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Effects of reinforcement content and shape on cavitation and failure in metal-matrix composites
Effects of r e i n f o r c e m e n t c o n t e n t and shape on cavitation and failure in m e t a l - m a t r i x composites A.F. WHITEHOUSE and T.W. CLYNE (University of Cambridge, UK) Received 17 June 1992; accepted in revised form 28 September 1992
Cavity development in alumina-reinforced aluminium composites during tensile loading at room temperature has been monitored using microstructural studies and precision density measurements. The materials examined were based on commercial purity aluminium, reinforced with 1 0 and 20 volume% of short fibres, conventional angular particles or spherical particles, produced by a thermal spraying process. The composites were made by a powder blending and extrusion route, involving no liquidation of the matrix and leaving arrays of fine oxide particles aligned parallel to the loading direction. In all cases, stable voids were found to form well before final failure. Significant void contents were developed earlier in the test for the higher reinforcement content and when fibres were present. However, extensive voiding, corresponding to approximately hemispherical voids being formed at most fibres or particles, occurred in all cases before final failure. Voids tend to form adjacent to the reinforcement, most readily when it is elongated in the direction of applied stress and when it has a relatively flat surface normal to the stress axis. Sharp corners do not themselves appear to be favoured sites for cavity formation. Consistent with this, cavities can form with spherical particles, although their incidence is somewhat less than with angular particles, presumably because of the absence of elongated shapes and surfaces which are actually flat. A simple model is proposed which allows prediction of the failure strain for a given reinforcement volume fraction and aspect ratio. This is based on the constraining effect of the reinforcement on plastic deformation in adjacent regions of matrix and the contribution of cavitation to the observed strain. Fairly good agreement is observed between the predictions of this model and the experimental data.
Key w o r d s : metal-matrix composites; reinforcement shape; reinforcement content; cavitation; failure strain; model Tensile failure of discontinuously reinforced metalmatrix composites (MMCS)has been shown ~ to be at least partly due to the nucleation and growth of cavities formed at reinforcing particles or fibres, followed by coalescence and fracture. Regions of the matrix adjacent to the ends of fibres or particles, along the line o f applied stress, are sites where high hydrostatic tension is generated and hence where nucleation o f cavities is expected ~7. Conditions have been proposed for the formation of a void at an isolated inclusion in a material under applied load 8-". It is rather unclear, however, how best to formulate a condition for the failure of the composite in terms of the nucleation and growth of voids. It has
been clearly shown ~2-14that stable voids can form in these materials, so that treatments of the nucleation process are unlikely to lead directly to ductility predictions. It seems clear that the growth and coalescence of voids, rather than their initial formation, will largely determine the final ductility of the material. Models have been proposed for the onset of instability in the growth and coalescence of voids, for example by considering local necking of matrix between debonded particles ~5 or between cracked particles ~6. These models tend to predict ductilities which are high for low volume fractions of reinforcement, but fall rapidly as the volume fraction is raised. Much experimental ductility data, at least in SiCp/
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COMPOSITES . VOLUME 24. NUMBER 3 . 1993
A1 composites 337,18, indicate that the ductility is quite low ( ~ 3 15%) even for low volume fractions ( ~ 10%), but does not fall off very sharply as the ceramic content is increased. Ductilities are usually observed to decrease somewhat as the particle size is increased, a factor which does not enter into most simple models. There is little information on the effect of interfacial bond strength, usually thought to be strong in SiC/A1, although in cast SiC/A1 7% Si4).4% Mg composites a sharp decrease in work hardening rate and a large increase in ductility has been reported ~9 to result from the prior formation of a silica layer on the SiC reinforcement. This apparently decreased the bond strength, encouraging interfacial sliding and possibly other stress relaxation mechanisms. It is not, however, clear whether the incidence of cavitation was affected by this change. In any event, changes in matrix precipitation induced by attraction of Mg to the interface may have influenced the behaviour 2°. The present paper is concerned with the effects of reinforcement content and shape, including the presence of angularities, on cavity formation and ductility. Following from some of the observations made, a simple model is proposed for the prediction of composite ductility.
EXPERIMENTAL PROCEDURE Material production Composite material was produced by dry powder blending, canning under vacuum and hot extrusion. The reinforcements used were (a) spherical A1203 (diameter of 10 p.m), (b) angular A1203 (approximately cuboids of side about 10-15p.m) and (c) chopped 'Saffi]' fibre ( ~ 3 lam diameter), which became broken up during extrusion into lengths of aspect ratio about four. Composite was produced with volume fractions of both 10% and 20%. The spherical alumina powder was manufactured by melting quantities of the angular powder, using low pressure plasma spray equipment. The molten droplets were allowed to refreeze in flight. Inert gas atomized commercial purity aluminium powder with a mean diameter of ~ 30 ~tm was used for the matrix. In all cases, the as-extruded microstructure consisted of well-dispersed particles in a matrix consisting of fine grains, elongated in the extrusion direction. These were formed by deformation of the original AI powder particles, and no recrystallization had taken place. All the composites contained about 0.08% by volume of fine platelets (d 50 nm, t ~ 10 nm) derived from the oxide skin on the A1 powder, broken up and aligned during extrusion. Mechanical testing Tensile testing was carried out ,~n a Schenck screw-driven machine, with a 10 kN load cell, on cylindrical specimens with a gauge length (parallel to the extrusion axis) of 20 mm and a diameter of 3.5 mm, under displacement control. The strain rate was 5 x 10 3 s-i. Specimen strain was measured using a linear variable displacement transducer (LVDT) mounted between two aluminium plates fixed above and below the specimen grips. In addition to this, strain gauges were used at low strains ( < 2%) where the LVDT results would not be accurate due to the compliance of the grips. Tests were periodically interrupted in order to measure any changes in specimen density as the test progressed. In view of the relatively
large failure strains observed in these specimens, data were converted to true stress/true strain plots.
Microstructural examination Specimens were examined using optical and scanning electron microscopies. Scanning electron microscope (SEM)examination of as-extruded material showed that initial porosity in the material was negligible. Standard preparation and imaging procedures were used, but the study of cavities and fine oxide particles in the SEM was done on carefully electropolished specimens, in order to minimize surface damage during preparation. Struers A2 electrolyte was used, with polishing for 10 s at 18 V and final etching for 7 s at 13 V, giving current densities of approximately 3 mA mm -2 and 2 mA mm -2 respectively. Specimens were given a thin coating of gold and examined with a low accelerating voltage of about 8 kV.
Density measurement The densities of specimens before and after tensile testing were measured by Archimedean pycnometry, using a Sartorius RC210P microbalance with a sensitivity of + 10 ~tg. A high density fluorocarbon was used as the immersion fluid. Changes in specimen density of 0.05% could be reliably measured. Measurements on the as-extruded specimens revealed them to be fully dense to the accuracy limits imposed by the precision to which the densities and volume fractions of the constituents were known. For strained specimens, a correction was made for the unstrained volume beyond the specimen shoulders, to obtain the density, and hence the void content, in the gadge length.
RESULTS Examination of electropolished sections taken from tensile-loaded specimens revealed that cavities could clearly be seen. These almost invariably formed in the matrix adjoining the reinforcement, approximately in line with the applied stress axis. Typical micrographs are shown in Fig. 1 for spherical, angular and fibrous reinforcements. Most of the voids are approximately hemispherical in shape, with a diameter largely dictated by the dimensions of the adjoining reinforcement. Only rarely were fractured fibres or particles observed. Data are shown in Fig. 2, for a composite containing 10 volume% (vol%) of angular particles, in the form of a stress/strain curve and the corresponding evolution of the void content during the test. It is clear from these data both that a significant degree of cavitation occurs only after a certain amount of plastic strain has been imposed and that specimen failure does not immediately follow the generation of voids. It is evident that cavities can remain stable while straining of the specimen continues. Further void content data are shown in Fig. 3, covering all three reinforcement types at both volume fractions. Several features are apparent in these plots. Firstly, it is evident that cavitation occurs earlier with the fibre reinforcement. This is consistent with an increased load being borne by the reinforcement (and hence higher peak stresses in the matrix) when it has a higher aspect ratio and is aligned parallel to the stress axis. Secondly, while
COMPOSITES. NUMBER 3. 1993
257
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COMPOSITES . NUMBER 3. 1993
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void contents are higher with angular particles than with the spheres, the difference is not very large. This is consistent with the observation that, in the angular case, there was a clear tendency for cavities to form at the ends of (elongated) particles, particularly when this end had a flattish surface normal to the stress axis: sharp angularities do not themselves appear to be favoured sites. With the spherical particles, cavities were also observed adjacent to them (particularly the larger ones), along the line of the applied stress. Again it would appear that surfaces approximately normal to the stress axis form the preferred sites, with sharp corners not required. This is broadly consistent with finite element computations of the distribution of hydrostatic stress 5, as are micrographs such as Fig. 1(b) suggesting that cavities first formed, not on the fibre axis, but between the centre and edge of the fibre end surface.
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MODELLING OF CA VlTY FORMATION A N D FAILURE Activation of cavitation sites
The observation that extensive and progressive cavitation appears to precede failure can be used as the
starting point for a simple model describing the condition for specimen fracture. A possible view of the sequence of events would be that cavities first form at preferred sites, quickly growing until they reach a stable shape, when growth is arrested by the resultant local stress relaxation. While predicting the rate of growth of a void at a fibre/matrix interface is a complex problem, combination of expressions for an isolated spherical cavity with estimates of the local stress field confirms 2n,22 that it is expected to be rapid compared with the far-field strain rate. For a fibre, the stable void shape can probably be taken as a hemisphere with the same diameter. The formation of the cavity will relax the local constraint and effect a reduction in the stress level in its immediate vicinity. Assuming that the matrix is sufficiently ductile for this to be a more important effect than any stress concentration around the void, there will be a tendency for further cavitation events to be distributed fairly homogeneously throughout the material, rather than rapidly becoming extensive in a local area*. Failure will occur when a local density of voids is high enough for them to coalesce by a ductile tearing mechanism. The data presented in Fig. 3 can be used to obtain an idea of the critical void density for failure, since a measured void content, V, can be converted to a fraction, F, of the cavitation sites which have been activated. Slightly different geometrical models are needed for the three types of reinforcement. For a cylindrical fibre aligned along the stress axis, with sites for a hemispherical void on both ends, it is readily shown that: F(c)
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where s is the fibre aspect ratio (length/diameter) a n d f i s the reinforcement volume fraction. If the angular particles are taken as cuboids with a pair of square faces normal to the stress axis, on which hemispheres with a diameter equal to the side length can form, then the corresponding expression is: 6 s V( e) F(e) = t c f
(2)
where s is the ratio of the length of the cuboid in the applied stress direction to that in the other two directions. For the spheres, the voids may be taken as hemis-. pheres with half the diameter of the sphere (see, for example, Fig. l(a)), leading to:
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Fig. 4 Data shown in Fig. 3, replotted in the form of an estimate of the fraction of cavitation sites which have been activated, for reinforcement contents of (a) 1 0 vol% and (b) 20 vol%
examined here* (Reference 23). In order to predict the failure strain for a composite, failure can be assumed to occur when the fraction of cavitation sites which have been activated reaches a critical value. Clearly this critical fraction will be a function of many microstructural factors. However, a preliminary attempt to model the behaviour could be based on taking the strain at full cavitation (F = 1) as the failure strain.
Failure strain prediction (3)
which is approximate since the volume of the hemispheres occupied by the parent sphere has been taken as part of the cavity. Application of these three equations to the data in Fig. 3 leads to the plots shown in Fig. 4. It would appear from these plots that a large proportion of the available cavitation sites have become activated by the time that final failure occurs, for the composites
*This is plausible provided that pronounced necking is not occurring. For a necked region, the effective far-field strain is higher and so the whole necked region will show accelerated cavitation in any event. For the material studied here, necking was only apparent at strains close to that of final failure.
Taking the failure strain as that when full cavitation has occurred seems broadly consistent with the data in Fig. 4 and may also be rationalized on the basis of a state being reached where no further stress relaxation by void formation can occur. In order to predict the composite *This might be expected to depend on microstructural features, such as the interfacial bond strength. It may be noted that the powder route material used here contained aligned arrays of fine oxide particles (from the original AI particle surfaces) which may have promoted void formation. In fact, work 23 with cast fibrous composites has shown that cavitation starts later and the void content remains lower in this material, although it still reaches a relatively high level by the time that failure occurs. In general, the critical value of F should be regarded as a variable dependent on microstructural features.
COMPOSITES.
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1993
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(plastic) strain at this point, three factors are incorporated in the model: 1) only the matrix can deform plastically, so that a correction factor of (1 - J ) is needed to take account of the volume occupied by the reinforcement; 2) cavity formation will itself contribute to the observed composite strain, this contribution, ~cav, presumably being absent for the unreinforced matrix; and 3) a certain proportion,fcon, of the volume of the matrix will be constrained by the presence of the reinforcement and unable to flow plastically (or to cavitate). This is illustrated by Fig. 5, in which the reinforcement is taken as a fibre and the constrained region is shown as a triangular-section volume of revolution surrounding the fibre. It follows that an expression for the failure strain of the composite may be written as: e. = e.0(1 - f ) ( 1 + e~v)(1 --f~n,)
(4)
where e.0 is the failure strain of the unreinforced matrix. The value of eCav can be taken as the product of the relative axial length contribution of the cavities within the unit cell ( = d/L, see Fig. 5) and a normalization factor to account for the relative volume effect, which can be taken asf. This leads to:
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The value of f~o, is obtained as the ratio of the constrained volume to the matrix volume within the cell. Making an approximation for the volume of revolution, this may be written as
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C O M P O S I T E S . N U M B E R 3 . 1993
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Fig. 6 Dependence of the composite failure strain on the reinforcement content and aspect ratio. Plots are shown for the predictions obtained from Equation (7) over (a) a wide range of f a n d svalues and (b) a narrower range, together with some experimental data in this regime
where h is the height of the triangular constrained region. Some arbitrary geometrical approximation is needed here, since the constrained region is evidently not well defined in practice. For example, it might be regarded as physically reasonable to take the ratio z/h as having a value of five. If this is done, then the above equation reduces to: 2s f~o, - 5 (f-' - 1)
(6)
It may be noted that, particularly at large values o f f and s, the constrained volume may extend outside the unit cell; mathematically, this will appear to eliminate plastic flow (and cavitation) in regions of the cell above and below the fibre, but this is acceptable since it corresponds physically to constraint of those regions in neighbouring cells. Combination of Equations (4)-(6) now leads to an expression for the failure strain ratio, as a function of the reinforcement volume fraction and aspect ratio only:
:o
1
Predictions from this equation are shown in Fig. 6, which includes a comparison with experimental failure strain data for the six composites referred to in Figs 3 and 4, normalized by that for the unreinforced matrix made by the same route (,-~24.5%). As expected, high values of s a n d / o r f c a n lead to very low predicted failure strains. It
can be seen that the trends observed experimentally with changing s andfvalues are broadly in line with the model predictions and that the values of the failure strains are also of the correct magnitudes. Evidently, more data are required in order to explore the validity of the model systematically. CONCL USIONS
1) Accurate density measurements, together with observations on electropolished sections, have revealed how the void content changes during tensile straining of AI203/AI composites made by powder blending and extrusion. 2) High aspect ratios, alignment parallel to the stress axis and flat surfaces normal to the stress axis all encourage cavitation. Spheres therefore generate voids less readily than angular particles of the same size, but the difference is quite small and the failure strains are very similar. Cavities start to form at lower strains with fibrous reinforcement, and with higher reinforcement contents. By the time that failure occurs (by link-up of cavities), a significant fraction of the cavitation sites seem to have been activated for all of the composites studied. 3) A simple geometrical model has been proposed for prediction of the failure strain, as a ratio to that for the unreinforced matrix, based on the effects of constraint to plastic flow and cavitation imposed by the presence of the reinforcement and the contribution to straining from the cavitation itself. Good agreement has been observed between the predictions of this model, obtained using the assumption that all cavitation sites had been activated by the time that failure occurred, and the experimental data presented. A CKNO WL ED G E M E N TS
Financial support for one of us (AFW) is being provided by the SERC and by Alcan International. Useful discussions have taken place with Dr R.A. Ricks, of A l c a n Research Centre, Banbury. The authors are grateful to Mr K. Gray and Mr K.A. Roberts, of Cambridge University, and Mr A. Forno, of NPL Teddington, for assistance with the preparation of the composite materials, and to Ms E.A. Simons, of Cambridge University, for carrying out some of the experimental measurements.
4
5 6
7
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17
18
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21 22 23
microstructure and particle distribution on fracture of an AI MMC' Mater Sci and Engng AI07 (1989) pp 241-255 Manoharan, M. and Lewandowski, J.J. 'Crack initiation and growth toughness of an AI M MC' Aeta Metall et Mater 38 (1990) pp 489~196 Nutt, S.R. and Needleman, A. 'Void nucleation at fibre ends in AI SiC composites' Seripta Metall 21 (1987) pp 705-710 Chrlstman, T., Needleman, A. and Suresh, S. 'An experimental and numerical study of deformation in MMCs' Acta Metal137 (1989) pp 3029 3050 Needleman, A. and Nutt, S.R. 'Void nucleation in short fiber composites' in Advances in Fracture Research (Proe ICF7) edited K. Salama (Pergamon, Oxford, 1990) pp 2211 2218 Tanaka, K., Mori, T. and Nakamura, T. 'Cavity formation at the interface of a spherical inclusion in a plastically deformed matrix' Phil Mag 21 (1970) pp 267 279 Argon, A.S., lm, J. and Safoglu, F. 'Cavity formation from inclusions in ductile fracture' Metall Trans 6A (1975) pp 825-837 Brown, L.M. and Stobbs, W.M. 'The work hardening of copper silica V. Equilibrium plastic relaxation by secondary dislocations' Phil Mag 34 (1976) pp 351 372 Goods, S.H. and Brown, L.M. "The nucleation of cavities by plastic deformation' Aeta Metal127 (1979) pp 1 15 Whitehouse, A.F., Shahaoi, R.A. and Clyne, T.W. 'Cavitation during tensile deformation of powder route particle-reinforced aluminium' in Metal Matrix Composites." Processing. Mierostrueture & Properties, Proe 12th R&o lot Symp (Roskilde, Denmark, 1991) edited by N. Hansen el al (Rise National Laboratory, Denmark) pp 741 748 Mummery, P.M. and Derby, B. "Fracture in particulate-reinforced metal matrix composites; crack propagation' ibid pp 535 541 Hunt, W.H., Brockenbrough, J.R. and Magnusen, P.E. "An AI Si Mg composite model system: microstructural effects on deformation and damage evolution' Scripta Metal125 (1991) pp 15 20 Brown, L.M. and Embury, J.D. 'The initiation of growth of voids at second phase particles' in Proc ICSMA HI (Cambridge, UK, 1973) pp 164~168 Evensen, J.D. and Verk, A.S. 'The influence of particle cracking on the fracture strain of some AI Si alloys' Scripta Metall 15 (1981) pp 1131 1133 McDanels, D.L. 'Analysis of stress strain, fracture, and ductility of aluminium matrix composites containing discontinuous silicon carbide reinforcement' Metall Trans 16A (1985) pp 1105- I 115 Shang, J.K., Yu, W. and Ritchie, R.O. 'Role of SiC particles in fatigue crack growth in SiC-particulate-reinforced AI alloy composites' Mater Sei and Engng A102 (1988) pp 181 192 DaSilva, R., Caldemaison, D. and Bretheau, T. qnterface strength influence on the mechanical behaviour of AI-SiCp MMCs' in Proe lnterfacial Phenomena in Composite Materials '89 (Sheffield, UK, 1989) edited by F.R. Jones (Butterworth-Heinemann Ltd, Oxford) pp 235 241 Rihes, H. and Suery, M. 'Effect of particle oxidation on agehardening of A1 Si Mg/SiC composites" Seripta Metal123 (1989) pp 705 709 Rice, J.R. and Tracey, D.M. 'On the ductile enlargement of voids in triaxial stress fields' J Mech Phys Solids 17 (1969) pp 201 217 Clyne, T.W. and Withers, P.J. An Introduction to Metal Matrix Composites (Cambridge University Press, Cambridge, 1992) Whitehouse, A.F. and Clyne, T.W. 'Cavity formation during tensile straining of particulate and short fibre MMCs' Acta Metall (to be published)
REFERENCES 1 Logsdon, W.A. and Liaw, P.K. 'Tensile, fracture toughness and fatigue crack growth rate properties of SiCw and SiCp reinforced A1 MMCs' Engng Fract Mech 24 (1986) pp 737 751 2 Hunt, W.H., Richmond, O. and Young, R.D. 'Fracture initiation in particle hardened materials with high volume fraction' in Proc 1CCM6/ECCM2 edited by F.L. Matthews et al. (Elsevier, London, 1987) pp 209 223 3 Lewandowski, J.J., Liu, C. and Hunt, W.H. 'Effects of matrix
AUTHORS
The authors are with the Department of Materials Science and Metallurgy, University of Cambridge, Pembroke Street, Cambridge CB2 3QZ, UK. Correspondence should be addressed to Dr Whitehouse.
COMPOSITES. NUMBER 3 . 1993
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Cavity development in alumina-reinforced aluminium composites during tensile loading at room temperature has been monitored using microstructural studies and precision density measurements. The materials examined were based on commercial purity aluminium, reinforced with 1 0 and 20 volume% of short fibres, conventional angular particles or spherical particles, produced by a thermal spraying process. The composites were made by a powder blending and extrusion route, involving no liquidation of the matrix and leaving arrays of fine oxide particles aligned parallel to the loading direction. In all cases, stable voids were found to form well before final failure. Significant void contents were developed earlier in the test for the higher reinforcement content and when fibres were present. However, extensive voiding, corresponding to approximately hemispherical voids being formed at most fibres or particles, occurred in all cases before final failure. Voids tend to form adjacent to the reinforcement, most readily when it is elongated in the direction of applied stress and when it has a relatively flat surface normal to the stress axis. Sharp corners do not themselves appear to be favoured sites for cavity formation. Consistent with this, cavities can form with spherical particles, although their incidence is somewhat less than with angular particles, presumably because of the absence of elongated shapes and surfaces which are actually flat. A simple model is proposed which allows prediction of the failure strain for a given reinforcement volume fraction and aspect ratio. This is based on the constraining effect of the reinforcement on plastic deformation in adjacent regions of matrix and the contribution of cavitation to the observed strain. Fairly good agreement is observed between the predictions of this model and the experimental data.
Key w o r d s : metal-matrix composites; reinforcement shape; reinforcement content; cavitation; failure strain; model Tensile failure of discontinuously reinforced metalmatrix composites (MMCS)has been shown ~ to be at least partly due to the nucleation and growth of cavities formed at reinforcing particles or fibres, followed by coalescence and fracture. Regions of the matrix adjacent to the ends of fibres or particles, along the line o f applied stress, are sites where high hydrostatic tension is generated and hence where nucleation o f cavities is expected ~7. Conditions have been proposed for the formation of a void at an isolated inclusion in a material under applied load 8-". It is rather unclear, however, how best to formulate a condition for the failure of the composite in terms of the nucleation and growth of voids. It has
been clearly shown ~2-14that stable voids can form in these materials, so that treatments of the nucleation process are unlikely to lead directly to ductility predictions. It seems clear that the growth and coalescence of voids, rather than their initial formation, will largely determine the final ductility of the material. Models have been proposed for the onset of instability in the growth and coalescence of voids, for example by considering local necking of matrix between debonded particles ~5 or between cracked particles ~6. These models tend to predict ductilities which are high for low volume fractions of reinforcement, but fall rapidly as the volume fraction is raised. Much experimental ductility data, at least in SiCp/
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COMPOSITES . VOLUME 24. NUMBER 3 . 1993
A1 composites 337,18, indicate that the ductility is quite low ( ~ 3 15%) even for low volume fractions ( ~ 10%), but does not fall off very sharply as the ceramic content is increased. Ductilities are usually observed to decrease somewhat as the particle size is increased, a factor which does not enter into most simple models. There is little information on the effect of interfacial bond strength, usually thought to be strong in SiC/A1, although in cast SiC/A1 7% Si4).4% Mg composites a sharp decrease in work hardening rate and a large increase in ductility has been reported ~9 to result from the prior formation of a silica layer on the SiC reinforcement. This apparently decreased the bond strength, encouraging interfacial sliding and possibly other stress relaxation mechanisms. It is not, however, clear whether the incidence of cavitation was affected by this change. In any event, changes in matrix precipitation induced by attraction of Mg to the interface may have influenced the behaviour 2°. The present paper is concerned with the effects of reinforcement content and shape, including the presence of angularities, on cavity formation and ductility. Following from some of the observations made, a simple model is proposed for the prediction of composite ductility.
EXPERIMENTAL PROCEDURE Material production Composite material was produced by dry powder blending, canning under vacuum and hot extrusion. The reinforcements used were (a) spherical A1203 (diameter of 10 p.m), (b) angular A1203 (approximately cuboids of side about 10-15p.m) and (c) chopped 'Saffi]' fibre ( ~ 3 lam diameter), which became broken up during extrusion into lengths of aspect ratio about four. Composite was produced with volume fractions of both 10% and 20%. The spherical alumina powder was manufactured by melting quantities of the angular powder, using low pressure plasma spray equipment. The molten droplets were allowed to refreeze in flight. Inert gas atomized commercial purity aluminium powder with a mean diameter of ~ 30 ~tm was used for the matrix. In all cases, the as-extruded microstructure consisted of well-dispersed particles in a matrix consisting of fine grains, elongated in the extrusion direction. These were formed by deformation of the original AI powder particles, and no recrystallization had taken place. All the composites contained about 0.08% by volume of fine platelets (d 50 nm, t ~ 10 nm) derived from the oxide skin on the A1 powder, broken up and aligned during extrusion. Mechanical testing Tensile testing was carried out ,~n a Schenck screw-driven machine, with a 10 kN load cell, on cylindrical specimens with a gauge length (parallel to the extrusion axis) of 20 mm and a diameter of 3.5 mm, under displacement control. The strain rate was 5 x 10 3 s-i. Specimen strain was measured using a linear variable displacement transducer (LVDT) mounted between two aluminium plates fixed above and below the specimen grips. In addition to this, strain gauges were used at low strains ( < 2%) where the LVDT results would not be accurate due to the compliance of the grips. Tests were periodically interrupted in order to measure any changes in specimen density as the test progressed. In view of the relatively
large failure strains observed in these specimens, data were converted to true stress/true strain plots.
Microstructural examination Specimens were examined using optical and scanning electron microscopies. Scanning electron microscope (SEM)examination of as-extruded material showed that initial porosity in the material was negligible. Standard preparation and imaging procedures were used, but the study of cavities and fine oxide particles in the SEM was done on carefully electropolished specimens, in order to minimize surface damage during preparation. Struers A2 electrolyte was used, with polishing for 10 s at 18 V and final etching for 7 s at 13 V, giving current densities of approximately 3 mA mm -2 and 2 mA mm -2 respectively. Specimens were given a thin coating of gold and examined with a low accelerating voltage of about 8 kV.
Density measurement The densities of specimens before and after tensile testing were measured by Archimedean pycnometry, using a Sartorius RC210P microbalance with a sensitivity of + 10 ~tg. A high density fluorocarbon was used as the immersion fluid. Changes in specimen density of 0.05% could be reliably measured. Measurements on the as-extruded specimens revealed them to be fully dense to the accuracy limits imposed by the precision to which the densities and volume fractions of the constituents were known. For strained specimens, a correction was made for the unstrained volume beyond the specimen shoulders, to obtain the density, and hence the void content, in the gadge length.
RESULTS Examination of electropolished sections taken from tensile-loaded specimens revealed that cavities could clearly be seen. These almost invariably formed in the matrix adjoining the reinforcement, approximately in line with the applied stress axis. Typical micrographs are shown in Fig. 1 for spherical, angular and fibrous reinforcements. Most of the voids are approximately hemispherical in shape, with a diameter largely dictated by the dimensions of the adjoining reinforcement. Only rarely were fractured fibres or particles observed. Data are shown in Fig. 2, for a composite containing 10 volume% (vol%) of angular particles, in the form of a stress/strain curve and the corresponding evolution of the void content during the test. It is clear from these data both that a significant degree of cavitation occurs only after a certain amount of plastic strain has been imposed and that specimen failure does not immediately follow the generation of voids. It is evident that cavities can remain stable while straining of the specimen continues. Further void content data are shown in Fig. 3, covering all three reinforcement types at both volume fractions. Several features are apparent in these plots. Firstly, it is evident that cavitation occurs earlier with the fibre reinforcement. This is consistent with an increased load being borne by the reinforcement (and hence higher peak stresses in the matrix) when it has a higher aspect ratio and is aligned parallel to the stress axis. Secondly, while
COMPOSITES. NUMBER 3. 1993
257
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COMPOSITES . NUMBER 3. 1993
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void contents are higher with angular particles than with the spheres, the difference is not very large. This is consistent with the observation that, in the angular case, there was a clear tendency for cavities to form at the ends of (elongated) particles, particularly when this end had a flattish surface normal to the stress axis: sharp angularities do not themselves appear to be favoured sites. With the spherical particles, cavities were also observed adjacent to them (particularly the larger ones), along the line of the applied stress. Again it would appear that surfaces approximately normal to the stress axis form the preferred sites, with sharp corners not required. This is broadly consistent with finite element computations of the distribution of hydrostatic stress 5, as are micrographs such as Fig. 1(b) suggesting that cavities first formed, not on the fibre axis, but between the centre and edge of the fibre end surface.
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MODELLING OF CA VlTY FORMATION A N D FAILURE Activation of cavitation sites
The observation that extensive and progressive cavitation appears to precede failure can be used as the
starting point for a simple model describing the condition for specimen fracture. A possible view of the sequence of events would be that cavities first form at preferred sites, quickly growing until they reach a stable shape, when growth is arrested by the resultant local stress relaxation. While predicting the rate of growth of a void at a fibre/matrix interface is a complex problem, combination of expressions for an isolated spherical cavity with estimates of the local stress field confirms 2n,22 that it is expected to be rapid compared with the far-field strain rate. For a fibre, the stable void shape can probably be taken as a hemisphere with the same diameter. The formation of the cavity will relax the local constraint and effect a reduction in the stress level in its immediate vicinity. Assuming that the matrix is sufficiently ductile for this to be a more important effect than any stress concentration around the void, there will be a tendency for further cavitation events to be distributed fairly homogeneously throughout the material, rather than rapidly becoming extensive in a local area*. Failure will occur when a local density of voids is high enough for them to coalesce by a ductile tearing mechanism. The data presented in Fig. 3 can be used to obtain an idea of the critical void density for failure, since a measured void content, V, can be converted to a fraction, F, of the cavitation sites which have been activated. Slightly different geometrical models are needed for the three types of reinforcement. For a cylindrical fibre aligned along the stress axis, with sites for a hemispherical void on both ends, it is readily shown that: F(c)
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where s is the fibre aspect ratio (length/diameter) a n d f i s the reinforcement volume fraction. If the angular particles are taken as cuboids with a pair of square faces normal to the stress axis, on which hemispheres with a diameter equal to the side length can form, then the corresponding expression is: 6 s V( e) F(e) = t c f
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where s is the ratio of the length of the cuboid in the applied stress direction to that in the other two directions. For the spheres, the voids may be taken as hemis-. pheres with half the diameter of the sphere (see, for example, Fig. l(a)), leading to:
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Fig. 4 Data shown in Fig. 3, replotted in the form of an estimate of the fraction of cavitation sites which have been activated, for reinforcement contents of (a) 1 0 vol% and (b) 20 vol%
examined here* (Reference 23). In order to predict the failure strain for a composite, failure can be assumed to occur when the fraction of cavitation sites which have been activated reaches a critical value. Clearly this critical fraction will be a function of many microstructural factors. However, a preliminary attempt to model the behaviour could be based on taking the strain at full cavitation (F = 1) as the failure strain.
Failure strain prediction (3)
which is approximate since the volume of the hemispheres occupied by the parent sphere has been taken as part of the cavity. Application of these three equations to the data in Fig. 3 leads to the plots shown in Fig. 4. It would appear from these plots that a large proportion of the available cavitation sites have become activated by the time that final failure occurs, for the composites
*This is plausible provided that pronounced necking is not occurring. For a necked region, the effective far-field strain is higher and so the whole necked region will show accelerated cavitation in any event. For the material studied here, necking was only apparent at strains close to that of final failure.
Taking the failure strain as that when full cavitation has occurred seems broadly consistent with the data in Fig. 4 and may also be rationalized on the basis of a state being reached where no further stress relaxation by void formation can occur. In order to predict the composite *This might be expected to depend on microstructural features, such as the interfacial bond strength. It may be noted that the powder route material used here contained aligned arrays of fine oxide particles (from the original AI particle surfaces) which may have promoted void formation. In fact, work 23 with cast fibrous composites has shown that cavitation starts later and the void content remains lower in this material, although it still reaches a relatively high level by the time that failure occurs. In general, the critical value of F should be regarded as a variable dependent on microstructural features.
COMPOSITES.
NUMBER
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1993
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(plastic) strain at this point, three factors are incorporated in the model: 1) only the matrix can deform plastically, so that a correction factor of (1 - J ) is needed to take account of the volume occupied by the reinforcement; 2) cavity formation will itself contribute to the observed composite strain, this contribution, ~cav, presumably being absent for the unreinforced matrix; and 3) a certain proportion,fcon, of the volume of the matrix will be constrained by the presence of the reinforcement and unable to flow plastically (or to cavitate). This is illustrated by Fig. 5, in which the reinforcement is taken as a fibre and the constrained region is shown as a triangular-section volume of revolution surrounding the fibre. It follows that an expression for the failure strain of the composite may be written as: e. = e.0(1 - f ) ( 1 + e~v)(1 --f~n,)
(4)
where e.0 is the failure strain of the unreinforced matrix. The value of eCav can be taken as the product of the relative axial length contribution of the cavities within the unit cell ( = d/L, see Fig. 5) and a normalization factor to account for the relative volume effect, which can be taken asf. This leads to:
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The value of f~o, is obtained as the ratio of the constrained volume to the matrix volume within the cell. Making an approximation for the volume of revolution, this may be written as
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C O M P O S I T E S . N U M B E R 3 . 1993
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where h is the height of the triangular constrained region. Some arbitrary geometrical approximation is needed here, since the constrained region is evidently not well defined in practice. For example, it might be regarded as physically reasonable to take the ratio z/h as having a value of five. If this is done, then the above equation reduces to: 2s f~o, - 5 (f-' - 1)
(6)
It may be noted that, particularly at large values o f f and s, the constrained volume may extend outside the unit cell; mathematically, this will appear to eliminate plastic flow (and cavitation) in regions of the cell above and below the fibre, but this is acceptable since it corresponds physically to constraint of those regions in neighbouring cells. Combination of Equations (4)-(6) now leads to an expression for the failure strain ratio, as a function of the reinforcement volume fraction and aspect ratio only:
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1
Predictions from this equation are shown in Fig. 6, which includes a comparison with experimental failure strain data for the six composites referred to in Figs 3 and 4, normalized by that for the unreinforced matrix made by the same route (,-~24.5%). As expected, high values of s a n d / o r f c a n lead to very low predicted failure strains. It
can be seen that the trends observed experimentally with changing s andfvalues are broadly in line with the model predictions and that the values of the failure strains are also of the correct magnitudes. Evidently, more data are required in order to explore the validity of the model systematically. CONCL USIONS
1) Accurate density measurements, together with observations on electropolished sections, have revealed how the void content changes during tensile straining of AI203/AI composites made by powder blending and extrusion. 2) High aspect ratios, alignment parallel to the stress axis and flat surfaces normal to the stress axis all encourage cavitation. Spheres therefore generate voids less readily than angular particles of the same size, but the difference is quite small and the failure strains are very similar. Cavities start to form at lower strains with fibrous reinforcement, and with higher reinforcement contents. By the time that failure occurs (by link-up of cavities), a significant fraction of the cavitation sites seem to have been activated for all of the composites studied. 3) A simple geometrical model has been proposed for prediction of the failure strain, as a ratio to that for the unreinforced matrix, based on the effects of constraint to plastic flow and cavitation imposed by the presence of the reinforcement and the contribution to straining from the cavitation itself. Good agreement has been observed between the predictions of this model, obtained using the assumption that all cavitation sites had been activated by the time that failure occurred, and the experimental data presented. A CKNO WL ED G E M E N TS
Financial support for one of us (AFW) is being provided by the SERC and by Alcan International. Useful discussions have taken place with Dr R.A. Ricks, of A l c a n Research Centre, Banbury. The authors are grateful to Mr K. Gray and Mr K.A. Roberts, of Cambridge University, and Mr A. Forno, of NPL Teddington, for assistance with the preparation of the composite materials, and to Ms E.A. Simons, of Cambridge University, for carrying out some of the experimental measurements.
4
5 6
7
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21 22 23
microstructure and particle distribution on fracture of an AI MMC' Mater Sci and Engng AI07 (1989) pp 241-255 Manoharan, M. and Lewandowski, J.J. 'Crack initiation and growth toughness of an AI M MC' Aeta Metall et Mater 38 (1990) pp 489~196 Nutt, S.R. and Needleman, A. 'Void nucleation at fibre ends in AI SiC composites' Seripta Metall 21 (1987) pp 705-710 Chrlstman, T., Needleman, A. and Suresh, S. 'An experimental and numerical study of deformation in MMCs' Acta Metal137 (1989) pp 3029 3050 Needleman, A. and Nutt, S.R. 'Void nucleation in short fiber composites' in Advances in Fracture Research (Proe ICF7) edited K. Salama (Pergamon, Oxford, 1990) pp 2211 2218 Tanaka, K., Mori, T. and Nakamura, T. 'Cavity formation at the interface of a spherical inclusion in a plastically deformed matrix' Phil Mag 21 (1970) pp 267 279 Argon, A.S., lm, J. and Safoglu, F. 'Cavity formation from inclusions in ductile fracture' Metall Trans 6A (1975) pp 825-837 Brown, L.M. and Stobbs, W.M. 'The work hardening of copper silica V. Equilibrium plastic relaxation by secondary dislocations' Phil Mag 34 (1976) pp 351 372 Goods, S.H. and Brown, L.M. "The nucleation of cavities by plastic deformation' Aeta Metal127 (1979) pp 1 15 Whitehouse, A.F., Shahaoi, R.A. and Clyne, T.W. 'Cavitation during tensile deformation of powder route particle-reinforced aluminium' in Metal Matrix Composites." Processing. Mierostrueture & Properties, Proe 12th R&o lot Symp (Roskilde, Denmark, 1991) edited by N. Hansen el al (Rise National Laboratory, Denmark) pp 741 748 Mummery, P.M. and Derby, B. "Fracture in particulate-reinforced metal matrix composites; crack propagation' ibid pp 535 541 Hunt, W.H., Brockenbrough, J.R. and Magnusen, P.E. "An AI Si Mg composite model system: microstructural effects on deformation and damage evolution' Scripta Metal125 (1991) pp 15 20 Brown, L.M. and Embury, J.D. 'The initiation of growth of voids at second phase particles' in Proc ICSMA HI (Cambridge, UK, 1973) pp 164~168 Evensen, J.D. and Verk, A.S. 'The influence of particle cracking on the fracture strain of some AI Si alloys' Scripta Metall 15 (1981) pp 1131 1133 McDanels, D.L. 'Analysis of stress strain, fracture, and ductility of aluminium matrix composites containing discontinuous silicon carbide reinforcement' Metall Trans 16A (1985) pp 1105- I 115 Shang, J.K., Yu, W. and Ritchie, R.O. 'Role of SiC particles in fatigue crack growth in SiC-particulate-reinforced AI alloy composites' Mater Sei and Engng A102 (1988) pp 181 192 DaSilva, R., Caldemaison, D. and Bretheau, T. qnterface strength influence on the mechanical behaviour of AI-SiCp MMCs' in Proe lnterfacial Phenomena in Composite Materials '89 (Sheffield, UK, 1989) edited by F.R. Jones (Butterworth-Heinemann Ltd, Oxford) pp 235 241 Rihes, H. and Suery, M. 'Effect of particle oxidation on agehardening of A1 Si Mg/SiC composites" Seripta Metal123 (1989) pp 705 709 Rice, J.R. and Tracey, D.M. 'On the ductile enlargement of voids in triaxial stress fields' J Mech Phys Solids 17 (1969) pp 201 217 Clyne, T.W. and Withers, P.J. An Introduction to Metal Matrix Composites (Cambridge University Press, Cambridge, 1992) Whitehouse, A.F. and Clyne, T.W. 'Cavity formation during tensile straining of particulate and short fibre MMCs' Acta Metall (to be published)
REFERENCES 1 Logsdon, W.A. and Liaw, P.K. 'Tensile, fracture toughness and fatigue crack growth rate properties of SiCw and SiCp reinforced A1 MMCs' Engng Fract Mech 24 (1986) pp 737 751 2 Hunt, W.H., Richmond, O. and Young, R.D. 'Fracture initiation in particle hardened materials with high volume fraction' in Proc 1CCM6/ECCM2 edited by F.L. Matthews et al. (Elsevier, London, 1987) pp 209 223 3 Lewandowski, J.J., Liu, C. and Hunt, W.H. 'Effects of matrix
AUTHORS
The authors are with the Department of Materials Science and Metallurgy, University of Cambridge, Pembroke Street, Cambridge CB2 3QZ, UK. Correspondence should be addressed to Dr Whitehouse.
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