Strengthening of nitrided FeTi alloys

Strengthening of nitrided FeTi alloys

Arta metall. Vol. 34, No. IO, pp. 1911-1923, Printed in Great Britain. All rights reserved 1986 STRENGTHENING Copyright OF NITRIDED D. S. RICKERB...

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Arta metall. Vol. 34, No. IO, pp. 1911-1923, Printed in Great Britain. All rights reserved







OOOI-6160/86 $3.00 +o.oo ci” 1986 Pergamon Journals Ltd



Wolfson Research Group for High-Strength The University of Newcastle-upon-Tyne,

Materials, Crystallography Newcastle-upon-Tyne,

Laboratory, England

(Received 20 Oclober 1985; in revised form 5 February 1986)

Abstract-The temperature dependence of the yield and flow stresses of nitrided FeeTi alloys have been investigated in the range 77-900 K for a number of particle dispersions. In as-nitrided or underaged alloys, from the magnitude of the strengthening, its dependence on solute concentration and temperature it is concluded that strengthening is due to chemical factors arising when new interfaces are created as titanium-nitrogen atom clusters (GP zones) are cut by glide dislocations. Such alloys have poor ductility due, in part, to their high strength and the coarse slip distribution which develops as a result of particle shear. When overaged, the titanium-nitrogen atom clusters transform to the equilibrium precipitate (TiN) and a change in deformation mechanism from cutting to looping occurs which is accompanied by a rapid increase in work hardening rate and an improvement in ductility. The strength of overaged alloys can be adequately accounted for by Orowan hardening. R&um&Nous avons 6tudi6 la variation de la limite tlastique et de la contrainte d’Ccoulement en fonction de la tempirature dans des alliages Fe-Ti nitrurCs entre 77 et 900 K, pour un certain nombre de dispersion de particules. Dans des alliages bruts de nitruration ou sous-vieillis, on peut dkduire de la grandeur du durcissement et de sa variation en fonction de la concentration en soI& et de la tempkrature, que le durcissement est dtYiaux facteurs chimiques qui apparaissent lorsque de nouvelles interfaces sont cr&s lors du cisaillement d’amas d’atomes de titane et d’azote (zones GP) par des dislocations de glissement. De tels ailiages prksentent une faible ductilitC due en partie B leur rCsistance 6levte et $ la distribution grossikre du glissement qui se dCveloppe $ la suite du cisaillement des particules. Lors d’un sur vieillissement, les amas d’atomes de titane et d’azote se transforment en prCcipit6 d’kquilibre (TiN) et il se produit un changement du mCcanisme de d&formation, de cisaillement a contournement, accompagnt: par une augmentation rapide de la vitesse d’tcrouissage et par une amtlioration de la ductilitk. On peut rendre compte de manikre satisfaisante de la resistance des alliages sur vieillis par le mCcanisme d’orowan.


Temperaturabhingigkeit der kritischen und der FlieBspannung von nitrierten Fe-Ti-Legierungen wurde im Temperaturbereich zwischen 77 und 900 K fiir eine Anzahl verschiedener Teilchen-Dispersionen untersucht. In den wie-nitrierten oder unteralterten Legierungen 15l3t sich aus der HGhe der Hirtung und deren Abhlngigkeit von Konzentration und Temperatur schlieDen. daL3 die HLrtung auf chemischen Faktoren beruht. Diese riihren davon her, daO Gleitversetzungen TitanStickstoff-Cluster (Guinier--Preston-Zonen) schneiden und so neue GrenzflCchen schaffen. Solche Legierungen weisen eine schlechte Duktilitit auf, teilweise wegen ihrer hohen Festigkeit und der groben Gleitverteilung, die sich wegen der Scherung der Teilchen entwickelt. Im iiberaltertem Zustand wandeln sich die Titan-Stickstoff-Cluster in die Gleichgewichtsausscheidung TIN urn. Damit wechselt der Verformungsmechanismus vom Schneiden zum Bilden von Versetzungsringen, wodurch die Verfestigung rasch ansteigt und die Duktilitit sich verbessert. Die Festigkeit der iiberalterten Legierungen kann mit dem Orowan-Mechanismus gut erkllrt werden.

1. INTRODUCTION With the advent of energy and material shortages, a need has developed for lightweight, high-strength, formable sheet steels. These steels, known as high strength low alloy steels, have a ferrite microstructure which is strengthened by fine-scale precipitation of carbides and carbonitrides formed by elements such as niobium and vanadium. Nitriding of iron and steels to produce a dense homogeneous dispersion of small particles is also a highly efficient means of strengthening the ferritic matrix [l, 21. The formation of mixed substitutional-interstitial clusters or GP tPresent address: Materials Development Division, AERE, Harwell. Didcot, Oxfordshire, England.

zones at nitriding temperture forms the basis of a new steel strengthening mechanism [3] and is the first stage of a continuous transformation sequence that ends with the equilibrium precipitate. Strengthening due to these particles, which are similar to the GP zones that occur in some facecentred cubic alloys, is consistent with a model in which the zones are cut by glide dislocations in their initial and underaged states. There is some disagreement, however, as to the exact nature of this extra resistance to dislocation movement, and modulus, coherency and chemical hardening have been proposed as factors contributing to the high strengths of nitrided Fe-Ti alloys [4-61. Beyond peak strength the yield stress is close to that predicted by the Orowan






mechanism and by-passing of the particles occurs by dislocation bowing [7, 81. The objective of the present study was to investigate the temperature dependence of the yield and flow stress of nitrided Fe-Ti alloys, when (i) the obstacles to deformation are sheared by dislocations and (ii) they are by-passed. Using the theory of thermally activated flow, and with the aid of friction stress calculations, the results are discussed in terms of the various models already proposed in the literature and the dominant strengthening mechanism for various particle dispersions identified.


1000 N


Flat tensile specimens of 20 mm gauge length and 5 mm width, and coupons for hardness testing, were stamped from 0.6 mm plate obtained from alloy bar. Annealed specimens were obtained by hot-rolling to 2 mm followed by cold-rolling and then annealing in hydrogen to give a uniform grain size of ASTM 7-8. Samples were nitrided in NH,-H, gas mixtures and air cooled or quenched after the nitriding treatment; selected specimens were hydrogen reduced after nitriding. For tensile tests an Instron 1115 machine was used at a nominal strain rate of 4.2 x 10m4s-i in a nitrogen-atmosphere furnace for high-temperature measurements up to 600°C and in cooled liquid baths for sub-zero temperatures. Room-temperature hardness measurements were made on metallographic specimens using a standard microhardness tester fitted to a Reichart microscope with loads of 20 or 50 g on the diamond indentor. Hot-hardness measurements were carried out in a Wilberforce Scientific Developments high-temperature microhardness tester in the Department of Metallurgy, University of Cambridge. Thin foils for transmission electron microscopy in a Philips EM300 were prepared from nitrided 100 pm thick foil or from the gauge length of tensile specimens. Scanning electron microscopy was carried out on the fracture faces of tensile specimens using a Cambridge Stereoscan S600 instrument. 3. RESULTS 3.1. Mechanical properties and structure Nitriding Fe-Ti alloys in the temperature range 40&65O”C leads to the homogeneous formation of small, coherent, disc-shaped particles on the {loo} matrix planes of ferrite. The disc is essentially a monolayer cluster of titanium and nitrogen atoms with each nitrogen co-ordinated by four Ti atoms in the layer and one Fe atom above and below it; see [9]. These substitutional-interstitial GP zones have associated with them excess nitrogen, that is, nitrogen above that required to form stoichiometric titanium nitride, which can be removed by hydrogen reduction or can be precipitated as a”-Fe,,N, at low temperatures leaving the clusters unchanged [lo]. The



900 / t? -___.-‘, t



1 _.-






l;k--;/;-/‘j:: 0.01





Fig. 1. Yield stress as a function of nitriding potential R for Fe-O. 15 wt% Ti. As-nitrided specimens: 0; nitrided and hydrogen reduced specimens: 0. The dashed line represents solid-solution hardening by excess nitrogen.

structure of nitrided iron-titanium alloys, and the various octahedral sites which nitrogens occupy within clustered materials, is described elsewhere [ 111. In Fig. 1 the variation of yield strength as a function of nitriding potential (R = pNH,/pHi’*) is shown for an FM.15 wt% Ti alloy nitrided at 650°C. On hydrogen reduction there is a decrease in yield strength which is proportional to the excess nitrogen concentration. Indeed, if the excess nitrogen concentrations for various nitriding potentials at 650°C [see Fig 2(b)] are multiplied by 575 MN/m* per at.% N, the solid-solution strengthening of ferrite by interstitial nitrogen [12, 131, the dashed line in Fig. 1 results. This line is approximately parallel to the data for as-nitrided materials (see Fig. 1) showing, to a first approximation, that the contribution to yield strength from excess nitrogen is as though the nitrogen atoms were occupying octahedral sites in pure m-iron. Although clustering results in a large increase in strength the material has limited ductility and at high nitriding potentials brittle fracture occurs in tensile testing; see Fig. 2(a) where the full curve represents the variation in elongation for a constant nitriding time of 5 h, while the dashed curve shows the effect of prolonged nitriding (18 h). When nitrided, the fracture behaviour of the alloys changes from microvoid coalescence, typical of unnitrided material [shown by Fig. 3(a)], to intergranular fracture with some cleavage for nitrided and for nitrided and hydrogen reduced material [see Fig. 3(b) and (c) respectively]. On the grain boundary facets of nitrided samples which fractured intergranularly, there are “dimples” which are assumed to be the result of grain-boundary precipitation of titanium nitride. Clearer evidence of such precipitation is given by transmission electron microscopy, and Fig. 4 shows grain-boundary precipitation and associated precipitate-free zones. This sample was overaged to




(a) 10

and HENDRY: VoTi


- As above,


- Fe-O.?!5

OS nltrided,

then hydrogen YoTi



OS nitridsd,


in pun

Sh reduced 18 h iron



01 0






OF NITRIDED similar behaviour



when alloys were nitrided

and hydrogen reduced at 585°C with subsequent aging at 800°C. It is suggested that the aging response of nitrided material reflects subtle changes in the composition of the titanium-nitrogen GP zones formed during nitriding. In the more dilute FeTi alloys, the titanium monolayers which constitute the GP zones contain iron atoms whose concentration increases with a reduction in nitriding temperature and decreasing titanium in the alloy. The rejection of these iron atoms from the zone during aging is thought to change the obstacle strength, or perhaps the distribution of the GP zones at a fixed composition, thereby increasing the resistance of the Ti-N zones to deformation by glide dislocations. At the higher nitriding and aging temperatures the GP

I 0.04




Code, see




t s

0.06 L

-t i .o

Ilj !




/ 002





,’ / 0 & ,3







1 0.04


Fig. 2. Variation of (a) uniform elongation and (b) weight gain, as a function of nitriding potential R for FeeO. I5 wt% Ti.

transform in situ the homogeneous clusters on the three cube planes to disc-shaped TIN precipitates; only two orientations are visible edge-on with the third lying in the plane of the foil. While Fig. 2 shows that time at a given nitriding temperature influences the resulting mechanical properties of a nitrided Fe-Ti alloy, several investigations have reported strength differences attributed to variations in processing temperature [Z, 51. This point is clearly illustrated by Fig. 5, which in addition shows that the aging response of nitrided and hydrogen reduced Fe-Ti alloys depends on the initial nitriding conditions, titanium concentration and subsequent aging temperature. While all alloys treated at 400°C and aged at 650°C show gains in strength with increasing aging time, only the Fe-O. 18 wt% Ti alloy

Fig. 3. Scanning electron micrographs of fracture surfaces of nitrided Fe-O.15 wt% Ti; (a) un-nitrided; (b) nitrided in 2NH,:98H, at 650°C; (c) nitrided as in (b). then hydrogen reduced at 5OO’C.




Fig. 4. Transmission




electron micrograph of Fe-O.18 wt% Ti nitrided in 7NH,:93H, reduced at 585”C, aged at 800°C for 112 h.

zones formed are quite stable, and any changes in zone composition and/or dispersion are small. As a consequence no strength increases are observed. The microhardness data presented in Fig. 5, obtained from Vickers pyramid impressions taken within a single ferrite grain, whilst useful for determining the general aging response of materials, reflect both the flow stress and work-hardening behaviour of the material under test, and as such are related to the intergranular friction stress. To differentiate between particle cutting and looping mechanisms, measurements of work-hardening rate (WHR) independent of

the flow or yieid stress are necessary. Figure 6 shows the results of tensile testing on F&.18 wt% Ti samples nitrided and hydrogen reduced at 585°C and subsequently aged for various times at 800°C; the WHR was determined at a strain of 2%. During the early stages of aging yield is controlled by a cutting mechanism, as characterised by a low WHR, while the higher WHR typical of the overaged material reflects the change from a particle cutting to a bypassing mechanism beyond peak strength. The particle strengthening mechanism operative at any stage of aging was found to influence the way in which the




mtrided & [email protected]



LOdC .qed








and hydrogen

18 (t+l) / h

(b) (4 Fig. 5. Variation of microhardn~s with aging time and temperature for nitrided Fe-Ti alloys; (a) nitrided in RJH, : 93H, and subsequently hydrogen reduced at 585°C: aged at 800°C; (b) nitrided in 29NH, : 71H, and subsequently hydrogen reduced at 400°C: aged at 650°C.





(t+l)/h Fig. 6. Variation in yield stress and work-hardening rate with aging time at 800°C for Fe4.18 wt% Ti nitrided in 7NH,:93H, and subsequently hydrogen reduced at 585°C prior to aging.

material deformed. For example, although the yield strengths of the Fe-0.18 wt% Ti alloy prior to aging and after aging for 11.5 h are approximately identical (see Fig. 6), the fracture behaviour which characterised these two particle dispersions was quite different as shown in Fig. 7. For as-nitrided materials or alloys aged for short times, long, straight, screw dislocations with b = :( 111) cut the particles causing a reduction in particle resistance along the glide plane and, by making it easier for slip to continue on this plane, give rise to a coarse slip distribution as described by




Hornbogen and ZumGahr [14]; a more detailed discussion on the dislocation-particle interactions and deformation behaviour of nitrided alloys is given by Rickerby and Hendry [15]. Such a slip distribution, when combined with the high stresses necessary for plastic flow, brings about a reduction in specimen ductility as measured by uniform elongation in a tensile test; see Fig. 7(a) and (b), where for time zero uniform elongations of typically 1% were observed. Overaging of the substitutional-interstitial zones causes glide dislocations to loop the particles and the Orowan loops harden the slip plane which causes the slip distribution to become finer with resulting increases in ductility; see Fig. 7(c) and (d), where uniform elongations of 6-l 3% were observed during tensile testing. The poor ductility which accompanies particle shear has also been observed in nitrided Fe--V alloys by Jones et al. [16]. Other alloy systems which show reduced ductility as a consequence of deformation by particle shear include, age-hardening Fe-S Ti [17] and age-hardened Ti-Mo alloys [IS]. In such systems crack nucleation occurs where slip bands intersect with one another and with grain boundaries. In the later stages of aging nitrided Fe-Ti alloys, the particles act as impenetrable barriers and force the dislocations to bow out and by-pass the obstacles. At this point it is possible to identify, by transmission electron microscopy, disc-shaped particles of titanium nitride [l 11. If an Orowan relationship applies, the increase in yield stress compared with the

Fig. 7. Scanning electron micrographs of fracture surfaces of Fe&I. 18 wt% Ti nitrided in 7NH,: 93H, and subsequently hydrogen reduced at 585°C. aged at 800°C for the times indicated.




a&y should be a linear function of the inverse of the planar spacing (L). For the Orowan regime Brown and Ham [19] suggest the use of annealed

0.8 Gb AX=~COS for

[I $

0 < 4, G 100”

where G is the shear modulus of the matrix, b the Burgers vector and & the breaking angle, which is relat,ed to the obstacle strength and is taken to be zero for impenetrable obstacles (Qrowan hardening). As shown in Fig. 8, where the mean free path A has been substituted for L, this relationship is valid. Equation (I) refers to shear stresses which must be converted to tensile stresses in a polycrystal. The alloys used in the present work have unknown texture and the effective Schmit or Taylor factor by which the shear stress must be multiplied (m) to find the tensile stress lies between 2.2 and 3.1 [20,21]. The gradient (y) of the straight line shown in Fig. 8 is therefore given by y = Mm Gb .

‘L, 05

(Ti,~~a)‘,2 ”


Fig. 9. &x&se in rnj~~~ard~~s with square root of atomic percentage titanium for alfoys nitrided in 7NH,:93H, at 585°C and hydrogen reduced at 585°C. Henderson [5]: 0; present work: a.


Taking typical values for C and b the theoretical gradient of the straight line is in the range 3.85.4 x 10m5MN/m {the chief uncertainty being in the Taylor factor) which is in reasonabb agreement with the results of Chen (4.9 x 10m5MN/m; [7]) and those of the present investigation (6.2 x lo-* MN/m) but in poorer agreement with Hamano and Tsuya (8.4 x 10-s MN/m; @I). 3.2. Temperature dependence of yield strength The increase in microhardness on nitriding and hydrogen reduction of iron-titanium alloys when pIotted against the square root of atomic percentage

titanium give a straight line; see Fig. 9 which includes the work of Henderson [5]. Similar behaviour is reported by Kirkwood er al. [4]. Such a dependence of strength on volume fraction may occm- for several of the possible sources of hardening by deformable particles e.g. coherency, modulus, and chemical hardening. Thus, in order to differentiate between these three alternatives it is necessary to consider the temperature dependence of yieId strength. Figure 10 shows the variation ofyield strength with temperature for polycrystalline Fe-Ti alloys nitrided and hydrogen reduced at 585°C to give Ti-N clusters. The plot can be divided into three distinct regions labelled (a), (b) and (c). In region (a) there is a strong dependence of yield stress on temperature identical to that observed when testing pure iron 122,231 and annealed [email protected] I8 wt% Ti, which is a consequence of the Peierls-Nabarro force for body-centred cubic iron. Note that a 77 K no yield was observed for Fe0.18wt% Ti due to brittle grain-boundary failure. The present results and those of Spitzig ]6] show that in region (9) the hardening which results from

TO-'m/h Fig. 8. Variation of yield strength with reciprocal mean free path (A), for Fe-X alloys nitrided and aged at high temperatures. Chen [?j: m; Hamano and Tsuya [g]: 0; present work: l t.

Fig. 10 Variation of yield stress with t~~rat~re un-nitrided and nitrided iron-titanium alloys.






nitriding Fe-Ti alloys is linearly additive to the lattice friction stress, in agreement with the views of Orowan 1241. The friction stress (go) is generally consist of two components fl,) = a’(T.i)






\ LOO-

+ 0’


where o ‘(T,i) and n’ are, respectively, the temperature dependent and temperature independent components of the friction stress. The yield or flow stress of a polycrystalline material can be expressed as

I \



g 300.-

b \


8 \




where k,(T,t)&” is the grain size contribution. For temperatures less than approximately 400 K the temperature dependence of k, is slight [25,26] and varies with temperature as the modulus [23]. For this reason equation (4) may be written as a,=a’(T,i)+[o’+k,.d


for T<400K


where the term contained in brackets may be regarded as athermal without a significant error being introduced in the evaluation of T,, the critical temperature beyond which only athermal mechanisms are operative [23,27]. In order to evaluate T, the slopes of the curves of Fig. IO, dg),ldT, for temperature less than 400 K are plotted against T and are given in Fig. 11. The transition between thermally activated and athermal regions (where da,/dT = 0) is found to occur at 350 f 20 K for the range of alloys investigated and is independent of the nitriding treatment and titanium concentration. This result is in good agreement with the value of 365 K given by Chen et al. [23] for pure iron with a similar grain size to that used in the present investigation. Once T, is known, values of o’ can be obtained from equation (5) and its variation with temperature for the variously treated alloys is given in Fig. 12. Clearly, the magnitude and temperature dependence of (r’ for the nitrided alloys, although these contain quite different dispersions of titanium-nitrogen GP zones, is identical to that of the annealed alloy. In region (b) the yield stress is independent of temperature, but as the temperature is increased a


0 100

200 Temperature.





Fig. Il. Stress differential, da/dT, as a function of temperafor un-nitrided and nitrided FeeTi alloys. Un-nitrided FeeO.18 wt% Ti: 0; nitrided Fe4.18 wt% Ti: 0; nitrided Fe4.07 wt% Ti: n .



"\ m\, OO




Temperature, K

Fig. 12. Effective stress, c ‘, as a function of test temperature for un-nitrided and nitrided Fe-Ti alloys. Un-nitrided Fe4). 18 wt% Ti: 0; nitrided Fea. 18 wt% Ti: 0; nitrided Fe4.07 wt% Ti: n .

third region (c) is observed where the yield strength again varies with temperature. This latter region is similar to that observed by Jones et al. [16] for nitrided Fe-O.15 wt% V and attributed by these authors to the thermal activation of chemical-bond rupture in the substitutional-interstitial mixed atom clusters formed by nitriding. However, while it is justified to assume a temperature independence of k, for T < 400 K, its temperature dependence becomes significant at higher temperatures and equation (4) should be used in preference to equation (5). As a result, the (c) regions of the curves shown in Fig. IO suggest thermal activation of an unlocking process (k, effect), in addition to the temperature dependence resulting from dislocation glide over localised obstacles, and from the present data it is impossible to separate these two thermally activated processes. A simple way of eliminating the temperature dependence of k.y is to use microhardness measurements taken within single grains of a polycrystal, and Fig. 13 shows the temperature dependence of Row stress (i.e. microhardness) for a range of Fe-Ti alloys nitrided and hydrogen reduced at 585°C. Clearly, there is a very marked temperature dependence of flow stress, and of the mechanisms proposed to explain the high strength of nitrided materials, only chemical strengthening should be accompanied by a strong temperature dependence [19,28]. The results of Fig. 13 therefore confirm the suggestions made by Kirkwood et al. [4] and Henderson [S], and the experimental work of Jones et al. [ 161, that a chemical strengthening mechanism accounts for the high strengths of nitrided materials. The modulus model proposed by Spitzig [6] does not account for the observed temperature dependence of yield strength. Since this dependence changes with the distribution of Ti-N zones in the material, an increased titanium concentration at a constant nitriding temperature gives a finer distribution of zones and hence an increased temperature dependence; this is also ob-






nltnded 8 hydrogen reduced -.-







a gradual decrease in the temperature dependence of flow stress. Any temperature dependence of flow stress for the Orowan process, Fig. 14, line (c). arises from variation of elastic moduli with temperature and is therefore slight.






Fig. 13. Change in microhardness with temperature for Fe-Ti alloys nitrided in 7NH,: 93H, at 585°C and hydrogen reduced at 585°C.

served in Fig. 13. The influence titanium concentration has on zone distribution has been explained in terms of classical nucleation theory and further details are given in Rickerby et al. [l 11.As shown by Fig. 6, aging the as-nitrided structure at 800°C leads to a change from cutting to a by-passing mechanism, and Fig. 14 shows that this change is accompanied by

natrlded 8 hydrogen reduced Fe-016 Wc TI aged 8OO’C


\ \



11.5 h




2 -y---yYbi 3







, K

Fig. 14. Change in microhardness with temperature for Fe.18 wt% Ti nitrided in 7NH,:93H, at 585°C and hydrogen reduced at 585”C, aged at 800°C for the times indicated.

The above results show that in as-nitrided Fe-Ti alloys and during the early stages of aging, the prominent deformation mechanism is particle shear by screw dislocations. In general, when precipitate particles are sheared by dislocations during deformation the strengthening of the alloy can be due to (a) coherency strain hardening, (b) order or chemical hardening, (c) modulus hardening, (d) surface hardening and (e) stacking fault hardening mechanisms (see for e.g. [29, 301). In nitrided Fe-Ti alloys it is proposed that coherency, modulus and chemical strengthening contribute to this hardening, while strengthening by other mechanisms is either negligible or not applicable to the system under investigation [&6]. Due to the complex microstructure of nitrided alloys it seems probable that more than one mechanism will control their yield behaviour and strength. The relative contributions of the cutting mechanisms to AZ, the critical resolved shear stress (CR%), is therefore of interest. 4.1. Coherency hardening An estimate of coherency hardening (Ar,), which arises from the interaction of slip dislocations with the stress fields resulting from the coherency strains of the titanium-nitrogen GP zones, can be made by regarding the stress field around the particle as being equivalent to a loop of edge dislocation. The force required to move a dislocation through the zone is then equivalent to that necessary to move it through a forest of dislocations intersecting the slip plane [3 11, with an applied stress given by

where 1 is the average separation of fixed dislocations (i.e. substitutional-interstitial zones) threading the glide plane, b, is their Burger’s vector (taken to be the discontinuity in elastic displacement obtained when a Burger’s circuit is made through the zone and matrix) and G is the shear modulus. The mean nearest neighbour distance has been used as an estimate of the separation of the zones on the slip plane, and is given by [32] z


WI”* 4v

where D is the diameter, t the thickness and V the volume fraction of the substitutional-interstitial zones.





I. Estimates

of the


hardening to be expected from models in nitrided AT,, MN/m* [equation (6)]

Zone parameters D=12nm, r=h b, = 0.05 nm D = 12nm, I = 1nm b, = 0.05 nm D=4nm, /=b b, = 0. I “m D=4nm. f=lnm b, = 0. I nm “Value of friction hValue of friction


Aa,, MN/m’



coherency alloys


and chemical

AT,,,MN/m’ [equation



























stress estimated stress estimated

from grain-size analysis [26]. from yield stress, with k, = I MN/m”’



Estimates of b, were obtained by imaging the Ti-N clusters in a [IOO] matrix zone; with g = 200 Ashby-Brown strain contrast is observed with a line of no contract perpendicular to g [33,34]. Values from such an analysis were found to lie in the range 0.040.1 nm and these are used in Table 1, along with two values for zone thickness (t), to estimate the strengthening due to coherency hardening; the actual increases in CRSS have been multiplied by a Taylor factor of 3.1, the upper limit in b.c.c. and f.c.c. materials [20, 211. Although the results depend on the value of zone thickness, they indicate coherency hardening has its greatest influence at small zone sizes. With particle coarsening this contribution falls quickly, accounting for approximately 15-30% of the observed strength of nitrided Fe-O.18 wt% Ti nitrided at 6.50-C.

lus effect is about ATm z 35 MN/m’, corresponding to a tensile stress of 110 MN/m’. An additional estimate can be made using an equation derived by Mclander and Persson [36], which gives an increment in yield stress of 150 MN/m2. Thus, modulus hardening could account for about 30% of the observed strength increases in nitrided Fe-O. 18 wt% Ti. These calculations are in agreement with the work of Ncmbach [38], where the contribution to hardening due to differences in the shear modulus between matrix and precipitate are small and only noticeable if it is the only mechanism operative. However, if, as is the case for nitrided iron-titanium alloys. the precipitates interact with dislocations via the modulus effect and simultaneously via another mechanism I.C. chemical or coherency hardening, then strengthening due to the modulus difference will be negligible.

4.2. Modulus hardening

4.3. Chemical hardening

Recent work suggests that modulus hardening (AT,,,) when combined with coherency hardening accounts for the total strengthening in nitrided Fe-Ti alloys [6]. Although modulus hardening has been used to explain the strengthening in several systems (for e.g. Fe-Cu [29, 351 and Al-Zn-Mg [36]), its temperature dependence results from the variation of the elastic moduli of matrix and precipitate with temperature, this variation being small [37]. For this reason it seems improbable that such a mechanism could account for the strong temperature dependence of yield strength observed in the present work. Due to the lack of a rigorous analysis for disc-shaped particles, the equation due to Kelly [29] for spheres of radius (u) will be used to estimate At,,,; this approach should be valid for small zones [36]

The stress required to force dislocations through deformable spherical particles at room temperature [28] has been modified by Stephenson [39] for discshaped particles to give




where AG, is the difference in shear modulus between matrix and precipitate and G is the matrix shear modulus. Using accepted values of the shear moduli, for 4 nm particles the strength increment due to a modu-


I Gbys’T[ (9)

where yp is the internal interface energy, ;‘, the surface energy, n the unit vector of the matrix lattice and a the angle between the dislocation line and its Burgers vector. The first term in equation (9) is due to disordering and is known as chemical or order hardening. The remaining terms are due to (i) the creation of a new surface interface, that is. surface hardening, and (ii) the energy required to increase the length of the dipole of edge dislocation arising from production ot jogs when the dislocation enters the particle. In a chemical strengthening model all energy terms arc small relative to yr, the energy required to shear bonds within the particle. To obtain values of ‘Jonecessary for an estimate ot‘ Arci, 9the data presented in Fig. 13 has been analyscd in terms of thermal activation theory [40]. For shortrange obstacles, which are specially sensitive to thermal activation, the force-distance profile for the




interaction between a dislocation may be generalised as


and an obstacle


(a) Fleischer


l-Fe-007VaT1 a-Fe-018VoT1



where AG is the activation free enthalpy, F, is the total free energy necessary to overcome the obstacle without the aid of thermal fluctuations, p and q are positive integers which describe the “tail” and “top” of the peak in the glide resistance profile, z”the local glide resistance, and tr the applied stress. In order to consider the temperature or strain-rate dependence of the flow stress for any obstacle profile, equation (10) is substituted into the strain-rate equation

(11) where i is the strain-rate, i, is assumed to be constant, T is the absolute temperature, and k is Boltzmann’s constant. Each obstacle profile will be defined by particular values of p and q which result in various stress-temperature relationships. Of the interaction profiles available in the literature [41], two appear to approximate to the force/area profile experienced by a dislocation as it approaches a Ti-N cluster. The first is the Fleischer potential, Fig. 15(a), which may be expressed as







lb) Mott - Nabarro






and which gives a linear plot of a”* against T”*; neglecting the variation in obstacle spacing with applied stress. The second is the Mott-Nabarro potential, Fig. 15(b), expressed as

20 1


(13) giving a linear plot of fr213against T2j3 if the variation in obstacle spacing with applied stress is taken into account. Both expressions give straight lines in their respective experimental a/T plots, showing that the interactions which occur in as-nitrided material are short-range and confirming that chemical hardening makes a major contribution to the strength of nitrided Fe-Ti alloys. In the present work the o/T relationships are merely used to confirm that the interactions which occur during deformation of nitrided materials are short-range in nature, and not, as is the case with modulus hardening, long-range. As Fig. 15 shows, it is feasible for the same set of experimental data to give straight lines in several a/T plots making it impossible to decide, on the basis of a linear relationship between o and Tin a given plot, the mechanism responsible for hardening. Considering the Fleischer potential, which may be expressed as

(yL,_(JJ where cr is the yield strength at temperature

(14) T, z^is the

Fig. 15. Hardness (AH)/temperature relationships derived from the data of Fig. 13. yield stress at 0 K, and To is the temperature at which the obstacle can be overcome by thermal fluctuations alone. The following relationship holds at 0 K u.z^ =F,=y,6A


where F, is related to the work expended during yielding in the creation of new surface area (aA), and u is the activation volume. The average area intersected by a random cross-section through a matrix containing a dispersion of disc-shaped particles of diameter (D) and thickness (t) is Dt [42] and by putting v = lb*, where 1 is the separation of particles on the slip plane, equation (15) may be re-written, to yield values of yP z^Ib* ?Jp=Df.


Substituting the values of z^obtained from Fig. 15(a) into equation (16), along with estimates of the other zone parameters, the calculated values of y,, lie in the range 0.62-1.10 J/m* for nitrided Fe-Ti alloys.




Similarly, the tensile data of Fig. 10 gave values of yp = 0.94 J/m*, neglecting the temperature dependence of k,, or 0.74 J/m2 if its variation is considered. Further estimates of yp can be obtained from the expression


Fll k In (i,&)


with the logarithmic term given a value of 30 [40]. The value of yp obtained by applying equation (17) to Figs 10 and 15 is 0.90 J/m*, in excellent agreement with the previous estimates. These are maximum values of yp since they are based on the assumption that chemical strengthening is the only mechanism operative i.e. they neglect the influence of stress fields around or in the zones. If a value of yp equal to 1 J/m* is assumed, substituting the data from Table 1 into equation (9) results in calculated strength increments which can account for at least 50% of those observed; see Table 1. The values of yp calculated for nitrided Fe-Ti alloys are similar to those found in other precipitation hardening systems: 0.53-1.53 J/m2 in AlKu [43]; 0.5-1.28 J/m2 in Fe-Si-Ti [44,45]; 1.3&1.70 J/m* in nitrided Fe-V [16]. When coherency hardening was considered earlier, the temperature dependence of yield strength was not evaluated. The treatment is complex and depends on whether the interaction is considered to be long-range or short-range in nature [46]. For the case of longrange stress fields the problem is one of overcoming a mean internal stress [19], and the various treatments given in the literature differ in the way in which this “averaging” is carried out; see for e.g. [47]. The temperature dependence of yield strength predicted by these various formulae, for the particle sizes usually encountered in precipitation hardening systems, will vary modestly in proportion to the shear modulus of elasticity due to the large energies needed to surmount such long-range obstacles to dislocation motion [46]. However, values of activation energy for coherency hardening may be estimated by considering the interaction between a screw dislocation and a prismatic dislocation loop to vary as [48]

AG -$R

[I -(;yl’


where R is the loop radius, zT. the yield stress at temperature T and z,, is the yield stress. Substituting values for the various parameters in equation (18) shows that for the zone sizes of interest in dilute iron-titanium alloys (approximately 4 nm diameter zones for the Fea.18 wt% Ti alloy, as measured by transmission electron microscopy), the calculated activation energies are in excess of 7 eV; this estimate is greater than the value considered to be capable of thermal activation, typically a few electron volts [49]. Therefore, in nitrided Fe-Ti alloys although a coherency strengthening model could account for the strength increases which result from GP zone




formation (see Table 1) it does not explain the marked temperature dependence of yield strength. In contrast, for irradiated iron, where the obstacles responsible for strengthening are < 1 nm in diameter. values for the activation energies calculated from equation (18) are 1-2 eV and as a consequence these obstacles to dislocation movement give rise to reasonable strengthening and a measurable temperature dependence of yield stress for a coherency hardening model [50]. On this basis, it is reasonable to assume that the yield strength of nitrided Fe-Ti alloys is dominated by chemical strengthening, as evidenced by the marked temperature dependence of yield strength, with a contribution from coherency hardening at small particle diameters whose temperature dependence becomes more significant with decreasing zone size. However, as Fig. 10 shows, the temperature dependence of yield strength of nitrided materials falls into two main regimes-when tested below room temperature, the Pierels-Nabarro force of the iron matrix dominates, with the GP zones adding a constant fraction to the athermal component of the friction stress. while with increasing temperature. the particle cutting mechanisms themselves account for the temperature dependence of yield strength. Such behaviour can be interpreted by the theoretical predictions of Guiu [51], who proposed a model for the glide of a dislocation through a square array of localised obstacles, in the presence of a friction stress. When the friction stress is large, as it is for nitrided Fe-Ti alloys, the localised obstacles are almost transparent to the glide dislocation; for this behaviour to predominate the following condition must be satisfied H,,*- v,* t, < Ho, + Dk T


where Ho, and H,,&are the total activation enthalpies of the Peierls and localised barriers, CT is the aciivation volume of the localised obstacles, 5, is the applied stress, and D is a logarithmic term of magnitude close to zero. Using typical values for H,,, and D for the Peierls mechanism in a-iron, Guiu [51] has shown that equation (19) is satisfied for values of H,, < -2 eV. Approximate values of H,,, evaluated from Figs 10 and 15 along with equation (17), show that for nitrided iron-titanium alloys containing ~0.32 wt% Ti this condition is satisfied (H,), for the Fe-Ti alloys -2.5 eV). For such alloys, the iemperature dependence of the effective stress of the matrix is so strong that precipitates contribute only by increasing the athermal component of the stress; in accord with the experimental findings of this, and previous investigations into precipitation hardening of b.c.c. materials [6, 521. When nitrided materials are overaged, a change in deformation mechanisms from cutting to looping occurs which is accompanied by a rapid increase in work-hardening rate. The contribution of Orowan hardening, by platelets of titanium nitride in a b.c.c.







of such alloys is attributed to chemical strengthening and the proposal is supported by detailed friction stress calculations. 2. Iron is rejected from the initially formed Ti-N zones when nitrided alloys are aged at the nitriding or higher temperatures. These changes in zone composition cause an increase in yield strength through changes in zone strength (i.e. yp), and alter the fracture behaviour of underaged alloys. 3. Yielding of the overaged alloys is accompanied by an increase in work hardening, caused by dislocation bowing around titanium nitride platelets, and by a reduction in the temperature dependence of the flow stress. The strength of these alloys can be adequately accounted for by Orowan hardening. Fig. 16. Observed increases in yield strength against those predicted from equation (20). Chen [7]: 0; Hamano and Tsuya [8]: n ; present work: 0.

matrix (A7,,), can be calculated expression [29, 531 AT,, =

0.83 Gb 2x(1 -v)“21

by the following

1 -1nA



authors gratefully acknowledge the support of the Science Research Council for the provision of a research support grant (DSR). We also offer our thanks to Drs T. F. Page and M. Naylor of the Department of Metallurgy, University of Cambridge for the use, with their help, of the hot-hardness testing equipment. We are also indebted to Professor K. H. Jack for discussion, encouragement and provision of facilities



where v is Poisson’s ratio, 1 the interparticle spacing, and Y,,the dislocation core radius taken equal to the Burger’s vector. The theoretical values of AT,, were determined by using the observed values of 1 and are plotted against the observed values (AT,~) in Fig. 16. The chief uncertainty when converting values of CRSS calculated from equation (20) to yield stresses is the value of the Taylor factor; for the results of the present work and those of Humayo and Tusya [8] a value of 3.1 was used, while the results of Chen [7] are better described by a value of 2.6. If the Orowan strengthening mechanism is responsible for the observed increase in strength for overaged alloys the slope of the straight line given in Fig. 15, should be unity passing through the origin. The slope of the best fitting line was found to be 1.013 and the value of the y-axis intercept was 6.6 MN/m*. Therefore, it is seen that Orowan hardening, as represented by equation (20) for flat discs, accounts quite satisfactorily for the observed strengthening in overaged Fe-Ti alloys. 5. CONCLUSIONS

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1. In nitrided F+Ti alloys the zones formed on nitriding are initially cut by long, straight screw dislocations of Burger’s vector ;(lll), and the yield strength is highly temperature dependent. The temperature dependence of nitrided iron-titanium alloys, at T < 400 K, is unaffected by the presence of

these zones in agreement with the theoretical work of Guiu [51]. When tested above 400 K, where the Peierls-Nabarro force for b.c.c metals is no longer effective, the temperature dependence of the strength

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