Low cycle fatigue behaviour of a ferritic steel strengthened with nano-meter sized precipitates

Materials Science & Engineering A 756 (2019) 198–212

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Low cycle fatigue behaviour of a ferritic steel strengthened with nano-meter sized precipitates

T

S. Majumdara,∗, A.D. Gandhia, M.S. Bishtb a b

R&D Division, Tata Steel Ltd., Jamshedpur, 831 007, India Department of Mechanical Engineering, National Institute of Technology, Raipur, 492013, India

A R T I C LE I N FO

A B S T R A C T

Keywords: Feeiritic steel Nanometer-sized precipitates Low-cycle-Fatigue Dislocation structure Coffin-Manson relationship Microcleavage

Low-cycle-fatigue behaviour (Δεt/2 = ± 0.002 to ± 0.01) of a ferritic-steel (tensile strength ∼ 800 MPa) strengthened with nano-meter-sized-precipitates has been examined. The selected steel is a hot-rolled Ti-Mobearing low-carbon steel (grain size ∼ 3 μm) strengthened predominantly with Ti-Mo-C and Ti-C type precipitates of size ≤ 30 nm distributed randomly on the grain-boundaries and the matrix. The spread of cyclic-plasticity is negligible in the steel till Δεt/2 = 0.0025 leading to cyclically-stable behaviour and excellent fatigue-life (no failure till 105 loading cycles). At Δεt/2 = 0.003, significant initial-cyclichardening is noticed followed by minor amount of cyclic-softening. The latter is attributed to formation of lowenergy-dislocation-structures e.g. dislocation-walls and channels. At Δεt/2 = 0.004–0.01, predominantly cyclichardening is noticed till failure; the intensity of hardening increases with increase in Δεt/2. The cyclic-hardening is attributed to increase in dislocation-density and dislocation-precipitate-interaction, formation of subgrains, microbands and dislocation-clusters within both ferrite-grains and microbands. All the above types of dislocation-substructures hinder movement of dislocations and reduce opportunity for cyclic-strain-hardening at Δεt/ 2 ≥ 0.004 compared to that at Δεt/2 = 0.002–0.003. This phenomenon leads to two stages of cyclic-hardening with two distinct values of cyclic-strain-hardening-exponents (n1′ = 0.3 at low Δεt/2 and n2′ = 0.04 at Δεt/ 2 ≥ 0.004). Two-stage cyclic-hardening is also reflected in the bilinear Coffin-Manson-relationship and fatiguefracture. In sharp contrast to fatigue-fracture-surface at Δεt/2 = 0.003, that at Δεt/2 ≥ 0.004 are characterised by multiple-origins of fatigue-crack, absence of fatigue-striations and occurrence of microcleavage/river-pattern indicating faster brittle-fracture at higher Δεt/2.

1. Introduction The present work revolves around the low cycle fatigue behaviour of a ferritic steel strengthened with nano-meter sized precipitates to achieve a tensile strength of 800 MPa. The usage of high strength formable steels is increasing in the automotive components such as long and cross members of heavy duty vehicles [1]. The nano-precipitate strengthened ferritic steel exhibits great potential to replace conventional micro-alloyed steels (tensile strength ∼ 500 MPa) [2] in the above application to achieve reduction in vehicle-weight. Some of the new generation high strength steels such as dual phase steels do offer the required level of strength but suffer from poor formability. The latter is attributed to local stress concentrations at harder second phase e.g. martensite dispersed in the soft ferrite-matrix [3]. A fully ferritic steel can obviously be the best option to overcome the above limitation. However, in a conventional ferritic steel, the highest level of strength

∗

that can be achieved with a combination of solid solution, grain boundary and conventional precipitation strengthening is known to be of the order of 500 MPa [2]. Funakawa et al. [4] demonstrated for the first time, the possibility of achieving tensile strength of 800 MPa in a ferritic steel. The additional contribution of 300 MPa could be achieved by strengthening the ferrite with nano-meter sized carbide precipitates. These investigators [4] established that in a low-carbon Ti- bearing steel (Ti ∼ 0.08–0.9 wt%), it is possible to achieve thermally stable nano-meter sized carbide precipitates of primarily Ti-Mo-C type by lowering the austenite to ferrite transformation temperature (through addition of ∼1.5 wt% Mn) and by retarding the formation of pearlite and large cementite (through addition of ∼0.2 wt% Mo) [4]. It was reported that the fine carbides are precipitated from the supersaturated ferrite solid solution at the austenite-ferrite interface in linear rows [4]. It is evident from a review of literature that following the first report of Funakawa et al. [4], several investigators [5–10] have made

Corresponding author. E-mail address: [email protected] (S. Majumdar).

https://doi.org/10.1016/j.msea.2019.04.043 Received 2 October 2018; Received in revised form 7 March 2019; Accepted 10 April 2019 Available online 14 April 2019 0921-5093/ © 2019 Elsevier B.V. All rights reserved.

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contributions in reinforcing the above concept. Yen et al. [5] revealed the chemical nature, crystal structure and lattice parameters of Ti-Mo-C precipitates formed in the above kind of high strength ferritic steel. These investigators identified the above precipitates as MC carbides with NaCl-type crystal structure. Chen et al. [6] examined the effects of Ti, Ti–Mo, and Ti–Nb microalloying additions on precipitation strengthening in HSLA steels. These investigators inferred that complex carbide, (Ti, Mo) C sustain nanometer-scaled size, exhibit thermal stability and contribute maximum towards the hardness as compared to TiC or complex carbide, (Ti, Nb) C. Wang et al. [7] examined the effect of austenite to ferrite transformation temperatures ranging from 650 °C to 750 °C, on the precipitation kinetics of nano-meter size TiC precipitates in the ferrite matrix. They inferred that at 700 °C, majority of nano TiC precipitates tend to distribute along the austenite/ferrite interface in linear rows imparting excellent strength to ferrite although at higher temperatures coarsening of precipitates occur. The nano-meter size TiC precipitates also formed at lower temperatures of 650 °C and 675 °C. However, these precipitates were found to be randomly dispersed in the matrix, at the point defects, grain boundaries, and at dislocation intersections. Shen et al. [8] inferred that in a high strength ferritic steel of 800 MPa TS, fine TiC precipitates (MC) of 10 nm size are dispersed in the ferrite matrix along with some square or spherical precipitates (M23C6) of 30–50 nm size located at the vicinity of grain boundaries and interior of grains. They inferred that the dual precipitate structure provides effective matrix strengthening. The above precipitates could strengthen the steel by both pinning the dislocations and retarding the recovery and annihilation of dislocations. They also concluded that the work-hardening behaviour of the steel could be correlated to observed accumulation of dislocations resulting from the dispersed nano-scale precipitates. Further, Funakawa [9] examined the effect of austenite to ferrite transformation temperature on size and row-spacing of carbide precipitates and their combined effect on mechanical properties of the steel. Funakawa et al. [10] also investigated the effect of cooling rate after hot rolling to evaluate the influence of rapid cooling on the nature of precipitates and consequent precipitation strengthening. It emerges from the above review that the contributions till date [4–10] are primarily on the effect of processing parameters on the nature of nano-precipitates. Barring a few reports [8], that on mechanical behaviour and especially fatigue behaviour of nano-precipitate strengthened ferritic steel are extremely limited in the literature. But it is known that an automotive component is subjected to cyclic loading in service. Therefore, the fatigue properties of this steel must be assessed in detail. The present work is a step towards addressing this cause. For the present work, an industrially hot rolled Ti-Mo bearing low carbon ferritic steel, strengthened with nano-meter sized precipitates, was selected. The as-received steel, addressed henceforth as HS-800 steel, was characterised with respect to microstructure and tensile properties. Low cycle fatigue (LCF) tests were carried out under total strain amplitude (Δεt/2) ranging from ± 0.002 to ± 0.01. The cyclic stress response, cyclic hardening and softening behaviour, fatigue life and the nature of fracture surfaces were examined. The evolution of dislocation structure during LCF was examined through transmission electron microscopy of as-received and fatigued samples. The aim was to establish the micro-mechanism of fatigue failure in the selected HS800 steel through a detailed study of dislocation sub-structures and fractographic features.

Table 1 Chemical composition of as received steel (wt%). C

Mn

S

P

Si

Al

N2 ppm

V

Ti

Mo

0.06

1.58

0.003

0.02

0.135

0.039

30

0.007

0.097

0.22

transformation temperature. The microalloying elements titanium and vanadium are added for grain refinement. Molybdenum is added to restrict the formation of cementite and large carbides. The steel was produced as slabs through LD steel making and vacuum degassing route. The slabs were hot rolled in a commercial hot rolling mill with finish rolling temperature of 900 °C and coiling temperature of 630 °C respectively. The metallographic samples collected from the selected steel were prepared by standard technique of polishing and etching with 2% Nital. General microstructure of the steel was examined using OM and FEGSEM. The volume fraction of phases and ferrite grain size (GS) were determined using image analysis software associated with OM. The tensile properties of the steel was evaluated using longitudinal specimens of 50 mm gauge-length machined as per ASTM E08M [11] and tested at cross head speed of 10 mm/min which corresponds to nominal strain rate of 3.33 × 10−3 s −1. The value of monotonic strain hardening exponent ‘n’ was estimated from the slope of the plot between log σ (true stress) and log ε (true strain) by linear regression method in accordance to ASTM E646 [12]. 2.2. Low cycle fatigue (LCF) tests LCF tests were carried out using longitudinal specimens of 17.5 mm parallel length fabricated following the guidelines of ASTM E606 [13]. Strain controlled fatigue tests were carried out at room temperature (≈300K) in the laboratory air using a servo-electric test machine. Tests were conducted under fully-reversed triangular wave-form under a constant strain-rate of 0.002 s−1 with the first load-reversal in tension. Total strain amplitude (Δεt/2) was controlled during the tests and the tests were conducted using various values of Δεt/2 as 0.002, 0.0025, 0.003, 0.004, 0.005, 0.006, 0.007, 0.008, 0.009 and 0.01. The elongation of the specimens was monitored with a dynamic-extensometer. Specimen-failure was defined as the state where the stress-amplitude dropped to 20 pct. with reference to the stable stress amplitude. The cyclic stress response or the variation of cyclic stress-amplitude (Δσ/2) with the number of loading cycles (N) was automatically recorded during each test. The cyclic hardening and softening behaviour of a material is generally identified by examining the cyclic stress response as described above. In addition, in the present work, the concept of strain ratio and hardening factor based on strain ratio was used to examine the nature of cyclic hardening and softening more quantitatively following some of the prior investigators [14]. The concept of strain ratio and the associated hardening factor can be described as follows. It is known that the shape of stress-strain hysteresis loop generated during a typical LCF test changes continuously due to cyclic hardening and softening of the material. Each hysteresis loop has a definite geometry defined by the width of the loop which is double the plastic strain amplitude (Δεp/2) and the height of the loop which is double the stress amplitude (Δσ/2). The elastic strain amplitude (Δεe/2) is proportional to the stress amplitude Δσ/2. Hence, the geometry of a typical hysteresis loop can be expressed by the ratio of Δεp/2 and Δεe/2. The above ratio is termed as strain ratio and is defined as

2. Experimental details

Strain ratio = 2.1. General characterisation of selected steel

Δεp Δεe

(1)

The total strain amplitude (Δεt/2) has two components: elastic and plastic strain amplitude (Δεe/2 and Δεp/2 respectively). It is known that during LCF tests, cyclic hardening leads to the increase in the value of stress amplitude. On the other hand, Δεe/2 is proportional to stress amplitude. With cyclic hardening, due to increase in the value of stress

A hot rolled sheet of 7 mm thickness was selected for the present work. The chemical composition of the selected steel is shown in Table 1. The steel is alloyed with manganese which imparts solid solution strengthening and helps in lowering austenite to ferrite 199

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amplitude, Δεe/2 increases with a concomitant decrease in the value of Δεp/2. Hence, it is evident from equation (1) that when cyclic hardening occurs Δεp/2 decreases and Δεe/2 increases leading to decrease in the value of strain ratio. Similarly, with cyclic softening, the value of strain ratio is expected to increase. Hardening factor (H) can be described as the strain ratio at saturated cycle (SRs) to the strain ratio at fist cycle (SR1) as

H=

SRs SR1

fatigued samples, adequate care was taken to collect the samples such that the measurement surface was as close to the fracture surface as possible. The microhardness of ferrite grains was measured using a Vickers indenter at 50-gmf load for indentation duration of 15 s. The average microhardness was estimated from at least ten nos. of readings. Appropriate care was taken during each measurement to ensure that the distance between two successive indentations was more than thrice the average diagonal length of the indentations.

(2) 2.5. Fractography

From equations (1) and (2), it can be stated that H < 1 for cyclic hardening and H > 1 for cyclic softening. Further, in the present work, the rate of change of stress response (dσ/dN) during each LCF test was examined following the report of Sivaprasad et al. [15]. The stress–strain cycle corresponding to a constant value of dσ/dN was selected as the stable hysteresis loop. From the latter, the corresponding values of cyclically stable stress amplitude (Δσ/2) and cyclically stable plastic strain amplitude (Δεp/2) for each test were recorded. The stable Δσ/2 and Δεp/2 data were compared with corresponding monotonic stress-strain data (obtained from uniaxial tensile tests) to bring forth the predominant cyclic behaviour of the steel. Next, the values of stable Δσ/2 and Δεp/2 were plotted in logarithmic co-ordinates to generate the cyclic stress-strain (CSS) curve and to estimate the value of cyclic strain hardening exponent (n’) from the slope of the CSS plot. The average fatigue lives (number of loading cycles to failure, Nf) of the sheet specimens at selected Δεt/2 were determined. Each test was repeated at least three times. The strain-life curve and Coffin-Manson (C-M) plot were represented as double-logarithmic plots of total strain-amplitude (Δεt/2) vs. Nf and plastic strain amplitude (Δεp/2) vs. Nf respectively. Linear regression was performed during the plotting of CSS and strain-life curves using analysis menu of Origin, a data analysis and technical graphics software.

Fractographic examinations were carried out on the specimens which failed in LCF tests using FEGSEM. The main aims of fractography were (a) to locate the origin of the fatigue crack and the nature of crack growth path along with the associated macroscopic features and (b) to understand the mechanism of crack propagation. 3. Results 3.1. General characteristics of selected steel The microstructure of the selected steel is shown in Fig. 1. The microstructure predominantly consists of equiaxed ferrite grains with less than 1.5 pct. volume fraction of pearlite. The average ferrite GS is 3 ± 2 μm while the maximum and minimum GS recorded is 1 and 16 μm respectively. The tensile properties of the steel are shown in Table 2. The selected steel exhibits good combination of strength and ductility. The yield strength (YS) is high at 728 MPa and tensile strength (TS) is more than 800 MPa with total strain to fracture at 24.4 pct. The value of monotonic strain hardening exponent (n) is 0.091. 3.2. Results of LCF tests

2.3. Transmission electron microscopy The results of LCF tests in terms of (a) cyclic stress response, (b) strain ratio and hardening factor, (c) cyclic stress-strain plot and (d) strain-life and Coffin-Manson plots are presented in Figs. 2-5 respectively. It emerges from the cyclic stress response (Fig. 2) that at low strain-amplitudes of 0.002 and 0.0025, the stress amplitude remains stable for major part of the fatigue life although there is minor amount of initial hardening. At intermediate values of Δεt/2 such as 0.003 and 0.004, there is moderate amount of initial cyclic hardening; although towards the end, there is minor amount of softening. At higher values of Δεt/2 such as 0.008–0.01, the nature of the Δσ/2 vs. N plot is considerably different. At these values of strain amplitudes, the steel predominantly undergoes cyclic hardening. Further, the variation of strain ratio and hardening factor (based on strain ratio) with number of loading cycles, N, are shown in Fig. 3. In Fig. 3(a), strain ratios pertaining to LCF tests at Δεt/2 = 0.002, 0.0025

Transmission electron microscopy was carried out using thin foils prepared from as-received and fatigued samples to reveal the evolution of dislocation structures during LCF. For examination of the precipitates thin foils as well as carbon extraction replica were used. In case of as received steel, foils were prepared perpendicular to the rolling direction along the cross section of the sheet. In case of fatigued samples, foils were prepared perpendicular to the loading axis from the gauge section. In case of samples, which did not fracture till 105 cycles in LCF tests, samples were collected from the middle of the gauge section whereas in case of fractured samples, foils were prepared from a location well clear of the fracture area. Thin foils were prepared by standard method of mechanical thinning followed by twin-jet electro-polishing in a solution of 10 pct. perchloric acid in acetic acid at temperature of 10 °C, maintaining the voltage at 36–45 V. To prepare the carbon extraction replica, a 200–300 Å layer of pure graphite particles was deposited on the polished and etched (with nital) sample under high vacuum. The surface of the sample (with the carbon layer on the top) was then etched once again and scored. Next, the carbon layer with the embedded precipitates on it was fished out on Cu-grids after dipping the double etched samples in a bowl of distilled water. TEM examinations were carried out mostly at 200 kV operating voltage using primarily brightfield (BF) imaging mode. At least three thin foils were examined for each specimen. 2.4. Evaluation of microhardness The microhardness of fatigue-tested and as-received samples were evaluated using polished and etched sample. In case of as received steel, samples were prepared perpendicular to the rolling direction along the cross section of the sheet. The fatigued samples were prepared perpendicular to the loading axis from the gauge section. In case of

Fig. 1. Microstructure of selected steel. 200

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Table 2 Mechanical properties of selected steel. Yield Strength (MPa)

Tensile strength (MPa)

Total strain to fracture, %

Uniform elongation, %

Strain hardening exponent ‘n’

728 ± 11

826 ± 15

24.4 ± 1

11.3 ± 0.4

0.091

cycles (without failure). At Δεt/2 = 0.003, the rate of decrease in strain ratio values is steeper which indicates higher intensity of initial cyclic hardening compared to that at lower Δεt/2 of 0.002 and 0.0025. After around 800 number of loading cycles, cyclic softening begins in samples tested at Δεt/2 = 0.003. On comparing the values of strain ratios in the y-axes of Fig. 3(a) and (b), it is evident that the amount of cyclic hardening is considerably higher in samples tested at Δεt/2 ≥ 0.004. It emerges from Fig. 3(b) that Δεt/2 ≥ 0.004, the values of strain ratios fall continuously indicating the predominance of cyclic hardening throughout the fatigue life of these samples. It is also evident from Fig. 3(b) that with increase in the values of Δεt/2 from 0.004 to 0.01, especially when Δεt/2 = 0.008–0.01, the intensity of initial cyclic hardening increases considerably. The variation of hardening factors with number of loading cycles pertaining to LCF tests carried out at Δεt/ 2 = 0.002–0.007 is shown in Fig. 3(c) whereas that for Δεt/ 2 = 0.008–0.01 are shown in Fig. 3(d). In the above plots, hardening factors of less than unity indicate cyclic hardening and vice versa. The data plotted in Fig. 3(c) indicate that in case of Δεt/2 ≤ 0.003, there is initial hardening followed by tendency of cyclic softening in the samples whereas in case of Δεt/2 > 0.003, there is predominantly cyclic hardening. Similarly, data in Fig. 3(d) also indicate continuous cyclic hardening throughout the fatigue life although at Δεt/2 ≥ 0.008, hardening factors decrease more rapidly indicating significant increase in initial hardening at this stage. It is evident from the above plots of strain ratios and hardening factors that the values of Δεt/2 play a decisive role in the nature of cyclic hardening and softening behaviour of the selected HS-800 steel.

Fig. 2. Variation of cyclic stress amplitude with number of loading cycles (cyclic stress response) in the selected steel.

and 0.003 are shown whereas in Fig. 3(b) strain ratios pertaining to LCF test at higher Δεt/2 (≥0.004) are presented for clarity of presentation. In these plots, the decrease in the values of strain ratios indicates cycling hardening whereas an increase in the values of strain ratios indicates cyclic softening. It emerges from Fig. 3(a) that the nature of variation of strain ratio in case of Δεt/2 = 0.002 and 0.0025 are similar in nature. In both, there is minor amount of initial hardening till around 500–600 cycles followed by minor amount of cyclic softening till 105

Fig. 3. Variation of (a)–(b) strain ratios and (c)–(d) hardening factors with number of loading cycles, N, during various LCF tests carried out. 201

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Fig. 5. (a) Strain-life curve and (b) Coffin-Manson plot of selected steel.

Fig. 4. (a) Comparison of monotonic and cyclic-stress-strain data and (b) cyclicstress-strain plot of selected steel wherein two stages of cyclic hardening are shown; stage 1 (n1′ = 0.3) and stage 2 (n2′ = 0.04) at low and high plastic strain amplitude respectively.

number of loading cycles. The drastic fall in fatigue life beyond Δεt/ 2 = 0.003, can possibly be attributed to disproportionate tendency of cyclic hardening. The C-M plot of the selected steel is shown in Fig. 5(b). It is evident that the C-M plot is also better represented as a bi-linear plot as in case of CSS curve. There is difference in the slopes of the two regimes in C-M plot. On comparison, it becomes evident that transition from stage 1 to stage 2 in CSS curve (Fig. 4(b)) and regime 1 and regime 2 in C-M plot (Fig. 5(b)) occurs at approximately same value of Δεp/2 = 0.00046 which corresponds to a Δεt/2 = 0.004. It can, therefore, be inferred that there is certain correspondence between cyclic hardening and C-M plot and that the deviation in the C-M relationship and the change in the cyclic strain-hardening exponent n’ are related effects.

The values of cyclic stress and cyclic plastic strain (stable Δσ/2 and stable Δεp/2) obtained from LCF tests are compared with corresponding monotonic stress-strain data obtained from uniaxial tensile tests in Fig. 4(a). It emerges that the cyclic stress-strain plot is considerably above the monotonic plot. This observation denotes that within the range of present experimental data, the selected steel exhibits cyclic hardening. To evaluate the cyclic strain hardening exponent (n’), the cyclic stress-strain data are plotted in double-logarithmic coordinates to generate the cyclic stress-strain (CSS) plot as shown in Fig. 4(b). It emerges that the CSS curve of the selected steel can be better represented as two distinct stages depicted by two straight lines with different slopes. The values of the cyclic strain-hardening exponents for the two stages are 0.3 (denoted as n1′ at low Δεp/2) and 0.04 (denoted as n2′, at higher Δεp/2) respectively as shown in Fig. 4(b). Such transitions in the cyclic stress strain curves are known to reflect two stages of cyclic strain hardening [16]. The strain hardening is basically the strengthening of metallic materials through plastic deformation. The above strengthening is caused by generation, movement and rearrangement of dislocations. As n1′ > n2′, it can be inferred that opportunity for dislocation movement and rearrangement are far more at lower Δεp/2 and vice versa. Although amount of dislocation generation is expected to be higher at higher Δεp/2. The strain-life curve and C-M plot of the selected steel are shown in Fig. 5. It is evident from strain-life curve (Fig. 5(a)) that the selected steel exhibit superior fatigue life at Δεt/2 = 0.002 and 0.0025 and no failure takes place till 105 cycles. This observation can be attributed to cyclically stable behaviour at low Δεt/2. However, at Δεt/2 of 0.003, there is an order of magnitude decrease in fatigue life and when Δεt/ 2 > 0.003, fatigue failure takes place even faster at remarkably lower

3.3. Results of TEM study 3.3.1. Dislocation structure and nature of precipitates in as received steel The dislocation structure in the as received HS-800 steel is shown through representative micrographs in Fig. 6 and in Fig. 7 respectively. The dislocation structure in as received steel is primarily characterised by non-uniform distribution of dislocation density as shown in Fig. 6 (a). The dislocation density varies from one ferrite grain to the other and even in a single ferrite grain the dislocation density is significantly high close to a grain boundary compared to interior of the grains which is relatively free of dislocations. In the areas of high dislocation density, dense dislocation clusters/tangles are formed as marked in Fig. 6(a). Long, straight dislocations emerging from the grain boundaries (Fig. 6 (b)) as well as abundance of dislocation segments and intersecting dislocations within the grains (Fig. 6 (c)) are also noticed. It is revealed that there is significant amount of dislocation-precipitate interaction in areas of low dislocation density as shown in Fig. 6(d–f). Some of the dislocation-precipitate interactions are marked in the above 202

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Fig. 6. Typical dislocation structuresin as received HS-800 steel: (a)overallview, (b) dislocations emergingfrom a ferrite grain boundary,(c) dislocation segments and intersecting dislocations (marked), (d) to (f) dislocation-precipitate interaction in areas of low dislocation density (d) BFimage,(e) BFimage and (f) corresponding DFimage of(e).

representative micrographs in Fig. 8. In Fig. 8 (a), bright field image of a representative location within ferrite matrix along with EDAX spectrum and SAD pattern (inset) captured from the same area shown. The presence of precipitates is identified through the peaks of titanium and molybdenum in the EDAX spectrum along with the peak of iron. The latter appear predominantly from the matrix. The corresponding DF image of Fig. 8(a) captured using a spot (which is less bright and considered to be arising from the precipitates) in the SAD pattern (inset in Fig. 8(a)) is shown in Fig. 8 (b). It is evident from Fig. 8(b) that the fine precipitates are randomly distributed in the ferrite matrix. Although size of these fine precipitates could not be measured with accuracy, but these are very fine and of approximately 10–30 nm in size. Similarly, in Fig. 8(c) and in Fig. 8(d), a ferrite grain boundary decorated with fine precipitates is shown. The size and exact chemical nature of typical precipitates which are larger than 30 nm in size could be better identified through extraction replica study; typical results of this study are shown in Fig. 9. The most abundantly occurring

micrographs. The dislocation-precipitate interactions are also evident within the dislocation clusters as shown through representative micrographs in Fig. 7. The bright field image of a dislocation cluster area is shown in Fig. 7(a). The corresponding dark field image in Fig. 7(b) is captured using a less bright spot in the SAD pattern (inset in (b)) which is considered to arise from the precipitates. The numerous dislocationprecipitate interactions are evident in the DF image (some are marked). It is possible that during the phase transformation from austenite to ferrite and the subsequent cooling process, the ferrite grains undergo deformation due to increase in volume as well as due to the formation of precipitates [17]. As a result, mobile dislocations are generated which interact with fine precipitates. It emerges from the thin foil study that, an abundance of fine precipitates (size < 30 nm) are present at the grain boundaries as well as in the matrix. There are larger precipitates of size ranging between 40 and 200 nm as well which are predominantly found in the matrix. The locations of occurrence of finer precipitates are shown through 203

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Fig. 7. Dislocation-precipitate interaction within a dislocation cluster in as received HS-800 steel: (a) BFimage and (b) corresponding DFimage using a point in SAD pattern (inset in (b)) from region shown in (a).

Fig. 8. Location of precipitates in the selected HS-800 steel (a)–(b) precipitation in matrix and (c)–(d) precipitation in grain-boundary. (a) and (c) BFimage withEDS spectrum and SAD patternas inset, (b) DF image using spot 1 in (a) and (d) DF image using spot in (c).

3.3.2. Dislocation structure in fatigued samples In the fatigued samples, the characteristic dislocation structures are found to be governed by the values of Δεt/2. Accordingly, distinctly different types of dislocation structures are found in samples tested at low (Δεt/2 = 0.002–0.0025), intermediate (Δεt/2 = 0.003) and high (Δεt/2 ≥ 0.004) values of Δεt/2 as described below.

precipitate is Ti-Mo-C type (Fig. 9(a)). These precipitates are of regular geometrical shape such as trapezoidal and rhombic. The next most abundantly occurring precipitates are Ti-C type (Fig. 9(b)) and these precipitates are mostly equiaxed or spherical or elliptical in shape. Along with abundantly occurring Ti-Mo-C and Ti-C particles, few precipitates of Ti-C-N and Ti-C-S type are also present in the selected steel as shown in Fig. 9(c) and in Fig. 9(d) respectively. The T-C-N precipitates are of regular geometrical shape e.g. rectangular or trapezoidal whereas Ti-C-S precipitates are roughly spherical or equiaxed in shape.

3.3.2.1. At low Δεt/2. In the present work, the samples tested at low Δεt/2 of 0.002 and 0.0025 did not fail till 105 cycles as stated above. The dislocation structures in un-failed sample (Δεt/2 = 0.0025) are 204

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Fig. 9. Typical precipitates with size larger than approximately 30 nm along with semi quantitative chemical analysis as obtained from EDS spectrum acquired from middle of the precipitate particle (a)Ti-Mo-C, (b) Ti-C, (c) Ti-C-N and (d) Ti-S type precipitates.

totally replaced by new features unlike that in sample tested at low Δεt/ 2 of 0.0025. Therefore, Δεt/2 = 0.003 is considered as that value of intermediate Δεt/2 where the dislocation structure undergoes a complete transition from as received structure to fatigued structure. At this stage (Δεt/2 = 0.003), some of the ferrite grains are full of dense dislocation clusters/tangles (Fig. 11(a)). In addition, there is predominance of dislocation walls separated by channels (Fig. 11(b and c)) within some of the ferrite grains. These walls are approximately 100–150 nm in width. The channels between the walls are free of dislocations at some places as seen in Fig. 11(b). In many instances, numerous gliding dislocations are observed in the channels (Fig. 11(c and d)). There is abundance of subgrains (Fig. 11(e–f)) in some of the ferrite grains. Some of the subgrains are not fully-formed as shown in Fig. 11 (e) while in some cases the entire ferrite grain is covered by fullyformed subgrains Fig. 11(f). The number of subgrains increases considerably and subgrains of various sizes e.g. 500 nm to 1.0 μm could be recorded. One of the remarkable feature at this stage is occurrence of long microbands or deformation bands which are 2.5–5 μm in length and (Fig. 11(g–i)). The dislocation density inside these microbands vary. At few locations, dense dislocation clusters are found whereas some other locations are dislocation free. Within the microbands, subgrains are found to form. These subgrains are surrounded by dislocation walls while the interior of the subgrains are relatively dislocation free. The subgrains formed within microbands are either rectangular or square shaped. Typical square shaped subgrains are 400–500 nm in size whereas rectangular subgrains have longer side of 400–900 nm and short side of 400–500 nm. Generally, set of subgrains are found to form by development of boundaries across microbands and dividing the microbands along their length by sub boundaries. At few locations,

shown in Fig. 10. At this stage, largely, the characteristics of as received steel are prevalent. For example, there are intersecting dislocations (Fig. 10 (a)) as well as long and straight dislocations emerging from grain boundaries. There are thick dislocation clusters close to the grain boundaries while the interior of the grains is largely dislocation-free as evident from grain 1 in Fig. 10 (b). In addition, approximately 100 nm thick dislocation walls separated by 400–500 nm wide dislocation channels form within ferrite grains as seen in grain 2 in Fig. 10(b). The dislocation channels are totally free of dislocations at this stage. In general, the dislocation density is marginally higher compared to as received sample and few of the ferrite grains are full of dislocation cluster as seen in grain 3 in Fig. 10(b). The two most important phenomenon that are noticed at this stage are moderate amount of increase in dislocation density and signatures of dislocation rearrangement. The latter is evident from the formation of alternate regions of dislocation clusters followed by totally dislocation free areas as shown in Fig. 10(c). At many locations, the dislocation walls divide the ferrite grains into subgrains. An emerging subgrain is shown in Fig. 10(d). The walls surrounding the subgrains are very sharp, distinct and curved at limited locations as shown in Fig. 10(e). The subgrains are mostly rectangular; the longer dimension is 400–500 nm while the shorter dimension is 100–200 nm as shown in Fig. 10(f). The interior of the subgrains are free of dislocations. However, at this stage, most of the subgrains are not fully formed or compact and are somewhat loosely bounded by dislocation walls/sub-boundaries. 3.3.2.2. At intermediate Δεt/2. The saturation dislocation structures observed in the failed sample tested at Δεt/2 = 0.003 are shown in Fig. 11. At this stage, the characteristics of as received sample are 205

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Fig. 10. Dislocation structure in samples fatigued at Δεt/2 = 0.0025 (a) intersecting dislocations, (b) dislocation walls separated bychannels; channel is marked with dotted arrow,(c) dislocation clusters adjacent to dislocation-free areas,(d) initiation of a subgrain,(e) a distinct curved subgrain boundary and(f) subgrains.

dislocations as shown inFig. 12(c). At this stage, for the first time, limited number of finer equiaxed cell-like structures are recorded. These cell-like structures are approximately of 100–200 nm in size as shown in Fig. 12(d and e). However, the boundaries of these cells are not very well defined or distinct and are somewhat diffused in appearance. The interior of these cell-like structures is relatively free of dislocations. These cell-like structures are remarkably different from dislocation cells reported in low carbon formable steels e.g. mild steel or interstitial free steels [19]. Unlike samples tested at intermediate Δεt/2 = 0.003, fewer number of microbands could be recorded in this sample. One such microband is shown in Fig. 12(f) The microband is full of dense dislocation clusters. Although there is some indication of subdivision of these microbands but formation of distinct subgrains bounded by sub-boundaries with interiors free of dislocation could not be recorded.

dense dislocation clusters are found adjacent to the microbands in the neighbouring ferrite grains. Increased dislocation density may be due to stress concentrations and can cause faster initiation of microcracks. The microbands generally have sharp boundaries. Roven and Nees [18] opined that the microbands can act as microcrack initiation site. 3.3.2.3. At high Δεt/2. The saturation dislocation structures observed in the failed sample tested at Δεt/2 = 0.008 are shown in Fig. 12. At high Δεt/2, dislocation density increases remarkably and most of the ferrite grains are found to be full of dense dislocation clusters as shown in Fig. 12(a) The dislocation structure at this stage primarily consists of clusters. Apart from that, the dislocation walls and division of ferrite grains by these walls leading to formation of subgrains are also noticed at this stage as shown in Fig. 12(b). At high Δεt/2, fully formed compact subgrains with more distinct and well-defined subgrain-boundaries are observed; interior of these subgrains is cleaner and is totally free of 206

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Fig. 11. Dislocation structure in sample tested at Δεt/2 = 0.003(a) dense dislocation clusters in ferrite grains, (b–c) dislocation walls separated by channels, (d) gliding dislocations between twodislocation walls, (e–f) subgrains and (g–i) microbands(MB); subgrains within microbands are markedin blue colour. (For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.)

features vary with distance from the crack origin as shown in Fig. 14(c)–14(f). The area close to crack origin is generally flat and featureless. However, this region exhibits some characteristic marks on the grains (Fig. 14 (d)). These marks produce an impression of rubbing of the crack-faces. It is envisaged that considerable crack closure effect during compression part of the loading cycle results into the formation of these characteristic marks in the grains. With further increase in crack-length, transgranular ductile fatigue-striations are noticed in the grains as shown in Fig. 14(e). Following initial propagation of the fatigue crack, significant amount of transverse cracking (marked with white arrow in Fig. 14(c–e) is also noticed which continues till final failure. Prior to final failure, tendency of transverse cracking increases (Fig. 14(e)). Final failure occurs though shallow dimples as shown in Fig. 14(f). At higher Δεt/2 (≥0.004), multiple origins of fatigue crack are noticed as shown in Fig. 15(a). There are characteristic flow lines emerging from the fracture origins. Following initiation, the crack propagates though rubbing of crack faces as also noticed in fracture surface at Δεt/2 = 0.003. However, at higher Δεt/2, these characteristic marks are sharper and assume a tooth-like appearance as shown in

3.4. Microhardness The microhardness values of as received and fatigued samples are shown in Fig. 13. The hardness values increase linearly with Δεt/2.

3.5. Results of fractography The fractography carried out on the failed LCF tested samples brings forth the fact that the microscopic features in fatigue fracture surfaces are distinctly different for sample tested at Δεt/2 = 0.003 and those tested at Δεt/2 ≥ 0.004. The main fractographic features of the two types of samples are, therefore, discussed separately. The representative fractographs of samples tested at Δεt/2 = 0.003 and at Δεt/2 = 0.007 are presented in Figs. 14 and 15 respectively. The direction of crack propagation is horizontal in the above figures. In samples tested at low Δεt/2 = 0.003, fatigue crack generally originates on the surface; close to a corner of the specimen as shown in Fig. 14(a). The fracture-origin can be traced back following the characteristic flow-lines emerging from the origin and progressing in the direction of crack propagation as shown in Fig. 14(b). The microscopic 207

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Fig. 12. Dislocation structures in samplefatigued at Δεt/2 = 0.008 (a) dislocation clusters within a ferrite grain, (b) dislocation walls and subdivision of ferrite grains into subgrains, (c) fully formed subgrain, (d) initiation of smaller subgrainsor cell-like structures, (e) smaller subgrains or cell-like structures, and (f) micro-band.

Fig. 15(b and c). Beyond this initial region, the crack propagation occurs through microcleavage for most part of the crack length before final failure through dimples (Fig. 15(d)). The cleavage fracture creates distinct river pattern on the fracture surface as shown in Fig. 15(e and f). The river pattern covers most part of the fracture surface over a wide range of Δεt/2 = 0.004–0.01. It can be mentioned here that growth of fatigue crack through microcleavage is a lower energy process and is an undesirable fatigue crack growth mechanism [20]. The predominance of cleavage in fatigue fracture surfaces indicate that fatigue failure at Δεt/2 > 0.003 is a brittle one. The fracture surfaces at higher Δεt/2 (≥0.004) are characterised by multiple origins of fatigue crack initiation, total absence of transgranular, ductile, fatigue striations (as observed at Δεt/2 = 0.003) and predominance of microcleavage/riverpattern on the fracture surface. All the above characteristics indicate faster brittle failure at higher Δεt/2 = 0.004–0.01. Fig. 13. Variation of Vickers microhardness values with total strain amplitudes (Δεt/2).

4. Discussion The evolution of dislocation substructure in a metallic material is 208

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Fig. 14. Fatigue fracture surface of sample tested at Δεt/2 = 0.003 (a) origin of fracture (marked), (b) flow lines emerging from fracture origin(marked), (c) characteristic marks in the grains, (d) striations, (e) transverse cracking prior to failure and (f) dimples in final failure zone.

only minor amount of initial hardening followed by cyclic softening at low Δεt/2 = 0.002–0.0025. The initial hardening can be attributed to the generation of few mobile dislocations during the fatigue cycling and the subsequent interaction of the newly generated dislocations with the precipitate particles and other dislocations in addition to the formation of few compact subgrains. The minor amount of softening can be attributed to the rearrangement of dislocations into low energy stable dislocation structures (LEDS) e.g. walls, channels and large loosely bound subgrains. At intermediate value of Δεt/2 = 0.003, cyclic plasticity increases leading to higher and more uniform distribution of dislocation density in the matrix compared to samples fatigued at lower Δεt/2. At Δεt/2 = 0.003, the characteristic dislocation substructure of as received steel is completely replaced by (i) newly formed microbands, (ii) dense dislocation clusters within the ferrite grains and the microbands and (iii) more number of subgrains within the ferrite grains and the microbands as evident from Fig. 11. It is possible that there is significant amount of dislocation-dislocation and dislocation-precipitate interaction within the clusters. The higher initial hardening in samples tested at Δεt/2 = 0.003 than that tested at Δεt/ 2 = 0.002–0.0025 (Fig. 3) can be attributed to the above dislocation structures. The cyclic softening towards the end of fatigue life can be attributed to the rearrangement of dislocations to form LEDS such as dislocation walls and channels. It is possible that after the initial hardening, the process of softening becomes predominant and balances the process of cyclic hardening. At higher Δεt/2 = 0.004–0.01, increasingly more number of dislocation sources start operating as Δεt/2 increases. As a result, the mobile dislocation density increases remarkably fast with increase in Δεt/2. This phenomenon leads to more homogeneous distribution of high dislocation density in the matrix

the fundamental process that governs the progress of monotonic and cyclic plastic deformation and the mechanical properties [18,21,22]. The dislocations are the main carriers of plasticity and the phenomena of yielding and strain hardening are controlled by the movement of and the interactions between dislocations. The evolution of dislocation substructures is, however, a complex process which is determined by the chemistry, initial microstructure and the processing history of the material. It is important to examine systematically the effect of dislocation substructure on fatigue behaviour of a structural steel and obtain a greater insight into the alloy design and the end applications. An effort has been made here to explain the cyclic behaviour of the selected HS-800 steel in terms of dislocation substructure evolving during LCF. It emerges that the cyclic stress response, variation of strain ratios and hardening factors, nature of cyclic hardening, bi-linear C-M relationship as well as the nature of fatigue fracture could all be correlated with the characteristic dislocation structures at various values of Δεt/2. The dislocation structure of as received HS-800 steel is characterised by non-uniformly distributed dislocation density and dislocation-precipitate interactions (Figs. 6 to 7). Most of these characteristics of as received structure are largely retained in the samples till Δεt/2 = 0.0025 (Fig. 10). This phenomenon implies that the spread of cyclic plasticity through dislocations is limited till Δεt/2 = 0.0025. The stabilised value of stress amplitude (Δσ/2) at Δεt/2 = 0.0025 is around 507.5 MPa as evident from Fig. 4. The corresponding value of cyclic plastic strain is found to be negligible. The overall cyclically stable behaviour and the superior fatigue life exhibited by the selected steel at Δεt/2 = 0.002–0.0025 (Fig. 2) can, therefore, be attributed to the limited dislocation activity. The latter is also reflected in the magnitude of strain ratios and the hardening factors (Fig. 3) which indicates 209

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Fig. 15. Fatigue fracture surface of sample tested at Δεt/2 = 0.007(a) origin of fatigue crack(marked), (b–c) region close to fracture origin, (d) final failure zone, (e–f) cleavage fracture (river pattern).

mean free-path. This phenomenon leads to reduced opportunity for cyclic strain hardening with consequent decrease in the value of n′. The selected steel exhibits bi-linear C-M relationship (Fig. 5(b)) with a transition at around Δεt/2 = 0.004; the same value of Δεt/2 at which second stage of cyclic hardening starts (Fig. 4(b)). It is, therefore, evident that the two stages of cyclic hardening and the bilinear C-M relationship are related effects. It emerges from the study of dislocation structures and fracture surfaces that two different micro-mechanisms of fatigue failure are prevalent in the selected steel at Δεt/2 = 0.003 and that at Δεt/2 ≥ 0.004. Till Δεt/2 ≤ 0.003, there is better opportunity for cyclic hardening which leads to superior fatigue life ∼105 to 104 cycles. At Δεt/2 = 0.003, some amount of cyclic softening is observed towards the end of fatigue life due to the formation of LEDS and the subsequent fatigue fracture occurs in a more ductile manner predominantly through striations (Fig. 14). At Δεt/2 ≥ 0.004, plastic strain in the matrix increases significantly and more and more dislocations are generated which form dense dislocation clusters filling most of the ferrite grains. The accommodation of cyclic plastic strain becomes increasingly difficult primarily because of the dislocation-clusters in addition to the formation of compact subgrains and microbands (Fig. 12). These dislocation structures lead to significant increase in hardness at this stage (Fig. 13). It can be conjectured that at this stage, the glide of dislocations from one grain to another becomes difficult due to significant reduction in the dislocation mean free path. This phenomenon leads to incompatibility effect during cyclic plastic deformation and produces intergranular stress and stress localization leading to intergranular cleavage fracture. The faster fatigue failure in a brittle manner predominantly through microcleavage (Fig. 15) leads to much lower fatigue life at higher Δεt/2 = 0.004–0.01. The predominance of

leading to formation of dense dislocation clusters (Fig. 12) within most of the ferrite grains and it is possible that there is concomitant increase in dislocation-dislocation and dislocation-precipitate interactions within the clusters. In addition, there is formation of compact subgrains, microbands and few dislocation cell-like structures (Fig. 12). All the above types of structures are known to cause significant amount of cyclic hardening [23]. Hence, the predominance of cyclic hardening throughout the fatigue life (Fig. 2) and increasingly higher intensity of cyclic hardening with increase in the values of Δεt/2 (Fig. 3) can all be attributed to the nature of dislocation substructures forming at this stage. It can be mentioned here that in fatigued low carbon ferritic steels, formation of well-defined dislocation cell structure with distinct cell-boundary is widely reported [19,24]. The conspicuous absence of compact dislocation cells is an exceptional feature exhibited by the selected ferritic steel. The selected HS-800 steel exhibits two different values of cyclic strain hardening exponents such as n1′ = 0.3 at low Δεt/2 and n2′ = 0.04 at Δεt/2 > 0.003 (Fig. 4(b)). The values of n′ basically denote the opportunity for generation, movement and rearrangement of mobile dislocations during cyclic deformation. Moderate amount of mobile dislocations is generated during cycling at Δεt/2 ≤ 0.003, and the newly generated dislocations can move unhindered for greater distances and rearrange themselves into dislocation walls, channels and large loosely bound subgrains. At increasingly higher Δεt/ 2 = 0.004–0.01, dislocation density increases remarkably fast with more and more dislocations getting pinned by precipitate particles along with the formation of significant number of dislocation clusters, microbands and subgrains which obstruct further movement and rearrangement of dislocations by significantly reducing the dislocation 210

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2 = 0.002–0.0025. This phenomenon can be attributed to high lattice friction arising primarily due to solid solution strengthening by manganese. In addition to the solid solution strengthening, the fine GS and the nano-meter sized precipitates play significant role in restricting dislocation glide length at low strain. With increase in Δεt/2 to 0.003 and beyond, dislocations are unlocked to greater extent to form stable dislocation structures. It emerges that the lack of well-defined dislocation cell formation and the predominance of microcleavage in the fatigue fracture exhibited by the selected HS-800 steel can be attributed to the microalloying elements in the steel and the resulting finer GS. Future work should be directed towards evaluating more precisely the contributions of the solid solution strengthening and the grain size on the overall micro-mechanism of fatigue failure in the selected steel. It emerges from the results of TEM examination that the finer precipitates (size ≤ 30 nm) in the selected steel are distributed in the grain boundaries as well as in the matrix in addition to few coarser precipitates of size 40–200 nm distributed randomly in the matrix. The value of cyclic yield strength calculated from the cyclic stress strain data shown in Fig. 4(b) by considering Δεp/2 = 0.002 emerges to be around 805.3 MPa which is higher than the monotonic yield strength of 728 MPa. It can be inferred that the nano-meter sized precipitates along with the solid solution strengthening provided by manganese and the grain boundary strengthening provided by the microalloying elements in the selected steel are effective in enhancing both cyclic and monotonic yield strength. There is no direct evidence of any detrimental effects of few larger precipitates (40–200 nm) present in the selected HS-800 steel. It can be mentioned here that Shen et al. [8] also inferred that in a high strength ferritic steel of 800 MPa TS, nano-meter sized precipitates could strengthen the steel by both pinning the dislocations and retarding the recovery and annihilation of dislocations. Further, it is noticed that barring minor amount of softening at low Δεt/2 ≤ 0.003, the selected HS-800 steel predominantly exhibits cyclic hardening. Generally, it is considered that when the ratio of tensile strength to yield strength is less than 1.2, cyclic softening is expected. The above ratio of selected HS-800 steel is 1.13. Hence one can naturally expect cyclic softening. However, it emerges from the above results that the selected steel predominantly exhibits cyclic hardening. The above attribute can be of great benefit from application point of view. The steel exhibit very less amount of plasticity, cyclically stable behaviour and excellent fatigue life at low Δεt/2 of 0.002–0.0025. The fatigue life at Δεt/2 of 0.003–0.007 is also moderately good. However, at Δεt/ 2 ≥ 0.008, the fatigue performance deteriorates due to excessive hardening leading to faster brittle failure. The latter can be a concern during end use.

microcleavage as the main fatigue fracture mechanism over a wide range of strain amplitudes in the selected ferritic steel is a unique feature. The fatigue fracture in low carbon ferritic steel is known to occur predominantly through striations [25]. The contrasting nature of (a) cyclic strain hardening behaviour and (b) the mechanism of fatigue failure at low Δεt/2 ≤ 0.003 and higher Δεt/2 = 0.004–0.01 leads to bilinear C-M relationship in the selected ferritic steel. It can be mentioned here that prior investigators have reported linear C-M relationship at room temperature in a wide variety of low carbon ferritic steels meant for various structural applications [26–31]. The number of prior works on fatigue behaviour of nano-precipitate strengthened ferritic steel are limited in the literature. The absence of well-defined dislocation cell structures, the predominance of microcleavage in the fatigue fracture and the bi-linear C-M relationship exhibited by the selected steel are not reported in detail so far and these observations contrast with what is generally reported in case of ferritic steels [24–31]. Therefore, these observations can be regarded as new findings and should be discussed further. The lack of dislocation cell formation is attributed to the lack of cross slip of screw dislocations [21,22] which in turn is attributed to the presence of solid solution strengthening elements in the steels [32–35] as well as to ferrite grain size [36,37]. The presence of solid solution strengthening elements is reported to make the movement of dislocations more difficult, the deformation more planar and the dislocation glide more homogeneously distributed with less cross-slip [32]. Sestak et al. [33] reported that the addition of silicon to iron single crystals lead to dislocation wall formation in contrast to pure iron where dislocation cell formation takes place. The difference was attributed to solid solution hardening which increased the friction stress in Fe–Si compared to that in iron leading to a smaller mobility of edge dislocations. The lattice friction stress is the stress needed to move the dislocations along the slip plane. It is known [38] that the friction stress depends strongly on the nature of alloying elements, the applied strain etc. Adding atoms of another element that occupy interstitial or substitutional positions in parent lattice increases the strength of the parent material as the stress fields generated around the solute atoms interact with the stress fields of a moving dislocation, thereby increasing the stress required for plastic deformation [38]. The results similar to that of Sestak et al. [33] were reported by Ushioda et al. [34] in polycrystalline Fe–1%Si alloy where vein structure developed in fatigue in contrast to silicon free steel where dislocation cells were formed. Ushioda et al. [33] also reported transgranular fracture in silicon free steel and intergranular crack in Fe–1%Si steel. Similar results were also reported by Schayes et al. [35]. Further, during cyclic plastic deformation, dislocations pile-up against the grain boundaries with consequent increase in stresses near boundary regions. These stress fields are expected to govern the slip processes in the grains on either side of the boundary. Keller et al. [35] demonstrated that in a low carbon ferritic steel, GS has a decisive influence on the slip process at the two adjoining grains. In a fine-grained (GS ∼ 6 μm) steel, stress fields in the two adjoining grains overlap and the resultant stress field controls the overall slip behaviour. This phenomenon promotes homogeneous single or planar slip in the grains. In a coarse-grained (GS ∼ 85 μm) steel, on the other hand, the stress fields near the grain boundary region cannot strongly affect the central portion of the grain. As a result, slip sources on opposite sides of a grain may activate independently and multiple slip may occur within a grain. It is known that accommodation of cyclic plastic strain through formation of LEDS is promoted predominantly by multiple slip. Hence, more LEDS are expected to form in the coarse-grained steel and vice-versa. In the same line, Lopes and Charlier [36] also inferred that a reduction in the ferrite grain size promote homogeneous single slip and decreases the grain boundary affected zone. Keller et al. [30] also showed that with reduction in GS, the possibility of intergranular fracture increases due to increased constraint experienced by the grains during cyclic deformation. In the selected HS-800 steel, dislocation mobility is difficult and the formation of stable dislocation structure is rather slow at low Δεt/

5. Conclusion General characteristics and low-cycle-fatigue behaviour (Δεt/ 2 = ± 0.002 to ± 0.01) of a ferritic-steel strengthened with nanometer-sized-precipitates have been examined. The main conclusions are as follows:

• The selected steel is a hot-rolled Ti-Mo-bearing low-carbon steel. •

• 211

The microstructure comprises predominantly of ferrite (average GS ∼ 3 μm) with less than 1.5% of pearlite. The yield strength and tensile strength are 728 MPa and 826 MPa respectively with total strain to fracture of 24.4 pct. The dislocation substructure in the as received steel exhibits low density of non-uniformly distributed dislocations. The dislocationprecipitate interactions are evident in areas of both high and low dislocation density. The precipitates are predominantly Ti-Mo-C and Ti-C type and are of size ≤30 nm. The precipitates are distributed randomly on the grain-boundaries and in the matrix. The spread of cyclic-plasticity is negligible in the selected steel till Δεt/2 = 0.0025 leading to predominantly cyclically-stable behaviour as well as excellent fatigue-life (no failure till 105 loading

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cycles).

• At Δε /2 = 0.003, significant initial-cyclic-hardening is followed by t

•

• • • •

[8]

minor amount of cyclic-softening. The latter is attributed to formation of low-energy-dislocation-structures e.g. dislocation-walls and channels; numerous gliding dislocations are noticed within the channels. At Δεt/2 = 0.004–0.01, predominantly cyclic-hardening is noticed till failure. The cyclic-hardening at Δεt/2 ≥ 0.003 is attributed to (a) increase in dislocation-density and dislocation-precipitate and dislocation-dislocation interaction, (b) formation of microbands, (c) formation of dislocation-clusters (both within ferrite-grains and within microbands) and (d) formation of subgrains. At Δεt/2 ≥ 0.004, smaller and more compact subgrains with well-defined sub-boundaries form along with equiaxed cell-like structures leading to higher intensity of cyclic hardening. The microhardness of the LCF tested samples increase significantly with increase in Δεt/2. The selected steel exhibits two stages of cyclic strain hardening with two different values of strain hardening exponents (n1′ = 0.3 at low Δεt/2 and n2′ = 0.04 at Δεt/2 > 0.003). The selected steel exhibits bilinear Coffin-Manson-relationship which is attributed to two-stages of cyclic hardening as the transition in Coffin-Manson plot occurs at Δεt/2 = 0.004 where the second stage of cyclic strain hardening begins. The bilinear Coffin-Manson-relationship and the two-stage cyclichardening is also reflected in the fatigue-fracture which is also governed by Δεt/2. In sharp contrast to fatigue-fracture-surface at Δεt/2 = 0.003, that at Δεt/2 ≥ 0.004 are characterised by multipleorigins of fatigue-crack, complete absence of transgranular fatiguestriations and predominance of microcleavage/river-pattern indicating faster brittle-failure.

[9] [10]

[11] [12] [13] [14]

[15]

[16]

[17] [18] [19]

[20] [21]

[22] [23] [24]

Acknowledgement

[25] [26]

The authors are grateful to Dr. Bhupesh Mahato (Scientist, CSIRNational Metallurgical Laboratory, Jamshedpur, India) for his kind help in carrying out the TEM work.

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