Materials Science & Engineering A 673 (2016) 467–475

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Materials Science & Engineering A

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Effects of tempering mode on the structural changes of martensite

D.C. Saha a,n, E. Biro b, A.P. Gerlich a, Y. Zhou a

a Centre for Advanced Materials Joining, Department of Mechanical & Mechatronics Engineering, University of Waterloo, 200 University Avenue West,Waterloo, Ontario, Canada N2L 3G1b ArcelorMittal Global Research, 1390 Burlington Street East, Hamilton, ON, Canada L8N 3J5

a r t i c l e i n f o

Article history:Received 9 June 2016Received in revised form20 July 2016Accepted 22 July 2016Available online 25 July 2016

Keywords:Martensite temperingTransmission electron microscopyCrystallographyDislocation densityNanoindentationStrength

x.doi.org/10.1016/j.msea.2016.07.09293/& 2016 Elsevier B.V. All rights reserved.

esponding author.ail address: dcsaha@uwaterloo.ca (D.C. Saha).

a b s t r a c t

Tempered martensite obtained from four different tempering modes were characterized using trans-mission electron microscopy, high-angle annular dark field scanning transmission electron microscopy,and nanoindentation techniques. Crystallographic analysis of tempered martensite revealed that ferrite(α) and cementite (θ) obtained via furnace and Gleeble heat treatment obeyed the Isaichev orientation(or close to it) with [ ̅ ]θ311 0.91° from [ ̅ ]α111 and the ||[ ̅ ]α θ

⎡⎣ ⎤⎦112 001 Bagaryatsky orientation relationship.A strict orientation relationship between ferrite and cementite could not be determined on the temperedstructure extracted from the sub-critical heat affected zone of two different laser beam welded samples.Extensive recovery and reduction of boundary regions was identified on the structure tempered slowly,whereas rapidly tempered structures retained a high density of dislocation and less decomposition of thelath structure. The relationship between dislocation density and modified tempering parameter wasdetermined and their contributions on tensile strength were evaluated.

& 2016 Elsevier B.V. All rights reserved.

1. Introduction

Tempering of martensitic steels is essential to suppress brittlefracture and ensure a desired combination of strength and ducti-lity. During tempering, the strength of martensitic steel decreasesdue to ejection of carbon atoms from the carbon supersaturatedmartensite phase [1]. Martensite tempering involves a series ofprocesses. In the first stage of tempering which occurs betweentemperature 80–200 °C, the segregation and redistribution ofcarbon atoms take place into lattice defects such as dislocations,lath boundaries, and prior-γ grain boundaries. In addition, thetransitional epsilon-carbides (ε-Fe2.4C) also formed in this tem-pering stage [2–4]. The interlath film like retained austenite de-composes into ferrite (α) and cementite (θ-Fe3C) in the secondstage of tempering (200–300 °C). In the third stage of tempering,segregated carbon and transitional carbides transform into stablecarbides such as cementite (Fe3C), which occurs at higher tem-perature, in the range of 250–350 °C [4]. At temperatures above350 °C, the cementite spheroidizes and coarsens [4]. There arenumerous factors which influence the martensite tempering pro-cess, such as: tempering temperature [5,6], tempering time [5,6],heating rate [7–9], and the steel chemistry [10,11]. Tempering isused in variety of applications, these can be divided broadly intorapid tempering applications and slow (or conventional)

tempering applications. In rapid tempering, the tempering occurson the order of seconds or less. Industrial examples of rapidtempering include: induction heating, laser heat treatment, andtempered heat-affected zone (HAZ) transformations duringwelding and joining [10–12]. Slow tempering is typically used infurnace post weld heat treatments, and tempering parts made ofquench and temper steels. Tempering technique can also affectprocess costs. For example, induction heating process is cost ef-fective due to the shorter processing time [7,9,13,14]. On the otherhand, a conventional tempering cycle is used to obtain a desiredhomogeneous microstructure with a uniform optimum mechan-ical property [15]; therefore, the conventional furnace temperingprocess is suitable for a large-scale component which requiresslow cooling to obtain a homogeneous microstructure.

Typical microstructural features such as crystal defect sites(especially with high dislocation densities), lath sizes, and block orpackets sizes are influenced by the mode of heating and heatingrate. Hernandez et al. [10] studied the consequences of isothermaland nonisothermal tempering process on dual-phase steel. Theyreported that the nonisothermal process employed using a re-sistance spot welder produces finer cementite and lesser recoveryin the ferrite structure compared to that obtained in a furnace heattreatment (isothermal tempering) process. It has been also re-ported that steel containing rich alloying elements such as Mn,and Cr has higher resistance to softening compared to a lean Mnand Cr containing steels [11].

The objective of the present study is to examine the temperedstructures of 0.24% C containing fully martensitic steel produced

D.C. Saha et al. / Materials Science & Engineering A 673 (2016) 467–475468

with various tempering modes such as a furnace heat treatment(FHT), Gleeble heat treatment (GHT), diode laser welding (DLW),and fiber laser welding (FLW) via transmission electron micro-scopy (TEM), high-angle annular dark-field scanning TEM (HAADF-STEM) imaging, and nanoindentation study. Crystallographicanalysis using selected area diffraction (SAD) patterns and na-noscale microstructure-properties correlations are evaluated. Inaddition, the strength contribution from high dislocation densitiesand precipitation are evaluated for the four tempering conditionsconsidered.

Fig. 1. Thermal cycles imposed on martensitic steels during tempering using aGleeble heat treatment (GHT), fiber (FLW), diode laser welder (DLW), and furnaceheat treatment (FHT).

2. Experimental

A 1.20 mm thick 0.24% C containing fully martensitic steel wereused; the chemical compositions of the investigated steel is shownin Table 1. In order to obtain various tempered structures, differenttempering methods were employed with different heating andcooling rates, temperatures, and times (Fig. 1, and Table 2). Toproduce a FHT sample, tempering was carried out in a mufflefurnace at 500 °C for 1 h; and a GHT sample was obtained byheating the sample at a heating rate, temperature, and time of100 °C/s, 495 °C, and 1 s, respectively (Fig. 1). Two other sampleswere prepared from the sub-critical HAZ (Ac1 isotherm line) ofdiode and fiber laser welded samples, which are henceforth re-ferred as the DLW, and FLW sample, respectively (Fig. 1). It can benoted that the thermal profiles presented in Fig. 1 were measured(using a thermocouple welded to the sheet surface) directly fromthe HAZ during diode laser and fiber laser welding. Due to thenarrow HAZ width (about 400 mm) of FLW, it was not possible torecord the temperature close to the Ac1 isotherm line; however,the heating and cooling sections of the thermal profile was suc-cessfully predicted (using a suitable curve fitting method) andextended to Ac1 line (725 °C) as shown in Fig. 1. The cooling rate inthe sub-critical HAZ of the laser welded samples were estimatedusing the Rosenthal Eq. (1) [16]:

( )Θ πα

υ Θ Θ∂∂

=− ∆ −( )

⎛⎝⎜

⎞⎠⎟t

kQ

2 x1

s2 2

03

where ∂Θ/∂t is the cooling rate, ks is the thermal conductivity ofthe steel (30 W/m/K), α is the thermal diffusivity of the steel(5.613�10�6 m2/s), υ is the welding speed (m/s), Δx is the sheetthickness (mm), Q is the power input (J/mm2), Θ, and Θ0 aretemperature (K) of the sub-critical HAZ (998 K) and the ambienttemperature (298 K), respectively [17]. The parameters used totemper the samples such as heating rates, cooling rates, tem-perature, and time are presented in Table 2. In this work, the FHTand DLW processes are categorized as slow tempering modes, andthe FLW and GHT are regarded as fast tempering modes due to thedifferences in heat input, and heating rates.

The microstructure of the tempered structure of the sampleswere analyzed using a field-emission scanning electron micro-scope (FE-SEM, Model: Zeiss Leo 1550), and TEM. The particle sizeswere measured using an image analysis software (imageJ) fromseveral high-resolution FE-SEM micrographs with a magnificationof 100,000� ; more than 1000 particles were measured for eachcondition. The carbide sizes presented here are the equivalentcircular diameter of the particles with the equivalent area. TEM

Table 1Nominal composition of the martensitic steel used in this investigation.

C Mn P S Si Cr Mo Ti

0.24 0.4 0.01 0.01 0.20 o0.1 o0.1 0.04

samples were prepared using twin-jet electropolishing of the3 mm disks punched from the foils of o50 mm thickness. Micro-structure was analyzed using a JEOL 2010F (Japan Electron OpticsLtd., Tokyo, Japan) electron microscope operated at 200 kV.

Vickers microhardness measurements were carried out using aload of 1 kg with 15 s dwell time; the microhardness value pre-sented here is the average value of 12 individual indents (thetolerance limit represents 95% confidence interval) separated witha spacing of 200 mm. To estimate nanoscale properties of thetempered structures, same Vickers microhardness indented sam-ples were used for the nanoindentation; the study was performedusing a Hysitron Triboindenter TI-900 equipped with a scanningprobe microscope in a load control condition with a loading rate of500 μN s�1 up to a maximum load of 5000 mN. 12 nano indents(3�4 matrix) were made in a 50 mm�50 mm area with a spacingof about 10 mm between indents.

3. Results and discussion

3.1. As-received martensitic microstructure

Fig. 2 shows the microstructure of as-received material whichcontains fully autotempered [18] typical lath-like martensite withan estimated prior-γ grain size (measured using a linear interceptmethod [19]) of about 6.370.72 mm (marked with arrows in Fig. 2(a)). Each prior-γ grain is divided into four packets as outlinedwith dotted lines in Fig. 2(a). Two kinds of laths were developedduring martensitic transformation due to the differences intransformation sequences and temperatures [20]. The coarse lathswere formed at the beginning of the martensite formation withrelatively high temperature and exhibited reasonably low dis-location density due to greater recovery of dislocations throughoutthe extended period of transformation [20,21]. On the other hand,thin martensite laths formed at a later stage of martensite trans-formation which maintained a high dislocation density (Fig. 2(b)).The intralath carbides associated with the autotempered marten-site are also delineated in Fig. 2(a). It was observed that the au-totempered carbide likely to be precipitated on the coarse mar-tensite laths (thickness: 4500 nm) whereas thin laths with anapproximate width of 200 nm were free of autotempered carbides(Fig. 2(b)). TEM micrograph of lath martensite (Fig. 2(b)) indicateddifferent contrast of martensite variants (bright and dark) undercertain incident directions of the electron beam. SAD patterns ta-ken from the martensite laths were indexed by following the

Table 2The parameters used to temper the samples.

Sample ID Heating rate (°C/s) Temperature (°C) Time (s) Cooling rate (°C/s) Tempering parameter

FHT Isothermal 500 3600 Air cooled 15,460DLW 115 725 Nonisothermal 1248 18,740GHT 100 495 1 50 13,000FLW 517 725 Nonisothermal 10,856 13,550

Fig. 2. Typical martensitic microstructure of as-received material; (a) FE-SEM micrograph of a prior-austenite grain of martensite with four packets and several blocks,(b) TEM image with indexed SAD pattern (inset) of lath martensite showing the zone axis of [ ]α′013 ; the faint diffraction spots corresponding to nanoscale autotemperedcarbides are marked with circles.

D.C. Saha et al. / Materials Science & Engineering A 673 (2016) 467–475 469

body-centered tetragonal (bct) structure of martensite (α′) show-ing the projection plane of [ ]α′013 . The faint diffraction spots(marked with circles on the inset SAD) were also observed illus-trating the presence of autotempered carbides as identified on theFE-SEM micrograph (Fig. 2(a)). The carbide spots were indexed tobe orthorhombic crystal structure of cementite (Pnma) with a d-spacing of 2.102 Å corresponding to < >θ211 cementite reflection as

Fig. 3. Representative high-resolution FE-SEM micrographs of the tempered martensite

marked on inset SAD pattern in Fig. 2(b).

3.2. Characterization of tempered martensite

The sheet was tempered using various tempering methods andparameter as described in the experimental section (Table 2) andthe resulting high-resolution FE-SEM micrographs are shown in

obtained via various tempering methods; (a) DLW, (b) FHT, (c) FLW, and (d) GHT.

Table 3Carbide size measurements at different samples obtained with different temperingmodes.

Temperingmode

Sampleconditions

Low-angleboundaries(nm)

High-angleboundaries(nm)

Inter-par-ticle dis-tance(nm)

Particledensity(nm�2)

Slow heat-ing mode

DLW 4571.23 17073.51 245 1.6E�5FHT 5872.10 14573.68 201 2.5E�5

Fast heatingmode

FLW 3571.05 9571.58 100 10.0E�5GHT 3970.61 5671.49 134 5.6E�5

D.C. Saha et al. / Materials Science & Engineering A 673 (2016) 467–475470

Fig. 3. The micrograph from the DLW sample (Fig. 3(a)), indicates aseverely tempered structure, and the GHT sample (Fig. 3(d)) ex-hibits a comparatively less tempered structure. The DLW sampleshows highly decomposed martensite with spheroidized carbidesat laths boundaries (with particle diameters: 4571.23 nm,marked with smaller arrows) and prior-γ grain boundaries (withparticle diameters: 17073.51 nm, marked with bigger arrows). Inthe DLW sample, the intra-lath carbides are almost dissolved (lessparticle density: 1.6�10�5 nm�2 compared to other conditions(Table 3)) representing a greater reduction of dislocation densityas intra-lath carbides mainly precipitated at dislocation cellstructures.

In addition, the inter-particle distance (245 nm) was also largeron the DLW sample compared to the other conditions (Table 3)suggesting less Orowan looping effect [22,23]. While the samplewas tempered in a furnace at 500 °C for an hr (FHT sample, Fig. 3(b)), similar morphologies of spheroidized carbides were identi-fied. However, some of the smaller intra-lath carbides in the FHTsample (marked with small arrows) were also observed indicatingthe presence of a low dislocation density, which was further ob-served via TEM and HAADF-STEM imaging as will be discussed in alater section. The FLW (Fig. 3(c)) and GHT (3(d)) showed more

Fig. 4. Bright-field TEM micrographs and HAADF-STEM images and their correspondinsample.

dispersedly distributed finer carbides; however, the carbides in theGHT sample had an elongated shape with an aspect ratio of about3.8570.47. On the other hand, many small quasi-spherical car-bides were observed in the FLW sample with a diameter of about3571.05 nm. The morphological differences of the carbidesamong these two samples (FLW and GHT) were solely related todifferences in heating rates (Table 2), where heating rate in theFLW process was about five times higher than the one applied inthe GHT process (100 °C/s). The spherical shape of carbides on theFLW sample representing short range carbon diffusion due tohigher particle density and shorter inter-particle spacing. It iswell-known that the maximum number of precipitates is directlyproportional to the density of nucleation sites [24]; therefore, itcan be presumed that the precipitates nucleated at dislocationsites maintain an identical size and shape distributions (Fig. 3(c)).As per Perrard et al. [24], when there is a high dislocation density,the nucleation process is accelerated due to greater solute con-sumption; as a result, the growth period is ceases and the particlesdirectly go from nucleation to coarsening. Conversely, directionaldiffusion of carbon may occur along the length axis of carbidesfound on a GHT sample; therefore, an elongated shape of carbideswas precipitated.

3.3. TEM and HAADF-STEM analysis of matrix and precipitates

In order to investigate the influences of the tempering modeson subtle microstructural changes of martensite, TEM and HAADF-STEM imaging were performed and the results are presented inFigs. 4 and 5. TEM study revealed disc-shape, and spherical-shapecarbides at high- and low-angle boundaries, in the DLW and FHTsamples, respectively. In the HAADF-STEM images (Fig. 4(b) and(e)), the precipitated carbides appeared to be brighter in contrastresulting from very high-angle, incoherently scattered electrons.The carbides observed on the DLW sample are well-developed,

g indexed matrix-precipitates SAD patterns; (a)–(c) DLW sample, and (d)–(f) FHT

Fig. 5. Bright-field TEM micrographs and HAADF-STEM images and their corresponding indexed matrix-precipitates SAD patterns; (a)–(c) FLW sample, and (d)–(f) GHTsample.

D.C. Saha et al. / Materials Science & Engineering A 673 (2016) 467–475 471

coarser, and randomly distributed. Similar coarser carbides athigh-angle boundaries were identified on the FHT sample (Fig. 4(d) and (e)); in addition, spherical intralath carbides (diameter:o100 nm) are also observed. The presence of these intralathcarbides may be attributed to: (i) precipitation at the final stage ofcarbide precipitation or (ii) a dissolution state (as per classicalnucleation theory) due to smaller than the critical carbide size[25,26]. On the other hand, the high-angle boundary carbides areinterconnected (Fig. 4(e)) illustrating a short-circuit diffusion path[26]. The carbides observed in the tempered martensite structureswere indexed to be orthorhombic crystal structure of cementite(θ-Fe3C) whereas the matrix phase was identified as body-cen-tered cubic (bcc) phase of ferrite. The orientation relationships(OR) between ferrite (α) and cementite (θ) were determined to be

||[ ] [ ]α θ023 110 , and ||[ ̅ ] [ ̅ ]α θ111 311 for the DLW (Fig. 4(c)), and FHTsample (Fig. 4(f)), respectively. The ferrite and cementite OR in theFHT sample was matched with Isaichev OR [27,28] (or close to it)with [ ̅ ]θ311 at an angle of 0.91° from [ ̅ ]α111 .

Conversely, intra- and inter-lath carbides became extremelyfine and densely spaced when rapid thermal cycles were em-ployed using a fiber laser and Gleeble thermal cycling (Fig. 5(a) and (d)). It was noticeable that the size distribution of carbidesat low-angle boundaries were similar for both the FLW and GHTsamples; however, the size of the carbides located at the high-angle boundary in the FLW was about three times larger thanthose from the GHT sample (Table 3). Interestingly, the intra-lathcarbides found on the FLW sample were randomly distributed andspherical in shape (Fig. 5(b)); however, the carbides in the intra-lath position of the GHT sample maintained a specific orientationrelation with the adjacent laths. It was observed that the multi-variate carbides were oriented along o1124 direction of theferrite matrix with an approximate angular position of 33° to thelath boundary (inset of Fig. 5(d)). The indexed SAD patterns pre-sented in Fig. 5(c) and (f) confirmed the OR of ||[ ] [ ¯ ]α θ012 241 , and

||[ ̅ ]α θ⎡⎣ ⎤⎦112 001 for the FLW, and GHT sample, respectively. It is

noted that the cementite precipitated on the GHT sample main-tained a well-defined Bagaryatsky orientation relationship [29,30].

TEM study of the slowly tempered structures (Fig. 4) revealed alow dislocation density on the ferrite structure, suggesting that therecovery of dislocation substructure was more pronounced in thecase of slowly heated samples [10]. Conversely, the faster thermalcycles provided less tempering time, retained more dislocation cellstructures (Fig. 5) [7]; with some of the dislocation lines markedwith arrows for example in Fig. 5(e). In addition, the dislocationlines observed on the GHT sample are almost parallel to the lengthaxis of the cementite platelets attributing the growth of the plate-like cementite occurred along the dislocation line.

3.4. Dislocation density and tempering parameters

The dislocation density is an important parameter which im-pedes the lattice movement, thus increases the strength of thesteels. To estimate the dislocation density, several experimentalmethods are usually employed such as X-ray diffraction line-broadening method [31], TEM [32], electron backscattered dif-fraction (EBSD) [9,33]. In the present investigation, the dislocationdensity of untempered martensite was estimated using a syn-chrotron X-ray measurement at the 33-ID-D beamline of the Ad-vanced Photon Source (APS) at the Argonne National Laboratory.The dislocation density of the steel sample was estimated to be inthe order of 4.9070.5�1015 m�2, which is about three timescompared to other studies (about 1.6�1015 m�2 [32,34]) for theidentical martensitic steel carbon content (0.2%). It is well-knownthat dislocation density is not uniform throughout the sample,therefore, the values measured using TEM and EBSD techniquemay provide local dislocation density. On the other hand, thesynchrotron measurement is considered a bulk area analysis

Fig. 6. (a) Relationship between dislocation density and the carbon content of lath martensite, and (b) a plot of dislocation density as a function of the modified temperingparameter.

D.C. Saha et al. / Materials Science & Engineering A 673 (2016) 467–475472

which provides more representative values of the average throughthe thickness.

Fig. 6(a) shows a relationship between dislocation density andthe carbon content of steels [7,9,32,35,36], which indicates thatdislocation density increases with carbon content due to localdistortion induced by the interstitial carbon atoms. Aside fromcarbon content, dislocation density is also influenced by coolingrate, and martensite start temperature during transformation [32].However, when a highly dislocated martensite phase is exposed toan elevated temperature, then dislocation density decreases due toannihilation and recovery process [1,23]. Dislocation density isexpected to decrease with tempering temperature, and holdingtime; however, a slow heating cycle results in more annihilationand recovery rate than rapid heating as observed in Figs. 4 and 5are in accordance with other studies [7,9].

In the present study, the tempering processes considered havedifferent heating rate, temperature, and time (Table 2); therefore,the influences of these factors were combined in the form of amodified tempering parameter as proposed by Tsuchiyama [37].The proposed model applies the additivity rule for time in order toconsider heating and cooling time during tempering. In thismethod, the heating and cooling cycles are divided into severalsmall isothermal time (tn) segments at Tn temperature. After nisothermal steps, the tempering parameter (TPn) can be presentedas:

Fig. 7. (a) Vickers microhardness and nanohardness of tempered martensite plotted as ato Vickers microhardness.

)(= + ( )TP T t20 log 2n n n

( )= +∆ ( ){ + − }−

−t t10 3n

TT

t20 log 20nn

n1

1

α= + ∆ ( )−T T t 4n n 1

where α and Δt are the heating or cooling rate and the isothermaltime step at Tn�1 temperature, respectively. By plotting dislocationdensity as a function of modified tempering parameters of fullymartensitic steels [7,9], it is found that the dislocation density ofthe tempered martensite varied as a cubic function (fitting coef-ficient, R2¼0.96) of the modified tempering parameter (Fig. 6(b)).Using the fitted function, the dislocation density of the studiedsamples are predicted based on their modified tempering para-meter as shown in Fig. 6(b); the highest recovery of dislocations ispredicted for the DLW sample which is due to greater heat inputand higher tempering parameter [12]. Conversely, the GHT sampleexperiences less recovery and a high amount of dislocation densityis retained as observed experimentally via TEM as shown in Fig. 5(d) and (e).

function of tempering conditions, and (b) plot of hardness ratio (Hn/HV) with respect

D.C. Saha et al. / Materials Science & Engineering A 673 (2016) 467–475 473

3.5. Micro- and nano-scale properties

Microhardness and nano-scale properties of the temperedmartensite were further assessed using Vickers microhardness andnanoindentation tests as shown in Fig. 7. There are four micro-structural units in a low carbon lath martensite, prior-γ grains,packets, blocks, and laths. The prior-γ grain is typically dividedinto four packets (Fig. 2(a)), which is composed of six blocks withidentical crystal orientation, and each block is further subdividedinto several parallel laths (Fig. 2(b)) with a high density of latticedefects [38–41]. The lath boundaries are considered to be low-angle grain boundaries (θmin¼2.8–2.9°) and do not provide ef-fective dislocation barriers. On the other hand, block boundarieseffectively impede dislocation propagation; therefore, these areconsidered major boundaries in lath martensite [42]. The hardnessmeasured using a Vickers indentation combines all of the micro-structural units including high- and low-angle boundaries, dis-location, solid solution, precipitation. Conversely, using a na-noindenter (Berkovich type) with a smaller tip size (about 50 nmtip diameter) which is less than the lath width (about 200 nm);therefore, the effects of high-angle boundaries (θminZ15°) on thenanohardness may be disregarded [43,44].

Fig. 7(a) illustrates the Vickers micro- and nanohardness of fourtempered martensite structures considered here; in which themicrohardness values are converted to GPa for comparison. Bothhardness measures increase as heat input decrease (signifying alower tempering parameter (Table 2)), due to a fewer structuralchanges, a larger boundary area, and the higher matrix strength.Nanohardness measured on the samples are higher than adjacentmicrohardness tests which is due to the effect of various bound-aries present on a martensite phase as reported by Ohmura et al.[43–45]. The structure containing a large amount of boundarieshas a higher hardness compared to the structure with a fewerboundaries. The largest hardness differences were measured onthe DLW sample which was due to the absence of a high amount ofdislocation density in the vicinity of boundaries. It has been re-ported that nano-indents located at a boundary exhibit highernanohardness than inside the laths [20,21,46]; therefore, the ab-sence of boundaries resulted in a lower microhardness value onthe DLW sample. However, the deviation of hardness values de-creases as it approaches to rapidly heated condition; it is notice-able that for the GHT sample, both hardness values are similar dueto less softening of the boundary areas. It may be concluded thatwhen the structure is heated slowly, the high-angle boundaryregions softened more than the low-angle boundaries as carbondiffusion occurred much faster in the high-angle boundaries dur-ing tempering [4,7,47].

Fig. 7(b) shows a plot of hardness ratio (Hn/Hv) as a function ofVickers microhardness; the hardness ratio represents the con-tribution of matrix strength on the total macroscopic hardness ofthe structure as can be approximated by the following relation-ship.

= −′

( )

−HH

k dH

15

n

V V

12

Where, the locking parameter k′ is a constant, and d is the grainsize. Ohmura et al. [43–45] reported that the higher the Hn/Hv

ratio, the greater the reduction of the grain boundary effect onmacroscopic strength. Therefore, from Fig. 7(b), it may be con-cluded that DLW sample has higher destruction of the boundaryregions (greater recovery) so in this sample, grain boundarystrengthening will give less contribution to overall strength as tothe FLW and GHT samples.

3.6. Contribution of dislocations and precipitates on martensitestrength

Typically, the yield strength of lath martensite is correlatedfrom the contributions of lattice friction stress of pure iron, thesolid solution strengthening, the precipitation strengthening (spct),grain boundary strengthening, and forest dislocation densitystrengthening (sρ) at lath and sub-block boundaries. However,considering the tempering effect on the strength, in this study,only dislocation density and precipitation strengthening areevaluated. The solid solution hardening effects on the tensilestrength have been disregarded as only a single steel chemicalcomposition was used and negligible carbon remained in the solidsolution after tempering. A separate study carried out using Dila-tometry confirmed that the carbide precipitation has completedwhen the sample was tempered with a tempering parameter of13,000 (GHT sample) which was the lowest tempering parameteramong the four types of the sample considered. Therefore, it canbe presumed that all of the carbon atoms already diffused andcombined with the iron atoms to form stable cementite, justifyingthe decision to omit the effect of solid solution strengthening ontensile strength. The strength contribution in relation to the dis-location density is estimated using Taylor formula [48]:

σ α ρ∆ = ( )ρ M Gb 6

where M¼3 is the Taylor factor, α¼0.25 is a fitting constant re-lated to the interaction between forest dislocations [49],G¼76 GPa is the elastic isotropic shear modulus of lath martensite[50], b is the Burgers vector, and ρ is the dislocation density. Theferrite lattice constant of the investigated steel was estimated fromthe TEM selected area diffraction patterns to be a¼2.91570.015 Å.The value of b is considered to be 2.52 Å along o1114 slipdirection.

The strength of lath martensite can be correlated from thecontributions of the carbide precipitation which may increase thestrength by impeding dislocation glide [22,51]. The contribution ofprecipitation strengthening is predicted using the Orowan-Ashbymodel [22,23] as presented in Eq. (6).

σ = ( ) ( )f

dd10. 8 ln 1630 7pct

where, f and d are the volume fraction of precipitate and meanparticle diameter (mm), respectively. The volume fraction and themean particle diameter are estimated from the high-resolution FE-

Fig. 8. Dislocation density and precipitation strength predictions as a function ofthe modified tempering parameter for four different tempered martensite samples.

D.C. Saha et al. / Materials Science & Engineering A 673 (2016) 467–475474

SEM and TEM micrographs by following the formula as describedin Ref. [22].

The contribution of strength due to a high density of forestdislocations and precipitation are plotted in Fig. 8 with respect tothe modified tempering parameter. The graph shows that thedislocation density has prominent contribution over that of thecarbide precipitation, and the observation is consistent with otherresearchers [42]. The structure heated with rapid nonisothermalprocess (FLW sample) possessed the highest precipitation hard-ening effect due to highest particle density (10�10�5 nm�2) re-sulting from a short carbon diffusion and shorter growth period,although the high-angle boundary carbides were larger than theone on GHT sample (Table 3). In overall, rapidly tempered GHT andFLW samples have higher precipitation strength contributionscompared to the slowly tempered FHT and DLW samples; a similarphenomenon was observed by Biro et al. [52]. As expected, dis-location density strength contribution declined as a function oftempering parameter (Fig. 8), which was reported by other re-searchers [42,53,54] as a function of tempering temperature.

4. Conclusions

In-depth characterization of the tempered martensite obtainedfrom various thermo-mechanical processing methods were char-acterized using TEM and nanoindentation study. The major find-ings are summarized as follows:

1. Crystallographic analysis of the tempered martensite confirmedBagaryatsky and near Isaichev OR between ferrite and ce-mentite on the sample produced via Gleeble thermomechanicalsimulator and isothermal furnace heat treatment, respectively.On the other hand, ferrite and cementite observed on thenonisothermally produced laser welded samples do not obey astrict OR.

2. The growth kinetics of precipitated carbides are suppressedwhen samples were subjected to rapid thermal cycle employedvia fiber laser welding. In addition, a rapidly tempered structuremaintains a high density of dislocation and less destruction ofboundary regions.

3. Microscopic structural softening was more pronounced onsamples subjected to slow heated cycles; conversely, micro-scopic and nanoscale hardness was found to be in the samelevel when rapid thermal cycle was employed.

4. The tempering mode has a prominent effect on the softening ofthe high-angle boundaries compared to the low-angle bound-aries due to the faster carbon diffusion at high-angle bound-aries. Therefore, when the slow heated cycle was applied, thehigh-angle boundary carbides become coarser and spher-oidized; conversely, the size of the low-angle boundary carbideswas less influenced by the mode of thermal cycle.

5. Structures subjected to rapid thermal cycles showed less ferritegrain recovery. After tempering, a higher dislocation densitywas retained in rapidly tempered structures due to the shortertempering duration.

6. The strength contribution due to dislocation density was higherthan that of precipitation strengthening for the temperedmartensite. Rapidly tempered samples have higher precipitationstrength contributions compared to the slowly temperedsamples.

Acknowledgments

Authors would like to acknowledge AUTO21, Canada's Auto-motive Research and Development Program, NSERC, Canada and

Innovation in Automotive Manufacturing Initiative (IAMI) in Ca-nada for financing this project. Authors are thankful to Arce-lorMittal Dofasco Inc. in Hamilton, Canada for providing the ma-terials to carry out this work. The authors would like to thank Dr.Levente Balogh from the Department of Mechanical and MaterialsEngineering, Queen's University, for the dislocation density mea-surements from the Synchrotron data, and Dr. Yuquan Ding fromthe Mechanical and Mechatronics Engineering Department, Uni-versity of Waterloo for his kind cooperation with the na-noindentation study.

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