On the plasticity mechanisms of lath martensitic steel

Author’s Accepted Manuscript On the plasticity mechanisms of lath martensitic steel Kyoung-Rae Jo, Eun-Jung Seo, Dimas Hand Sulistiyo, Jin-Kyung Kim, Seong-Woo Kim, Bruno C. De Cooman www.elsevier.com/locate/msea

PII: DOI: Reference:

S0921-5093(17)31030-4 http://dx.doi.org/10.1016/j.msea.2017.08.024 MSA35372

To appear in: Materials Science & Engineering A Received date: 13 April 2017 Revised date: 4 August 2017 Accepted date: 6 August 2017 Cite this article as: Kyoung-Rae Jo, Eun-Jung Seo, Dimas Hand Sulistiyo, JinKyung Kim, Seong-Woo Kim and Bruno C. De Cooman, On the plasticity mechanisms of lath martensitic steel, Materials Science & Engineering A, http://dx.doi.org/10.1016/j.msea.2017.08.024 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting galley proof before it is published in its final citable form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

On the plasticity mechanisms of lath martensitic steel Kyoung-Rae Jo1, Eun-Jung Seo1, Dimas Hand Sulistiyo1, Jin-Kyung Kim1,*, Seong-Woo Kim2, Bruno C. De Cooman1 1

Materials Design Laboratory, Graduate Institute of Ferrous Technology, Pohang University of Science and Technology, Pohang 37673, Republic of Korea 2

POSCO Technical Research Laboratories, Gwangyang 57807, Republic of Korea

* Corresponding author: Jin-Kyung Kim, [email protected]

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Abstract The plasticity mechanisms of press hardening steel with a fully lath martensite microstructure were examined experimentally by strain rate sensitivity measurements, repeated relaxation tests and internal friction measurements. The analysis of relaxation tests suggests that the micro-plasticity could be due to the motion of mobile non-screw dislocations, based on mobile dislocation exhaustion observed in the micro-plastic range. In the macro-plastic range, the plasticity is thought to be due to the generation of mobile screw dislocations. The solute carbon-dislocation interaction results in a negative strain rate sensitivity and a Snoek-KösterKê peak in the internal friction spectrum of the lath martensitic press hardening steel. The magnitude of the effective activation volume and its stress dependence indicate that plastic deformation is most likely controlled by screw dislocation motion by formation and lateral movement of kink pairs dragging solute carbon atom atmospheres. Both isotropic and kinematical hardening seem to play a role in the strain hardening behavior of lath martensitic steel.

Keywords: Press hardening steel; Plastic deformation; Strain rate sensitivity; Martensite; Stress relaxation test 2

1. Introduction 

Press hardening steel (PHS) is an ultra-high strength steel used for the production of passive safety-related structural parts of car bodies. The untempered low-carbon (0.2-0.4 wt. % carbon) lath martensitic PHS has superior strength and toughness. PHS parts are produced by the hot press forming (HPF) of austenitized blanks in special forming presses equipped with water cooled quenching dies. During the HPF process the initial ferrite-pearlite microstructure is transformed into a fully lath martensitic microstructure. The final in-service microstructure and mechanical properties are obtained after vehicle assembly and paintbaking. The paint-baking is considered as a low temperature tempering treatment.

The stress-strain curves of lath martensitic steel reveal a low conventional 0.2% proof yield strength, a high tensile strength and a remarkably high initial strain hardening rate [1-11]. In lath martensitic steel, the stress for initial plastic yielding is often much lower than the 0.2% proof YS [3, 10]. An analysis of the available literature reveals that there is no single explanation for the above mentioned characteristics of lath martensite plasticity.

Allain et al. [1] considered lath martensite as a heterogeneous, composite-like material consisting of soft low-carbon areas, and hard high-carbon areas. The soft areas, carbondepleted ferrite, have a YS in the range of 400-500 MPa. The hard areas, lath martensite strengthened by carbon in solid solution, have a YS of approximately 4 GPa. They reported that the soft areas were responsible for micro-plastic yielding and that the hard areas remained elastic and provided the high work hardening. The strain hardening of lath martensite was suggested to be achieved by the generation of a large internal stress (kinematic hardening), rather than by the standard dislocation storage mechanism. In support of their view, the authors carried out Bauschinger backstress measurements, showing that the kinematic hardening contributed approximately 80 % of the total strain hardening. The nanohardness measurements reported by Zhang et al. [2] however showed that the hardness of martensite was spatially homogeneous. This is in contradiction to the model proposed by Allain et al. [1]. Zaccone and Krauss [3, 4] suggested that the presence of soft retained austenite was the cause 3

of plasticity of lath martensite at low strains and stresses. This point of view is supported by Maresca et al. [5], who studied the orientation dependence of the ductile behavior of lath martensite deforming by dislocation glide. They showed, by crystal plasticity modeling, that the presence of 5 vol.-% inter-lath retained austenite could be the cause of the very low YS of lath martensite. Their results showed that yielding in lath martensite containing inter-lath austenite was initiated at a low applied stress in the softer austenite, which had a YS of 265 MPa as compared to a YS of 510 MPa for ferrite. The deformation was reported to occur by in-lath-plane dislocation glide.

Morsdorf et al. [6] have examined the deformation mechanisms in as-quenched Fe-0.13C5.0Ni and Fe-0.30C-5.1Ni (in wt. %) lath martensite. They argued that during the martensitic transformation, i.e. during the cooling in the Ms-Mf temperature range, auto-tempering effects [7] did not occur at the same temperature throughout the material. This resulted in compositional, crystallographic and morphological heterogeneities in the microstructure. Lath martensite contained regions with soft coarse laths formed closer to the Ms temperature, and regions with hard fine laths formed closer to the Mf temperature. They showed that lath martensite was deformed by dislocation glide, and that strain localization occurred during deformation. Strain bands were predominantly observed along the laths which had their longitudinal direction oriented at 45q to the tensile direction. The activation of in-lath-plane slip was reported to enable this localized deformation because of the larger mean free path available to dislocations in the longitudinal direction of the laths. Strain was localized at high angle block and packet boundaries. The retained austenite transformed to martensite during deformation and it could therefore only affect plasticity in the very early stages of deformation. Michiuchi et al. [8] also reported the preferred activation of in-lath-plane slip systems in Fe-0.13C-0.92Mn-0.25Si-0.83Cr-0.32Mo (in wt. %) lath martensite. They observed that slip bands were developed along martensite laths. Dislocation cell formation was proposed to be the origin of the local hardening of the in-lath-plane slip system.

Leslie and Sober [9] suggested that the apparent high strain hardening observed for lath martensite was due to the elimination of internal stresses introduced by the austenite-tomartensite transformation. This suggestion was further developed by Hutchinson et al. [10], who also argued that the low YS and continuous yielding of as-quenched lath martensite was entirely due to internal stresses close to the plastic flow stress of martensite. Assuming that 4

the peak broadening observed for X-ray diffraction (XRD) peaks of lath martensite was entirely due to internal stresses, they deduced that the internal stress had a value approximately equal to half the tensile strength. In agreement with Allain et al. [1], they considered that the properties of lath martensite were heterogeneous, with regions that yielded plastically at different strains depending on residual stresses present in each region. While Hutchinson et al. [10] considered the reduction of XRD peak broadening by straining as a clear proof of the reduction of internal stresses during straining, Takaki et al. [11] have given an entirely different interpretation of the same observation. Takaki et al. [11] argued that the reduction of XRD peak broadening was due to a reduction of dislocation density. The view that the observed peak broadening for martensite diffraction peaks is only related to strain, i.e. the dislocation density, is also shared by Christien et al. [12]. Akama et al. [13] analyzed the XRD peak broadening for Fe-18Ni-0.002C (in wt. %) lath martensite by means of the modified Williamson-Hall method [14] considering dislocation arrangement. In contrast to the report by Takaki et al. [11], which was based on the conventional Williamson-Hall method, they did not find a reduction of dislocation density when lath martensite was deformed to a small strain. They reported that the percentage of screw dislocations in as-quenched lath martensite was about 88 %, and that cold rolling of the lath martensite increased the percentage of edge dislocations. The dislocation density was reported to be almost unchanged by straining. The initial dislocation arrangement of random dislocations was changed to a cell structure during straining. They argued that the plastic train was entirely due to the slight movement over an average distance of about 21 nm, of a high density of mobile dislocations (2.1u1015 m-2) that changed the initial random dislocation distribution into the tangled dislocation cell structure.

Although this has so far not been considered, there is still a possibility that the properties of lath martensite may simply be the result of normal dislocation-mediated plasticity. The present work was therefore undertaken to analyze whether the tensile behavior of lath martensitic steel could be the result of normal dislocation-mediated plasticity and to offer new insights on the plasticity mechanisms of lath martensitic steel.

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2. Experimental Procedure 2.1 Materials

An industrially produced cold-rolled 0.35 wt. % C PHS was used in the present study. The composition of the steel is given in Table 1. The following procedure was used to simulate the hot press forming (HPF) of the PHS. ASTM E8 standard size tensile specimens with a gauge length of 50 mm were prepared. The samples were first given an austenitization treatment of 5 min at 900 qC in an electric furnace. The specimens were then transferred to a laboratory hydraulic HPF simulator where the specimens were quenched between two flat water-cooled dies to room temperature. During the die-quenching the initial ferrite-pearlite microstructure of the continuously annealed PHS specimen was transformed to lath martensite.

2.2 Microstructure analysis

The PHS microstructure was observed by means of electron backscattering diffraction (EBSD) and transmission electron microscopy (TEM). EBSD samples were prepared by standard mechanical polishing followed by a final polishing using colloidal silica. The EBSD analysis was done in an FEI Quanta 3D FEG. TEM samples were prepared as 3 mm diameter disks which were mechanically polished to a thickness less than 100 Pm and thinned by the electrolytic double jet technique at room temperature. A mixture of 5 % perchloric acid and 95 % acetic acid was used as electrolyte. The TEM observations were carried out in a JEOL JEM-2100F TEM operating at 200 kV.

2.3 Mechanical tests

The specimens were tested in tension in an electromechanical universal testing machine using a strain rate in the range of 3×10-5 to 5×10-3 s-1. Tensile tests at a strain rate of 10-3 s-1 were repeated four times and the stress-strain curves were almost identical. Repeated stress relaxation tests were carried out by stopping the crosshead of tensile testing machine after a specific stress was reached, and maintaining a constant crosshead displacement. All the stress relaxation tests were conducted at a strain rate of 10-5 s-1. During a first relaxation lasting 30 s, the stress decreased gradually. The specimen was then reloaded to the same stress for the next 6

30 s relaxation. The relaxation and reloading test was repeated four times, and the time evolution of the stress was recorded during each relaxation stage. Small stress drops 'V(t) were measured during the four successive relaxations. Stress relaxation tests were repeated twice at each stress level and the stress-time curves were almost identical. The equations used for the analysis of the stress relaxation tests are summarized in Section 1 of Supplementary materials.

2.4 Internal friction measurements

The internal friction (IF) spectra was measured with an IMCE RFDA LTVP800 resonant frequency damping analyzer operated in the free flexural vibration mode. The dimensions of the specimen used for the IF measurement were 20 mm in width, 80 mm in length and 1.5 mm in thickness. The specimen was suspended between two thin thermocouples and excited to oscillate at its resonant frequency by means of impulse excitation. The room temperature resonance frequency was approximately 1.2 kHz. During the IF measurements, the specimen was heated in a vacuum infrared furnace with a vacuum better than 10-5 mbar. A heating rate of 5 °C min-1 was used to heat the sample from 25 °C to 450 °C. The Fouss-Kirkwood modified Debye equation was fitted to the measure damping peaks by taking into account peak broadening [15]:

‫ڃڌ ڬ‬Z‫ڇ‬W ‫˜ ' ڄ‬

‫ڃ‬ZW ‫ڄ ۍ‬D c ‫ڃ  ڌ‬ZW ‫˜ ڍڄ ۍ‬D c

(1)

Here Δ is the relaxation strength, i.e. the peak maximum amplitude, and τr is the relaxation time. ω is the angular frequency, given by ω = 2πf, where f is the resonant frequency. α' is the peak broadening parameter. When α' = 1, the peak is a classical Debye peak. When α' < 1, the peak is broader as compared to a normal Debye peak. The α' parameter does not have a welldefined physical meaning. In the present case, the main peak in the IF spectrum of lath martensite is the Snoek-Köster-Kê (SKK) relaxation peak which is due to the motion of kinks dragging interstitial carbon atoms [16]. The components of the SKK peak have an α' value less than 1, as they are associated with a distribution of relaxations times.

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3. Results 3.1 Microstructure evolution of the lath martensitic PHS steel during deformation

The flow curve of as-quenched PHS in uni-axial tension reveals the characteristic features of lath martensite plasticity. These are illustrated in Fig. 1(a) with the stress-strain curve of a 1.8 GPa PHS tested at a strain rate of 10-3 s-1. The flow curve shown in Fig. 1(a) has no clear yield point. Instead there is a smooth and continuous elasto-plastic transition from the microplastic domain into the macro-plastic domain. The material fractures in a fully ductile manner as shown in the SEM image of fractured surface of the material in Fig. 1(a), and the initial strain hardening is remarkably high (Fig. 1(b)). Fig. 2 shows SEM and EBSD micrographs of the lath martensite microstructure of the investigated PHS in the as-quenched condition and in the deformed condition, i.e. after fracture in a tensile test. The phase map in Fig. 2(c) indicates that the initial retained austenite volume faction is very low, i.e. less than 2 vol. % in the as-quenched condition, and that austenite is almost absent after deformation to fracture as shown in Fig. 2(d). This indicates that the role of retained austenite on the plasticity of the investigated PHS is rather limited.

The inverse pole figure (IPF) maps shown in Fig. 2(e) and (f) illustrate the hierarchical microstructure of lath martensite microstructure, distributed over five length scales consisting of prior austenite grain boundaries (PAGS), packets, blocks, sub-blocks and laths. The IPF maps show that the block size is small (block width: 1-2 Pm) and that the blocks are degenerate, i.e. the block structure is not very clear. Similar microstructures were observed by Morito et al. [17] for Fe-0.38%C lath martensite and by Kitahara et al. [18] for Fe-0.2%C lath martensite. Morito et al. [17] reported that prior austenite grains (PAG) were sub-divided in packets. All the laths in the same packet were characterized by the same habit plane, i.e. (011)D'//(111)J. The packets were subdivided into blocks. Each block contained sub-blocks, consisting of two laths belonging to two Kurdumov-Sachs related variants with a misorientation of 10.53°. The laths are single crystals which contain a high density of dislocations. Sandvik and Wayman [19] have analyzed the microstructure of Fe-20%Ni5%Mn lath martensite, which is very comparable to low carbon lath martensite. They reported both the Kurdumov-Sachs (0° deviation between <101>J and <111>D') and the Nishiyama-Wassermann (5.26° deviation between <101>J and <111>D') orientation 8

relationships between parent austenite grains and product martensite laths.

According to Wasaka and Wayman [20], laths form independently of each other as the presence of inter-lath retained austenite suggests that laths do not form self-accommodating groups during a cooperative growth process. A large density of dislocation is created during the austenite-to-martensite transformation [20]. Three families of dislocations are formed during the transformation: (a) a/12<110>J-type transformation dislocations associated with the structural ledges, (b) a/2 <111>D'-type screw misfit dislocations at the austenite-martensite interphase boundary, and (c) a/2<110>J-type dislocations in austenite, resulting from deformation of austenite during the martensitic transformation. The dislocations in austenite are subsequently inherited by martensite. Sandvik and Wayman [19] indicate that most of dislocations in lath martensite are in the screw orientation. This is in agreement with the dislocation analysis in lath martensite reported by Moritani et al. [21]. According to Akama et al. [13], 88 % of the a/2<111>D'-type dislocations segments in lath martensite are in the screw orientation. The TEM micrographs showing dislocation structures of the investigated PHS in the as-quenched state and in the deformed state for an engineering strain of 7 % are presented in Fig. 3. The dislocation arrangement, observed in the [111]D' zone axis in both cases, is characterized by a high density of dislocations. The dislocation density is much higher in the deformed PHS as compared to the as-quenched PHS, which is an indication of dislocation multiplication in the lath martensite during deformation.

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3.2 Strain rate sensitivity and stress relaxation behavior of the lath martensitic PHS steel Fig. 4(a) and (b) show the engineering and true stress-strain curves measured with an applied strain rate of 5u10-4, 1u10-3 and 5u10-3 s-1. The YS, the ultimate tensile strength (UTS) and the total elongation (TE) increase with decreasing strain rate. The YS increases from 1336 MPa to 1489 MPa, the UTS increases from 1847 MPa to 1962 MPa, and the TE increases from 5.7 % to 6.3 %, when the strain rate is changed from 5u10-3 to 5u10-4 s-1. No postuniform elongation is observed for the stress-strain curve with a strain rate of 5u10-3 s-1. The uniform elongation is similar in all cases, i.e. about 4 %. Fig. 4(c) shows the strain dependence of strain rate sensitivity. The results show that the PHS has a negative strain rate sensitivity, and that the strain rate sensitivity is more negative when measured at lower strain rates. This is evidence for a short-range, diffusion-controlled dynamic strain aging process at room temperature.

The stress-strain curves of the as-quenched PHS do not have a clear yield point as shown in Fig. 4(a). The conventional 0.2 % offset stress is therefore defined as the YS of the asquenched PHS. The assumption here is that, at a 0.2 % strain, the majority of grains contributes to plastic strain. Micro-plastic deformation does however take place when strain is smaller than 0.2 %. Stress relaxation tests were therefore carried out for an applied stress VA < V0.2% (VA=1 GPa, WA=330 MPa), VA close to V0.2% (VA=1.2GPa, W=390 MPa), and VA > V0.2% (VA=1.5 GPa, W=490 MPa). Four successive relaxation tests were carried out, and time dependence of the small stress drops was recorded during successive relaxations. Repeated relaxation test curves for an applied stress of 1000, 1200 and 1500 MPa are shown in Fig. 5. A reduction of the size of the successive stress drops is observed, indicating that mobile dislocation density decreases during the relaxation test [22]. Note that time in Fig. 5 refers to time after the first relaxation.

Fig. 6 shows the shear stress-test time curves for four consecutive relaxation cycles. There is a reduction of the stress drop in each successive relaxation in both the micro-plastic and macro-plastic range. In the micro-plasticity region and macro-plasticity region, the rate of stress relaxation at the end of each relaxation is higher than that at the start of the subsequent relaxation as shown in the derivative dW/dt in Fig. 6(a) and (b). This indicates that dislocations 10

may be pinned by a diffusive process during the quasi-elastic reloading and that they then move more slowly at the start of the following relaxation.

According to Eq. (S.14) in Section 1 of Supplementary materials, the stress drops in each successive relaxation are related to a decrease of mobile dislocation density. The evolution of mobile dislocation density is shown in Fig. 7. Fig. 7(a) shows that the rate of mobile dislocation exhaustion is very effective in the pre-yield micro-plasticity region. Standard mobile dislocation exhaustion processes include (a) dislocation cell formation, (b) sessile dislocation segment formation and (c) solute pinning, i.e. by Cottrell atmosphere formation. As reported in earlier works [13, 19, 21], most of the dislocations in lath martensite are in the screw orientation. The screw dislocations are known to display much lower mobility than non-screw segments in bcc metals at moderate to low stresses [23]. The micro-plasticity in the as-quenched lath martensite is therefore provided by the most mobile dislocation segments, i.e. the non-screw dislocation segments. The non-screw dislocation exhaustion is most likely due to the fact that the screw dislocations segments to which the edge segments are attached, simply do not move. Fig 7(c) shows that the rate of mobile dislocation annihilation is lower in the macro-plastic deformation range. This could be due to the fact that the critical stress to initiate screw dislocation motion is reached and the screw dislocations become mobile, which can result in the activation of dislocation sources and the multiplication of dislocations.

The effective activation volume was determined using Eq. (S.11) in Section 1 of Supplementary materials, and the results are shown in Fig. 8. The results indicate that the activation volume decreases with increasing applied stress. The transition from microplasticity (VAV0.2%) in lath martensite is associated with a large decrease of the effective activation volume, from approximately 250ub3 to 100ub3. Fig. 8 shows that the effective activation volume is relatively large and stress dependent. This supports the view that dislocation motion is controlled by the kink pair mechanism. As the critical kink pair separation is stress-dependent, the activation volume varies from a larger value at low stress, to a smaller value at high stress [24]. Note that the : value used in Eq. (S.17) in Section 1 of Supplementary materials for the first cycle of the four consecutive relaxation cycles was the average value of the three last cycles. 11

The : values for each cycle used in the present study are shown in Fig. 9. Viguier et al. [25] reported that repeated stress relaxation tests were satisfactorily analyzed when the : values deduced from the stress drops measured at the end of each relaxation in a series of a repeated relaxation test were constant. 3.3 Internal friction analysis of the as-quenched lath martensitic PHS steel 

The IF spectrum of martensitic steel has been reported to contain five distinct peaks [26, 27]. The peak labelling proposed in the work of Tkalcec et al. [27] on high C ferrous martensite was used in the present work. Tkalcec et al. [27] labelled the relaxation peaks as P1, P2, M3, P4 and P5. They made a clear distinction between the M3 peak and the other four peaks. They showed that the M3 peak was not a thermally activated peak, i.e. the position of the M3 peak did not change with frequency, and observed following peak maximum temperatures: P1 at -143 °C, P2 at -13 °C, P3 at 107 °C, P4 at 237 °C, and P5 at 327 °C. These peak temperatures are for a resonant frequency of 1.5 kHz. Fig. 10 shows the IF spectrum for the as-quenched investigated PHS. The three relaxation peaks are observed at a resonant frequency of 1.2 kHz. The peaks are labelled as P3, P4 and P5, which correspond to M3, P4 and P5 peaks in the work of Tkalcec et al. [27]. The P3 peak has a maximum at 125 °C, the P4 peak has a maximum at 265 °C and the P5 peak has a maximum at 320 °C.

The P3 peak is related to the solute C in martensite, and it is affected by the transition carbides precipitation during the first stage of tempering [28]. The P3 peak of martensite is almost coincident with the Snoek peak at 120 °C. The Snoek peak is due to the rearrangement of solute C atoms between the three equivalent octahedral interstitial sites during cyclic straining [29]. The Snoek peak is observed in steels which have a low dislocation density and which contain C in supersaturation.

The P5 peak was identified as the Snoek-Kê-Köster (SKK) peak reported previously for ferritic steels [30]. According to Speich [31] and Kehoe and Kelly [32], close to 90 % of the carbon atoms was segregated to dislocations and lath boundaries. The SKK relaxation peak is commonly observed in the IF spectrum of deformed carbon steel and as-quenched ferrous lath martensite containing carbon. The SKK peak is due to double kink formation on screw dislocations in the presence of solute carbon atoms. According to Tkalcec et al. [27], the broad P4 peak is part of the P5 peak. Sulistiyo et al. [16] however reported that the origin for 12

P4 peak was still not clear and that this peak only appeared in connection with the P5 peak.

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4. Discussion 4.1 Interactions between dislocations and carbon atoms in lath martensitic steel

The investigated as-quenched lath martensitic PHS steel shows a clear SKK peak as shown in IF spectrum of Fig. 10. According to Schoeck’s “String model” [33, 34], the SKK peak is due to the movement of dislocations dragging interstitials. In Seeger’s “Double kink model” [35], it is due to the formation of thermally activated kink pairs and their lateral movement, on a/2<111>-type screw dislocations in the presence of solute carbon atoms, with kinks dragging interstitials along. The peak occurs at a significantly higher temperature than the equivalent relaxation peak for the dislocation motion when no solutes are present (J-peak) [36]. The observed SKK peak broadening is most likely due to the wide distribution of dislocation segment lengths.

The activation enthalpy of relaxation associated with the SKK peak is the sum of 2HK, the formation enthalpy of a kink pair on a a/2<111> screw dislocation, (2HK=0.63 eV), and the migration enthalpy HD of the interstitial carbon, (HD=0.87 eV) [37]:

H SKK

2˜ HK  HD

0.63  0.87eV

1.5eV

(2)

Note that in the case of lath martensite, the activation energy for the SKK relaxation is not a function of binding energy of carbon atoms to dislocations. This is due to a saturation effect since the carbon atmospheres contain a large number of carbon atoms occupying dislocation sites with a range of binding energies [38]. As it takes more time to form a kink pair than it takes for the carbon atoms to re-arrange when the dislocation moves, the dislocation does not tear itself free of the atmosphere [35]. In the case of lath martensite, dislocation unpinning is therefore unlikely to take place and, instead, the dislocation drags the carbon atmosphere along when it moves. Fig. 11 presents a schematic illustrating the dislocation motion on {110} slip planes for lath martensitic steel. The screw components of the dislocation are characterized by kink-pairs that drag carbon atoms along. Note that the carbon atoms diffuse and interact with moving dislocations rather than occupying true octahedral solid solution sites.

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The interaction between dislocations and interstitial carbon atoms could give rise to two interactions in the investigated lath martensitic PHS. During quenching, the auto tempering [37] can result in the formation of clusters of solute C atoms by their diffusion to the dislocations. During deformation, screw dislocations could play an essential role by dragging carbon atoms along during their motion. In the immediate vicinity of the moving dislocations, i.e. at the dislocation cores, an instantaneous stress-induced re-ordering of the solute carbon atoms can occur. This process, known as Snoek ordering, does not involve long range diffusion, as it only requires a single diffusional hop in the vicinity of the dislocation core to a more energetically favorable position.

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4.2 Deformation mechanisms of lath martensitic steel 

Overcoming the combined effect of the Peierls lattice friction and the presence of interstitials is usually considered to be rate-controlling mechanisms of dislocation movement in D-Fe. The process of overcoming the Peierls barrier has a small activation volume, i.e. in the range of 5ub3-50ub3. In case of the investigated lath martensitic PHS, the effective activation volume is approximately 250ub3 in the pre-yield range, and 100ub3 in the plastic deformation range (Fig. 8). The stress-dependence of the effective activation volume shown in Fig. 8 suggests that the plasticity is mediated by nucleation and propagation of kink-pairs on screw dislocations. In addition, the negative strain rate sensitivity of the PHS (Fig. 4) is an indication of a pronounced dislocation-solute carbon interaction. No serrations are observed on the flow curves of the investigated lath martensitic PHS at ambient temperature (Fig. 4). This implies that the dislocation breakaway from the carbon atom atmospheres is not expected for the conventional tensile test conditions used in the present work. The dislocation-solute carbon interaction is further supported by the internal friction measurements which reveal the presence of a prominent SKK peak (Fig. 10) due to the movement of screw dislocations dragging carbon atoms along (Fig. 11). These observations suggest that the solute carbon atoms exert a “solute drag” effect on the dislocation motion. This interaction leads to a re-organization of a relatively large number of carbon atoms close to the moving dislocation.

The present work also offers a new insight into the dislocation density evolution. In the micro-plastic range, i.e. for stress below the macroscopic yield stress, the flow is very likely due to the motion of the non-screw dislocation as these are highly mobile as compared to screw dislocations [22]. According to Hivert et al. [39], the onset of micro-plasticity in high purity D-Fe is due to the glide of non-screw dislocations. In the macro-plastic range, the applied stresses could be high enough to move the less mobile screw dislocations, and dislocation multiplication can take place. The interactions between screw dislocations of different slip systems can lead to a frequent jog formation, which rapidly reduces the dislocation mean free path, and dislocation annihilation due to cross slip [40]. The plasticity of lath martensitic steel is therefore expected to be affected by standard dislocation density evolution resulting from dislocation multiplication and annihilation. The observed rate of mobile dislocation exhaustion is much smaller in the macro-plasticity range than in the 16

micro-plastic range as shown in Fig. 7(c). The dislocation multiplication and annihilation lead to a reduction of the strain hardening in the macro-plasticity range [41].

Dislocation multiplication has so far been considered based on the analysis of diffraction peaks as proposed by Ungár et al. [42] and Ribárik et al. [43], which makes it possible to study the change of the dislocation arrangement in lath martensite during straining. Harjo et al. [44] reported that the initially random arrangement of dislocations in lath martensite rapidly evolved to a correlated arrangement of dislocations during straining. Akama et al. [13] reported that the dislocations arrangement in as-quenched martensite was unstable, and that a small amount of deformation by cold rolling resulted in a tangled dislocation arrangement. Both reports indicate that the dislocation density remains almost unchanged during the straining, i.e. there is no dislocation multiplication. The results of the relaxation test and TEM observations in the present work however confirm that the dislocation density increases during the deformation of the investigated lath martensitic PHS. 

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4.3 Unresolved issues in lath martensite plasticity

The observations made in the present work shed light on the relation between the strength and the C content of lath martensite. The well-known relation between the YS and square root of the carbon content in martensitic steel is often related to the solid solution strengthening effect of carbon [45-48]. While a higher carbon content results in an extreme strengthening effect in ferrous martensite, it may be wrong to assign this effect to solute carbon only. This assumption ignores the effect of (1) the carbides (transition carbides or cementite) formed during auto-tempering [49], (2) the extremely high dislocation density [50], (3) the high density of boundaries resulting from the transformation [51] and (4) the presence of excess vacancies [52].

The solute carbon content dependence of the strength of untempered lath martensite needs to be reinvestigated. The early theoretical works [53, 54] suggest that C atoms tend to concentrate inside dislocation core due to the strain field of dislocations, rather than forming a random solid solution. Three-dimensional atom probe tomography (3D APT) has also revealed that carbon atoms do not form a random solute solution when D-Fe or martensite contains dislocations. The studies of the solute carbon atom distribution around dislocations by 3D ATP of Wilde et al. [55], Chang et al. [56] and Smith et al. [57] show that there are approximately 30 carbon atoms per nm along the dislocation core, a region with a diameter of about 4ub centered on the dislocation line. The cylindrical region extending to a distance of 7.0-7.5 nm from the dislocation core contains a total of about 100 carbon atoms per nm as illustrated in Fig. 12(a). The 3D ATP data of the investigated as-quenched lath martensitic PHS steel shown in Fig. 12(b) and (c) also illustrate this inhomogeneous distribution of carbon atoms and show the segregation of carbon atoms along dislocation-like structures. The carbon solid solution strengthening in the sense of the Fleisher-Friedel model [58] is therefore unlikely in lath martensite. The detailed review on the effect of carbon on yield strength of martensite is available in the Section 2 of Supplementary materials.

Further insights on the deformation behavior of lath martensitic steel can be gained by comparison of stress-strain behavior of the PHS and ultra-low carbon bake-hardening (ULC BH) steel grade. Fig. 13(a) shows the comparison of the true stress-strain curves for the PHS and an ULC BH steel grade. The stress-strain curve of PHS is characterized by a high flow 18

stress and a low total elongation while the ULC BH steel shows a low YS and a gradual increase of flow stress. The strain hardening behavior of the PHS and ULC BH steel is clearly different as shown in Fig. 13(b). The strain hardening rate of the ULC BH steel shows a steep decrease during the elasto-plastic deformation regime and maintains a low level during plastic deformation. On the other hand, the PHS has a considerably higher strain hardening rate in the initial stages of the plastic deformation and the decrease of the strain hardening during deformation is much more gradual. This characteristic strain hardening behavior makes it difficult to identify the yield point of martensitic steel.

As dislocation multiplication is clearly taking place, a dislocation density-based constitutive model was used to analyze whether standard dislocation density evolution could explain the high strain hardening behavior of lath martensite. The details of the modeling results are presented elsewhere [59]. The dislocation density-based models could not describe the high initial work hardening rate of the investigated lath martensitic PHS. The high initial work hardening rate of martensitic steel can therefore not solely be due to a gradual increase of the dislocation density up to a constant saturation level, and a high kinematical strengthening mechanism from microstructural origin must therefore also be considered. As the strain hardening of lath martensite includes both a kinematical and an isotropic contribution to strengthening, the present work therefore provides support for a strengthening mechanism combining (1) the development of a pronounced backstress as proposed by Allain et al. [1], with (2) dislocation multiplication and storage. While evidence for the kinematical strengthening is provided by the backstress measurements of Allain et al. [1], the present work also identifies dislocation multiplication and storage as an isotropic strengthening contribution.

19

5. Conclusions

1. The dislocation density is much higher in the deformed PHS as compared to the asquenched PHS. This provides evidence for dislocation multiplication in the lath martensite during deformation.

2. The investigated lath martensitic PHS has a negative strain rate sensitivity. This observation is evidence for a short-range, diffusion-controlled dynamic strain aging process at room temperature.

3. The dislocation-solute carbon interaction is supported by internal friction measurements that reveal the presence of a prominent SKK peak, due to the movement of screw dislocations dragging carbon atoms along.

4. Stress-relaxation tests suggest a transition of deformation mechanisms from the microplastic range to the macro-plastic range. In the micro-plastic range, the flow is very likely due to the motion of the non-screw dislocation as these are highly mobile as compared to screw dislocations. In the macro-plastic range, the applied stresses could be high enough to move the less mobile screw dislocations, and dislocation multiplication can take place. The stressdependence of the effective activation volume suggests that the plasticity is mediated by the mechanism of nucleation and propagation kink-pair on screw dislocations.

5. Both isotropic and kinematical hardening play a role in the strain hardening behavior of lath martensitic steel.

Acknowledgements The authors gratefully acknowledge the support of the POSCO Technical Research Laboratories, Gwangyang, South Korea.

20

References [1] S. Allain, O. Bouaziz, M. Takahashi, Toward a new interpretation of the mechanical behaviour of as-quenched low alloyed martensitic steels, ISIJ Int. 52 (2012) 717-722. [2] L. Zhang, T. Ohmura and K. Tsuzaki, Application of Nanoindentation Technique in Martensitic Structures, Nanoindentation in Materials Science, Dr. Jiri Nemecek (Ed.), InTech, 2012 [3] M. Zaccone, G. Krauss, Elastic limits and microplastic response in ultrahigh strength carbon steels, Metall. Trans. A 20 (1989) 188-191. [4] G. Krauss, Martensite in steel: strength and structure, Mater. Sci. Eng. A 273 (1999) 40-57. [5] F. Maresca, V.G. Kouznetsova, M.G.D. Geers, Subgrain lath martensite mechanics: A numerical-experimental analysis, J. of the Mech. and Phys. of Solids 73 (2014) 69-83. [6] L. Morsdorf, O. Jeannin, D. Barbier, M. Mitsuhara, D. Raabe, C.C. Tasan, Multiple mechanisms of lath martensite plasticity, Acta Mater. 121 (2016) 202-214. [7] B. Hutchinson, J. Hagström, O. Karlsson, D. Lindell, M. Tornberg, F. Lindberg, M. Thuvander, Microstructures and hardness of as-quenched martensites (0.1–0.5%C), Acta Materialia 59 (2011) 5845-5858. [8] M. Michiuchi, S. Nambu, Y. Ishimoto, J. Inoue, T. Koseki, Relationship between local deformation behavior and crystallographic features of as-quenched lath martensite during uniaxial tensile deformation, Acta Mater. 57(18) (2009) 5283-5291. [9] W. Leslie, R. Sober, The strength of ferrite and of martensite as functions of composition, temperature, and strain rate, Trans. Am. Soc. Met. 60 (1967) 459-484. [10] B. Hutchinson, D. Lindell, M. Barnett, Yielding behaviour of martensite in steel, ISIJ Int. 55 (2015) 1114-1122. [11] S.Takaki, Y. Fujimura, K.Nakashima, T.Tsuchiyama, Effect of dislocation distribution on the yielding of highly dislocated iron, Mater. Sci. Forum 207 (2006) 539-543. [12] F. Christien, M.T.F. Telling, K.S. Knight, Neutron diffraction in situ monitoring of the dislocation density during martensitic transformation in a stainless steel, Scr. Mater. 68 (2013) 506-509. [13] D. Akama, T. Tsuchiyama, S. Takaki, Change in dislocation characteristics with cold working in ultralow-carbon martensitic steel, ISIJ Int. 56 (2016) 1675-1680. [14] T. Ungar, A. Borbely, The effect of dislocation contrast on x-ray line broadening: A new approach to line profile analysis, Appl. Phys. Lett. 69 (1996) 3173-3175. [15] R.M. Fuoss, J.G. Kirkwood, Electrical properties of solids. VIII. Dipole moments in polyvinyl chloride-diphenyl systems, J. of the Am. Chem. Soc. 63(2) (1941) 385-394. [16] D.H. Sulistiyo, L. Cho, E.J. Seo, B.C. De Cooman, Internal friction analysis of lath martensite in press hardening steel, Mater. Sci. and Technol. 33 (2016) 879-892. [17] S. Morito, H. Tanaka, R. Konishi, T. Furuhara, T. Maki, The morphology and crystallography of lath martensite in Fe-C alloys, Acta Mater. 51 (2003) 1789-1799. [18] H. Kitahara, R. Ueji, N. Tsuji, Y. Minamino, Crystallographic features of lath martensite in low-carbon steel, Acta Mater. 54 (2006) 1279-1288. [19] B. Sandvik, C. Wayman, Characteristics of lath martensite: Part I. Crystallographic and substructural features, Metall. Trans. A 14 (1983) 809-822. [20] K. Wakasa, C.M. Wayman, The morphology and crystallography of Ferrous lath martensite. Studies of Fe-20%Ni-5%Mn—II. Transmission electron microscopy, Acta Metall. 29 (1981) 991-1011. [21] T. Moritani, N. Miyajima, T. Furuhara, T. Maki, Comparison of interphase boundary structure between bainite and martensite in steel, Scr. Mater. 47 (2002) 193-199. 21

[22] D. Calliard, J.L. Martin, Thermally activated mechanisms in crystal plasticity, First ed., Pergamon, 2003. [23] M.R. Gilbert, S. Queyreau, J. Marian, Stress and temperature dependence of screw dislocation mobility inα-Fe by molecular dynamics, Phys. Rev. B 84(17) (2011). [24] A. Sato, M. Meshii, Solid solution softening and solid solution hardening, Acta Metall. 21 (1973) 753-768. [25] B. Viguier, J. Bonneville, J.L. Martin, The mechanical properties of single phase gamma Ti47Al51Mn2 polycrystals, Acta Mater. 44 (1996) 4403-4415. [26] I. Tkalcec, D. Mari, Internal friction in martensitic, ferritic and bainitic carbon steel; cold work effects, Mater. Sci. Eng. A 370 (2004) 213-217. [27] I. Tkalcec, D. Mari, W. Benoit, Correlation between internal friction background and the concentration of carbon in solid solution in a martensitic steel, Mater. Sci. Eng. A 442 (2006) 471-475. [28] J.J. Hoyos, A.A. Ghilarducci, D. Mari, Evaluation of dislocation density and interstitial carbon content in quenched and tempered steel by internal friction, Mater. Sci. Eng. A 640 (2015) 460-464. [29] J.L. Snoek, Effect of small quantaties of carbon and nitrogen on the elastic and plastic properties of iron, Physica 8 (1941) 711-733. [30] I.-C. Jung, D.-G. Kang, B.C. De Cooman, Impulse excitation internal friction study of dislocation and point defect interactions in ultra-low carbon bake-hardenable steel, Metall. Mater. Trans. A 45 (2014) 1962-1978. [31] G. Speich, Tempering of low-carbon martensite, Trans. Metall. Society of AIME. 245 (1969) 2553-2564 [32] M. Kehoe, P. Kelly, The role of carbon in the strength of ferrous martensite, Scr. Metall. 4 (1970) 473-476. [33] W. Köster, L. Bangert, R. Hahn, Das Dämpfungsverhalten von gerecktem technischem Eisen, Steel Res. Int. 25 (1954) 569-578. [34] G. Schoeck, The cold work peak, Scr. Metall. 16 (1982) 233-239. [35] A. Seeger, A theory of the SnoekǦKöster relaxation (coldǦwork peak) in metals, Phys. status solidi A 55 (1979) 457-468. [36] M. Shimada, K. Sakamoto, Internal friction of D-iron deformed at low temperatures, Scr. Metall. 13 (1979) 1177-1182. [37] M. Weller, The Snoek-Köster relaxation in body-centred cubic metals, J. Phys. Colloq. 44 (1983) C9-63-C9-82. [38] G.R. Speich, W.C. Leslie, Tempering of steel, Metall. Trans. B 3 (1972) 1043-1054. [39] V. Hivert, P. Groh, I. Ritchie, P. Moser, W. Frank, Internal friction peaks due to dislocation relaxations in plastically deformed and/or irradiated high-purity α-iron. 2, Phys. Status solidi A, 46 (1978) 89-98. [40] M. Tang, L.P. Kubin, G.R. Canova, Dislocation mobility and the mechanical response of B.C.C. single crystals: a mesoscopic approach, Acta Mater. 46 (1998) 3221-3235. [41] P. Astié, J. Peyrade, P. Groh, Pics de relaxation des dislocations dans le fer apres deformation a basse temperature, Scr. Metall. 14 (1980) 611-616. [42] T. Ungar, J. Gubicza, G. Ribarik, A. Borbely, Crystallite size distribution and dislocation structure determined by diffraction profile analysis: principles and practical application to cubic and hexagonal crystals, J. of Appl. Crystallogr. 34 (2001) 298-310. [43] G. Ribarik, J. Gubicza, T. Ungar, Correlation between strength and microstructure of ball-milled Al-Mg alloys determined by X-ray diffraction, Mater. Sci. Eng. A 387 (2004) 343347. [44] S.Harjo, T. Kawasaki, W.Gong, K.Aizawa, Dislocation characteristics in lath martensitic 22

steel by neutron diffraction, J. Phys. Conf. Ser. 746 (2016) 1-7. [45] J. Chilton, P. Kelly, The strength of ferrous martensite, Acta Metall. 16 (1968) 637-656. [46] M. Roberts, W. Owen, Unstable flow in martensite and ferrite, Metall. Trans. A 1 (1970) 3203-3213. [47] G. Speich, H. Warlimont, Yield strength and transformation substructure of low-carbon martensite, J. Iron and Steel Inst. 206 (1968) 385-392. [48] P. Winchell, M. Cohen, Solid solution strengthening of Martensite by carbon, Electron Microscopy and Strength of Crystals (1963) 995. [49] H. Matsuda, R. Mizuno, Y. Funakawa, K. Seto, S. Matsuoka, Y. Tanaka, Effects of autotempering behavior of martensite on mechanical properties of ultra high strength steel sheets, J. Alloy. Comp. 577S (2013) S661-S667. [50] M. Kehoe, P. Kelly, The role of carbon in the strength of ferrous martensite, Scr. Metall. 4 (1970) 473-476. [51] L. Norstrom, Yield strength of quenched low-C lath martensite, Scand. J. of Metall. 5 (1976) 159-165. [52] K. Sugita, Y. Mutou, Y. Shirai, Vacancy clustering behavior in hydrogen-charged martensitic steel AISI 410 under tensile deformation, J. Phys. Conf. Ser. 674 (2016) 012006 1-6. [53] A.H. Cottrell, B.A. Bilby, Dislocation theory of yielding and strain aging of iron, Proc. Phys. Soc. A 62 (1949) 49-62. [54] N.F. Fiore, C.L. Bauer, Binding of solute atoms to dislocations, Prog. Mater. Sci. 13 (1968) 85-134. [55] J. Wilde, A. Cerezo, G.D.W. Smith, Three-dimensional atomic-scale mapping of a cottrell atmosphere around a dislocation in iron, Scr. Mater. 43 (2000) 39-48. [56] L. Chang, S. Barnard, G. Smith, The segregation of carbon atoms to dislocations in lowcarbon martensites: studies by field ion microscopy and atom probe microanalysis, Gilbert R. Speich symposium proceedings: fundamentals of aging and tempering in bainitic and martensitic steel products, 1992, pp. 19-28. [57] G.D.W. Smith, D. Hudson, P.D. Styman, C.A. Williams, Studies of dislocations by field ion microscopy and atom probe tomography, Philos. Mag. 93 (2013) 3726-3740. [58] R.L. Fleischer, Solution hardening by tetragonal distortions: Application to irradiation hardening in FCC crystals, Acta Metall. 10 (1962) 835-842. [59] K.-R. Jo, E.-J. Seo, D.H. Sulistiyo, J.-K. Kim, S.-W. Kim, B.C. De Cooman, Dislocation density-based constitutive modeling of the tensile behavior of lath martensitic press hardening steel, Data in Brief, submitted. 

23

Tables

Table 1. Composition of the press hardening steel used in the present work, in wt.-%. 

Element

C

Mn

Si

B

Ti

Mo

Fe

wt.-%

0.31

0.87

0.28

0.003

0.028

0.096

bal.



24

Figure captions

Fig. 1. (a) Engineering stress-strain curve, and (b) true stress-strain and strain hardening rate curves for 1.8GPa PHS, at a strain rate of 10-3 s-1. The inset in (a) presents a SEM image of the fractured surface of the material showing ductile fracture. Fig. 2. Microstructure of the 1.8GPa PHS. (a) SEM micrograph, (c) EBSD phase map showing martensite (red) and austenite (green) and (e) EBSD orientation map for martensite (BCC) before deformation. (b) SEM micrograph, (d) EBSD phase map and (f) EBSD orientation map for martensite (BCC) after uni-axial deformation to an engineering strain of 7%. Fig. 3. TEM micrographs of the 1.8GPa PHS showing the dislocation structure in the lath martensite (a) in the as-quenched state and (b) in the deformed state for an engineering strain of 7%. The electron beam was parallel to the [111]D' direction. The micrographs illustrate the increase of dislocation density during straining. Fig. 4. (a) Engineering stress-strain curves and (b) true stress-strain curves for different strain rates. (c) Strain and strain rate dependence of strain rate sensitivity as a function of true strain. Fig. 5. Repeated stress relaxation and reloading tests for different values of the target stress VA. (a) VA =1000 MPa, in the micro-plasticity range. (b) VA =1200 MPa and (c) VA =1500 MPa, in the macro-plasticity region. Fig. 6. Shear stress-time curves of the stress drop for four consecutive relaxation cycles. (a) Stress relaxation cycles in the micro-plasticity range. (b) Stress relaxation cycles in the macro-plastic range. Fig. 7. Relative mobile dislocation density evolution during four consecutive stress relaxation cycles (a) in the micro-plastic range for VA =1000 MPa, (b) in the macro-plastic range for VA =1200 MPa and (c) in the macro-plastic range for VA =1500 MPa. Fig. 8. Applied stress dependence of the effective activation volume. Fig. 9. The value of the correction term : as a function of the relaxation number during repeated stress relaxation experiments.

25

Fig. 10. IF spectrum of the as-quenched 1.8GPa PHS. The ranges of the reported peak maximum temperatures for the J-peak and the SKK peak are indicated in grey. The peak maximum temperatures of the Snoek peak and the DES peak are indicated with dashed lines. The fitted parameters are as follow: W0=1.5 x 10-15 s, H=0.87 eV and D'= 0.60 for the P3 peak. W0=6.0 x 10-18 s, H=1.43 eV and D'= 0.81 for the P4 peak.W0=1.3 x 10-18 s, H=1.65 eV and D'= 0.47 for the P5 peak. The P3 peak is related to the interstitial carbon in martensite and the P5 peak is related to the kink pair formation on screw dislocations dragging carbon atoms. Fig. 11. Schematic illustrating dislocation motion on {110} slip planes in a lath martensitic steel. The screw components of the dislocation are characterized by kink-pairs that drag carbon atoms along. Fig. 12. (a) Schematic illustration of the structure of the C-atmospheres in lath martensite based on experimental atom probe tomography data. (b) 3D APT result of carbon mapping for the as-quenched 1.8GPa PHS. (c) Atomic profile of carbon from the region of interest indicated in (b). Fig. 13. (a) Comparison of the true stress-true strain curves and (b) corresponding shear strain hardening rate-shear strain curves for 1.8 GPa PHS and an ultra-low carbon bake-hardening (ULC BH) steel.

26

Fig.1

(b)

2500

True Shear Stress, W, MPa

Engineering Stress, MPa

(a)

- No upper/lower yield point - Smooth elasto-plastic transition

2000

Ductile fracture

1500

V0.2%

1000 500 5 Pm

0 0

2

4

6

Engineering Strain, %

8

50000 40000

dσ ε dε

G 2

High initial strain hardening rate

30000 20000 G 4

10000 0 0.00

dτ ε dγ

WH  0.01

0.02

0.03

τ γ

0.04

True Shear Strain, J

0.05

Fig.2

(a)

(b)

1 Pm

1 Pm

(c)

Ferrite

(d)

Austenite

(e)

(f)

111 111 5 Pm

5 Pm

100 110 100 110

Fig.3

(a)

(b)

100 nm

Fig.4

2000 1500 1000 ε

500

ε

5 u 10 3 s 1 3

1

4

1

1 u 10 s

ε

5 u 10 s

4

6

0

(c)

2500 2000 1500 1000 ε

500

5 u 10 3 s 1 3

1

ε

1 u 10 s

ε

5 u 10 4 s 1

0 0

2

8

Engineering Strain, %

0 0.01 0.02 0.03 0.04 0.05

True Strain

Strain Rate Sensitivity

(b)

2500

True Stress, MPa

Engineering Stress, MPa

(a)

0.00 m= -0.009±0.001

-0.05

-0.10

m= -0.094 ±0.007 'H : 5 u10 3 s 1 o 1u10 3 s 1 'H : 1u10 3 s 1 o 5 u10  4 s 1

-0.15 0

0.01 0.02 0.03 0.04

True Strain

Fig.5

(b) V$: 1000 MPa W: 330 MPa

1010

1000

990

1220

Engineering Stress, MPa

Engineering Stress, MPa

1020

(c) V$: 1200 MPa W: 390 MPa

1210

1200

1190

1520

Engineering Stress, MPa

(a)

1180

980 0

50 100 150 200

Time (s)

V$: 1500 MPa W: 490 MPa

1510

1500

1490

1480 0

50 100 150 200

Time (s)

0

50 100 150 200

Time (s)

Fig.6

Shear stress (MPa)

(a)

328.5 n=1

328.0

n=2 W2

327.5

dτ dt

W1 327.0 dτ dt

326.5

n=3

n=4

W3

W4 dτ dt

2

: = 1.16

dτ dt 3

: = 1.17

4

: = 1.15

1

V: 1000 MPa W: 330 MPa

:ave = 1.16

326.0 0

50

100

150

200

Time (s)

Shear stress (MPa)

(b)

494.5 n=2

n=1

n=3

494.0

493.0

492.0 491.5

dτ dt

W1 dτ dt

492.5 dτ dt

W4

W3

W2

493.5

n=4

3

: = 1.10

dτ dt

4

: = 1.06

2

: = 1.07 1

V: 1500 MPa W: 490 MPa

:ave = 1.08

491.0 0

50

100

Time (s)

150

200

Fig.7

n 

n  n  n  V: 1000 MPa W: 330 MPa 0

50 100 150 200

Time (s)

1.00 0.96 0.92 0.88 0.84 0.80 0.76 0.72 0.68 0.64 0.60

n 

n 

n 

(c)

n 

U/U0

1.00 0.96 0.92 0.88 0.84 0.80 0.76 0.72 0.68 0.64 0.60

U/U0

U/U0

G

(b)

(a)

V: 1200 MPa W: 390 MPa 0

50 100 150 200

Time (s)

1.00 0.96 0.92 0.88 0.84 0.80 0.76 0.72 0.68 0.64 0.60

n 

n 

n 

n 

V: 1500 MPa W: 490 MPa 0

50 100 150 200

Time (s)

Effective Activation Volume , b3

Fig.8

300 250

V0.2%

: 

200 150

: 

: 

100 50 0

1000

1100

1200

1300

1400

Applied Stress, MPa

1500

Fig.9

Correction Term, :

1.3

VA: 1500 MPa VA: 1200 MPa VA: 1000 MPa

1.2

1.1

T = 273 K (25 °C) 1.0

0

1 2 3 4 Number of Relaxation Test Cycle 

5

Fig.10 J-peak

0.005

Snoek peak

SKK-peak DES peak

Damping, Q-1

0.004

0.003 P5

0.002 P4 Background

0.001 P3

0.000 0

100

200

300

Temperature, °C

400

500

Fig.11

True solid solution C

b [

b

0.234nm

d110

0.204nm

Mobile dislocation dragging C atoms along

b

Fig.12

C atoms atmosphere ~100 C atoms/nm

(b)

7.0 - 7.5 nm

Dislocation core region ~30 C atoms/nm

Depth Depth (nm)

12

100

100

200

300

300

400

400

500

500

Dislocation core 1nm ≈ 4·b (b = 0.248 nm)

14

(nm)

200

~ six {111}a lattice planes

(c)

Atomic %

(a)

10 8 6 4 2 0 0

2

4

6

8 10 12 14 16 18 20

Distance (nm)

Fig.13

(a)

(b) 2000

10000 8000

1500

dW/dJ , MPa

True Stress, MPa

PHS

1000 500

ULC BH

PHS

6000 4000 G/40

2000 ULC BH

0 0.00

200 0.01

0.02

0.03

True strain

0.04

0.05

0.00

0.02

G/400 0.04

0.06

0.08

True shear strain

0.10