Martensite in Steels - Department of Materials Science and Metallurgy
Martensite in Steels - Department of Materials Science and Metallurgy
Martensite in Steels - Department of Materials Science and Metallurgy
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<strong>Materials</strong> <strong>Science</strong> & <strong>Metallurgy</strong>http://www.msm.cam.ac.uk/phase-trans/2002/martensite.htmlH. K. D. H. Bhadeshia<strong>Martensite</strong> <strong>in</strong> <strong>Steels</strong>The name martensite is after the German scientist Martens. It was used orig<strong>in</strong>ally to describethe hard microconstituent found <strong>in</strong> quenched steels. <strong>Martensite</strong> rema<strong>in</strong>s <strong>of</strong> the greatesttechnological importance <strong>in</strong> steels where it can confer an outst<strong>and</strong><strong>in</strong>g comb<strong>in</strong>ation <strong>of</strong> strength(> 3500 MPa) <strong>and</strong> toughness (> 200 MPa m 1 2 ). Many materials other than steel are now knownto exhibit the same type <strong>of</strong> solid-state phase transformation, known as a martensitic transformation,frequently also called a shear or displacive transformation. <strong>Martensite</strong> occurs <strong>in</strong>, forexample, nonferrous alloys, pure metals, ceramics, m<strong>in</strong>erals, <strong>in</strong>organic compounds, solidifiedgases <strong>and</strong> polymers (Table 1). We shall review first the experimental facts about martensite<strong>and</strong> then proceed to expla<strong>in</strong> them.Composition M S / K Hardness HVZrO 2 1200 1000Fe–31Ni–0.23C wt% 83 300Fe–34Ni–0.22C wt% < 4 250Fe–3Mn–2Si–0.4C wt% 493 600Cu–15Al 253 200Ar–40N 2 30Table 1: The temperature M S at which martensite first forms on cool<strong>in</strong>g, <strong>and</strong>the approximate Vickers hardness <strong>of</strong> the result<strong>in</strong>g martensite for a number <strong>of</strong>materials.Diffusionless CharacterMartensitic transformations are diffusionless, but what evidence is there to support this?<strong>Martensite</strong> can form at very low temperatures, where diffusion, even <strong>of</strong> <strong>in</strong>terstitial atoms,is not conceivable over the time period <strong>of</strong> the experiment. Table 1 gives values <strong>of</strong> the highesttemperature at which martensite forms <strong>in</strong> a variety <strong>of</strong> materials; this temperature is knownas the martensite–start, or M S temperature. It is obvious that although martensite can form1
at low temperatures, it need not do so. Therefore, a low transformation temperature is notsufficient evidence for diffusionless transformation.<strong>Martensite</strong> plates can grow at speeds which approach that <strong>of</strong> sound <strong>in</strong> the metal. In steelthis can be as high as 1100 m s −1 , which compares with the fastest recorded solidification frontvelocity <strong>of</strong> about 80 m s −1 <strong>in</strong> pure nickel. Such large speeds are <strong>in</strong>consistent with diffusiondur<strong>in</strong>g transformation. Note that martensite need not grow so rapidly. For example, <strong>in</strong> shape–memory alloys or <strong>in</strong> s<strong>in</strong>gle–<strong>in</strong>terface transformations, the <strong>in</strong>terface velocity is small enough toobserve.The chemical composition <strong>of</strong> martensite can be measured <strong>and</strong> shown to be identical tothat <strong>of</strong> the parent austenite. The totality <strong>of</strong> these observations demonstrate conv<strong>in</strong>c<strong>in</strong>gly thatmartensitic transformations are diffusionless.The Habit PlaneThis is the <strong>in</strong>terface plane between austenite <strong>and</strong> martensite as measured on a macroscopicscale (Fig. 1), for example by us<strong>in</strong>g one or two–surface crystallographic trace analysis onmetallographic samples. For unconstra<strong>in</strong>ed transformations this <strong>in</strong>terface plane is flat, butstra<strong>in</strong> energy m<strong>in</strong>imisation <strong>in</strong>troduces some curvature when the transformation is constra<strong>in</strong>edby its surround<strong>in</strong>gs. Nevertheless, the macroscopic habit plane is identical for both cases, asillustrated <strong>in</strong> Figure 1.Figure 1: An illustration <strong>of</strong> the habit plane between austenite (γ) <strong>and</strong> martensite(α ′ )2
<strong>Steels</strong> <strong>of</strong> vastly different chemical composition can have martensite with the same habitplane (Table 2), <strong>and</strong> <strong>in</strong>deed, other identical crystallographic characteristics.Composition /wt.%Low–alloy steels, Fe–28NiPlate martensite <strong>in</strong> Fe–1.8CFe–30Ni–0.3CFe–8Cr–1Cɛ–martensite <strong>in</strong> 18/8 sta<strong>in</strong>less steelApproximate habit plane <strong>in</strong>dices{1 1 1} γ{2 9 5} γ{3 15 10} γ{2 5 2} γ{1 1 1} γTable 2: Habit plane <strong>in</strong>dices for martensite. With the exception <strong>of</strong> ɛ–martensite, the quoted <strong>in</strong>dices are approximate because the habit planes are<strong>in</strong> general irrational.Orientation RelationshipsThe formation <strong>of</strong> martensite <strong>in</strong>volves the coord<strong>in</strong>ated movement <strong>of</strong> atoms. It follows thatthe austenite <strong>and</strong> martensite lattices will be <strong>in</strong>timately related. All martensitic transformationstherefore lead to a reproducible orientation relationship between the parent <strong>and</strong> productlattices. It is frequently the case that a pair <strong>of</strong> correspond<strong>in</strong>g close–packed† planes <strong>in</strong> the ferrite<strong>and</strong> austenite are parallel or nearly parallel, <strong>and</strong> it is usually the case that correspond<strong>in</strong>gdirections with<strong>in</strong> these planes are roughly parallel (Fig. 2):{1 1 1} γ ‖ {0 1 1} α< 1 0 1 > γ ‖ < 1 1 1 > αKurdjumov–Sachs{1 1 1} γ ‖ {0 1 1} αNishiyama–Wasserman< 1 0 1 > γ about 5.3 ◦ from < 1 1 1 > α towards < 1 1 1 > α{1 1 1} γ about 0.2 ◦ from{0 1 1} αGren<strong>in</strong>ger–Troiano< 1 0 1 > γ about 2.7 ◦ from < 1 1 1 > α towards < 1 1 1 > α† The body–centred cubic lattice does not have a close–packed plane but {0 1 1} α is themost densely packed plane.3
Note that these have been stated approximately: the true relations are irrational, mean<strong>in</strong>gthat the <strong>in</strong>dices <strong>of</strong> the parallel planes <strong>and</strong> directions cannot be expressed us<strong>in</strong>g rational numbers(the square root <strong>of</strong> 2 is not a rational number).Fig. 2: Stereographic representation <strong>of</strong> the Kurdjumov–Sachs <strong>and</strong> Nishiyama–Wasserman orientation relationships. The stereograms are both centred on(1 1 1) γ ‖ (0 1 1) α . It is seen that the NW orientation can be generatedfrom KS by an appropriate small rotation (5.25 ◦ ) about [0 1 1] α . Only afew <strong>of</strong> the poles are marked to allow a comparison with the Ba<strong>in</strong> orientationrelationship. The neighbour<strong>in</strong>g pairs <strong>of</strong> poles would superpose exactly for theBa<strong>in</strong> orientation.Athermal Nature <strong>of</strong> TransformationIn the vast majority <strong>of</strong> cases, the extent <strong>of</strong> reaction is found to be virtually <strong>in</strong>dependent<strong>of</strong> time:1 − V α′ = exp{β(M S − T)} where β ≃ −0.011 (1)V α′ is the fraction <strong>of</strong> martensite <strong>and</strong> T is a temperature below M S . This is the Koist<strong>in</strong>en <strong>and</strong>Marburger equation; notice that time does not feature <strong>in</strong> this relation, so that the fraction <strong>of</strong>martensite depends only on the undercool<strong>in</strong>g below the martensite–start temperature. Thisathermal character is a consequence <strong>of</strong> very rapid nucleation <strong>and</strong> growth, so rapid that thetime taken can <strong>in</strong> normal circumstances be neglected.Isothermal martensite is possible when nucleation is h<strong>in</strong>dered, although the growth rate<strong>of</strong> <strong>in</strong>dividual plates <strong>of</strong> martensite can still be rapid.4
Structure <strong>of</strong> the InterfaceAny process which contributes to the formation <strong>of</strong> martensite cannot rely on assistance fromthermal activation. There must therefore exist a high level <strong>of</strong> cont<strong>in</strong>uity across the <strong>in</strong>terface,which must be coherent <strong>and</strong> semi–coherent. A stress–free fully coherent <strong>in</strong>terface is impossiblefor the γ → α ′ transformation s<strong>in</strong>ce the lattice deformation BR is an <strong>in</strong>variant–l<strong>in</strong>e stra<strong>in</strong>. Asemi–coherent <strong>in</strong>terface must be such that the <strong>in</strong>terfacial dislocations can glide as the <strong>in</strong>terfacemoves (climb is not permitted). It follows that the Burgers vectors <strong>of</strong> the <strong>in</strong>terface dislocationsmust not lie <strong>in</strong> the <strong>in</strong>terface plane unless the dislocations are screw <strong>in</strong> character.There is an additional condition for a semi–coherent <strong>in</strong>terface to be glissile. The l<strong>in</strong>evectors <strong>of</strong> the <strong>in</strong>terfacial dislocations must lie along an <strong>in</strong>variant–l<strong>in</strong>e, i.e. a l<strong>in</strong>e which jo<strong>in</strong>sthe parent <strong>and</strong> product crystals without any rotation or distortion. Why is that? If there isany distortion along the dislocation l<strong>in</strong>e, then other dislocations are needed to accommodatethat misfit. It will then be necessary to have more than one set <strong>of</strong> non–parallel dislocations<strong>in</strong> the <strong>in</strong>terface. These non–parallel dislocations can <strong>in</strong>tersect to form jogs which render the<strong>in</strong>terface sessile.It follows that for martensitic transformation to be possible, the deformation which changesthe parent <strong>in</strong>to the product must leave one or more l<strong>in</strong>es <strong>in</strong>variant (unrotated, undistorted). Adeformation which leaves one l<strong>in</strong>e <strong>in</strong>variant is called an ‘<strong>in</strong>variant–l<strong>in</strong>e stra<strong>in</strong>’.The Shape DeformationThe passage <strong>of</strong> a slip dislocation through a crystal causes the formation <strong>of</strong> a step where theglide plane <strong>in</strong>tersects the free surface (Fig. 3a,b). The passage <strong>of</strong> many such dislocations onparallel slip planes causes macroscopic shear (Fig. 3c,d). Slip causes a change <strong>in</strong> shape butnot a change <strong>in</strong> the crystal structure, because the Burgers vectors <strong>of</strong> the dislocations are alsolattice vectors.Dur<strong>in</strong>g martensitic transformation, the pattern <strong>in</strong> which the atoms <strong>in</strong> the parent crystalare arranged is deformed <strong>in</strong>to that appropriate for martensite, there must be a correspond<strong>in</strong>gchange <strong>in</strong> the macroscopic shape <strong>of</strong> the crystal undergo<strong>in</strong>g transformation. The dislocationsresponsible for the deformation are <strong>in</strong> the α ′ /γ <strong>in</strong>terface, with Burgers vectors such that <strong>in</strong>addition to deformation they also cause the change <strong>in</strong> crystal structure. The deformationis such that an <strong>in</strong>itially flat surface becomes uniformly tilted about the l<strong>in</strong>e formed by the<strong>in</strong>tersection <strong>of</strong> the <strong>in</strong>terface plane with the free surface. Any scratch travers<strong>in</strong>g the transformed5
egion is similarly deflected though the scratch rema<strong>in</strong>s connected at the α ′ /γ <strong>in</strong>terface. Theseobservations, <strong>and</strong> others, confirm that the measured shape deformation is an <strong>in</strong>variant–planestra<strong>in</strong> (Fig. 3e–g) with a large shear component (≃ 0.22) <strong>and</strong> a small dilatational stra<strong>in</strong> (≃ 0.03)directed normal to the habit plane.Fig. 3: (a, b) Step caused by the passage <strong>of</strong> a slip dislocation. (c, d) Manyslip dislocations, caus<strong>in</strong>g a macroscopic shear. (e) An <strong>in</strong>variant–plane stra<strong>in</strong>with a uniaxial dilatation. (f) An <strong>in</strong>variant–plane stra<strong>in</strong> which is a simpleshear. (g) An <strong>in</strong>variant–plane stra<strong>in</strong> which is the comb<strong>in</strong>ed effect <strong>of</strong> a uniaxialdilatation <strong>and</strong> a simple shear.Ba<strong>in</strong> Stra<strong>in</strong>We now consider the nature <strong>of</strong> the stra<strong>in</strong> necessary to transform the c.c.p. lattice <strong>of</strong> γ<strong>in</strong>to the b.c.c. lattice <strong>of</strong> α ′ . Such a stra<strong>in</strong> was proposed by Ba<strong>in</strong> <strong>in</strong> 1924 <strong>and</strong> hence is known6
as the ‘Ba<strong>in</strong> Stra<strong>in</strong>’ (Fig. 4). There is a compression along the z axis <strong>and</strong> a uniform expansionalong the x <strong>and</strong> y axes.Fig. 4: The Ba<strong>in</strong> stra<strong>in</strong> (not all lattice po<strong>in</strong>ts illustrated)The deformation describ<strong>in</strong>g the Ba<strong>in</strong> Stra<strong>in</strong> is given byB =⎛⎝ ɛ 0 0 00 ɛ 0 00 0 ɛ ′ 0⎞⎠ɛ 0 =√2aα ′ − a γa γɛ ′ 0 = a α ′ − a γa γwhere a α′ <strong>and</strong> a γ are the lattice parameters <strong>of</strong> martensite <strong>and</strong> austenite respectively. Thecontraction is therefore along the [0 0 1] γ axis <strong>and</strong> a uniform expansion on the (0 0 1) γ plane.The Ba<strong>in</strong> stra<strong>in</strong> implies the follow<strong>in</strong>g orientation relationship between the parent <strong>and</strong>product lattices:[0 0 1] fcc ‖ [0 0 1] bcc [1 1 0] fcc ‖ [1 0 0] bcc [1 1 0] fcc ‖ [0 1 0] bcc7
ut <strong>in</strong> fact, the experimentally observed orientation relationships are irrational, as discussedearlier. We shall deal with this <strong>in</strong>consistency later.Temporarily neglect<strong>in</strong>g the fact that the Ba<strong>in</strong> orientation is <strong>in</strong>consistent with experiments,we proceed to exam<strong>in</strong>e whether the Ba<strong>in</strong> stra<strong>in</strong> leaves at least one l<strong>in</strong>e <strong>in</strong>variant. After all,this is a necessary condition for martensitic transformation.In Fig. 5a,b, the austenite is represented as a sphere which, as a result <strong>of</strong> the Ba<strong>in</strong> stra<strong>in</strong> B,is deformed <strong>in</strong>to an ellipsoid <strong>of</strong> revolution which represents the martensite. There are no l<strong>in</strong>eswhich are left undistorted or unrotated by B. There are no l<strong>in</strong>es <strong>in</strong> the (0 0 1) fcc plane whichare undistorted. The l<strong>in</strong>es wx <strong>and</strong> yz are undistorted but are rotated to the new positions w ′ x ′<strong>and</strong> y ′ z ′ . Such rotated l<strong>in</strong>es are not <strong>in</strong>variant. However, the comb<strong>in</strong>ed effect <strong>of</strong> the Ba<strong>in</strong> stra<strong>in</strong>B <strong>and</strong> the rigid body rotation R is <strong>in</strong>deed an <strong>in</strong>variant–l<strong>in</strong>e stra<strong>in</strong> (ILS) because it br<strong>in</strong>gs yz<strong>and</strong> y ′ z ′ <strong>in</strong>to co<strong>in</strong>cidence (Fig. 5c). This is the reason why the observed irrational orientationrelationship differs from that implied by the Ba<strong>in</strong> stra<strong>in</strong>. The rotation required to convert B<strong>in</strong>to an ILS precisely corrects the Ba<strong>in</strong> orientation <strong>in</strong>to that which is observed experimentally.Fig. 5: (a) <strong>and</strong> (b) show the effect <strong>of</strong> the Ba<strong>in</strong> stra<strong>in</strong> on austenite, whichwhen undeformed is represented as a sphere <strong>of</strong> diameter wx = yz <strong>in</strong> three–dimensions. The stra<strong>in</strong> transforms it to an ellipsoid <strong>of</strong> revolution. (c) showsthe <strong>in</strong>variant–l<strong>in</strong>e stra<strong>in</strong> obta<strong>in</strong>ed by comb<strong>in</strong><strong>in</strong>g the Ba<strong>in</strong> stra<strong>in</strong> with a rigidbody rotation through an angle θ.As can be seen from Fig. 5c, there is no rotation which can make B <strong>in</strong>to an <strong>in</strong>variant–plane stra<strong>in</strong> s<strong>in</strong>ce this would require two non–parallel <strong>in</strong>variant–l<strong>in</strong>es. Thus, for the fcc → bcc8
transformation, austenite cannot be transformed <strong>in</strong>to martensite by a homogeneous stra<strong>in</strong>which is an IPS. And yet, the observed shape deformation leaves the habit plane undistorted<strong>and</strong> unrotated, i.e. it is an <strong>in</strong>variant–plane stra<strong>in</strong>.The phenomenological theory <strong>of</strong> martensite crystallography solves this rema<strong>in</strong><strong>in</strong>g problem(Fig. 6). The Ba<strong>in</strong> stra<strong>in</strong> converts the structure <strong>of</strong> the parent phase <strong>in</strong>to that <strong>of</strong> the productphase. When comb<strong>in</strong>ed with an appropriate rigid body rotation, the net homogeneous latticedeformation RB is an <strong>in</strong>variant–l<strong>in</strong>e stra<strong>in</strong> (step a to c <strong>in</strong> Fig. 6). However, the observed shapedeformation is an <strong>in</strong>variant–plane stra<strong>in</strong> P 1 (step a to b <strong>in</strong> Fig. 6), but this gives the wrongcrystal structure. If a second homogeneous shear P 2 is comb<strong>in</strong>ed with P 1 (step b to c), thenthe correct structure is obta<strong>in</strong>ed but the wrong shape s<strong>in</strong>ceP 1 P 2 = RBThese discrepancies are all resolved if the shape chang<strong>in</strong>g effect <strong>of</strong> P 2 is cancelled macroscopicallyby an <strong>in</strong>homogeneous lattice–<strong>in</strong>variant deformation, which may be slip or tw<strong>in</strong>n<strong>in</strong>g asillustrated <strong>in</strong> Fig. 6.The theory expla<strong>in</strong>s all the observed features <strong>of</strong> the martensite crystallography. Theorientation relationship is predicted by deduc<strong>in</strong>g the rotation needed to change the Ba<strong>in</strong> stra<strong>in</strong><strong>in</strong>to an <strong>in</strong>variant–l<strong>in</strong>e stra<strong>in</strong>. The habit plane does not have rational <strong>in</strong>dices because theamount <strong>of</strong> lattice–<strong>in</strong>variant deformation needed to recover the correct the macroscopic shapeis not usually rational. The theory predicts a substructure <strong>in</strong> plates <strong>of</strong> martensite (either tw<strong>in</strong>sor slip steps) as is observed experimentally. The transformation goes to all the trouble <strong>of</strong>ensur<strong>in</strong>g that the shape deformation is macroscopically an <strong>in</strong>variant–plane stra<strong>in</strong> because thisreduces the stra<strong>in</strong> energy when compared with the case where the shape deformation mightbe an <strong>in</strong>variant–l<strong>in</strong>e stra<strong>in</strong>.Thermodynamics <strong>of</strong> Martensitic Transformations<strong>Martensite</strong> is not represented on phase diagrams because the latter deal with equilibrium.<strong>Martensite</strong> deviates from equilibrium <strong>in</strong> two important ways:<strong>Martensite</strong> grows without diffusion, so it <strong>in</strong>herits the chemical composition <strong>of</strong> the parentaustenite. In an equilibrium transformation the chemical elements partition <strong>in</strong>to the parent<strong>and</strong> product phases <strong>in</strong> a manner which leads to a m<strong>in</strong>imisation <strong>of</strong> free energy.Secondly, the shape deformation associated with martensitic transformation causes stra<strong>in</strong>s;the result<strong>in</strong>g stra<strong>in</strong> energy has to be accounted for before the transformation can happen.9
Fig. 6: The phenomenological theory <strong>of</strong> martensite crystallographyThese deviations can be represented on a free energy plot as illustrated <strong>in</strong> Fig. 7.The relationship with the phase diagram is illustrated <strong>in</strong> Fig. 8. Martensitic transformationis only possible below the T ′ 0 temperature.10
Fig. 7: The distance ac represents the free energy decrease when austenite <strong>of</strong>composition x decomposes <strong>in</strong>to an equilibrium mixture <strong>of</strong> ferrite <strong>and</strong> austenite<strong>of</strong> compositions x αγ <strong>and</strong> x γα respectively. The distance ab is the smaller decrease<strong>in</strong> free energy when martensite forms without any composition change,tak<strong>in</strong>g <strong>in</strong>to account the stra<strong>in</strong> associated with the transformation.J mol −1Stra<strong>in</strong> energy 600Tw<strong>in</strong> <strong>in</strong>terface energy 100γ/α ′ <strong>in</strong>terface energy 1Stored energy due to dislocations 20Table 3: Typical energies associated with martensitic transformation.11
Fig. 8: Schematic illustration <strong>of</strong> the orig<strong>in</strong> <strong>of</strong> the T 0 curve on the phase diagram.The T 0 ′ curve <strong>in</strong>corporates a stra<strong>in</strong> energy term for the ferrite, illustratedon the diagram by rais<strong>in</strong>g the free energy curve for ferrite by an appropriatequantity.12