Ratcheting strain in interstitial free steel

Materials Science & Engineering A 575 (2013) 127–135

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Ratcheting strain in interstitial free steel Krishna Dutta a,n, K.K. Ray b a b

Department of Metallurgical and Materials Engineering, National Institute of Technology, Rourkela 769008, India Department of Metallurgical and Materials Engineering, Indian Institute of Technology, Kharagpur 721302, India

art ic l e i nf o

a b s t r a c t

Article history: Received 24 December 2012 Received in revised form 22 February 2013 Accepted 25 February 2013 Available online 6 March 2013

This investigation illustrates ratcheting phenomenon, in-situ substructural variations during ratcheting and post-ratcheting tensile properties of interstitial free steel at ambient temperature (≈300 K). The results highlight that the nature of strain accumulation is dependent on the magnitude of the employed combinations of mean stress (sm) and stress amplitude (sa); this phenomenon has been explained considering the asymmetry of loading cycles and substructural variations as delineated by TEM. Tensile strength increases while ductility decreases for ratcheted samples with increasing sm and/or sa and these variations in tensile properties are correlated with the induced cyclic hardening. & 2013 Elsevier B.V. All rights reserved.

Keywords: Ratcheting Interstitial free steel Substructure Tensile strength

1. Introduction Engineering components are often subjected to symmetric or asymmetric type of fatigue loading in their service. Fatigue damage is particularly detrimental when there is asymmetric cyclic loading associated with positive mean stress. From the perspective of deformation behaviour, application of positive mean stress in stress-controlled fatigue tests gives rise to ratcheting which results in accumulation of plastic strain during low cycle fatigue. Strain accumulation by ratcheting limits the predictive capability of well-known Coffin Mansion relation [1] and it is known that accumulation of ratcheting strain usually degrades fatigue life of structural components [2,3]; the extent of degradation depends on the imposed stress parameters and the nature of the material. Investigations related to experimental and simulation studies in this direction have therefore got considerable attention of several research groups over the past few years [4–21]. The existing reports are more focussed to achieve understanding related to uniaxial and multiaxial ratcheting behaviour of metallic as well as polymeric materials [9,22–24] primarily from the viewpoint of mechanistic approach. However, emphasis towards understanding ratcheting behaviour of metallic materials and specifically for low carbon steels like interstitial free (IF) steel with attendant variations in its substructure is insufficient. Interstitial free steels are currently being extensively used for manufacturing car bodies and different parts of the car, where effect of asymmetric cyclic loading and the consequent

n

Corresponding author. Tel.: þ91 661 2462568; fax: þ 91 661 2462015. E-mail addresses: [email protected], [email protected] (K. Dutta).

0921-5093/$ - see front matter & 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.msea.2013.02.052

deformation behaviour of the steel after ratcheting are important issues. As plastic strain gets accumulated during ratcheting, it is expected to cause variations in the post-ratcheting properties of a material as a natural consequence. But, this expected phenomenon has not been carefully examined so far especially for IF steel. Thus it is necessary to understand ratcheting and post-ratcheting tensile behaviour of IF steel, which are the primary aims of this report. In this investigation, uniaxial ratcheting behaviour of an IF steel has been examined for different combinations of mean stress sm) and stress amplitude (sa) at room temperature of ≈300 K. Examinations have been carried out to understand tensile behaviour of ratcheted samples. An attempt has also been made to correlate variations in tensile strength of ratcheted samples with their cyclic hardening phenomenon induced during ratcheting deformation. Further a few ratcheted specimens have been studied using transmission electron microscopy to examine the variations in the substructures due to ratcheting deformation. 2. Experimental procedure 2.1. Material, microstructure and conventional mechanical properties The selected interstitial free steel was obtained as courtesy of Tata Steel, Jamshedpur, India and it was available in the form of 31 mm thick plate. Chemical composition of the selected steel is: C—0.003, Mn—0.13, Ti—0.052, P—0.012, Ni—0.01, Si—0.009, S—0.009, Nb—0.001, Mo—0.001, V—0.001 and balance Fe (all in wt%). The as-received steel plates were subjected to stress relief

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annealing by soaking these at 673 K for 1 h followed by furnace cooling. Specimens with approximate height of 10 mm with cross section of 12 mm  12 mm were cut from the annealed materials for microstructural characterizations and determination of hardness. Microstructural examinations were carried out with the help of an optical microscope (Leica, model: DMILP, Bannockburn, IL 60015, USA) connected to an image analyzer (Software: Biovis Material Plus, Version: 1.50, Expert Vision Labs Private Limited, Mumbai, India). Hardness measurements were done with the help of a Vickers hardness tester (Leco, model: LV 700, Michigan, USA) using an indentation load of 10 kgf. Tensile tests were carried out on cylindrical specimens of 5 mm diameter and 25 mm gauge length at a cross-head speed of 1 mm/min. The employed crosshead speed corresponds to nominal strain rate of 3.3  10−3 s−1 at the room temperature of ≈300 K. 2.2. Procedure of uniaxial ratcheting test The specimens for ratcheting tests were of configuration similar to cylindrical tensile blanks with 6 mm diameter and 12.5 mm gauge length. Uniaxial ratcheting experiments were carried out at room temperature using a servo-hydraulic universal testing machine (Instron, model: 8800R, High Wycombe, Buckinghamshire, UK). Cyclic loading was carried out using a triangular waveform in stress-control mode, as schematically shown in Fig. 1. The loading rate for all ratcheting tests was 50 MPa/s. Based on the employed test controls, these tests could be classified into two categories as: (i) constant sa with varying sm, and (ii) constant sm with varying sa. The different combinations of the employed sa and sm values for these tests are listed in Table 1. The strain measurements during cyclic deformation were made using an axial extensometer having 12.5 mm gauge length. The data pertaining to stress-extension as well as actuator displacement were continuously recorded during each test; attempts were made to acquire at least 200 data points per cycle for further analyses. After completion of 100 loading cycles of ratcheting deformation, a set of specimens were subjected to tensile tests under identical manner as described in the previous section. Fractographic studies of the broken samples were carried out by using scanning electron microscope (Zeiss, model: Evo 60, Germany). 2.3. Transmission electron microscopy To understand the substructural variations associated with ratcheting deformation, transmission electron microscopic (TEM) studies were carried out on a set of ratcheted specimens. For this

study, thin slices of about 0.5 mm thickness were cut from the gauge portions of the ratcheted specimens using a slow speed precision cutter (Buehler, Lake Bluff, Illinois, USA). The slices were next thinned sequentially by manual polishing on emery paper followed by dimpling and ion milling prior to TEM studies. TEM studies were carried out using a 200 keV transmission electron microscope (JEOL, model: JEM 2100, Tokyo, Japan).

3. Results and discussion 3.1. Microstructure, hardness and tensile properties of the material The microstructure of the investigated IF steel is depicted in Fig. 2. It exhibits equiaxed ferrite grains; the grain size is estimated as 64.4 7 1.3 μm. The selected steel contains inclusions of low volume fraction of the order of 0.06 70.02%. Vickers hardness (HV10) of the steel is found to be 71 71.8. The estimated standard deviation in hardness is o3%, which supports the contention that the steel is relatively clean and is single phase in nature, as discussed by Ray and Mondal [25]. Typical engineering stress– strain plot for the investigated steel is illustrated in Fig. 3, which exhibits continuous yielding behaviour; the yield strength value thus has been determined using 0.2% strain offset procedure as suggested in ASTM standard E-8M [26]. The average tensile properties of the steel can be summarized as – yield strength: 90.77 2.5 MPa, tensile strength: 2407 2 MPa, %uniform elongation: 36.4 70.8, %total elongation: 51.470.5 and strain hardening exponent (n): 0.407 0.01. The obtained values of the tensile parameters are in good agreement with some reported results on IF steels of similar chemical compositions [27,28]. 3.2. Uniaxial ratcheting: shifting of hysteresis loops Accumulation of ratcheting strain is known to occur during asymmetric cyclic loading with non-zero mean stress [23,29–31]. Based on the imposed level of mean stress, the nature of stressstrain hysteresis loops vary. Typical cyclic stress-strain hysteresis loops generated from ratcheting experiments on the investigated IF steel samples under positive mean stress levels of 10, 20 and 30 MPa, with constant stress amplitude of 140 MPa are presented in Fig. 4(a–c). All these experiments were carried out till 100 cycles. The results indicate that the hysteresis loops shift more towards positive plastic strain for increasing mean stress. For the mean stress levels of 10 MPa, 20 MPa and 30 MPa, the magnitudes

Stress σa σm Time Fig. 1. Schematic loading path for ratcheting test.

Table 1 Selected sm and sa values for ratcheting tests of IF steel. Serial no.

sm (MPa)

sa (MPa)

1 2 3

10 20 30

130, 140, 150 130, 140, 150 130, 140, 150

200μm Fig. 2. Microstructure of the investigated interstitial free steel.

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129

250

Engineering stress, MPa

200

150

100

50

0 0

10

20 30 40 Engineering strain, %

50

Fig. 3. Engineering stress–strain plot of the selected steel.

of plastic strain are 3.6%, 5.3% and 6.1%, respectively. Similar experiments were done under different mean stress levels but using alternate stress amplitudes of 130 MPa and 150 MPa, which also yielded similar results. It is thus evident that increase in mean stress at any constant stress amplitude increases the accumulation of plastic strain in the material. The increase in the magnitude of plastic strain with mean stress is discussed in the next section. 3.3. Accumulation of ratcheting strain: effect of mean stress and stress amplitude Variations of strain accumulation with number of cycles for varying sm and at constant sa values of 130, 140 and 150 MPa for the investigated IF steel are shown in Fig. 5(a–c). The results in these figures indicate that accumulation of ratcheting strain increases with increasing number of cycles for any combination of sm and sa. In addition to that, for any constant sa and at any specific number of cycles, the magnitude of accumulated ratcheting strain increases with increasing sm. The variations in accumulated ratcheting strain up to 100 cycles (εr100) of loading for all the combinations of sm–sa are plotted in Fig. 5(d); the results in this figure illustrate that εr100 increases with increasing sa as well as with increasing level of sm. When sm is altered between 10 and 30 MPa, the magnitudes of εr100 increase from 0.42 to 5.94 % at sa ¼130 MPa, from 3.72 to 6.19 % at sa ¼140 MPa and from 5.63 to 7.52 % at sa ¼ 150 MPa. The observed nature of increase in εr100 with sm is in good agreement with the trend of results reported by Gupta et al. [32] for SA333 Gr. 6 piping steel and that by Kang et al. [7] for SS304 stainless steel. A comparison of the magnitudes of εr100 for different materials indicates that it is about 3.5% for AISI 304LN stainless steel [30], 1.2% for 304 stainless steel [7] and 0.1% for copper alloy [33] over similar cyclic loading parameters; in-depth comparison of these results is difficult due to varied combinations of loading parameters that have been employed in different investigations. In order to understand ratcheting behaviour of the selected IF steel at any particular cycle for the different employed test parameters, hysteresis loops generated during each cycle of the uniaxial ratcheting tests were recorded and analyzed subsequently. Typical nature of the hysteresis loops at constant stress amplitude of 140 MPa for mean stress levels of 10, 20 and 30 MPa is depicted in Fig. 6 for the tenth cycle. The results in Fig. 6 indicate that for a given stress amplitude, smax increases with increase in

Fig. 4. Typical hysteresis loops generated from uniaxial ratcheting tests for varying mean stress levels of 10, 20 and 30 MPa at constant stress amplitude of 140 MPa.

sm for any specific cycle, as expected. Any increase in smax would induce higher extent of plastic deformation to the material, and as a consequence, strain accumulation is naturally expected to increase with increasing sm. This phenomenon can be correlated to the dislocation substructure of the material that forms during cyclic loading. As the nature of cyclic loading is asymmetric (with positive mean stress), the number of dislocations generated during the loading cycles is reported to be higher than that generated during the unloading cycles [30]. But, only a part of the generated

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6

6

4

4 σm = 10MPa, σa = 130 MPa σm = 20MPa, σa = 130 MPa

2

2

σm = 10MPa, σa = 140 MPa

σm = 30MPa, σa = 130 MPa

σm = 20MPa, σa = 140 MPa σm = 30MPa, σa = 140 MPa

0

0 0

20

40

60

80

0

100

20

40

60

80

100

Number of cycles 8

8

6

6

4

4

σm = 10MPa, σa = 150 MPa

2

σa = 130 MPa

2

σa = 140 MPa

σm = 20MPa, σa = 150 MPa σm = 30MPa, σa = 150 MPa

0 0

20

40

60

80

100

σa = 150 MPa

0 10

20

30

Fig. 5. Variation of ratcheting strain with number of cycles for varying levels of mean stresses and at constant stress amplitude values: (a) 130 MPa, (b) 140 MPa, (c) 150 MPa and (d) total accumulation of ratcheting strain up to 100 cycles of loading.

200 160 MPa

150 MPa

170 MPa

Stress, MPa

100

0

-100 -130 MPa σ m = 10 MPa,

-200 1.2

1.6

2.0

-110 MPa

-120 MPa

σ m = 20 MPa,

2.4 2.8 Strain, %

σ m = 30 MPa

3.2

3.6

Fig. 6. Typical stress–strain hysteresis loops (N ¼ 10) showing variations in their relative positions.

dislocations gets annihilated during load reversal; as a consequence, considerable number of the generated dislocations remains as residuals in the substructure of the material. It is well known that higher is the remnant dislocation density in a material, higher is the accumulation of plastic strain and vice versa. Hence, it can be inferred that with increasing sm for a particular sa, total strain accumulation will increase because of the increase in the remnant dislocation density. Typical bright field TEM images for cyclic loading conditions of ‘sm ¼ 30 MPa and sa ¼140 MPa’ and ‘sm ¼ 30 MPa and sa ¼150 MPa’ are illustrated

in Fig. 7(a and b), respectively. Examination of these figures indicates that dislocation density increases with increase in stress amplitude for constant sm in agreement with the earlier report [30]. Hence, it is inferred that with increasing sa for a particular sm, strain accumulation would increase because of the increase in the remnant dislocation density. To understand the influence of the variation of stress amplitude at constant sm levels on the nature of strain accumulation with number of cycles for the investigated IF steel, the obtained results were reanalyzed and presented in Fig. 8. The results in Fig. 8(a) show that nature of strain accumulation with increasing number of cycles at constant sm for varied sa is similar to that for constant sa and varying sm conditions; strain accumulation increases with increasing number of cycles for any combination of sa and sm. Variations of εr100 for all the investigated combinations of sa and sm are depicted in Fig. 8(b). The results lead to infer that εr100 increases with increasing sa for any specific sm. 3.4. Saturation of ratcheting strain Ratcheting deformation is known to take place at different rates in different intervals of time [7]. Analogous to strain ratetime curves of creep deformation, the rate of accumulation of ratcheting strain is very sharp in initial few cycles of asymmetrical cyclic loading, which eventually becomes saturated attaining a steady state in strain accumulation. The phenomenon is commonly termed as stable ratcheting or can be termed as plastic shake down when rate of accumulation of ratcheting strain tends to zero [34,35]. Typical variations in the rate of accumulation of ratcheting strain (dεr/dN) with number of cycles for the investigated IF steel are presented in Fig. 9. The results in Fig. 9 indicate that dεr/dN decreases sharply during the initial few cycles and

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131

Ratcheting strain, %

6

σ

Total ratcheting strain, εr100, %

Fig. 7. Typical variation in dislocation density for the cyclic loading conditions of sm ¼ 30 MPa with (a) sa ¼ 140 MPa and (b) sa ¼ 150 MPa.

m = 10MPa, σa = 130 MPa m = 10MPa, σa = 140 MPa

σ

5

σ

4

m = 10MPa, σa = 150 MPa

3 2 1 0 -1 0

20

40

60

80

100

8 150

7 150

6

130

150

5 4

140

140 130

140

3 2 1

130

0

10

20

30

Mean stress, MPa

Number of cycles

Fig. 8. (a) Variation of ratcheting strain with number of cycles for varying stress amplitudes and at a constant mean stress value of 10 MPa and (b) bar chart showing total accumulation of ratcheting strain up to 100 cycles of loading (values with the bars correspond to stress amplitudes in MPa).

0.8

σm = 10MPa, σa = 130 MPa

0.7

σm = 10MPa, σa = 140 MPa

0.6

σm = 10MPa, σa = 150 MPa

sa. The observed nature of attainment of steady state in strain accumulation is similar to that observed in existing literature for cyclic stabilizing materials such as annealed 42CrMo steel [36] and carbon steel [37]. Based on these observations, the experiments on the investigated IF steel have been carried out only up to 100 cycles. The attainment of steady state in dεr/dN can be explained by the formation and distribution of dislocations associated with cyclic deformation. When a material is subjected to cyclic deformation, dislocations get generated resulting strain hardening. These dislocations initially form tangles and subsequently lead to the formation of dislocation cells with increasing number of cycles [29]. After certain number of cycling, depending on the magnitude of the accumulated cyclic strain, the newly generated dislocations assume a relatively stable configuration which leads to initiation of the steady state in rate of strain accumulation.

dεr /dN

0.5 0.4 0.3 0.2 0.1 0.0 0

20

40 60 Number of cycles

80

100

Fig. 9. Variation in the rate of accumulation of ratcheting strain with increasing number of cycles for the investigated steel.

attains a saturation plateau after about 70 cycles for all combinations of sm and sa. In brief, it can be inferred that rapid accumulation of ratcheting strain in the initial few cycles followed by attainment of a steady state value in dεr/dN are the characteristic features of the asymmetric cyclic deformation behaviour of IF steel. Similar phenomenon has been observed for all the ratcheting experiments irrespective of the employed combinations of sm and

3.5. Substructural variation in interstitial free steel Variations in the substructures of ratcheted samples of metallic materials are commonly manifested by dynamic changes in dislocation density through generation, annihilation and interactions of dislocations, dislocation distributions, formation of dislocation tangles, subcells etc. In order to understand the substructure of the ratcheted specimens, representative bright field TEM images were captured from the transverse sections of the ratcheted specimens of the investigated IF steel and are illustrated in Fig. 10. Fig. 10(a–c) shows the images of the specimens which were subjected to ratcheting deformation with sm ¼30 MPa and sa ¼ 140 MPa, whereas

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PSB

PSB

Discrete dislocation tangles

Wavy slip line

PSB Planar slips

Subcell

Subcell Subcell

Fig. 10. Typical variation in dislocation substructure showing (a) planar slips, (b) persistent slip band (PSB), (c) and (d) dislocation cells.

Fig. 10(d) is that for a specimen tested with sm ¼30 MPa and sa ¼150 MPa. In general, these figures exhibit planar slips with discrete tangles of dislocations (Fig. 10a), persistent slip bands (Fig. 10b) as well as dislocation subcells (Fig. 10c and d). An overview of all these figures indicate that persistent slip bands and planar slips are predominant in specimens subjected to ratcheting at low stress amplitude, whereas formation of dislocation cells appears to be the characteristics of specimens subjected to high stress amplitude. Mao et al. [38] have reported that IF steel shows formation of dislocation cells when it is subjected to low cycle fatigue under various strain amplitudes. These authors have extended evidences of distinct substructure formation in IF steel loaded for 1000 to 10,000 cycles. It is interesting to note from the current TEM results that dislocation cells tend to form even within the investigated 100 cycles during ratcheting deformation. Gaudin and Feaugas [29] have provided evidences for subcell formation during ratcheting of 316L stainless steel. Kang et al. [39] have examined evolution of dislocation features in 316L stainless steel and have reported different stages of dislocation substructure formation. Dislocation pattern changes from dislocation tangles to incomplete dislocation cells to stable dislocation cells. Cell formation was also reported for 304LN stainless steel in an earlier report by the present authors [30], but those were diffused dislocation subcells. In contrast, distinct dislocation subcells are observed in the substructure of the investigated IF steel as a result of ratcheting deformation. It is well-known that materials having bcc crystal structures produce wavy slip lines upon deformation. Similar features were recorded in this investigation too as depicted in Fig. 10(b). In addition, Kang et al. [37] have reported evolution of dislocation substructure in a bcc low carbon steel at various

extents of cyclic loading during ratcheting deformation. After 300 cycles of ratcheting deformation, dislocation veins form in association with some incipient sub-grains inside some dislocation cells; but with increase in ratcheting deformation (after 1200 cycles), number of sub-grains increased. In comparison to their work, IF steel is found to exhibit formation of dislocation cells only after 100 cycles, with no sub-grain formation inside the cells. The differences may be attributed to the differences in material characteristics as well as the effect of constraint due to presence of multiple phases in low carbon steel as compared to that in the single phase IF steel. In generalization, it may be inferred that features associated with substructure evolution in IF steels incorporate formation of dislocation tangles and their subsequent conversion to sub-cells in ratcheting deformation at higher imposed stress amplitudes whereas at lower stress levels substructures depict only persistent slip bands with planar slips. 3.6. Post-ratcheting tensile behaviour It is established in the preceding sections that uniaxial ratcheting deformation induces considerable amount of plastic damage in materials. Naturally it is necessary to understand the associated effect of this plastic damage on the resultant tensile properties of ratcheted specimens. In order to fulfil this motivation, tensile tests were carried out on a series of specimens after 100 cycles of asymmetric fatigue cycling, subjected to both “constant stress amplitude varying mean stress” and “constant mean stress varying stress amplitude” conditions; the estimated tensile strength values are summarized in Fig. 11. The results in Fig. 11 indicate that the

280

280

240

240

Strength, MPa

Strength, MPa

K. Dutta, K.K. Ray / Materials Science & Engineering A 575 (2013) 127–135

200 160 YS UTS

120

133

200 160 YS UTS

120

Stress amplitude: 140 MPa

Mean stress: 30 MPa

80

80 Un-ratcheted 10

20

30

Mean stress, MPa

Un-ratcheted 130

140

150

Stress amplitude, MPa

Fig. 11. Comparison of yield strength and tensile strength values of unratcheted and ratcheted specimens for the investigated IF steel: (a) at constant stress amplitude and varying mean stresses and (b) at constant mean stress and varying stress amplitudes.

2.6 log (σ) = 2.65+0.19log ( ε)

log(True stress)

2.5

2.4

log(σ) = 2.73+0.40 log ( ε)

2.3

Ratcheted Un-atcheted linear fit

2.2

2.1 -1.5

-1.0 log(True strain)

-0.5

Fig. 12. Comparison of the Hollomon plots of the investigated IF steel under ratcheted and unratcheted conditions.

200

N=2

N=6

N = 24

N = 48

N = 80

N = 100

150

Stress, MPa

100 50 0 -50 -100 -150 1 .5

2 .0

2 .5

3 .0

3 .5

4 .0

4 .5

5 .0

5 .5

Strain, % Fig. 13. Variations in the width of hysteresis loops showing cyclic hardening phenomenon for the investigated IF steel.

magnitudes of yield strength (YS) of the ratcheted samples subjected to both “constant sa varying sm” and “constant sm varying sa” conditions are considerably higher in comparison to the YS of unratcheted samples. The increment in YS due to increase in sa or sm may be as high as 110% for the investigated IF steel. However, the corresponding variation in ultimate tensile

strength (UTS) is marginal, and the obtained results can be referred to as almost of identical magnitude within the range of experimental scatter. One may note from the results in Fig.11 that the magnitudes of YS and UTS are considerably higher compared to the unratcheted state, but variations in these strength values are however marginal among the different ratcheted states. The strain hardening behaviour of the steel under ratcheted and un-ratcheted condition is illustrated in Fig. 12 in which the experimental data is fitted using the Hollomon equation. The strain hardening exponent n, which was estimated from the slope of the true stress-true strain plot, for the un-ratcheted steel (n¼0.40) is considerably higher compared to that for the ratcheted steel (n¼0.19). Interestingly, specimens subjected to ratcheting deformation appear to exhibit almost identical values of n (0.18≤n≤0.20). This fact indicates that increase in strength of the ratcheted steel is primarily governed by increased strain hardening. The increase in YS and UTS can be correlated with cyclic hardening phenomenon. Typical sets of hysteresis loops at varying number of cycles generated from one of the ratcheting experiments are illustrated in Fig. 13. It can be observed from this figure that the width of hysteresis loops decreases continuously, which is indicative of cyclic hardening under stress controlled cyclic loading. Increase in the magnitude of strength of the ratcheted specimens can be considered to occur as a consequence of cyclic hardening of the investigated IF steel. The magnitude of %uniform elongation (%eu) of the ratcheted specimens, on the other hand, decreases as compared to %eu of unratcheted samples; about 39% decrease in %eu was observed (Fig. 14a and b). To the contrary, alteration in %total elongation (%et) values for specimens subjected to varied ratcheted states are within ≤5%. These observations lead to infer that there is considerable increase in elongation beyond necking of the specimens during tensile tests. This fact can be attributed to the nature of the dislocation sub-structure formed in the material. In some earlier reports on ratcheting behaviour of stainless steel, Gaudin and Feaugas [29] as well as the present investigators [30] have demonstrated that dislocation subcells form during ratcheting deformation. These subcells assist to initiate larger number of microvoids, but only a part of these microvoids can grow substantially providing larger elongation after necking; this is evident from the typical fractograph of ratcheted IF steel specimens (Fig. 15). The volume fraction of the microvoids which exhibits higher growth contributes to the %et of the specimens (Fig. 14a and b) in a significant manner. To examine the nature of the void formation near and below the fracture surface, a few broken tensile specimens were cut perpendicular to the fracture surface and were examined using SEM. A typical photograph depicting both void initiation and void coalescence is shown in Fig. 16. The voids are found to originate either at interfaces or at inclusions. It can be observed from Fig. 16 that microvoids have initiated from inclusions, which have joined subsequently. Several voids are also found to originate from the grain boundaries.

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60

60

50

50

40 % uniformation elongation % total elongation

30

%Elongation

%Elongation

134

40

% uniformation elongation % total elongation Mean stress: 30 MPa

30

Stress amplitude: 140 MPa 20

20 Un-ratcheted

10

20

Un-ratcheted

30

Mean stress, MPa

130

140

150

Stress amplitude, MPa

Fig. 14. Comparison of %uniform and %total elongation values of unratcheted and ratcheted specimens for the investigated IF steel: (a) at constant stress amplitude and varying mean stresses and (b) at constant mean stress and varying stress amplitudes.

in this investigation. Based on the results obtained from the current set of experiments, the following conclusions can be drawn:

 Accumulation of ratcheting strain for interstitial free steel is

 Fig. 15. Typical fractograph of the investigated steel: Ratcheted for a loading condition of sm ¼ 10 MPa and sa ¼140 MPa. The circled areas indicate larger growth of microvoids.



found to increase if the magnitude of stress amplitude gets increased from 130 to 150 MPa at constant mean stress. The ratcheting strain increases by 0.42–5.63% at sm ¼10 MPa, 4.49– 6.74% for sm ¼20 MPa and 5.94–7.52% for sm ¼30 MPa for different sa values. Similar orders of increase in strain accumulation are observed with increase in mean stress, for any constant value of stress amplitude. The increase in strain accumulation can be correlated with increased cyclic damage illustrated in terms of shift of the hysteresis loops towards higher plastic strain amplitudes; this phenomenon is considered to occur by increase in dislocation density in the samples due to ratcheting deformation. Both yield and tensile strength of the ratcheted samples are higher in comparison to those for unratcheted samples. Yield strength of IF steel can increase up to almost 110% by ratcheting deformation whereas the maximum increase in tensile strength is only about 15%. But interestingly, percentage of total elongation is found to either increase or marginally decrease for specimens subjected to ratcheting deformation; this is attributed to the nature of dislocation subcell formation during ratcheting, which could result in larger extent of microvoid growth leading to higher post-necking elongation. The substructures of ratcheted IF steel exhibit persistent slip bands, wavy slip lines at lower sa value whereas these show well developed subcells at higher sa.

References

Fig. 16. Photograph depicting microvoid coalescence beneath the fracture surface of the investigated IF steel. The EDS spectrum of the inclusion is shown as an inset.

4. Conclusions Uniaxial ratcheting behaviour and post-ratcheting tensile properties of interstitial free steel at room temperature have been explained

[1] Z. Xia, D. Kujawski, F. Ellyin, Int. J. Fatigue 18 (1996) 335–341. [2] U.C. Ozgen, Mater. Des. 29 (2007) 1575–1581. [3] N. Isobe, M. Sukekawa, Y. Nakayama, S. Date, T. Ohtani, Y. Takahashi, N. Kasahara, H. Shibamoto, H. Nagashima, K. Inoue, Nucl. Eng. Des. 238 (2008) 347–352. [4] R.J. Rider, S.J. Harvey, H.D. Chandler, Int. J. Fatigue 17 (7) (1995) 507–511. [5] F. Yoshida, Int. J. Plast. 16 (2000) 359–380. [6] X. Feaugas, C. Gaudin, Int. J. Plast. 20 (2004) 643–662. [7] G.Z. Kang, Y.G. Li, J. Zhang, Y.F. Sun, Q. Gao, Theor. Appl. Fract. Mech. 43 (2005) 199–209. [8] G.Z. Kang, Int. J. Fatigue 30 (2008) 1448–1472. [9] W. Liu, Z. Gao, Z. Yue, Mater. Sci. Eng.: A 492 (2008) 102–109. [10] S.C. Kulkarni, Y.M. Desai, T. Kant, G.R. Reddy, Y. Parulekar, K.K. Vaze, Int. J. Pressure Vessels Piping 80 (2003) 179–185. [11] D. Nouailhas, J.L. Chaboche, S. Savalle, G. Cailletaud, Int. J. Plast. 1 (1985) 317–330. [12] J.L. Chaboche, Int. J. Plast. 7 (1991) 661–678. [13] C. Holste, W. Kleinert, R. Giirth, K. Mecke, Mater. Sci. Eng.: A 187 (1994) 113–123.

K. Dutta, K.K. Ray / Materials Science & Engineering A 575 (2013) 127–135

[14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24] [25] [26]

Y. Jiang, H. Sehitoglu, Int. J. Plast. 10 (5) (1994) 579–608. P. Delobelle, P. Robinet, L. Bocher, Int. J. Plast. 11 (4) (1995) 295–330. Y. Jiang, P. Kurath, Int. J. Plast. 12 (1996) 387–415. N. Ohno, M.A. Karim, M. Kobayashi, T. Igari, Int. J. Plast. 14 (1998) 355–372. S. Bari, T. Hassan, Int. J. Plast. 16 (2000) 381–409. X. Chen, R. Jiao, Int. J. Plast. 20 (4–5) (2004) 871–898. X. Chen, R. Jiao, K.S. Kim, Int. J. Plast. 21 (1) (2005) 161–184. J.L. Chaboche, Int. J. Plast. 24 (2008) 1642–1693. T. Hassan, S. Kyriakides, Int. J. Plast. 10 (2) (1994) 185–212. G.Z. Kang, Q.H. Kan, J. Zhang, J. Mater. Sci. Technol. 21 (1) (2005) 5–9. X. Chen, S. Hui, Polym. Testing 24 (2005) 829–833. K.K. Ray, D.P. Mondal, Metall. Mater. Trans. A 23 (1992) 3309–3315. E 8M-03, Standard test method for tension testing of metallic materials (Metric), ASTM Annual Book of Standards, 03.01, West Conshohocken, PA, 2003. [27] K. Sekido, T. Ohmura, L. Zhang, T. Hara, K. Tsuzaki, Mater. Sci. Eng.: A 530 (2011) 396–401. [28] P.W. Liu, J.K. Wu, Mater. Lett. 57 (2003) 1224–1228.

135

[29] C. Gaudin, X. Feaugas, Acta Mater. 52 (2004) 3097–3110. [30] K. Dutta, S. Sivaprasad, S. Tarafder, K.K. Ray, Mater. Sci. Eng.: A 527 (2010) 7571–7579. [31] S.K. Paul, S. Sivaprasad, S. Dhar, S. Tarafder, Int. J. Pressure Vessels Piping 87 (2010) 440–446. [32] C. Gupta, J.K. Chakravartty, G.R. Reddy, S. Banerjee, Int. J. Pressure Vessels Piping 82 (2005) 459–469. [33] C.B. Lim, K.S. Kim, J.B. Seong, Int. J. Fatigue 31 (2009) 501–507. [34] G. Kang, Q. Kan, L. Qian, Y. Liu, Mech. Mater. 41 (2009) 139–153. [35] X. Yang, Int. J. Fatigue 27 (2005) 1124–1132. [36] G.Z. Kang, Y.J. Liu, Mater. Sci. Eng.: A 472 (1–2) (2008) 258–268. [37] G.Z. Kang, Y.W. Dong, Y.J. Liu, H. Wang, X.J. Cheng, Mater. Sci. Eng.: A 528 (2011) 5610–5620. [38] S.W. Mao, W.C. Lo, H.L. Huang, N.J. Ho, J. Mar. Sci. Technol. 19 (2) (2011) 115–119. [39] G. Kang, Y. Dong, H. Wang, Y. Liu, X. Cheng, Mater. Sci. Eng.: A 527 (2010) 5952–5961.