MMC geblaat

MR40CH10-Mortensen ARI 24 May 2010 15:28

Metal Matrix CompositesAndreas Mortensen1 and Javier Llorca2

1Institute of Materials, Ecole Polytechnique Federale de Lausanne (EPFL), CH-1015,Lausanne, Switzerland; email: [email protected] Institute for Advanced Studies of Materials (IMDEA-Materials) and Department ofMaterials Science, Polytechnic University of Madrid, E-28040, Madrid, Spain;email: [email protected]

Annu. Rev. Mater. Res. 2010. 40:243–70

First published online as a Review in Advance onMarch 26, 2010

The Annual Review of Materials Research is online atmatsci.annualreviews.org

This article’s doi:10.1146/annurev-matsci-070909-104511

Copyright c© 2010 by Annual Reviews.All rights reserved

1531-7331/10/0804-0243$20.00

Key Words

fiber-reinforced composites, particle-reinforced composites, layeredmaterials, strength, ductility, stiffness

Abstract

In metal matrix composites, a metal is combined with another, often non-metallic, phase to produce a novel material having attractive engineeringattributes of its own. A subject of much research in the 1980s and 1990s, thisclass of materials has, in the past decade, increased significantly in variety.Copper matrix composites, layered composites, high-conductivity compos-ites, nanoscale composites, microcellular metals, and bio-derived compositeshave been added to a palette that, ten years ago, mostly comprised ceramicfiber– or particle-reinforced light metals together with some well-establishedengineering materials, such as WC-Co cermets. At the same time, researchon composites such as particle-reinforced aluminum, aided by novel tech-niques such as large-cell 3-D finite element simulation or computed X-raymicrotomography, has served as a potent vehicle for the elucidation of themechanics of high-contrast two-phase elastoplastic materials, with implica-tions that range well beyond metal matrix composites.

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MMC: metal matrixcomposite

INTRODUCTION

Metals and alloys are generally produced and shaped in bulk form but can also be intimately com-bined with another material that serves to improve their performance: The resulting material is ametal matrix composite (MMC). This class of composites encompasses many different materialsthat can be distinguished according to their base metal (e.g., aluminum, copper, titanium); ac-cording to the other, reinforcement, phase (e.g., fibers, particles, whiskers); or according to theirmanufacturing process (e.g., powder metallurgy, diffusion bonding, infiltration, stir casting).

Bulk metals and alloys are economical high-performance materials. Why, then, combine thesewith another phase, as doing so will always add cost and cause complications (in recycling, notably)?Among the stronger drivers of MMC technology are the following basic facts.

The first is that the composite approach to materials design makes it possible to go beyondboundaries drawn in property space by basic attributes of the main materials classes. A classicalexample is the specific modulus of metals, defined as elastic modulus E divided by density ρ:(E/ρ). This parameter is a measure of the performance, in weight-critical deformation-limitedstructural applications, of linear elastic components subjected to uniaxial stress. Now, the mainengineering metals and alloys have roughly the same (E/ρ) ≈ 26 MJ kg−1. So essentially the onlyway to exceed this limit in a metallic material is to replace a significant fraction of the metal atomswith a phase made of atoms that are (a) situated in the top rows of Mendeleev’s periodic table and(b) strongly bonded to one another. Examples are ceramics such as Al2O3, B4C, or SiC and certainvariants of carbon (e.g., high-modulus carbon fibers or diamond). Figure 1 shows another exampleof property boundary transgression made possible by MMC technology.

The second reason why MMCs are interesting has to do with processing: Making a compositeis the only approach by which a significant volume fraction of oxide or carbide can be introducedinto some important metals. Iron is very frequently—and easily—reinforced with a wide arrayof carbides, nitrides, or (more rarely) oxides because carbon, nitrogen, and oxygen are solublein this molten metal. Liquid aluminum, magnesium, and copper, in contrast, have essentiallyno solubility for carbon. Therefore, the only way to introduce a carbide into these metals is bymaking a composite; the same holds for aluminum with oxides or nitrides. In other words, MMCtechnology holds the key, for aluminum, magnesium, or copper, to much of the wide spectrum ofmicrostructures and properties available with iron.

A third reason for interest in MMCs has little to do with metals: Some phases, ceramics inparticular, have far better properties in finely divided form. Notably, micrometer-sized ceramicfibers or ceramic particles can be much stronger than bulk ceramics. Additionally, small, single-crystalline ceramic particles can be excellent conductors of heat. Carbon, too, can in finely dividedform be very strong, stiff, and a good conductor of heat (as diamond, for example). Taking advan-tage of this in macroscopic materials therefore calls for the incorporation of such finely dividednonmetallic phases (as fibers, platelets, films, or particles) within a composite material, the ma-trix of which can advantageously be made of metal. Indeed, metals conduct better, are stronger,tougher, and more environmentally resistant than polymers—and of course are much tougherthan ceramics.

These basic considerations have driven sustained research on MMCs, initiated several decadesago by pioneering research such as the important contributions of Anthony Kelly and coworkers(e.g., 6). Research on the subject reached a high level of intensity in the late 1980s and early 1990sand continues today, albeit in a wider array of more distinct directions and hence less visibly.MMCs have also entered the “real world” of engineering applications, in several forms rangingfrom a few well-established engineering materials (such as WC-Co hard metal) to newer nichematerials; References 1–3 give recent surveys.

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Figure 1Electronic substrates hold electronic circuits in place and keep them cool. Electronic substrate materialsmust therefore conduct heat well and have a coefficient of thermal expansion (CTE) close to that ofsemiconductors used in electronic circuitry, in the range from roughly 3 ppm K−1 to 7 ppm K−1. Somemetals (e.g., copper or silver) and some ceramics (e.g., SiC or selected forms of carbon) are good conductorsof heat; however, their CTE falls on either side of the desired range. Because the CTE of metals tends to betoo high and that of ceramics too low, a mixture of the two provides the ideal material for this application—one of the success stories of MMC technology (1–4). Aluminum/SiC composites produced by infiltration arenow well-established high-performance composites for electronic substrate applications; their propertyrange is indicated in the figure. Carbon materials, however, offer far higher conductivities than does SiC.Over the past decade the price of synthetic diamond, an excellent conductor of heat, has decreased to levelsthat make diamond particles viable engineering materials. A new generation of MMCs combiningaluminum, copper, or silver matrices with diamond particles and featuring an engineered interface has thusemerged, with appropriate CTE values and thermal conductivities approaching 1000 W m−1 K−1, i.e., 2.5times that of pure copper. Figure adapted from recent work by L. Weber and R. Tavangar at EPFL(Lausanne, Switzerland) (5).

Thus, the topic of MMCs is wide-ranging; recent reviews of the subject are in References 2 and7. If we look at progress accomplished during this early twenty-first century, what first strikes theeye is that the subject has “defocused” significantly to become both broader and less visible as asubtopic in materials science and engineering. There are fewer conferences specifically devoted toMMCs, but a rapid look at data from bibliometric search engines indicates that the yearly numberof articles published on the subject has remained roughly steady during this past decade.

The subject has diversified in two directions. The first direction is driven by the invention ofinteresting new MMCs; microcellular metals (composites too) and bulk metallic glass composites

www.annualreviews.org • Metal Matrix Composites 245

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are examples. The other direction has grown out of the realization that these materials serve aswonderful vehicles for the exploration of the physics or the micromechanics of nonlinear multi-phase materials in general. MMCs have thus been the subject of much recent research that hasviewed these as near-ideal model materials, a role that MMCs have served well for many years[going back to one of the earliest papers on the subject (8)].

We give in what follows a glimpse at some selected areas of recent progress in both of these twodirections. The next section describes new materials and advances in processing, whereas recentprogress in micromechanics driven by MMC research is presented in the section entitled Mech-anisms of Deformation and Fracture. Discussion of MMC research can also be found elsewherein this volume (9).

PROCESSING AND MATERIALS

The past ten years have seen a significant enlargement in the palette of reinforcements that arecombined with metal. New particles have appeared, starting with fine-scale submicrometer (ornano-) particles. These tend to be intrinsically strong while also bringing Orowan hardeningor grain refinement to the metallic matrix. The difficulty with nanosized reinforcements is inprocessing: Nanoparticles are much harder to incorporate or to distribute uniformly within metal.Capillary forces, often important in MMC processing, are much higher with nanoparticles (becausethese forces scale with the inverse of the reinforcement size) (10). The same holds for carbonnanofibers or carbon nanotubes, another newer reinforcement with potential for the reinforcementof metals.

Despite the challenges posed in processing, some laboratories and companies have managed tosuccessfully incorporate nanoparticles or nanofibers into metal and to produce engineering-quality(i.e., nonporous) MMCs with attractive properties by pressure infiltration (11, 12), by stir casting(13), by electrodeposition (14), or by powder metallurgy (15). Another, relatively well-established,pathway to the production of nanoscale MMC structures is by attrition, generally involving ballmilling followed by consolidation. Reference 16 notably reports a cryomilled aluminum-basedMMC having a partly nanoscale microstructure that exhibits, after extrusion and annealing, acompressive yield stress above 1 GPa along the extrusion direction. Other methods that havebeen recently developed to this end are more chemical in nature; these are in situ methods,exemplified by internal oxidation (17). Here, nanoscale reinforcements are created by internalreaction between precursor materials that are finely combined within the composite; Reference18 gives a recent review of in situ MMC processing.

A few laboratories have explored variations in the intrinsic microstructural quality, rather thanthe scale, of the reinforcement, questioning the wisdom of using low-cost crushed (comminuted)abrasive grade ceramics for the reinforcement of metals, as is generally done. Comminuted particlescontain many internal defects, including cracks or sharp corners along their surfaces. Angularityproduces sites of elevated stress concentration within the composite when it is stressed, causingin turn an acceleration of damage accumulation within the material, which sharply reduces itsductility. Rounding comminuted particles to eliminate such sites of stress concentration has led tosignificant improvements in composite ductility (19, 20). Spectacular improvements in compositeproperties can be further obtained if one uses particles produced by other methods, with fewinternal defects and no sharp angles; a (rare) example of this is Sumitomo’s SumicorundumTM

particles (http://www.sumitomochem.co.jp/english/research/develop_basic.html).The wisdom of keeping the volume fractions of ceramic particles below roughly 30%, as

is usually done to minimize their deleterious influence on composite ductility, has also beenquestioned. Indeed, the benefit of adding ceramic to metal is, for many properties, nonlinear:


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6 mm

100 μm

Figure 2Combining metal and ceramic need not produce a brittle material, provided that the ingredients and theprocessing are of high quality. This is illustrated with a four-point bend bar of a composite combiningroughly 50% alumina with 50% aluminum. From current research at EPFL (Lausanne, Switzerland) byA. Hauert, A. Rossoll, and A. Mortensen (21).

IPC: interpenetratingphase composite

Adding 25% alumina particles to aluminum will raise the modulus by 50%, from 70 GPa to100 GPa, whereas 60% alumina will yield a 2.5-fold increase to 180 GPa in an isotropic materialhaving a density near that of aluminum. Defect-free composites of this class can be relativelyductile despite a high (≈50%) ceramic content (see Figure 2). If, in addition, high-quality aluminaparticles are used, both the ultimate tensile strength and the fracture toughness can reach valuesmatching those of engineering aluminum alloys (22–25). These results, together with their analysis(see next section), show that the potential held by strong ceramic particles for the reinforcementof metal remains essentially untapped.

Much innovative recent work has also focused on ceramic reinforcements having three-dimensionally percolating architectures. This is an area that has grown significantly over thepast decade, largely under the impulse of a parallel thrust in microcellular ceramics research (26).Once infiltrated with metal, open-pore microcellular ceramics become interpenetrating phasecomposites (IPCs), defined as composites in which both phases (metal and ceramic in the presentinstance) are three-dimensionally percolating (27). As a result of these advances, IPC-MMCsare now much more frequently produced and explored than they were ten years ago. Note-worthy in this regard are the unique structures that are produced by infiltration with metal of


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Growing ice crystals become,after infiltration, the (light) metal phase in the composite

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Suspension of ceramic particles in water becomes, after dryingand sintering, the (dark) ceramic in the composite

Figure 3Metal matrix composites from freeze-cast ceramic preforms. (Left) Ice crystals are made to grow directionallyin a slurry of water containing a high volume fraction of fine ceramic particles. Particle pushing by thegrowing ice crystals concentrates the ceramic into thin walls. After freeze drying and sintering, a porousceramic preform is obtained; the domain distribution and the spacing of lamellae are functions of slurrysolidification parameters. (Right) A cross section through a freeze-cast alumina–reinforced Al-12Si compositeproduced by squeeze casting the metal into pores of the ceramic preform, viewed perpendicular to thefreezing direction in one single domain of a polydomain sample. Micrograph kindly provided by S. Roy andA. Wanner of the University of Karlsruhe, Germany (29).

PCM: phase changematerial

freeze-cast ceramics (Figure 3) (28, 29), biomorphic ceramics obtained from pyrolized wood(Figure 4) (30–32), or ceramic preforms produced by three-dimensional printing (33).

Together with the exploration of radically new reinforcement architectures, the past decadehas seen a greater emphasis on the exploration of MMCs for functional applications. Experiencehas shown that many applications of MMCs are motivated by their ability to conduct electricityor heat: Electronic substrates, electrical contactors, and brushes are examples of applications inwhich MMCs excel. Such properties have motivated the exploration of new MMCs for functionalapplications, such as novel carbon-reinforced metals for high thermal conductivity (Figure 1) ornovel composite superconductors (Figure 5) (34).

New functional MMCs have also emerged from the current drive toward greater energy effi-ciency. A notable example is that of solid-oxide fuel cell anode materials, most frequently a porouscomposite combining nickel with yttria-stabilized zirconia (35–37). These are generally producedby blending, densifying, and cofiring mixtures of NiO and zirconia, followed by reduction ofthe NiO; the ensuing (25%) shrinkage of NiO creates the pore network. Cell performance ishighly dependent on the microstructure, and hence on the processing, of these complex anodemetal/ceramic/gas composites. One can thus expect these to remain a focus of intense researchactivity in the years to come.

The current drive toward energy research should motivate the exploration of new MMCs; asomewhat exotic example is phase change materials (PCMs). These materials can serve in ther-mal management by absorbing or releasing heat as they melt or solidify, respectively (38). Aclassical PCM is paraffin, the melting point of which is near ambient temperature (the melting-point temperature varies with the precise paraffin formulation). The efficiency of PCMs is often


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Figure 4Computed X-ray microtomography composite view of three orthogonal sections of an Al/SiC compositeproduced by pressure infiltration with an Al-13Si-9Mg alloy of a three-dimensional SiC honeycomb-likestructure made by reaction with Si of pyrolized beech wood. The bounding box measures approximately750 μm per side; the voxel size is 1.46 μm. In the (X-ray attenuation–based) color scale used, the Al-filledpores appear blue, the SiC appears yellow or black, and residual porosity appears red or black. Image kindlyprovided by T.E. Wilkes and K.T. Faber of Northwestern University, Evanston, Illinois; for details consultReference 30.

restricted by their capacity to transport heat to/from the melting/solidification front, that is, bytheir low heat conductivity. As a result, some of the best PCMs are composites combining thephase-changing material (say, paraffin) with another, more conductive phase (generally a metal).The resulting MMC-PCM can be made by infiltrating pores of an open-cell microcellular metalwith the molten PCM.

Microcellular metals, often called metal foams, are also MMCs. Research on highly porousmetals has grown in recent years to become a major thrust in metallurgy, covered by dedicatedconferences and books (and is now too broad to be covered in any detail within the present article)(39, 40; http://www.metfoam2009.sav.sk/index.php?ID=1859&pg=13).


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aa

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Figure 5Cross-polarized light micrograph of a composite consisting of MgB2 continuous fibers within a Mg matrix(a). The 190-μm-diameter MgB2 fibers are created by a reaction of 140-μm B fibers with liquid Mg underthermal cycling conditions (ten 600–900◦C cycles over 3 h). The inset shows a higher-magnification view ofa similarly reacted fiber (eleven 650–900◦C cycles over 4.5 h) highlighting (b) the MgB2 grains and (c) theW-B core of the fiber. Image kindly provided by J.D. DeFouw and D.C. Dunand of NorthwesternUniversity, Evanston, Illinois (34).

BMG: bulk metallicglass

MMC research has also expanded in recent years by incorporation of the approach into othercurrent areas of metallurgical research: Many major innovations in metallurgical research havebranched into novel MMC research. Bulk metallic glasses (BMGs) are inherently very brittlematerials; the MMC approach has proven to be a potent pathway toward addressing this limita-tion. Siegrist & Loffler (41), for example, have shown recently that if soft particles are combinedwith a BMG matrix, significant improvements in BMG (compressive) ductility can be achievedat minimal loss in yield stress. In related work, novel metals available in powder form, such asaluminum-based BMG (42) or quasicrystals (43), have been explored as reinforcements for alu-minum. Novel metallurgical processes, such as severe plastic deformation or friction stir welding,have also been adapted toward the processing of MMCs, notably as methods toward improvingthe spatial uniformity of reinforcement distribution (44–47).

Current interest in layered structures has motivated research on MMC multilayers at both themicro- and nanoscale. Figure 6 shows a metal/metal microlaminate material combining ductileaustenitic and brittle martensitic steel grades. In such composites, the more ductile metal stabilizesthe more brittle metal against tensile failure. As a result, as-quenched martensite can be “coached”to deform by more than 20% in tension without breaking. Through use of this approach, withappropriately strong interfaces, sufficiently small layer thicknesses, and optimized heat treatment,a steel sheet having an ultimate tensile strength of 1.35 GPa with a tensile fracture elongation of28% was demonstrated at the University of Tokyo (48). Nanoscale laminates (Figure 7) can alsoexhibit interesting properties; these materials serve notably as vehicles for research on plasticitysize effects or the role of interfaces in the deformation and fracture of fine-scale materials moregenerally (49, 50).

As for fiber-reinforced metals, recent engineering progress has been in large part drivenby 3M’s innovations in high-quality ceramic fibers suitable for the reinforcement of metals.Work during the past decade has notably introduced a continuous wire of aluminum rein-forced by Nextel 610TM alumina fibers designed for the overhead transmission of electrical


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200 μm

Figure 6Multilayered steel composite combining strongly bonded sheets of austenitic SS304 (0.04C-0.53Si-0.92Mn-8.07Ni-18.19Cr; lighter phase in the micrograph) and martensitic SS420J2 (0.34C-0.49Si-0.57Mn-0.12Ni-13.21Cr) steel. The composite is produced by stacking 25 layers of 1-mm-thick surface-ground steel sheets,sealing the stack by welding, preheating in inert gas, and hot rolling to a final thickness of approximately 3mm. After annealing and air cooling, the laminate is further thinned by cold rolling to a thickness of 1.0 mm.This particular composite exhibits a yield stress of 450 MPa, an ultimate tensile strength of 1250 MPa, and20% elongation at fracture. Micrograph kindly provided by S. Nambu and T. Koseki of the University ofTokyo, Japan (48).

power (shown in Figure 8) (http://solutions.3m.com/wps/portal/3M/en_US/Energy-Advanced/Materials/Industry_Solutions/MMC/).

The past decade has seen progress in our understanding of the fundamentals that underlieMMC processing. Noteworthy are advances in our understanding of in situ processes (18), of thewetting of ceramics by metals (good overviews of this topic can be found in References 51 and52), of transport phenomena that intervene in processes such as infiltration (53, 54), and of thelink between deformation processing and particle clustering in solid-state MMC processing (seenext section).

Finally, we have seen impressive and far-reaching advances in microstructural characterization.These developments have proven particularly well suited for MMCs because of the high contrast(both physical and mechanical) that can exist between phases in these materials. Advances in X-rayand neutron diffraction characterization of materials have thus largely benefited MMC research(55, 56), as has the advent of methods for the characterization of material microstructures inthree dimensions, including computed X-ray microtomography (Figures 4 and 9) (30, 57–59)and automated serial sectioning (Figure 10) (60).

MECHANISMS OF DEFORMATION AND FRACTURE

From the structural viewpoint, a main limitation to the industrial application of MMCs has beenthe embrittlement associated with the addition, to the metal, of brittle ceramic reinforcements. Thephysical phenomena that control this behavior occur at the micrometer scale and above in MMCs.


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+5.000e+02+4.167e+02+3.333e+02+2.500e+02+1.667e+02+8.333e+01+1.526e–05–8.333e+01–1.667e+02–2.500e+02–3.333e+02–4.167e+02–5.000e+02

Maximum princi-pal stress (MPa)

+2.000e+02+1.833e+02+1.667e+02+1.500e+02+1.333e+02+1.167e+02+1.000e+02+8.333e+01+6.667e+01+5.000e+01+3.333e+01+1.667e+01+0.000e+00

S22 (MPa)

Multilayers/Si interface

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Figure 7(a) Nanolayered composite of aluminum and SiC produced by magnetron sputtering onto a silicon substrate,tested by nanoindentation. The nominal thickness of each of the alternating Al and SiC layers is 50 nm. TheAl layers are polycrystalline with a columnar grain structure, and the SiC material is amorphous. The pictureon the left shows a scanning electron microscope image of a cross section of the postindented compositeprepared by the focused ion beam technique. A part of the Berkovich indentation mark behind the sectionedsurface is visible. One can see that a symmetric pattern of damage was caused by the indentation, comprisingshear fracture of (1) the SiC layers and (2) mid-level voids. Further below, cracking near the multilayers/substrate interface has also occurred. (b) The color contour plots show the results from a finite elementanalysis of nanoindentation on the multilayered structure. The model features axial symmetry about the leftvertical boundary. The material system is identical to that used in the experiment. The left figure shows thedistribution of normal stress along the vertical (indentation) direction. Directly underneath the indentation,the stress field is predominately compressive. The contour legend was adjusted to bring out the fact thatthere is a region, below and slightly outside the indentation edge, that is under significant tensile stress. Thisregion largely corresponds to the damage zone observed in the experiment as highlighted. The right contourplot of maximum principal stress further indicates a particularly highly stressed region near the interfacebetween the Al/SiC multilayers and the Si substrate, which can also explain the observation of interfacecracks. Adapted from figure kindly provided by N. Chawla of Arizona State University, Tempe, Arizona, andY.L. Shen of the University of New Mexico, Albuquerque, New Mexico (50).


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3M™ aluminum fiber core

Figure 83M’s unidirectional Nextel 610TM nanocrystalline alumina fiber–reinforced pure-aluminum composite has,along the fiber direction, roughly one-third the conductivity of copper in combination with a tensile strengthof roughly 1.5 GPa and a density near 3 g cm−3 (http://solutions.3m.com/wps/portal/3M/en_US/Energy-Advanced/Materials/Industry_Solutions/MMC/). When used instead of steel as thehigh-strength core of electrical power transmission cables (inset), the composite provides an attractivesolution to power transmission, for example, in environmentally sensitive river crossings such as thatdepicted in this figure. The composite features low sag and improved conductance and allows new towerconstruction to be avoided while boosting transmission capacity. Photographs courtesy of 3M CorporateCommunications, St. Paul, Minnesota.

DD: discretedislocation

FE: finite element

As mentioned above, these phenomena can now be observed and quantified accurately usingnovel three-dimensional microstructural characterization techniques. In addition, deformationand failure processes within MMCs can now be simulated using several novel tools and methods,including discrete dislocation (DD) dynamics, large-scale finite element (FE) simulation, andnonlinear homogenization theory. Driven by this combination of strong engineering motivationand novel methods, research on the nonlinear deformation and fracture of MMCs has led tosignificant advances in this general area during the past decade.

Particle-Reinforced Composites

The dispersion of stiff ceramic particles or fibers within a ductile metallic matrix leads to an in-crease in flow stress of the metal by load transfer across a strong interface from the matrix to thereinforcement. Constraint imposed by the ceramic reinforcements on matrix plastic deformationinduces large tensile hydrostatic stresses in the matrix. This enhances the load carried by the rein-forcements and hence the composite flow stress but also triggers the early development of internaldamage in the form of particle fracture, interface decohesion, and/or matrix void growth (61–64).


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0.3 mm

Pure-aluminum matrix Harder aluminum alloy matrix

Lower strainlevel

Higher strainlevel

Figure 9X-ray microtomographic in-situ observation of the evolution of damage at different strain levels in a modelcomposite material made of aluminum-based matrices reinforced with 4 vol% of ZrO2/SiO2. The figureshows tomographic slices extracted parallel to the tensile axis (vertical), at various levels of stress, increasingfrom top to bottom. (Left column) Damage in the model composite material made of a pure-aluminum matrixis mainly by decohesion along the particle/matrix interface. (Right column) The same material as in the leftcolumn, but with a harder aluminum alloy matrix. The damage mechanism changes to particle fracture. Inboth cases, initiation, growth, and coalescence of damage can be captured. Images kindly provided byE. Maire and V. Carmona, MATEIS Laboratory, INSA Lyon, France (57).


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Figure 10Three-dimensional finite element model corresponding to a region 200 × 140 × 60 μm wide based on theactual microstructure of a composite of 6061 reinforced by 27 vol% SiC particles. The model containsapproximately 1000 SiC particles. The three-dimensional microstructure of this powder metallurgy–processed material was generated via automated (robotic) serial sectioning and optical imaging, using theRobo-Met.3DTM device (60). The red feature is an extended region of higher-than-average equivalentplastic strain generated by applying a 2.5% tensile strain parallel to the long dimension, showing that themacroscopic deformation band is modified by the presence of the local heterogeneities in the spatialarrangements of the particles. Image kindly provided by J. Spowart of the Air Force Research Laboratory,Wright-Patterson Air Force Base, Ohio.

RVE: representativevolume element

The challenge to find how the microstructure of these materials can be tailored to improve theirductility and toughness has been addressed through a combination of simulation and experiment.

Realistic quantitative predictions of the mechanical response of particle-reinforced compos-ites can be obtained via computational micromechanics. The composite behavior is analyzedthrough the FE simulation of a three-dimensional representative volume element (RVE) of themicrostructure. The RVE size has to exceed a critical value to ensure that the simulation resultsare independent of both the RVE size and the spatial distribution of the reinforcements withinthe RVE. This strategy has been widely used to explore the effect of reinforcement volume frac-tion, spatial distribution, and shape on deformation and damage mechanisms of such composites(65–72). This approach is illustrated in Figure 11a, which shows a cubic RVE containing a non-homogeneous distribution of ceramic spheres dispersed in an aluminum matrix. Upon tensiledeformation, the ceramic particles constrain matrix plastic deformation within the cluster, whichincreases hydrostatic stresses in both the matrix and the particles (Figure 11b). These large stressesin turn promote interface decohesion (Figure 11c) as well as particle fracture (66) and/or matrixductile failure by void growth (67).

Such damage mechanisms reduce the strain hardening capacity of the material. This reductionin turn precipitates the onset of plastic instability, which often controls the tensile ductility ofthese materials (73, 74), to low strain values (<4%). Numerical predictions of the effect of particleclustering on the tensile properties of these materials have been corroborated by experimentalresults, which show significant improvements in ductility if the particle distribution is homoge-nized through friction stir processing, high-pressure torsion, or equal-channel angular pressing(44–47). In addition, techniques such as automated serial section and X-ray microtomographyprovide detailed information on the relationship between the nucleation or growth of damage andspecific features of the three-dimensional microstructure (57–60, 75–79). In particular, the wholeprocess of damage nucleation by either particle fracture or interface decohesion, followed by void


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a b

GPa

1.00.80.60.40.20.0

c

Figure 11Three-dimensional finite element simulation of the effect of particle clustering on the deformation anddamage micromechanisms in a model composite made of 15 vol% of ceramics spheres embedded in analuminum matrix (71). (a) Sphere spatial distribution within the cubic representative volume element (RVE)of the microstructure. Notice that the microstructure is periodic and that spheres are truncated where theyintersect the cube faces and reappear on the opposite sides of the cube. The spheres are grouped in clustershaving a higher local volume fraction of reinforcements (one of these is highlighted in dark blue). (b) Contourplot of the maximum principal stress in the ceramic particles when the composite has been subjected to atensile strain of 5%. Very large tensile stresses develop in particles within the clusters. (c) Development ofdamage by interface decohesion (marked with black arrows on a two-dimensional cut through a large RVE).Decohesion is localized between particles situated very close to each other within the clusters and orientedalong the loading direction. Interfacial fracture relieved large stress concentrations generated at the interfaceby this particle spatial distribution. The blue arrows in panels b and c indicate the direction of tensile loading.From research at the Polytechnic University of Madrid, Spain, by J. Segurado, C. Gonzalez, and J. Llorca.

growth and coalescence through the matrix, can now be followed directly within the material(see Figure 9).

These advances in experimental characterization have been accompanied by new developmentsin linear and nonlinear homogenization models. Linear homogenization is a proven methodologyto determine the effective properties of composite materials as a function of the phase propertiesand their spatial distribution. For instance, accurate approximations to the elastic constants of


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particle-reinforced isotropic composites were obtained by Torquato (80) by truncating after third-order terms an exact expansion series for the effective stiffness tensor, the first few terms ofthe series being given as a function of statistical correlation parameters that describe the phasearrangement (81). Extension to the plastic regime was not, however, immediate, and the accuracyof the predictions was limited by the localization of strain during plastic deformation and by thelimitations of the incremental methods (either tangent or secant) used to linearize the nonlinearproblem (82–84). Large stress and strain gradients develop during the elastoplastic deformationof composites, especially with elastic particles embedded in a soft matrix. The plastic behavior ofthe matrix is determined by a reference equivalent stress computed in the classic homogenizationmodels from the volumetric average of the matrix stress tensor. The appropriate equivalent stressis, however, significantly lower than the phase average of the equivalent stress, and hence thecomposite yield and flow stresses are overestimated using the classic homogenization approach.This problem has since been overcome by the so-called modified secant approximation, shown tobe equivalent to a variational estimate by Ponte Castaneda (85, 86) and amenable to simplificationinto relatively user-friendly expressions (87). In this approach, the reference equivalent stressin the matrix is determined from the volumetric average of the second-order moment of thestress tensor in this phase instead of the usual first-order moment (or average), an approximationthat takes into account the effect of the field fluctuations (strain localization). The accuracy ofthis new homogenization model was demonstrated by comparisons with quasi-exact numericalresults obtained through computational micromechanics (88, 89), and new versions of the tangentapproach also yielded good results (90, 91) (Figure 12).

These nonlinear homogenization approaches have served to develop physically based phe-nomenological models that include the effect of damage nucleation and growth (by either particlefracture or interface decohesion), addressing damage percolation as well (83, 92, 93, 96). These

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Figure 12Predicted stress-strain curve for an aluminum matrix composite reinforced with 25 vol% stiff ceramicparticles. (a) Tensile ( purple) and shear ( green) deformation of a composite reinforced with sphericalparticles. (b) Tensile deformation parallel (black) and perpendicular (blue) to the ellipsoidal reinforcements ina composite with aligned ellipsoidal reinforcements with an aspect ratio of 3. The solid circles correspond toquasi-exact numerical results obtained from computational micromechanics by averaging the resultsobtained in 12 different particle realizations. The continuous lines denote the homogenization resultsprovided by improved secant (spheres) and incremental (ellipsoids) methods (89, 91).


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models can be divided in two groups. The first is applicable to composites having a low particlevolume fraction (<30%) or having soft and ductile matrices, whose tensile ductility is controlledby the onset of plastic instability. In these composites the Considere criterion predicts the tensilefailure strain well. Simulations of the tensile deformation of such composites take into accountthe progressive reduction of the composite strain hardening rate due to damage and include theeffect of stress redistribution among the particles due to damage, using hypotheses consistent withhomogenization approaches that support the model (22, 73, 74, 83, 92–94). A different case isthat of composites with high particle volume fraction (≥40%) and hard matrices: Fracture is thenoften triggered before the onset of plastic instability by an abrupt percolation of damage across thematerial. This phenomenon starts from a cluster of broken particles, which grows unstably abovea certain stress. Treating both of these failure modes leads to the prediction of a ductile-to-brittle

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transition in tensile failure mode as the reinforcement volume fraction and/or the matrix strengthincrease, which has been reported experimentally (24, 93, 95) and is captured by a recent model(96).

The analyses presented above predict an effect of the particle size on the tensile strength andthe ductility because smaller particles tend to be stronger. This in turn diminishes the extentof particle fracture during composite deformation and increases the hardening rate in tension.Prior to the onset of particle fracture, however, for a given elastoplastic matrix, predictions ofthe composite initial flow stress and hardening rate are insensitive to particle size, if all else isconstant. These predictions differ from experimental findings (97–100), which show an increasein the yield stress and hardening rate as the particle size decreases, particularly for interparticledistances below 10 μm.

This plasticity size effect has been rationalized in terms of the strain gradients that appearin the matrix as a result of deformation incompatibility between the plastic matrix and the stiffceramic particles. For a given geometry of plastic flow, finer microstructures (shorter interparticlespacing) lead to greater strain gradients in the matrix, both during composite deformation and,before this, due to differential matrix/reinforcement thermal contraction during cooldown fromprocessing temperatures. Higher gradients in turn produce a greater density of geometricallynecessary dislocations, which harden the metal. The effect has been known for some time (100);however, its analysis has progressed significantly in recent years. Detailed models of the effect ofinterparticle distance of the flow stress of composites have been carried out using DD simulations(101–103). Figure 13 gives results from a fully three-dimensional coupled DD-FE simulationof dislocation flow between narrowly spaced parallel ceramic fibers. The increase in flow stressand work hardening rate as the interparticle distance decreases essentially takes, in the fine-scalestructures of this simulation, the form of a classical Orowan bowing mechanism. In addition,the accumulation of dislocations at the particle interface during plastic flow creates an internalstress larger than the resolved applied stress and of opposite sign near the interface, reducing theeffective interparticle distance for matrix plastic flow from d to deff (Figure 13c). This phenomenoncauses further hardening by what is, in effect, a source-shortening mechanism. In recent years

←−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−Figure 13Coupled dislocation dynamics–finite element (DD-FE) simulations of the effect of interparticle distance onthe flow stress of a continuously reinforced Al-Al2O3 composite deformed perpendicularly to the fibers.(a) Simulated dislocation microstructure projected on the (001) plane of the aluminum matrix, which isperpendicular to the axis of the fibers. The volume fraction of fibers is 45%. Longitudinal strain ε33 =0.16% applied along the vertical direction in the figure ([010] direction for the aluminum). Note theaccumulation of dislocations at the interfaces and in the channels with smallest width. (b) Size effect intransverse stress-strain curves for different reinforcement volume fractions (5%, 10%, and 45%); straining isalong the same direction as in panel a. The elementary simulation cells have the same size and contain thesame initial dislocation density. The solid red lines show the size effect predicted by the coupled discrete-continuum model. The dashed blue lines represent continuum FE predictions using, for the aluminummatrix, a stress-strain response fitted to a coupled DD-FE simulation of the single crystal. (c) Resolved shearstress profile (τ , normalized by the shear modulus of aluminum, μAl) across the aluminum matrix in thecomposite with the highest reinforcement volume fraction (45%) and the smallest spacing between fibers (inunits of x/b, where b is the Burgers vector) for the most active slip system in the matrix. The deformationconditions are the same as in panel a. The dashed black line is a profile extracted from simulation data, andthe solid black line is the corresponding regression curve. The accumulation of dislocations at the interfacesinduces a resistive internal stress larger than the resolved applied stress, which reduces the channel width d toan effective value deff . Figure kindly provided by L. Kubin of the CNRS-ONERA, Chatillon, France, andadapted with permission from Elsevier Science; full publication of this work is in Reference 102.


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Figure 14Two-dimensional finite element simulation of crack growth in a microstructure produced on the basis of micrographs of a SiCparticle–reinforced aluminum composite. (a) Color contours of the stress state in a two-dimensional image of a microstructure (toppanel: without particle fracture; bottom panel: with particle fracture). Several particles have cracked away from the crack tip. (b) Thepredicted crack profiles. As has been observed experimentally, when the particles crack, the crack profile is quite linear, with the crackpropagating through the particles. When the particles do not crack, crack deflection is more pronounced. The bottom plot of panel bshows the local stress intensity factor calculated at various points in the microstructure. This is plotted as a ratio of the mode I stressintensity for the actual microstructure, kI(AlSiC), normalized by that of a homogeneous model with circular particles (with the cracknot interacting with the particles), kI(cp). Thus, a value of less than 1 indicates crack shielding (a decrease in the driving force for crackgrowth), whereas a value greater than 1 indicates antishielding (an increase in the driving force for crack growth). Drawn from figurekindly provided by N. Chawla of Arizona State University, Tempe, Arizona (108).

investigators have tackled plasticity size effects, using approaches based on higher-order continuummicromechanics formulations incorporating one or more length scales to account for the role ofstrain gradients or compliant interfaces on the matrix flow behavior (104, 105).

Fracture mechanisms have also been the subject of continued investigation. The influence ofthe particle distribution has been quantified and modeled in three dimensions, showing a stronginfluence on damage accumulation within these materials (Figure 10) (60, 106, 107). Micromech-anisms governing the fracture toughness of these materials have also received attention in recentyears in simulation (Figure 14) (108) and also in experiment, where progress has notably beendriven by the advent of quantitative fractographic analysis tools (109, 110). High fracture tough-nesses have been demonstrated in gas-infiltrated Al-Al2O3 composites containing a high volumefraction (approximately 50%) of ceramic particles. When reinforced with strong polygonal Al2O3

particles, these composites present strength/toughness combinations that rival those of engineer-ing aluminum alloys. The surprisingly high toughness of these composites comes about by thesynergistic contribution to the fracture energy of several factors, namely, the increase in elasticmodulus (which is 2.5 times that of the unreinforced alloy), the formation of a large plastic zonearound the crack tip, and high bridging stresses between crack surfaces carried by the metal liga-ments as a result of the small interparticle distance and high local stress triaxiality (23–25, 110, 111).


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GLS: global loadsharing

LLS: local loadsharing

SCF: stressconcentration factor

Finally, current interest in Cu-C composites as heat sinks in microelectronics has led to newanalytical and numerical models to predict their thermal conductivity. New developments includethe influence of the polyhedral reinforcement geometry and spatial distribution as well as theinfluence of the crystalline orientation and of the electron/phonon interfacial conduction barrier(112–114).

Fiber-Reinforced Composites

In continuous parallel fiber-reinforced composites, progressive fiber fracture controls the longi-tudinal tensile strength. Two extreme situations can be found. Under global load sharing (GLS)conditions, the effect of the local stress concentration around the broken fibers is negligible: Loadshed by fractured fibers is redistributed equally among the intact fibers in the remaining cross-sectional area of the composite at that location. The stress-strain curve then exhibits a smoothmaximum, which arises from the competition between (a) hardening induced by matrix and fiberdeformation and (b) softening caused by fiber fragmentation. Under these assumptions, elegantanalytical solutions (115–118) and numerical models (119) have been developed to predict thecomposite strength, accounting for matrix/fiber load transfer and fiber fracture statistics.

GLS, however, represents an idealization because it ignores damage localization. Evidence ofdamage localization in MMCs is provided by in situ monitoring of damage using X-ray synchrotronradiation in a Ti/SiC composite tested in tension (120): Fiber fracture is localized near the fracturesurface, whereas most of the sample remains free of damage. In addition, GLS predicts failurewhen the tangent modulus reaches zero and does not account for size effects; both predictions areopposed to available experimental results in most fiber-reinforced MMCs (121–123).

Experimental evidence indicates that local stress concentrations around broken fibers tend tolocalize damage, leading to fracture at lower strengths by the unstable expansion of a cluster ofbroken reinforcements (120–123). This behavior can be captured by local load sharing (LLS)models, which rely on a stress concentration function (SCF) describing the redistribution ofload around a broken fiber, which governs the neighboring fiber fracture probability (124–127).Although elegant solution approaches exist, LLS models tend to be more complex and often relyon numerical simulations to compute the composite strength. Model predictions are sensitive tothe precise values of the SCF, which in turn depends on the actual fiber arrangement as well asthe interface and matrix properties. Accurate values for the SCF were obtained in specific MMCsystems using detailed FE simulations of the stress field around a broken fiber. These findingswere in turn used in rigorous experimental validations of LLS predictors of MMC strength (122,124, 128, 129).

From the modeling viewpoint, a more complex problem is to determine the strength of fiber-reinforced MMCs in the presence of a hole or a sharp notch. Two main failure mechanisms havebeen reported, depending on matrix and interface properties and on thermal residual stresses(130–132). With a ductile matrix having a high flow stress and good fiber/matrix bonding, failuretakes place by the propagation of a mode I crack from the notch root perpendicular to the fibersat moderate toughness levels. Composites with a weak, brittle matrix and/or a poor fiber/matrixbond exhibit a strong tendency toward mode II crack propagation along the fiber direction. Suchsplitting initiates and propagates at relatively high values of the applied stress intensity factor,leading to a low notch sensitivity for this class of composites.

Simulation of the behavior of notched specimens was initially carried out for SiCmonofilament–reinforced titanium within the framework of cohesive crack models, as matrixplastic deformation is localized in a thin strip in front of the notch. There, fibers fracture andare eventually pulled out from the matrix (131, 132). More recently, novel multiscale simulation


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Figure 15Multiscale modeling of fracture in SiC fiber–reinforced Ti.6A-4V matrix composites. (a) Schematic of the three-point bend testcomprising a notched beam showing the central region of length h used in the numerical simulations, together with the detailedmicrostructure in the central region of the notched beam ( planar view and lateral view). Matrix, fibers, and homogenized material areshown in different shades of gray. (b) Comparison of simulated and experimental P-CMOD (load–crack mouth opening displacement)curves for the notched beam tested at 20◦C. The initial notch length a0 was given by a0/D = 0.35, where D = beam height. The loadP on the ordinate of the plot was normalized by the beam dimensions (L = beam length between outer load application points, B =beam width, and D = beam height). (c) Contour plot of the accumulated plastic strain in the matrix at maximum load in the compositebeam tested at 20◦C. The black line shows the initial notch tip. (d) Idem for the longitudinal stress in the fibers. From research at thePolytechnic University of Madrid and IMDEA-Materials by C. Gonzalez & J. Llorca (135).


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strategies based on embedded cell models in three dimensions were used to predict the toughnessand notch sensitivity of fiber-reinforced MMCs (133). The representation of the material in frontof the notch tip—where damage is concentrated-–includes the actual fiber/matrix topology inthe composite, whereas the rest of the solid is modeled as a linear thermoelastic, transversallyisotropic homogeneous solid (Figure 15a). Damage and fracture micromechanisms that controlfracture (namely, plastic deformation of the matrix, brittle fiber fracture, and fiber/matrix fric-tional sliding) are all included in the simulation. Fiber fracture is modeled by introducing interfaceelements randomly placed along the fibers and with random strengths to simulate fiber fracturerealistically. It is assumed that the interface strength is negligible and that the fiber/matrix in-teraction is controlled by friction. Micromechanical parameters governing the behavior of fibers,matrix, and interfaces are independently measured. The mechanical response of the test beams inthree-point bending is then computed using the FE method, leading to results that are in goodagreement with experimental data, at both the microscopic level and the macroscopic level andfrom room temperature up to 400◦C (Figure 15b,c) (134, 135). These results demonstrate the po-tential of coupled multiscale three-dimensional simulation for predicting the fracture behavior ofMMCs.

Other than fiber-reinforced titanium composites, recent research has addressed alumina fiber–reinforced aluminium. Damage micromechanisms in tension (136) and fatigue (137), matrix hard-ening mechanisms (138), and the properties of complex composite architectures (139, 140) havebeen investigated.

CONCLUSION

Thus, a highly diverse picture of MMCs emerges from this brief overview of current researchon this materials class. First, the materials are more numerous than was the case ten years ago(although the same probably cannot be said of processes). Second, the toolkit available to the ma-terials scientist for the elucidation of structure/property relations in these interesting high-phasecontrast materials has expanded significantly in both experimental and analytical tools togetherwith underlying theory. Third, the range of explored properties has also expanded to include, forexample, a greater focus on thermal conductivity, a property for which MMCs are now amongthe top-performing bulk materials.

We expect this trend toward breadth and diversity to continue. Many new, interesting materialsare bound to be composites that combine a metal with another phase. As one example, MMCs,full of metal/dielectric interfaces as these materials are, may one day enter the field of opticalmaterials research. PCMs, mentioned above, are another class of emerging materials likely to becomposites with a metallic matrix. MMCs are a class of materials with a rich, albeit complicated,future.

SUMMARY POINTS

1. MMC research has branched into many new directions, and the range of materials itencompasses has expanded significantly.

2. Several new classes of MMCs have gained importance and have been studied in detailin the past ten years, including interpenetrating phase composites, biomorphic ceramic-reinforced metals, bulk metallic glass composites, nanoscale composites, layered metals,and microcellular metals.


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3. Research on MMCs for structural applications has progressed along two main direc-tions: (a) the exploration of new composites expanding the property range of MMCs and(b) the elucidation of structure/property relations in particulate and fiber MMCs.

4. Research on MMCs for functional applications has seen significant progress on materialsdesigned for thermal management.

5. MMC research has been, and remains, an important vehicle in nonlinear micromechanicsand three-dimensional microstructural characterization.

6. Our understanding of damage and fracture mechanisms in ceramic-reinforced metals,both fibrous and particulate, now enables the accurate prediction of their performanceand the definition of strategies for their optimization.

7. The potential offered by strong ceramic particles for the reinforcement of metals is veryhigh and remains untapped.

FUTURE ISSUES

1. With an increased drive toward energy saving, research on MMCs for structural appli-cations will surely gain new momentum, given the weight savings these materials offerin several critical applications. The accuracy of the modeling tools in establishing theconnection between microstructure and properties will be very useful in developing newmaterials with optimal properties.

2. For the same reason, many new composites combining a metal with another phase, oftenone of ceramic, will likely emerge for applications in the management, storage, andgeneration of energy as well as in novel functional applications.

3. A revitalization of research on the fundamentals of MMC processing, over and above theinvention of new systems, would be opportune.

DISCLOSURE STATEMENT

The authors are not aware of any affiliations, memberships, funding, or financial holdings thatmight be perceived as affecting the objectivity of this review.

ACKNOWLEDGMENTS

A.M. gratefully acknowledges support of his research on the subject at EPFL from core laboratoryfunding and from the Swiss National Science Foundation (project number 200020-107556), atMIT from the Office of Naval Research and the U.S. National Science Foundation, and in bothinstitutions from several industrial sponsors. J.L. acknowledges support from the Comunidadde Madrid (program ESTRUMAT), the Spanish Ministry of Science and Innovation (projectMAT2009-14396), and several industrial sponsors.


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