets can be considered as being increased, leading to a subsequent decrease in Young's modulus for the composite, as observed experimentally.

4.1.3. Effect of the volume fraction of reinforcement In Fig. 6, we reported the theoretical evolution of

Young's modulus E c of the composite as a function of the volume fraction of the platelets as well as the experimental evolution determined for aluminium alloy 6061 matrix composites. In both cases, a linear dependance of Young's modulus with the volume frac- tion is observed in the range of values investigated experimentally (between 20 and 35% of reinforce- ment), the law of evolution being (a) from the results of the theoretical study E¢ = 198.8F+63.2 GPa and (b) from the results of the experimental study E c = 2 0 3 F + 6 3 . 3 GPa. Good correlation between

TABLE 3. Comparison between experimental and calculated Young's moduli

Composite Experimental Calculated Young's modulus Young's modulus (GPa) (GPa)

AI alloy 6061/AI203 104 102.8 A1/AI203 95 95

E c (GPa) 101

o51

00-1

95"1

- Era= 69 GPa o Era= 62 GPa

f

E (AIzO 3 ) 90 1 . . . . . . . . . . . .

360 380 400 420 440 460 480

Fig. 4. Evolution of Young's modulus for aluminium alloy 6061 and aluminium matrix composites as a function of Young's modulus of the alumina particles.

Ec 110 1

(OPa) ] k~ T1T2

i : i OrO 0~2 Oz4 Or6

Eshelby

Exper iment

0,2 0,3 0,4

a 3 / a 1

i i

0r8 It0

Fig. 5. Evolution of Young's modulus for the composite as a function of the aspect ratio of the platelets.

L 12 V. Massardier et al. / Elastic behaviour ofA l-platelet-reinforced A l matrix composite

E c (GPa)

140 -1

60 0 1 ~0 2~0 30 4~0

E / I~ s * E(O.S.) / E s 1,20 -

• E(P.S.) / E s 1,15 "

1,10 •

1,05 •

1,00'

F(%) 0,95 , ~ , 2~0 2~5 0 5 10 15 30

Fig. 6. Experimental and theoretical evolutions of Young's modulus for the composite as a function of the volume fraction of platelets.

Fig. 7. Effect of the shape of the particulates on Young's modulus for the composite: O.S., oblate spheroid; ES., prolate spheroid.

theory and experiment appears once more, which validates the model as well as the choice of the elastic constants.

4.2. Theoretical study of the effect of the shape of the reinforcing phases on Young's modulus for the composite

In this section, we shall consider the influence of the shape of the inclusions on the modulus of a composite from a theoretical point of view, assuming isotropic elastic constants for the reinforcement. In addition to the case of oblate spheroids, we shall study the case where the inclusions have the shape of either spheres or prolate spheroids defined by a t = a : and as>a1. The prolate spheroids can simulate short fibres for example.

In order to establish the shape of the reinforcing phases (spheres, short fibres or platelets) which would best to obtain a high modulus, we calculated by the iterative method the modulus of a composite reinforced with a volume fraction F of spheres or of prolate spheroids or of oblate spheroids.

Our calculations were carried out considering that the matrix is aluminium alloy 6061. The elastic con- stants of the reinforcement were set equal to the values taken in the preceding calculations. Moreover, in all simulations, we chose a mean aspect ratio equal to 15 for the prolate spheroids and to 1/15 for the oblate spheroids. The reinforcing particles were assumed to be randomly oriented.

As the effect studied is only geometrical, we com- pared the values of Young's moduli E obtained with the different types of particle with Young's moduli E~ calculated in the case of spheres with the same elastic constants and same volume fraction. In Fig. 7, we thus report the evolution of the ratio E/E~ as a function of the volume fraction.

In the case of random orientation of the particles, it clearly appears that it is more advantageous, in order to obtain a high modulus, to use reinforcing phases having the shape of platelets (oblate spheroids) rather than short fibres (prolate spheroids) or spheres.

5. Conclusions

The main conclusions of our study are the following. ( 1 ) Good agreement was found between the experi-

mental values and the calculations of the iterative Eshelby method which allowed us to take into account all the parameters studied.

(2) One of the major interests of the morphology of the platelets used lies in their aspect ratio which places them in the range of values where the elastic moduli are high.

(3) In comparison with other types of reinforcement (spheres or short fibres), the shape of platelets appears to be more favourable to obtain a high modulus, in the case of random orientation of the reinforcement.

R e f e r e n c e s

1 R. Hamann, A. Mocellin, E E Gobin and R. Foughres, Scr. Metall. Mater., 26 (1992) 963.

2 J. Dinwoodie and I. Horsfall, Proc. 6th Int. Conf. on Com- posite Materials', London, July 20-24, 1987, Elsevier Applied Science, London, 1987, p. 2.390.

3 R. Y. Lyn, R. J. Arsenault, G. P. Martins and S. G. Fishmann (eds.), Interfaces in Metal Ceramics Composites', Metallurgical Society of A1ME, Warrendale, PA, 1990, p. 271.

4 W. D. Tefft, J. Res. Natl. Bur. Stand. A, 70(1966) 277. 5 International Handbook Committee, Metals Handbook, Pro-

perties of Wrought Aluminum and Aluminum Alloys, Vol. 2, 10th edn., American Society for Metals, Metals Park, OH, 1990, p. 65.

6 Fiber FP-Technical Data Sheet E56612, E.I. Dupont de Nemours, Wilmington, DE, 1989.