ELSEVIER Journal of Materials Processing Technology 56 (1996) 743-756

Journal of

Materials Processing Technology

MECHANICAL PROPERTIES OF ALUMINIUM METAL MATRIX COMPOSITES UNDER IMPACT LOADING

A.M.S. Hamouda and M.S.J. Hashrni

Advanced Materials Processing Centre School of Mechanical & Manufacture Engineering

Dublin City University, Dublin 9, Ireland

ABSTRACT A flow stress modd based on plasticity theory has been developed for two different types of aluminium metal matrix composite materials subjected to high strain rate. A combined experimental and numerical techniques are used to determine the flow model parameters. Experimental results consisting of cylindrical impact compression tests and conventional mechanical tests are presented. The parameters of the proposed flow stress model were evaluated based on satisfactory agreement between the predicted and measured final dimension of the test specimen. The model, in its general form, considers the combined effects of strain, strain hardening, strain rate, and thermal softening on the flow stress. Finally, for comparison, tests were also conducted on pure aluminum.

NOMENCLATURE A cross-section area f portion of the work of deformation converted into heat energy G temperature effect factor on strain hardening index G1 temperature effect factor on strength coefficient K strength coefficient [MPa] m material strain rate sensitivity constant [s -1] M mass per unit length n strain hardening index in the quasi-static test N axial force p material strain rate sensitivity constant [dimensionless] r current radius of an element R strain rate effect factor on strain hardening s specific heat 0 acceleration U displacement p density AS link length in numerical model At time interval

total true strain total strain rate[s -~]

a stress [MPa] a combined strain rate and temperature effects on strain hardening

Subscripts i the mass number and the number of the preceding link j instant of time

0924-0136/96/$15.00 © 1996 Elsevier Science S.A. All rights reserved SSDIO924-OI36(95)OI888-L

744 A,M.S. Hamouda, M.S.J. Hashmi / Journal of Materiab Processing Technology 56 (1996) 743-756

1.0 INTRODUCTION

Metal Matrix Composite (MMC) materials are currently experiencing active development in all over the world. The advantage of using MMC materials is in their property combinations, that results in a number of service benefits. The combination of high strength to density, high stiffness to density ratio, together with higher resistance to erosion and high service temperature make metal matrix composites (MMC s) the best choice for applications such as turbine blades and aerospace structures.

1.1 Background

Composite material consist of matrix and the reinforcement. In MMCs, the metal acts as the matrix, and its main function is to transfer and distribute the load to the reinforcements or fibres. This transfer of load depends on the interface bonding between the matrix and the reinforcement [1]. The fibres commonly used in MMC application have been boron, silicon carbide, and graphite. They all have high yield strength and high Young's modulus. Compared to these fibres, the matrice used in MMC system are relatively ductile low yield strength materials such as aluminum and titanium. The major differences as well as the similarities between the metals and MMCs are listed in Table [I][2].

TABLE[I] Comparison between the pure metals atut MMC materials[2].

METALS

Material is homogenous.

METAL MATRIX COMPOSITE I

Materials contains particles and particle/matrix interfaces.

Mechanical properties are constat and can Mechanical properties vary and are often be listed in standard tables, characterized in terms of reinforcement

ratios.

Compressive and tensile strengths are Compressive strength is greater than tensile approximately equal in magnitude, strength.

Fracture toughness and ductility are high. Fracture toughness and ductility are relatively low.

Material is ductile under both tension and Material is ductile under compression and compression, brittle in tension.

Failure is due to localization into shear Failure is either due to fracture and bands or necking, decohesion of the particles or ductile failure

within the bulk matrix.

Residual stresses due to cooling down from Residual stress are induced in the composite fabrication or annealing temperature are due to the mismatch of thermal expansion minimal, coefficients between the matrix and particle.

Compressive strength increases under Compressive strength increases under impact conditions, dynamic loading.

Metals exhibit work hardening. MMCs exhibit work hardening also.

Thermal softening is abrupt. Thermal softening is gradual. I I

A. M.S. Hamouda, M.S.J. Hashmi / Journal ofMaterials Processing Technology 56 (1996) 743-756

A characteristic of the mechanical behaviour of particulate MMC is that they are stronger in compression than they are in tension. This strength different increases with increasing volume fraction of the reinforcement [3].

745

The primary dis-advantages of many MMCs is that they exhibit low ductility and poor fracture toughness when they are under unconfined stress conditions. One of the mechanism that appears to contribute to low ductility of MMC involves the formation of voids at the reinforcement and matrix interface. These effects are well documented in the reference [4].

For many materials mechanical behaviour can be quite different under dynamic as opposed to static loading [5]. Thus, to design for resistance to impact loading, to dynamic penetration or for other dynamic conditions, it is important to know the dynamic stress-strain behaviour of the materials in question. For published information on the quasi-static mechanical properties of Aluminum metal matrix composite, the reader is referred to recent papers[4,6] and to the review by Nair et al. [7] which include fracture behaviour, stress- strain behaviour in tension, compression and shear, as well as fatigue and creep properties.

Dynamic behaviour, however, has received very little attention although it is of significant interest in numerous application. Wittman et al [8] conducted a compression test on tungsten-nickel based matrix alloy at strain rate up to 6xl0 ~ s -t and temperature ranging from room temperature to 850 °C. They compared the material properties of this MMC with those of pure tungsten and reported that the dominant material property for the MMC and pure tungsten is the material's propensity for self heating which results in a significant loss of the strength in the pure tungsten but less so in the composite.

Marchand et al. [9] conducted a series of experiments at room temperature to determine the dynamic fracture initiation behaviour and dynamic stress-strain behaviour of a metal matrix composite(2124-T6 aluminum reinforced with silicon carbide whiskers). They reported that fracture toughness in the reinforced material is sensitive to loading rate but that the stress-strain behaviour does not change with deformation rate in the range from quasi-static to strain rate of 3000 s ~. The stress-strain curves show only a small strain rate sensitivity either for the reinforced or for the un-reinforced materials. Harding [10] critically assessed various techniques for determining the mechanical behaviour of fibre-reinforced composite materials at impact rates of strain.

Rajendran and Kroupa [11] proposed damage model for ceramic material subjected to high strain rate. A1- Tounsi and Hashmi [12] used the constitutive model previously developed by Cowper-Symonds[13] for metallic materials to study the dynamic behaviour of iron powder compacts. One of the limitation of the Cowper- Symonds model is that it does not include temperature and strain hardening effects on strain rate sensitivity.

Recently, Vaziri et al [14] conducted experiments consisting of dynamic penetration of various reinforced and unreinforced materials by cylindrical tungsten projectiles fired at velocities ranging from 450 to 850 ms -t. They found that, the MMCs outperformed their unreinforced matrix materials in resisting penetration. The highly reinforced material exhibited brittle characterisation similar to ceramics. At high impact speed (750 ms-~), all MMCs, behaved much like unreinforced metals. They implemented two deformation models, Johnson-Cook model [15] and Zerilli-Armstrong model [16] into the DYNA2D hydrocode in an attempt to simulate the impact behaviour of MMC s.

This paper introduces the issue that must be addressed to develop a high strain rate behaviour of MMC's. The application of a combined experimental and numerical technique to establishing the mechanical properties of A1 MMC s were considered. First, briefly we will review the essential features of the technique, and then we dwell on developing constitutive equation for MMC s.

746 A.M.S. Hamouda, M.S.J. Hashmi / Journal of Materials Processing Technology 56 (1996) 743-756

2.0 EXPERIMENTAL TECHNIQUE

Tests were carried out quasi-statically and at high speed employing different test apparatus:

(i) Quasi-static tests were carried out using an Instron universal testing machine Model[4204] at a cross-head speed of 5 mm/ min. (ii) High Velocity tests were carried out using an air gun apparatus.

2.1 Procedure

QUASI-STATIC TESTS The nominal heights and diameters of the specimens were equal to 6.00 mm for all the materials investigated, the maximum compressive loads are determined as 50 kN for MMCs or 25 kN for pure aluminium and the compressive velocity is set as 5 mm/min for all the materials. In order to reduce the friction between the pressure head and the specimen, a lubricant film (0.2 mm thickness) has been used. The tests were performed for 4 to 5 times for each material.

Static compressive tests were performed with both reinforced and un-reinforced material. The curves presented in Fig. 1 indicate that the presence of reinforcement increases the compressive strength from 78 MPa for the un-reinforced to 408 MPa for the reinforced.

400 ~ulco~a,~c

24O [ Room Temperm~re

2O0

0.2 0,4 0.6 0.8 1 1.2 L4 1.6 1.8

Fig. 1 Static stress-strain behaviour in compression.

There is also a substantial effect on the fracture strain of MMC s as compared with the pure materials. For the pure material, the specimen was deformed upto strain equal 1.36 (75% reduction) and no crack was developed. However, in the case of A1/Li MMC a crack become evident at strain equal to 0.78. For the A1/Cu MMC crack occurs at a strain equal to 0.92.

Significant difference was found between the reported data for the standard tensile test (supplied by the company) and the compressive data obtained during this investigation from the Instron machine as shown in table [II]. This is in agreement with what Arsenault and Wu [4] observed. They reported a significant difference in the tensile and compressive strength of SiC-A1 composite.

A.M,S. Hamouda, M.S.J. Hashmi / Journal of Materials Processing Technology 56 (1996) 743-756 747

TABLE[H] Comparison between compression and tensile test

Elastic modulus [GPa]

Yield stress [MPa]

Max. Elongation/or Max. Reduction(%)

Tensile stress [MPa]

i

Al(pure)

I

70.6

10-35 (16) 1

(>75%)

II

A1/Cu Composite

I

100

40O (319)

6% (60%)

A1/Li Composite

I

lOO

5OO (308)

r

2.3% (52%)

50-90 (78) 610 550 (400) (359)

i i I

HIGH SPEED IMPACT TESTS The impact experiments were performed with an air-gun apparatus shown in Fig. 2. This set of experimental system mainly consists of a movable rig, the high pressure power system, the barrel parts, the anvil unit and projectile velocity measuring system.

~ t j 2

7

FIG. 2 Gas qun: (1) air cylinder, (2) pressure regulator, (3)air reservior, (4) valve, (5) barrel, (6) projectile, (7) velocity measuring device,(8) specimen, (9) anvil.

Procedure and Principal The gas gun has an air reservoir which was pressurised using an external pressure controller, with a nitrogen gas supply. The reservoir was pressurised and then a fast response valve was used to release the gas into the gun barrel to accelerate the projectile. This system produces projectile velocities of 30 to 1000 ms 1. The velocity of the projectile was measured using a laser beam device mounted near the end of the gun barrel.

I The numbers between the brackets are obtained from the compression tests.

748 A.M.S. Hamouda, M.S.J. Hashmi / Journal of Materials Processing Technology 56 (1996) 743-756

The basic experimental technique used here involved firing the cylindrical projectile from the smooth barrel of the air gun at speeds ranging between 35 to 120 ms -~ onto small cylindrical test specimen placed upon an anvil. The deformed specimen was removed and its final height and diameter were recorded. Three or four specimens were tested at nominally the same impact speed.

P r e p a r a t i o n o f t e s t s p e c i m e n s Extruded cylinders rods of the materials were purchased from commercial suppliers. The specimens were machined to size 6.0 mm in length and 6.0 mm in diameter. Both surfaces of the test specimen were finely ground and made as fiat as possible. Before the dynamic test was conducted, the contact faces of the specimen, anvil and the projectile were lubricated with Polythene sheet and petroleum jelly.

The materials tested were A1/Cu composite, AI/Li composite, and pure aluminum (99.99%). Results of chemical analysis for the reinforced and pure materials are given in table [III]. Mechanical properties for these materials as given in the literature, are shown in table [II]. As it is evident from table [II], the potential advantages of the composite as regards mechanical behaviour, lie in its Young's modulus and higher flow stress, while its disadvantages lies in low ductility. For the comparison between the static and dynamic ductility, pure aluminum and A1/cu MMC show nearly the same ductility under the dynamic and static deformation, but in the case of Al/li ductility appears to be less under dynamic deformation.

TABLE[IffJ C h e m i c a l A n a l y s i s

: ! :..Al(i~ir~) A1/Cu " A1/Li

AI: : i 99~99:% 77.9% 81% A g :~ !:! ::ppm . . . . . . . . :Ca: . ..:i:~:::l::ppm . . . . . . . .

C r . i <!!:IiPP m - . . . . . . . Cu: .7..::iO/:E!ppm 3.3% 1.2%

::Fe!: : : i : l O : . . ) p p m . . . . . . . .

..Mg : • ...::::12.:::.:: :~pm 1.2 % O. 8 % :Mn.! : . :?i2:!/i:ippm 0.4:% . . . . • Li. : :. : : : . . . . 2 . 0 %

SiC :i !5:: i:ppm 17:8% 15 %

3 . 0 M O D E L ANALYSIS

Generally, the theoretical analysis of an experimental system requires idealization of the system into a-form that can be analyzed, formulation of the governing equilibrium equations, and interpretation of the results. Therefore, it is necessary to establish a mechanical model of the experimental configuration. The model is first simplified based on the experimental system in which a small cylindrical specimen placed upon a hardened anvil is struck by projectile with a high speed as shown in Fig. (3a, 3b).

Idea l i za t ion o f t he S y s t e m 1. CASEI the projectile and anvil can be considered as a rigid in the process of impact due to their higher

yield stress and elastic modulus (Fig. 3a). CASEII considering the effect of elastic deformation of the projectile and anvil.

2. The stresses parallel to the central axis of the specimen are distributed uniformly over the cross section that is vertical to axis.

3. The friction at the interfaces is ignored.

4. Uniform strain occurs in each individual link.

A.M.S. Hamouda, M.S.J. Hashmi / Journal of Materials Processing Technology 56 (1996) 743-756

The equations of motion listed below are those used in the developed computer code. The derivation of the equations can be found in a paper by authors [17].

749

P r o j e c t g id

~stic--plastic Specin format ion

Figure 3

~ E l a s t i c

!" ~ E l a s t i e - p l a s t i e ~Deforrnat ion

I

E l a s t i c

(a) (b)

Shows the actual system and the lwnped mass representation.

Equation o f Motion The general equation of motion of an element of the specimen, soon after impact, can be derived by consider the internal and inertia forces acting on the element is given by,

aN = MU (1) OS

Equation(l) may be written in finite difference form and the resulting equation applies to the lumped mass discs. The finite difference equation for the concentrated disc at the ith location of the model is given by,

N m - Ni - AS o M 0 = 0 (2)

Equation (2) applies to all the masses in the system (projectile, specimen, anvil) and gives instantaneous values of Uij for any time t i when coupled with the following relationship between the acceleration(U) and displacement(U);

The time increment is defined through

Uij., = Oq (At) 2 + 2Uij - Uij_, (3)

a t = § - % (4 )

Strain and Strain Rate The difference in displacement of link between locations i and i+ 1 and hence its new length may be expressed by,

a s u , = ~ j . , - ~ , . , j . , (5 )

and the change in length, t~(AS)io+l, of the link occurring during the time interval At is given by;

(AS), j . , = AS, j , - aS, j ( 6 )

750 A.M.S. Hamouda, M.S.J. Hashmi / Journal of Materials Processing Technology 56 (1996) 743-756

Then the strain increment, total strain and strain rate occurring in each link during the time interval is given by,

( : [ ~(as)../.~

0e i , j+l [ /kSi, j*l

e, ij+l = C, ij + ?9~,ij.l

t3eij+l

e~j AT

(7)

Stress calculations The stress in the element is determined from the strain, strain rate, internal energy and the material property. Since the strain and strain rate are assumed to be constant within the element during the time interval At, the stress is also constant. The stress is obtained from the appropriate constitutive equation given by,

~,j,I = f ( e, ~, T ) (8)

In order to facilitate the calculation of stress which, due to friction and inertia effect, may vary across the cross section of the specimen. It is necessary to idealize the actual cross section to an equivalent cross section model which consists of a number of layers at which the stress is assumed to be uniform.

Force calculation In order to describe the elastic-plastic stress state in a layer of the model section, further idealization is made and each layer is assumed to consist of a number of sub-layers. The axial force is used to update the displacement and is given as,

~ j . , = ~A~j+, . %.÷~ (9) n=O

where or is the stress and A is the sub-layer area.

DEVELOPMENT OF COMPUTER CODE The solution of various finite difference equations was obtained by use of a computer. Computer program was developed to simulate the deformation behaviour of MMC's during the impact process. The computations have been performed on PC 386DX-33MHZ with 8 MB RAM, and 100 MB Hard disk. The specimen is divided into 160 element along the y axial direction.

Convergence of the calculations is ensured by selecting the time interval At in such a manner so that it is always smaller than the time needed for the elastic wave to propagate through the length of any deformed link.

Effect of Elastic Deformation of the Projectile and Anvil To study the effect of elastic deformation of the projectile and anvil (case II)due to stress wave propagation, the whole system was represented by lumped mass model as shown in Fig. 3b. The boundary condition for this new system is changed. The principal feature for this system is that, the projectile and the anvil deform only elastically due to their high yield stresses and the specimen deforms both elastically and plastically. It has been found that there is no significant difference between the two cases I & II, this means that the assumption of rigid anvil and projectile is valid, however, the result reported in this paper are based on case II.

A.M.S. Hamouda, M.S.J. Hashmi / Journal of Materials Processing Technology 56 (1996) 743-756 751

4.0 DEFORMATION FLOW MODEL To model material undergoing deformation using computer codes, constitutive equations are typically used to describe the plastic flow properties. Common to most constitutive equation for high strain rate applications are parameters describing an initial yield stress which increases due to strain hardening, strain rate, and decreases due to the thermal softening. One of such equation which utilizes material property data at high strain rates over a wide range of strains is previously proposed by the authors in reference [18] as follows:

tr d = KGle~,r~ [1 + (m~)P ] ( l o )

where

G ( T ) o~ - (11)

R ( ~ )

Temperature Rise in the Specimen When the metals and MMCs are deformed at very large strain and high strain rates such as in ballistic impact and penetration, machining, and high speed forging, leading to localization of heat generation. The temperature of the specimens rises during plastic deformation because of the heat generated by plastic work. The deformation energy per volume, w, is equal to the area under the stress strain curve

w = i c r ( e , ~ , T ) d e (12)

only small fraction of this energy is stored, the rest is released as heat. If the deformation is adiabatic, no heat transfers to the surroundings, and the stress is considered as a function of strain, strain rate and temperature, when the strain increase from e to e+Ae, the temperature rise (AT) during deformation is given by,

AT=---f0s [ tr ( e, k, T ) de _ f ~ s (13)

where ~ is the average value of a over the strain interval from e to e+Ae. For this particular case we make assumption that all the work is corrverted to heat ( f = 1), this will lead to some error as in reality a percentage of the work is not converted to heat. The values of s and 0 are given in Table [IV]. The specific heat, s, is assumed to be independent of the stress level and the material is treated as incompressible.

During the simulation process, at each strain increment the temperature rise is updated based on the plastic work using equation (13). The computation is done in small incremental steps, and this way allows the stress in equation (13) to be calculated as function of temperature.

The initial estimation of the maximum rise in the temperature, in the case of pure A1 is 95 °C at impact-speed of 86 ms 1, for A1/Li MMC, 144 *C at impact speed of 102 ms -~, and for A1/Cu MMC is 214 °C at impact speed 130 ms 1.

Determination o f Material Constants The deformation behaviour may be described isothermally or adiabatically for a range of strain and strain rates. The isothermal stress-strain curves produced from the quasi-static tests was used to fit the first term of equation (10), producing strain hardening exponent (n) and the strength constant (k). The temperature factors G and G1 are obtained from the ratio of room temperature flow stress to flow stress at high temperature (approximately 6000C) obtained from reference [19].

752 A.M.S. Hamouda, M.S.J. Hashmi / Journal of Materials Processing Technology 56 (1996) 743-756

Although most of the strain hardening data available in the literature relate to static conditions, it is likely that these would be applicable for high strain rate conditions with some changes. General form is established, for the effect of strain rate on strain hardening (R) using limited data from reference [20]. Knowing the dimensions of the test specimen together with the mass and impact speed of the projectile, the deformation is simulated using the developed computer code based on the proposed constitutive equation (10). By iterative computation the material constants m and P of the constitutive equation are established for close agreement between the experimental and simulated results in terms of the length and diameter of the deformed test specimen.

5.0 RESULTS AND DISCUSSION Values for a constitutive model were determined for pure aluminium material as well as for metal matrix composites. Table [IV] shows the best fit material constants for all the materials investigated here.

TABLE[IV] Material Constants for the Constitutive Equation.

MATERIAL DESCR! PTION

Aluminum(pure)

Al/Cu Composite

AI/Li Composite

CONSTITUTIVE CONSTANTS EQUATION [

Density Specific Heat Melting K n m p [Kg/m3l [J/Kg kl Temperature [°CI [MPal [sec.l

2700 900 660,4 78 0.37 0.0024 0.25

2850 875 512-660 408 0.054 8x10 s 0.075

2620 875 560-590 359.5 0.06 4x10 "9 0.06

The influence of strain rate on the stress level of the un-reinforced material is approximately what one would expect for pure aluminum, since in general, the strain rate sensitivity of aluminum depends on its purity, where high purity aluminum shows high strain rate sensitivity and aluminum alloys show low sensitivity [20]. Yoshida and Nagat [22] observed that the dynamic flow stress is always higher than the quasi-static one, when they conducted compression tests on pure aluminium (99 % purity) at room temperature and strain rates between 10 .2 to 103 s-t Bodner [23] also reported stress ratios of 3.11 to 3.46 for structural aluminium at strain rates ranging f rom 10 3 to 104 s -1.

The strain rate sensitivity may be defined as the ratio between the dynamic to static stresses at certain strain;

Strain rate sensitivity = gay (14) %,

In the present study, the stress ratio for pure aluminum investigated here has been found to vary between 3.34 to 9.6 at strain rates varying between 10 3 to 103 S ~ and strain equal to 0.1. At strain equal to 1 the ratio was found to be varying between 2.24 to 5.3 at strain rate 103 to lO s s k These results indicated that below the strain rate 103 s ~ the flow stress ratio corresponding to a certain strain value increases linearly with the logarithm of strain rate. This is generally acknowledged to be a consequence of the role of thermal activation in the control of the deformation mechanics. Above this critical strain rate (103)the stress ratio increases more rapidly with strain rate. This behaviour is interpreted to indicate the transition to visco-drag mechanism. Similar observations of transition to a visco-drag mechanism were reported for copper in references [24,25]. However, Follansbee et al [26] have observed the rapid increase of the flow stress after strain rate 104 s ~, but reported that transition to visco-drag is not a likely explanation, and that the observed behaviour can be more accurately interpreted as a change in the way that structure evolves with strain. Microstructural observation reported by Haque et al [27] and Chiem [28] supports this view by showing that the occurrence of twinning is much common in specimens deformed at strain rate above the critical rate 104 s t Figure 4 shows the

A.M.S. Hamouda, M.S.J. Hashmi / Journal o[ Materials Processing Technology 56 (1996) 743-756 753

6

. ~ 5 ° . . . . 1

° ~. .~ r .¢]

112} { ¢ 3

~d~4

° , . -~

r.1}3 ¸

2 -

1- A 1 / C u M M C 2- A 1 / L i M M C

=0.5 A l l a t s t r a i n ,._, /

/ /

/

1 0 a

1

2 t I

1 0 3 1 0 4 1 0 s

S t r a i n rate. [s -1]

400 ¸

"~ '300 n

ql ¢/1 ID

~ 200

(D i . . .

i--

1 0 0

AL(pure) ___ ~ _ _ ~ 10 5

/ /

. . . . . . . . . 1 0 4

, /

. . . . . . 1 0 3 / i f -

/

/

0

/

10-2

i I ' I ' I ' I ' I ' I 7 - ~ , I - ~

0.2 0.4 0.6 0,8 1 1.2 1.4 1.6 .8

True strain

Fig. 4 Variation of flow stress ratio with strain rate. Fig. 5 Stress-strain data in compression for pure Al.

700 - - -

6 0 0 -

500"

Q-

'---'400-

rio

N3oo- I11

200-

100-

(AI/Cu MMC) ( 10s

~- 10 4

- - 1 0 3

j ~ . /

10-2

0 ' [ I I I I

0 0.2 0.4 0.6 0.8 1 1.2

True strain

500

400-

t~ 13_ :~ 3oo- u)

(l) 1. - -

200-

100"

o+ 0

10 5 10 4

10 3

. . . . . . . . . 10 4

(AI/Li MMC)

0.2 0.4 0.6 0.8

True strain

1 1.2

Fig. 6 Stress-strain data in compression for Al/Cu MMC. Fig. 7 Stress-strain data in compression for Al/Li.

754 A.M.S. Hamouda, M.S.J. Hashmi / Journal of Materials Processing Technology 56 (1996) 743-756

relationship between the ratio of dynamic to static flow stress and the strain rate. This figure shows the degree of rate sensitivity obtained for all three materials investigated in this study at strain equal to 0.5. The strain rate sensitivity for the MMC at strain rate los to 10 s s -~ and strain equal to 0.12 was found to vary between 1.46 to 1.69 for A1/Cu MMC and between 1.26 to 1.46 for A1/Li MMC. At strain equal to 0.78 the rate sensitivity varies between 1.34 to 1.54 for A1/Cu MMC and between i. 19 to 1.33 for A1/Li MMC. The dynamic stress-strain curves for the pure aluminium investigated here is shown in Figure 5. Results for the reinforced materials A1/Cu and AI/Li are presented in Figures 6 and 7 respectively. In the range of the experiment, it appears that strain rate has a remarkable effect on the flow stress level. It can be seen that, the dynamic flow stress is affected differently at constant strain rate. As the strain increases the strain rate sensitivity decreases.

6.0 SUMMARY

An empirical plasticity-based constitutive model that contains the terms necessary to described the flow stress( e, 6, T ) of MMC and lends itself to an efficient implementation in hydrocodes is proposed. This model suggests that for pure aluminum the plastic deformation shows a transition from thermal activation mechanism to visco-drag mechanism at strain rate above 104 s 1. However, for the MMC's investigated here, no transition mechanism is evident even at strain rate of los s -~. The A1/Cu MMC shows more strain rate sensitivity and ductility than the AI/Li MMC.

The final dimensions of the test specimen is the only measured quantity which we rely upon in the materials modelling. Work in progress by the authors to match the experimental deformation history (force-time history) obtained from the impact test with the finite difference numerical solution based on constitutive model.

It can be concluded that a realistic flow deformation model, however accurate it may be, is not sufficient to guarantee a precise prediction of the impact behaviour of MMCs. The capability of any advanced model is also based on detailed knowledge of the failure mechanisms. A more physical approach than the one presented here must wait the development of more sophisticated yet practical, failure models.

Acknowledgements The authors wish to thank Mr Liam Domican at Dublin City University for his help in carrying out the experiments.

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