Barsoum Encyclopedia of Materials 1-16-2004

8/9/2019 Barsoum Encyclopedia of Materials 1-16-2004

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Mechanical Properties of the MAX Phases

By now it is fairly well established that the layeredternary carbides and nitrides with the general formulaMn1AXn (MAX), where n 1, 2, or 3, M is an earlytransition metal, A is an A-group element (mostly IIIAand IVA), and X is either C or N, represent a new classof solids (Barsoum 2000, Barsoum and El-Raghy2001a). These phases are layered with Mn1Xn layersinterleaved with layers comprised of pure hexagonalnets of the A-group element. The Mn1AXn unitcellsspace group P63/mmchave two formula unitsper unit cell. There are roughly 50 M2AX phases(Nowotny 1970); three M3AX2 (Ti3SiC2 (Jeitschko andNowotny 1967), Ti3GeC2 (Wolfsgruber et al. 1967),and Ti3AlC2 (Pietzka and Schuster 1994)), and oneM4AX3 namely, Ti3AlN4 (Barsoum et al. 1999a, Rawnet al. 2000). Mainly as a result of the way they deform(Fig. 1), they have been labeled polycrystalline nano-laminates (Barsoum et al. 1997).

The Mn1AXn phases combine an unusual, andsometimes unique, combination of properties (Bar-soum 2000). Like their corresponding binary carbidesand nitrides, they are elastically stiff, have relativelylow thermal expansion coefficients, good thermal andelectrical conductivities, and are resistant to chemicalattack. As this entry will show, however, mechani-cally they cannot be more different: they are relativelysoft (15 GPa) and most readily machinable, thermalshock resistant, and damage tolerant. Moreover,some are fatigue and creep, and oxidation resistant.At higher temperatures, they go through a ductile-to-brittle transition. At room temperature, they can be

compressed to stresses as high as 1 GPa and fullyrecover upon removal of the load, while dissipating25% of mechanical energy (Barsoum et al. 2003).

This entry summarizes our current understandingof the mechanical properties of the Mn1AXn phases,with emphasis on Ti3SiC2, which is the most studiedand best understood to date. However, based onlimited results on other phases there is little doubtthat what applies to Ti3SiC2 applies to the otherMn1AXn phases as well. A more complete review oftheir atomic structure and physical properties such aselastic moduli, electrical and thermal properties, etc.,appears in the article Physical and Chemical Proper-

ties of the MAX Phases.To understand the response of the Mn1AXn

phases to stress, it is imperative to understand thenature of their dislocations and concomitant slipsystems.

1. Atomistics of Deformation

1.1 Dislocation and Defects in the Mn1AXn Phases

The key to understanding the mechanical propertiesof the Mn1AXn phases is the fact that only basal

plane dislocations exist. These dislocations are mobileand multiply, even at temperatures as low as 77 K.Transmission electron microscopy (TEM) (Farberet al. 1998, Barsoum et al. 1999b) and high-resolutiontransmission electron microscopy (HRTEM) (Farberet al. 1998, 1999) studies of Ti3SiC2 revealed thepresence of only perfect dislocations lying in the basalplanes with a Burgers vector b 1

311%20

or 1.54 (Ain length. Every dislocation is of a mixed nature withan edge and screw component (Farber et al. 1999,Kooi et al. 2003).

Because they are confined to the basal planes, thedislocations arrange themselves either in arrays (pile-ups) on the same basal planes (Fig. 2(a)), or in walls(low- and high-angle grain boundaries) normal to thebasal planes (Fig. 2(a)). The walls have both tilt andtwist components (Farber et al. 1999, Kooi et al. 2003).

Figure 1Typical examples of the nanolaminated nature of theMAX phases. SEM micrographs of: (a) a Ti3SiC2surface scribed with a sharp point and (b) typicalkinking and delaminations observed on fracturedsurfaces of Ti3SiC2.

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Encyclopedia of Materials Science and Technology, Eds. Buschow, Cahn, Flemings, Kramer,

Mahajan and Veyssiere, Elsevier Science 2004.


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To account for both, the boundary was interpreted tobe composed of parallel, alternating, mixed perfectdislocations with two different Burgers vectors lyingin the basal plane at an angle of 1201 relative to oneanother. The boundary twist was provided for byhaving an excess of one type of dislocation (Farberet al. 1999, Kooi et al. 2003).

Dislocation interactions, other than orthogonal(Fig. 2(a)), are very unlikely to occur, and have notbeen reported to date. As discussed later this fact has

very far-reaching ramifications in that substantialdeformation can now occur without work hardeningin the classic sense. Given that nonbasal dislocationswould have Burgers vectors 4c (viz.41123 (A), theirpresence is highly unlikely. Furthermore, as a resultof their high c/a ratios, twinning is unlikely (Hessand Barrett 1949).

In addition to dislocations, stacking faults werealso observed (Farber et al. 1998). The stacking faultsare typically growth defects where locally an Si planeis missing and the stacking twin symmetry brokensuch that thin lamella with an Mn1Xn chemistryremain with identical stacking as [111] in the rock saltstructure (Yu et al. 2003, Kooi et al. 2003). Allstacking faults and their bounding dislocations alsolie in basal planes with their displacement vectorsparallel to [0001] (Faber et al. 1998, Yu et al. 2003).Grain boundaries are another planar defect present inpolycrystalline samples, but their structure is stilllargely an open question.

1.2 Deformation Mechanisms

The key mechanism without which the deformationof the Mn1AXn phases cannot be understood is the

formation of kink bands (KBs). It is thereforeimportant to briefly review what is known aboutKBs. KBs in crystalline solids were first observed inZn single crystals loaded parallel to their basal planes(Orowan 1942). Later, Hess and Barrett (1949)proposed a model to explain their formation by theregular glide of dislocations. Initially, upon loadingof a long, thin column of length L, elastic bendingcreates maximum shear stressesassuming perfectsymmetryat L/4 and 3L/4 (Fig. 2(b)). Above a

critical value this shear stress is sufficient to create,within the volume that is eventually to become theKB, a pair of dislocation walls of opposite signs thatmove in opposite directions (Fig. 2(c)). The end resultis two regions of severe lattice curvature, separatedfrom each other and from the unkinked crystal bywell-defined kink boundaries BC and DE (Fig. 2(d)).

Note that KBs are expected only in crystals that donot twin, such as hexagonal metals or alloys havingan axial c/a ratio greater than E1.73 (Hess andBarrett 1949). With c/a ratios that vary from 3 to 7, itis not surprising that Mn1AXn phases deform by thismechanism.

The Hess and Barrett model was qualitative; a fewyears later Frank and Stroh (1952) proposed a morequantitative model in which pairs of dislocations ofopposite sign nucleate and grow at the tip of a thinelliptical kink with dimensions, a and b, such thatacb (Fig. 3(a)). The precise mechanism responsiblefor nucleation of kinks has, to date not beenidentified. However, by assuming the local stressneeded to form a dislocation pair to beEG/30, whereG is the shear modulus, Frank and Stroh (1952)showed that at a critical kinking angle, gcE561, thedislocation walls will grow rapidly until they meet agrain boundary (interior grains) or surface (exterior

Figure 2Schematic of (a) dislocation walls (vertical) and arrays or pile-ups (horizontal) in the MAX phases. Both are confinedto the basal planes. The and signs denote the orientations of the screw dislocations in the wall (Farber et al.1998). (b) Elastic buckling and corresponding shear diagram, and (c) initiation of pairs of dislocations in areas ofmaximum shear. (d) KB and kink boundaries comprised of edge dislocations of one sign giving rise to the classic

stove-pipe shape.

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grains). In other words, the formation of an incipientkink band (IKB)like the growth of a crackisautocatalytic and sudden. The critical remote shearstress, tc, needed to convert a subcritical kink into anIKBi.e., render the former unstablewill dependon a, and is given by

tc %

ffiffiffiffiffiffiffiffiffiffiG2bg

a

r1

The most important ramification of Eqn. (1) is thatthe smaller the domain size a, or the volume availablefor the creation of an IKB, the larger the stressesrequired. Mechanistically, or phenomenologically,the response to stress of a grain in which an IKBforms is shown in Fig. 3(d); it will only kink when theapplied shear stress tki4tc is given by Eqn. (1). Onceit kinks, the domain or grain shrinks by a strain eki.

When the stress is reduced the friction associated withthe dislocation lines will ensure that the IKBdisappears at a stress tootc (Fig. 3(d)). Since tcdepends on a, finer-grained samples will form IKBs athigher stresses than coarse-grained samples. IKBs arethus the key microstructural hysteretic element.

In the Frank and Stroh analysis, it was assumedthat once an IKB nucleated it would immediatelyextend to a free surface, eliminating the mutualattraction and resulting in two parallel, mobilenoninteracting dislocation walls (i.e., Fig. 3(e)). It isthe repetition of this process that results in thegeneration of new dislocation walls whose coales-cence form the kink boundaries (Fig. 3(f)). The ideathat an IKB can reach a grain boundary and notdissociate (Fig. 3(b)) was not considered; as discussedbelow, it is crucial. At this juncture it is worth notingthat direct TEM evidence for the presence of parallel

Figure 3Schematic representation of: (a) thin elliptic cylinder with axes a and b and acb. The sides are comprised of twodislocation walls (shown in red) of opposite sign, and uniform spacing D. (b) Formation of an IKB in hard (red)grains adjacent to soft (blue) grains. The lines in the grains denote basal planes. At this stage it is fully reversible.(c) Three-dimensional representation of two pairs of dislocations in a wall, emphasizing the dislocation loop and howit can extend along the basal planes unimpeded. (d) Hysteretic element associated with IKBs based on Eqn. (1). Belowa certain stress, tk, that depends on grain size, the IKB is energetically unfavorable and does not nucleate. Upon

removing the load, friction associated with the dislocation lines ensures that the IKB will not collapse until a stresst0otk. (e) Multiple pile-ups and kink bands in a large grain. Dotted lines denote walls that have separated from thesource and are moving away from it. This only happens at higher temperatures and/or stresses. (f) Same as (d) afterremoval of stress, emphasizing formation of grain boundaries (dark lines). (g) Schematic of a delaminating grainshowing how a kink boundary can suppress further delamination.

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combination of KB formation at the corners of thetested cubes, delaminations within individual grains,and ultimately shear band formation (Fig. 4(b)).Note the KB visible on the bottom left-hand side ofthe cube in Fig. 4(b) did not result in the totaldelamination of the outermost grain in which it wasinitiated. This observation was taken to be the firstcompelling microstructural evidence that KBs are

potent suppressors of delamination (Barsoum andEl-Raghy 1999).

Polycrystalline samples of Ti3SiC2 subjected tocompressive loads and temperatures up to E900 1Cfail in a quasi-brittle manner by shearing, roughly at451 to the loading axis. Not all MAX phases failsuddenly; actually most exhibit graceful failurecharacteristics in that the stressstrain curves are

1 mm

Kink band

Shear band

Engineeringstress(M

Pa)

0 5 10 15

Engineering strain (%)

0

100

200

300

Compression

parallel to basal

planes(along z-

direction)

Compressionalong "easy"

x-direction

z

x

(a)

(b)

Figure 4(a) Engineering stressstrain curves of 2 mm cubes of highly oriented samples of Ti 3SiC2. Inset shows schematic ofcube and basal plane orientations. (b) Optical OM micrograph of polished and etched sample after deformation

parallel to the basal planes. Note kinking at corners. Inset shows a higher magnification view of lower left corneremphasizing the kink band and, as importantly, the genesis of the shear band that cuts across the cube face (Barsoumand El-Raghy 1999).

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closer to an inverted shallow V, than a sharp dropat a maximum stress (Barsoum et al. 2000, Tzenovand Barsoum 2000). The failure mode is still shearfailure across a plane, but presumably enoughligaments reach across the plane to result in a lesssudden loss in load bearing capability. This tendencyincreases with increasing grain size and reduced

loading rates.

2.2 IKBs and Kinking Nonlinear Elastic (KNE)Solids

The strongest evidence for the formation of IKBs isthe fully reversible nature of the deformationobserved when bulk Ti3SiC2 samples are loaded incompression (Barsoum et al . 2003) and recentnanoindentation results (Murugaiah et al . 2004).The room temperature stressstrain curves of macro-scopic polycrystalline cylinders of Ti3SiC2 outline

fully reversible, reproducible, closed loops whosesize, shape, and slopes depend on grain size, butnot strain rate (Fig. 5(a)). In this article, referencewill be made mostly to two different microstructures,fine- (35 mm) and coarse-grained (plate-like grains,50200 mm in diameter and 520 mm thick). Fine-grained (35 mm) samples can be compressed tostresses up to 1 GPa and fully recover upon theremoval of the load (inset in Fig. 5(a)). In one case, asample was cycled 100 times at 700 MPa, with noapparent difference between the first and last cycles(Barsoum et al. 2003).

The fully reversible deformation, its strong depen-

dence on grain size but not strain rate, the propen-sity of the MAX phases to form KBs, and the factthat the energy dissipated per cycle, Wd, increaseswith the square of the applied stress (Fig. 5(b))provide compelling, almost irrefutable, evidence forthe formation of IKBs (Barsoum et al . 2003).Assuming t in Eqn. (1) to be EG/1000 (for Ti3SiC2G 130 GPa), g 51, yields a value ofa ofE10 mm.It is thus not surprising that atE250 MPa, the elasticstrain contributions to the total strain of the FGsamples (with grains in the 35 mm range) is muchhigher than the corresponding values for the CGsamples in which large hexagonal plate-like grainswith diameters of 100300 mm andE10 mm thick areembedded in a fine-grained matrix (Fig. 5(a)). Inother words, the CG samples would rather formIKBs than elastically linearly deform.

The room temperature loss factors (Wd/2p) forTi3SiC2 are exceedingly high and are probably arecord for crystalline solids. They are several ordersof magnitude higher than those of other structuralceramics, higher than most woods, and comparableto polypropylene and nylon (Fig. 6). These highvalues (0.7 MJ m3 at 1 GPa) are consistent with asolid in which no work hardeningin the classicsenseis occurring. In other words, because the

dislocation lines are confined to the basal planes(Fig. 3(c)), they cannot entangle and thus can moveto and fro over distances that are significantly higherthan those in other solids. It is important to note herethat in contrast to most other crystalline solidswiththe notable exception of graphiteWd is propor-tional to s2 (Fig. 5(b)).

Recent nanoindentation work with a 13.5 mmspherical indenter (Murugaiah et al . 2004) onindividual Ti3SiC2 grains offers further compellingevidence that IKBs form at the grain level. Unlikethe nanoindentation response of crystalline materialsthat almost always results in plastic deformationand/or damage, Ti3SiC2 can be loaded up to stressesof E10 GPa, deform plastically and then recoverupon unloading to such an extent that the indenta-tions cannot be found. In that respect it is notunreasonable to think of the Mn1AXn phases asbehaving as dislocation-based elastomers, in thatthey can be loaded repeatedly, without damage,

and dissipate significant amounts of energy duringeach cycle.Here againbut this time because of the con-

fined nature of the deformation to much higherstressesthe loaddisplacement curves trace almostfully reversible loops that are a function of grainorientation. At low loads, fully reversible closedloops are obtained for the same reasons outlinedabove. At intermediate loads (10200 mN) thefirst loop is slightly open, but then all subsequentloops obtained from the same location taken to thesame stress are not only closed, but, as important,harder than the first (Fig. 7). The hardening observed

is key because it rules out microcracking. (Phasetransitions have not been observed and can beruled out.)

The simplest explanation for this observation isthat at sufficiently high ss the walls comprising theIKB split, become mobile and move away from thesource, accounting for the small plastic deformationrecorded during the first loadings. On subsequentloading the presence of these walls obviously hardensthe indented area. At high stresses, the mobiledislocation walls will create KBs that reduce a andthus increase the stress at which new IKBs form.Direct evidence for this grain refinement can befound in nanoindentation studies on single crystals ofgraphite (Barsoum et al. 2004a). The area under theindenter breaks up into submicron grains that arequite resistant to deformation. The same occurs inmica (Barsoum et al. 2004b).

When the nanoindentation results are convertedto stressstrain curves, Wd calculated and plottedon the same loglog plot as the bulk results, excel-lent agreement between the two sets of data isobtained (Fig. 5(b)). This clearly implies that thesame physics is occurring at the different lengthscales. Note here, because the deformation is con-fined, the values of Wd are of the order of 10 GJ m

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(Fig. 5(b)) and the expected Wd versus Es2 relation-

ship is valid over 6 orders of magnitude of Wd. Alsoplotted in Fig. 5(b) are results on graphite and mica,that, together with the MAX phases, and nonlinear

mesoscopic solids, NMEs (Guyer et al. 1995) layeredsilicates and oxides, belong to a much larger classof solidsKNE solidsthat deform by kinking(Barsoum et al. 2004b).

Figure 5

(a) Stressstrain curves for FG- and CG-grained Ti3SiC2. Dotted line is linear elastic response expected for Ti3SiC2had kinking not occurred. The loop labeled coarse-grained Ti3SiC2 represents three loading and unloading cycles thatdiffered from each other by a factor of 10 in loading and unloading rates. The reproducibility is noteworthy. Alsoincluded are the results on Al2O3 and Al for comparison. Inset shows successive loops obtained as the stress wasincreased up to 1 GPa. Note all loading curves are identical (Barsoum et al. 2003). (b) loglog Wd vs. s plot. Theresults in the lower left hand corner are for bulk samples; those in the upper right from nanoindentations (Murugaiahet al. 2004).

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The transformation of the IKB into two mobilewalls must be accompanied by the formation of a freesurface either at a grain boundary, or, much morelikely in this case, one that forms by delamina-tions. For graphite single crystals, it is the latter(Murugaiah et al. 2004). Note that direct TEMevidence for the formation of kink bands underBerkovich indenters has recently been published(Kooi et al. 2003, Molina-Aldareguia et al. 2003).

2.3 Hardness and Damage Tolerance

The Mn1AXn phases, unlike the MX carbides, arerelatively soft and exceedingly damage tolerant. The

hardness values of polycrystalline Mn1AXn phasesfall in the relatively narrow range of 15 GPa. Theyare thus softer than most structural ceramics, butharder than most metals (Barsoum 2000). The lowhardness persistsat least in Ti3SiC2 even attemperatures as low as 77 K (Kuroda et al. 2001).

Working with CVD single crystals, Nickl et al.(1972) were the first to note that the hardness ofTi3SiC2 was anisotropic and higher when loadedalong the c-direction. This was later confirmed byGoto and Hirai (1987), who also were the first toshow that the hardness was a function of indentationload. Both observations are characteristic of theMAX phases (Barsoum 2000). With decreasing load,the hardness increases (Fig. 8, top curve) and below a

Figure 6Ashby-map of loss factor defined as Wd/2p vs. Youngs modulus (Ashby 1989).

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certain load it is not measurable, since no trace of theindentations is found. These observations were notunderstood until the recent nanoindentation workin which the reversible nature of the IKBs waselucidated (see above).

Not surprisingly, given their plastic anisotropy, theresponse to nanoindentations is anisotropic; when

the basal planes are parallel to the surface, the extentof plastic deformation is higher than if the basalplanes are loaded edge-on (inset in Fig. 7) (Kooiet al. 2003, Murugaiah et al. 2004). In the formercase, it is easier to form KBs because the top sur-face is unconstrained (Kooi et al. 2003, Murugaiahet al. 2004).

The damage tolerance values of Ti3SiC2 (El-Raghyet al. 1997, 1999) and Ti3AlC2 (Tzenov and Barsoum2000) are best exemplified in Fig. 8 (bottom 3 curves)in which the functional dependencies of post-indenta-tion bend strengths are plotted versus Vickersindentation loads. Clearly, the post-indentation

flexural strengths of these ternaries are considerablyless dependent on the indentation loads than typicalbrittle ceramics (dashed line in Fig. 8). Similar toceramics, however, the damage tolerance of coarse-grained microstructures is superior to finer-grainedsamples.

Typically, Vickers indentations in brittle solidsresult in sharp cracks extending from corners ofthe indents that result in sharp reductions instrengths. As first reported by Pampuch et al. (1989,1993) it is difficult to induce cracks from the cornersof Vickers indentation in Ti3SiC2. Instead of theformation of cracks, delaminations, kinking of

individual grains, grain push-outs and pull-outs areobserved in the area around indentations (El-Raghyet al . 1997, Procopio et al . 2000, Tzenov andBarsoum 2000). In short, the main reason for thisdamage tolerance is the ability of the MAX phasesto contain and confine the extent of damage to asmall area around the indentations. The atomisticreasons for this state of affairs were discussed above(e.g., Fig. 3(g)).

The importance of such high damage tolerancecannot be overemphasized since it implies that theMn 1AXn phases are much more tolerant to proces-sing and service flaws, that are typically quitedetrimental to the mechanical properties of brittlesolids. This, in turn, should also greatly increasemanufacturing yields, since the need for full density isrelaxed.

2.4 Thermal Sock Resistance

Another characteristic feature of the MAX phases istheir excellent thermal shock resistances (Barsoumand El-Raghy 1996). The response of Ti3SiC2 tothermal shock depends on grain size (El-Raghy et al.1999); the post-quench flexural strengths of CG

Figure 7Typical load vs. depth-of-indentation response of aTi3SiC2 surface for which the basal planes were:perpendicular, or edge-on, to the surface. The loop areaassociated with the first indentation is larger thansubsequent indentations in the same location. Insetcompares first loops in both orientations; for the mostpart, the loop areas and depths of penetration are higherin the orientation for which the basal planes are parallelto the surface (Murugaiah et al. 2004).

Figure 8Vickers hardness versus indentation load (top curve):four-point flexural strength vs. indentation loadsfor fine- and coarse-grained Ti3SiC2 and Ti3AlC2with a E25 mm grain size. The inclined dashed line isexpected behavior for brittle solids (Tzenov andBarsoum 2000).

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samples are not a function of quench temperature andactually get slightly stronger when quenched from1400 1C (Fig. 9). The response of fine-grained Ti3SiC2samples is different; instead of exhibiting a criticalquenching temperature above which the strength isgreatly reduced as typical for ceramics, their post-quenching strengths gradually decrease over a 500 1Crange (Fig. 9). The same non-susceptibility to thermalshock is also exhibited by Ti3(SixGe1x)C2 solidsolutions (Ganguly et al. 2004). In one case, the

post-quench flexural strengths of a CG Ti3(Si0.5-Ge0.5)C2 sample were actually E20% higher thanthe as-sintered CG samples (not shown). The reasonsfor this quench hardening are not entirely clear at thistime, but are most probably related to the formationof smaller domains as a result of thermal residualstresses.

2.5 R-curve Behavior and Fatigue

Gilbert et al. (2000) reported on the fracture andcyclic fatigue crack growth behavior of Ti3SiC2. Boththe fine- and coarse-grained microstructures exhibitsubstantial R-curve behaviorwhere the stressneeded to extend a crack is a function of cracklengthat room temperature (Fig. 10(a)). The FGsamples initiated at a K1cE8 MPa m

1/2, rising toE9.5 MPa m1/2 after 1.5 mm of crack extension. TheCG samples exhibit substantially stronger R-curvebehavior, with crack growth initiation between8.5 MPa m

1/2and 11 MPa m

1/2, and peaking at

1416 MPa m1/2 after 2.74 mm crack extension(Fig. 10(a)). The latter value is believed to be one ofthe highest K1c values ever reported for monolithic,single-phase non-transforming ceramics.

Quench temperature (C)

Retainedflexuralstrength(MPa)

0

100

200

300

400

500

600

0 200 400 600 800 1000 1200 1400 1600

100200 m

35 m

Figure 9Thermal shock of Ti3SiC2 samples with two different

grain sizes.

Figure 10(a) Crack growth resistance, KR, plotted as a function ofcrack extension, Da, for both the fine- and coarse-grained Ti3SiC2 microstructures at ambient and elevatedtemperatures. The initial flaw size, a0, is indicated foreach measured R-curve. Note that KR drops above thebrittle-to-plastic transition temperature (Chen et al.2001). (b) Field-emission SEM image of a bridged crackin the coarse-grained Ti3SiC2 microstructure. Heavilydeformed lamella bridge the crack, and significantamounts of delamination and bending are observed.Such processes are highly unusual in ceramic systemsand must, at least partially, account for the extremelyhigh plateau K1Cs. Crack is growing from left to right(Gilbert et al. 2000).

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The cyclic fatigue study of coarse- and fine-grainedTi3SiC2 samples (Gilbert et al. 2000) confirmed a highdependence of cyclic fatigue crack growth rates,da/dN, on the applied stress intensity range, DK, thatis typical of ceramics. However, the fatigue crackgrowth thresholds, DKth, are comparatively higherthan those for typical ceramics and some metals

(e.g., 300 M alloy steel) tested under the sameconditions. The fatigue threshold of the CG samples(9 MPa m1/2) is one of the highest fatigue thresholdsever observed in monolithic, non-transforming cera-mics. For the FG structure, the fatigue thresholddrops to E6.5 MPa m1/2. With the increase of test-ing temperature, the fatigue thresholds for bothmicrostructures decrease slightly up to 1100 1C. At1200 1C which is above the brittle-to-plastic transition(BPT) (see below), the da/dN versus DK curves showthree distinctive regions that are more pronouncedfor the FG samples.

Evidence for elastic-ligaments bridging and fric-

tional pull-outs similar to those observed in otherstructural ceramics were found in all samples afterfracture toughness and cyclic-fatigue testing. How-ever, the excellent K1c and Kth values can be mostlyattributed to the unique KB induced lamellae(Fig. 10(b)) that serve as very tenacious crack bridges,somewhat reminiscent of wood.

3. High-temperature Response

All MAX phases tested to date go through a brittle toductile or BPT. The temperature of the transitionvaries from phase to phase, but for many Al-contain-

ing phases and Ti3SiC2, it is between 10001C and1100 1C. The fact that K1c drops above the BPTtemperature (Fig. 10(a)) (Chen et al. 2001) categori-cally rules out the activation of additional slip systems,which is why it is more accurate to label the transitionas a BPT transition, rather than the more commonductile-to-brittle transition. More details on the natureof this transition are discussed below.

3.1 Compressive Properties

Further compelling evidence for the KB-based modeldiscussed above can be found in the high-temperatureresponse of Ti3SiC2 to compressive cyclic loadings.Up to E900 1C, and consistent with the athermalmodel for the formation of IKBs, there is little changeto the shapes or areas of the stressstrain loops incompression (Barsoum et al. 2003). At temperatures41000 1C, however, the stressstrain loops are open(Fig. 11(a)) and the response becomes strongly strainrate dependent. Cyclic hardening at temperatures ashigh as 12001C has been observed for both FG(Fig. 11(a)) and CG samples; the effect on the latter,however, is more dramatic (Barsoum et al. 2003). Thehardening is manifested in two ways: First the areas

enclosed by the loops become smaller (Fig. 11(a)).Second, the initial slopes of the stressstrain curvesapproach the linear elastic limit as the number ofcycles increase (Fig. 11(a)). The latter clearly impliesthat the cycling results in microdomains that areharder to kink than the initial grains (i.e., reductionofa in Eqn. (1)).

Along the same lines, and for the same reasons,after cycling at high temperature the room tempera-ture response of the CG samples becomes comparableto those of the FG ones, and the latter approach thelinear elastic limit. Figure 11(b) plots room-tempera-ture stressstrain curves of a CG Ti3SiC2 samplebefore and after a 2% deformation at 1300 1C (insetin Fig. 11b). After deformation, the stress-strainloops are distinctly steeper (Zhen et al. 2004a). Asimportant, the first loop after deformation, traced inred in Fig. 11(b), is open, but subsequent ones (blue)are closed (Zhen et al. 2004a) The simplest interpreta-tion for these observations is that during the first cycle

the mobile dislocation walls (Fig. 3(e)) produced athigh temperature are swept into the kink boundaries,immobilizing them (Fig. 3(f)). On subsequent loadingonly IKBs are activated. From these results it isobvious that the deformation at high temperatureseffectively reduces the grain size. In other words, thereasons for hardening are similar to the ones invokedto explain hardening under the nanoindenter, namely,the transformation of IKBs to KB, and the reductionin the volume available to form new IKBs.

3.2 Tensile Properties

The response of Ti3SiC2 to tensile stresses is a strongfunction of temperature and strain rate. Below theBPT they are brittle, above they can be quite plastic,with strains to failure up to 25% in some cases,especially at low strain rates (Barsoum et al. 2001b)(Fig. 12(a)). The deformation occurs without neckingand the majority of the strain at failure is due todamage accumulation in the form of cavitations,pores microcracks, etc. (Radovic et al. 2000, 2001,2002, 2003).

The strain rate sensitivity ofE0.5 (Radovic et al.2000, 2002) determined for both coarse- and fine-grained microstructures of Ti3SiC2 is quite high andmore characteristic of superplastic solids than typicalmetals or ceramics. This does not imply, however,that the deformation of Ti3SiC2 is in any way similarto that of superplastic solids. The latter havecomparable strain rate sensitivities, but only at grainsizes that are at least 2 orders of magnitude smallerthan those of the CG Ti3SiC2 samples.

3.3 Creep

If the MAX phases are ever to be used as high-temperature structural materials in air, it is critical tounderstand both their creep behavior and oxidation

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resistance. The latter is dealt with separately inanother entry.

In the 100013001C temperature range, Ti3SiC2loaded in tension or compression exhibits primary,secondary, and tertiary creep (Radovic et al. 2001,2003, Zhen et al. 2004b). During the short primarycreep stage, the deformation rate decreases rapidly.This is followed by a secondary creep regime dur-ing which the creep rate, although not truly reachinga constant level, does not change significantly overa wide range. This secondary or minimum creeprate, emin, characterizes a plastic flow in which

hardening and softening are believed to be indynamic equilibrium.

The emin for the FG and CG samples in bothtension and compression of Ti3SiC2 can be describedby the following power-law equation (Radovic et al.2001, 2003, Zhen et al. 2004b):

emin e0As

s0

nexp

Q

RT

2

where A, n, and Q are, respectively, a stress-independent constant, stress exponent, and activation

Figure 11Fine-grain sample of Ti3SiC2 cycled in compression at 1200 1C. Inset shows the totality of cycles. Select, color-coded,cycles are extracted from the inset and plotted starting at zero strain for comparison (Barsoum et al. 2003). Note thesignificant cyclic hardening manifested by both reduction in dissipated energy, Wd, and stiffening at low loads. Thedashed line is the response predicted for purely elastic deformations. (Barsoum et al. 2003). (b) Comparison of theroom temperature compressive stressstrain curves of a coarse-grained Ti3SiC2 sample tested before and after a 2%deformation at 1300 1C (inset). The latter was loaded twice; the first loading resulted in an open loop, the second andsubsequent, only closed loops (Zhen et al. 2004a).

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energy for creep. R and T have their usual meanings;emin 1 s

1 and s0 1 MPa. A summary of thecreep results for the FG samples is shown inFig. 12(b). Table 1 summarizes the values of A, n,and Q obtained.

Based on these, and other results on the mechan-ical response of Ti3SiC2 in the 100013001C tem-perature and 10100 MPa stress ranges, one canconclude the following: (a) Based on the similaritiesin the values of n, especially at low stresses

(Fig. 12(b)), it is fair to conclude that the samemechanism is responsible for the creep of both theFG and CG microstructures. This claim is madedespite the differences in activation energies. At thistime it is not clear why the latter are a function oftype of loading or what their origin is. More work isneeded. (b) For both microstructures, at any given

temperature,

emin is at least an order of magnitudelower in compression than in tension (Fig. 12(b)).(c) Large internal stresses develop during testing(Radovic et al. 2001, 2003, Zhen et al. 2004b). Themost likely source of these stresses are dislocationpile-ups or arrays. (d) In tension, emin is a weakfunction of grain size, with grain size exponents o1.The same is true in compression, but only at lowstresses (Fig. 12(b)), which implies that the dominantcreep mechanism must be dislocation creep, despitethe fact that n is less than the exponents typicallyassociated with dislocation creep (Radovic et al.2001, 2003).

In compression, especially at relatively high stres-ses and/or temperatures, emin can actually be lowerfor the FG than the CG microstructures (Fig. 12(b))(Zhen et al . 2004b). In that regime, the stressexponents also become quite large (Fig. 12(b)). Thereasons for this unusual phenomenon are not totallyunderstood at this time, but post-testing microstruc-tural examinations of samples in that regime suggesta change in mechanism from dislocation creep tosubcritical crack growth. The latter regime is quitedifficult to document in tension most likely becausethe stress state is such as to quickly cause fastfracture. These comments notwithstanding, more

work is needed to better understand what isoccurring.At lower stresses, the times to failure measured

during tensile creep are considerably longer for thecoarse- than for fine-grained microstructures (Rado-vic et al. 2001, 2003). This is attributed to the higherdamage tolerance of the CG microstructure, i.e., tothe ability of CG structure to sustain higher bridgingstresses than the finer ones. Two different bridgingmechanisms were observed in creep. The firstinwhich grains whose basal planes are parallel to theapplied loadserves as classic crack bridges. Thesecond mechanism begins with delaminations that areinitiated at opposite ends of a single grain, but ondifferent basal planes. With further deformation thetorque separates the lamellae between the twodelamination cracks to ultimately form crack bridgesnot unlike the ones shown in Fig. 10(b).

The simplest explanation for these observations, aswell as to the fact that K1C actually decreases abovethe PBT, is the following: As in ice (Barsoum et al.2000) and for the same reason, viz. the paucity ofoperative slip systems, glide of basal plane disloca-tions takes place only in favorably oriented grains orsoft grains. During the short primary creep regime,basal plane dislocations glide and form pile-ups,

4

0

20

40

60

80

100

0.0 1.0 2.0 3.0 4.0 5.0

Stress(M

Pa)

Strain (%)(a)

(b)

1.38104

6.8310

1.38105

6.83106

1.38106

Coarse-grainedTi3SiC2

1200 C

Strain tofailure 25%

109

108

107

106

105

10 100

Stress (MPa)

Strainrate(s1)

1200 C1300 C

Tension

Comp.

1200 C 1100 C

1100 C

Fine-grainedTi3SiC2

104

103

Dislocation creep

Subcritical crackgrowth

Figure 12(a) Typical tensile stressstrain curves for coarse-grainedTi3SiC2 tested in air at 1200 1C as a function of strainrate. Note strong strain rate sensitivity; at high strainrates, samples are brittle. At low rates, deformations of25% are possible (Barsoum et al. 2001b). (b) Summaryof creep response of fine-grained Ti3SiC2 tested intension and compression at various temperatures(Radovic et al. 2000, Zhen et al. 2004b).

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resulting in large internal stresses. As the internalstresses increase, the creep rate decreases, leading to aquasi-steady-state. If the rate at which these stressesaccrue is significantly higher than the rate at which

they can relax, failure is brittle, insensitive to strainrate, and a function of grain size (Radovic et al.2002). At the lowest strain rates and/or highesttemperatures, the internal stresses can be accommo-dated by interlaminar decohesion, grain bending orkinking, and/or grain boundary decohesion andsliding. As the number of cavities and cracks increaseand coalesce, this naturally leads to an increase in eminand a transition from secondary to tertiary creep. Inother words, dislocation creep gives way to sub-critical crack growth rate (Radovic et al. 2003, Zhenet al. 2004b).

To put it most succinctly, the response of the MAX

phases to stress at elevated temperatures is directlyrelated to the rate at which the internal stresses arerelaxed (Radovic et al. 2000, 2001, 2002, 2003).

4. Solid Solution Hardening and Softening

Since substitutions can be made on either of the threesites in the MAX phases, the number of solidsolutions possible is quite high. It is thus notunreasonable to assume that once the effects suchsubstitutions have on the mechanical properties areunderstood, major improvements will accrue. Verylittle work exists on M

n1AX

nphase solid solutions,

but what little exists is intriguing. Based on a limiteddataset, it appears that only substitutions on theX-sites have a dramatic effect on properties. Sub-stitutions on the M-sites (e.g., (Ti0.5,Nb0.5)2AlC;Salama et al. 2002) or A-sites (e.g., Ti3(Si0.5,Ge0.5)C2;Ganguly et al. 2004) do not result in solid solutionhardening. In contradistinction, the solid solution,Ti2AlC0.5N0.5, is harder, more brittle, and signifi-cantly stronger, than the end-members Ti2AlC andTi2AlN, which can be deformed plastically up to 5%strain even at room temperature (Barsoum et al.2000). Interestingly, at temperatures E1200 1C a

solid solution softening effect is observed, the reasonsfor which are still unclear, but could be related to theaforementioned interlaminar decohesions.

5. Tribological Properties and Machinability

As early as 1996 (Barsoum and El-Raghy 1996), itwas noted that Ti3SiC2 shavings had a graphitic feelto them. This was later confirmed (Myhra et al. 1999,Crossley et al. 1999) when the friction coefficient, m,of the basal planes of Ti3SiC2 was measured bylateral force microscopy and found, at (25)103, tobe one of the lowest ever reported. Not only was thisvalue exceptionally low, but it remained that low forup to 6 months exposure to the atmosphere.Unfortunately, this low friction coefficient does not

translate to low friction in polycrystalline samples(El-Raghy et al. 2000). More recent results (Souchetet al. 2003), however, suggest that it may be possibleto obtain surfaces with ms against steel and Si3N4 aslow as 0.15, especially at low stresses. More work,however, needs to be carried out to better understandand ultimately exploit this important property.

Lastly, one would be remiss not to mentionprobably the most characteristic trait of the MAXphases and one that truly sets them apart from otherstructural ceramics or high-temperature alloys: easeof machinability (Barsoum and El-Raghy 1996,1997, Barsoum et al. 1997). The MAX phases arequite readily machinable with regular high-speedtool steels or even manual hacksaw. It is importantto note that the machining does not occur by plasticdeformation, as in the case of metals, but rather bythe breaking off of tiny microscopic flakes. In thatrespect, they are not unlike other machinableceramics such as Maycort. The analogy with ice isalso apt (Barsoum et al . 2001b); the Mn1AXncompounds do not machine as one scoops ice cream(as in metals), but rather as in shaving ice. The MAXphases have some of the highest specific stiffnessesfor readily machinable solids, with the exception ofBe and Be alloys.

Table 1Summary of creep results for Ti3SiC2.

ln A nQ

(kJ mol1)emin s

1

at 1200 1C and 50 MPa Refs.

CompressionCG 22 2 585720 2.3 107 Zhen et al. (2004b)

FG 14 1.9 768720 2.2 107 Zhen et al. (2004b)

TensileCG 17 2 458712 3.5 106 Radovic et al. (2003)FG 19 1.5 445710 1.0 105 Radovic et al. (2002)

a Note these results are not valid for stresses less than 70 MPa.

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6. Summary and Conclusions

In a relatively short time, our understanding of themechanical properties of these potentially technolo-gically important materials has deepened consider-ably. This can be traced to two factors. First, therealization that the properties of these materials have

a lot in common with two of the most widely studiedmaterials: ice and graphite. The more recent realiza-tion that the MAX phases are part of a much largerclass of solidsKNE solids (Barsoum et al. 2004a)that is quite ubiquitous in nature and includes ice,graphite, layered oxides and silicates, nonlinearmesoscopic solids, NMEs (Guyer et al. 1995), andmany more will indubitably result in even more rapidand deeper understanding. A sufficient condition tobelong to this class of solids is plastic anisotropy andthe absence of twinning, both almost guaranteed ifthe solid has a high c/a ratio (Barsoum et al. 2004a).

Second, and more important, must be the confine-ment of the dislocations to basal planes and theabsence of twinning, which greatly simplifies the pro-blem. Even in the unlikely eventuality that theMAX phases do not blossom into new applications,their study should greatly enhance our understandingof plastic deformation in other solids. These poly-crystalline nanolaminates are almost ideal modelmaterials for the study of dislocation dynamics andinteractions of walls or pile-ups with grain bound-aries, and other obstacles, without complicatingfactors, such a twinning, work hardening, formationof dislocations forests, etc., that have doggedmetallurgists and material scientists almost from theinception of the field. The further prospect ofstudying dislocation dynamics in more than 50MAX phases that exist, and the innumerablecombinations of solid solutions, is a wonderful oneindeed, and one that should prove to be of immenseimportance and benefit.

Acknowledgments

The progress made in understanding the mechanicalproperties of the MAX phases in a relatively shorttime is a testament to the graduate students, post-docs,and collaborators around the world, who have workedon these solids over the years. Foremost amongstthem is Dr. T. El-Raghy, who was the first to studythese phases and whose enthusiasm and productivitywere contagious. A. Procopio, L. Ho-Duc, I. Salama,A. Murugaiah, T. Zhen and A. Ganguly, and Drs.L. Farber, N. Tzenov, and P. Finkel of DrexelUniversity have also contributed much to our under-standing of their mechanical properties. Without thesupport of Drs. D. Stepp of the Army Research Office,L. Madsen and L. Schioler of the Division ofMaterials Research of the NSF the progress outlinedherein would not have been possible. My manyexcellent discussions with my colleagues at Drexel

UniversityR. Doherty, S. Kalidindi, Y. Gogotsi,and A. Zavailangoshave also been invaluable.

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M. W. Barsoum and M. Radovic

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