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Low cycle fatigue behavior of modified 9Cr–1Mo steel at room temperature
Materials Science & Engineering A 652 (2016) 30–41
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Low cycle fatigue behavior of modified 9Cr–1Mo steel at room temperature Preeti Verma a, N.C. Santhi Srinivas a, S.R. Singh b, Vakil Singh a,n a b
Centre of Advanced Study, Department of Metallurgical Engineering, Indian Institute of Technology (Banaras Hindu University), Varanasi, India School of Materials Science and Technology, Indian Institute of Technology (Banaras Hindu University), Varanasi, India
art ic l e i nf o
a b s t r a c t
Article history: Received 16 September 2015 Received in revised form 18 November 2015 Accepted 19 November 2015 Available online 27 November 2015
Low cycle fatigue (LCF) behavior of modified 9Cr–1Mo steel was studied in normalized and tempered condition at strain rates from 10 2 s 1 to 10 4 s 1 in the regime of low strain amplitude between 70.25% and 7 0.5% at room temperature. Cyclic softening was exhibited at the higher strain amplitudes of 7 0.375% and 7 0.50% after about 20–30 cycles and after 200–300 cycles at the lowest strain amplitude of 70.25%, at all the strain rates. There was mild tendency of hardening from 2 to 20 cycles at the highest strain amplitude of 7 0.50% and up to 200–300 cycles at the lowest strain amplitude of 7 0.25%. The rate of softening increased with increase in strain amplitude. Masing and non-Masing behavior was exhibited at the higher strain amplitudes (Z 70.375%) and lower strain amplitudes ( o 7 0.375%) respectively. Dependence of fatigue life, based on both plastic strain amplitude as well as plastic strain energy was linear and fatigue life decreased with lowering of strain rate. The unstable tempered martensitic structure was transformed into equiaxed dislocation cell structure under cyclic loading. The size of the cells and annihilation of dislocations increased with increase in strain amplitude. While the friction stress decreased with number of cycles at all the strain amplitudes, back stress was nearly constant at the high strain amplitudes and increased at the lowest strain amplitude. The observed cyclic softening was thus mainly due to decrease in friction stress, formation of low energy dislocation cell structure, and annihilation of dislocations. & 2015 Elsevier B.V. All rights reserved.
Keywords: Modified 9Cr–1Mo steel Cyclic softening Masing and non-Masing behavior Friction stress Dislocation cells Fatigue
1. Introduction Modified 9Cr–1Mo steel (with minor additions of V and Nb in conventional 9Cr–1Mo steel) is widely used for steam generator of nuclear reactors [1–7]. It is also a candidate material for future metallic fuel sodium cooled fast breeder reactor. High thermal conductivity, lower thermal expansion coefficient, high tensile and creep strength, good weldability, microstructural stability and higher resistance to stress corrosion cracking in water-steam systems of this steel compared to austenitic stainless steels are important features for its suitability in nuclear industry. Fine microalloyed precipitates of carbides, nitrides and carbonitrides of Nb and V such as Nb (C, N) and V (C, N) enhance the high temperature strength of this steel [1–6]. During service exploitation, the components of steam generators are often subjected to repeated thermal stresses as a result of temperature gradients occurring from heating and cooling during start-ups and shutdowns or thermal transients. These transient thermal stresses induce n
Corresponding author. E-mail address: [email protected] (V. Singh).
http://dx.doi.org/10.1016/j.msea.2015.11.060 0921-5093/& 2015 Elsevier B.V. All rights reserved.
cyclic strain and cause low cycle fatigue (LCF) damage in the material. There have been several studies on LCF behavior of this steel in normalized and tempered condition related to effect of strain amplitude, strain rate and temperature [2–6,8–11]. In general, there was exhibition of hardening during the initial cycles followed by continuous softening till failure at different temperatures and fatigue life was decreased with increase of temperature and it was more pronounced at the lower strain amplitudes [4]. Krishna et al. [11] studied LCF behavior of this steel at high strain amplitudes (70.7% to 71.2%) at room temperature (RT), 500 and 600 °C at strain rate of 10 3 s 1 and observed cyclic softening with rise in test temperature due to decrease in dislocation density, coarsening of martensitic laths and transformation of lath structure into dislocation cell and sub-grain structure. Cyclic softening exhibited during cyclic straining has been attributed to changes in dislocation substructure from the original lath martensite structure to subgrain and decrease in dislocation density [3,8,11]. Most of the LCF studies on this steel have been carried out at single strain rate and mostly in the regime of high strain
P. Verma et al. / Materials Science & Engineering A 652 (2016) 30–41
amplitude, at elevated temperatures. As part of evaluation of the effect of strain rate and temperature on LCF behavior of the modified 9Cr–1Mo steel for advance nuclear reactor applications, investigation was undertaken to study LCF behavior of this steel in the regime of low strain amplitude at different strain rates over a wide range of temperature from RT to 600 °C. This communication presents LCF behavior of this steel at room temperature including characterization of deformation, fracture, Masing and non-Masing behavior.
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Fig. 1. Schematic of low cycle fatigue test specimen. Table 2 Test matrix for LCF test at room temperature.
2. Material and methods Modified 9Cr–1Mo steel of the present investigation was supplied by IGCAR Kalpakkam, India, in the form of plate, in normalized and tempered condition. It was normalized at 1060 °C for 1 h, tempered at 780 °C for 1 h and cooled in air. The chemical composition of the steel is given in Table 1. Cylindrical LCF specimens with gage section of 5.5 mm diameter, 15 mm gauge length and threaded ends of 12 mm diameter and 35 mm length, on either side and curvature radii of 25 mm were machined with length in rolling direction of the plate as per the British standard (BS 121950). Schematic of the LCF specimen with all dimensions are shown in Fig. 1. LCF tests were conducted at RT under fully reversed triangular waveform (R ¼ 1) in total-strain control mode using servo-hydraulic testing system (MTS model 810, with flex test 40 controller). Room temperature extensometer (Model: Model: 632.03C 30 MTS) was used to measure the strain during the LCF test. The test data in terms of different strain components were displayed. LCF tests were performed at RT in regime of low strain amplitude at three strain amplitudes of 70.25%, 7 0.375% and 7 0.50% and three strain rates of 10 2 s 1, 10 3 s 1 and 10 4 s 1. Test matrix for LCF tests is given in Table 2. The initial microstructure was characterized by optical, scanning electron microscope (Model: FEI Quanta 200 FEG) and TEM (Model: FEI Tecnai 20 G2). TEM foils for the study of deformation behavior under LCF were prepared from transverse section of the fatigue tested specimens by electro polishing in an electrolyte containing 6% perchloric acid, 34% n-butanol in methanol at 22 V and 40 °C, using a twinjet electropolisher (Model: Struers Tenupol 5). Deformation behavior and dislocation substructure was assessed by transmission electron microscope.
3. Results 3.1. Microstructure Microstructure of the modified 9Cr–1Mo steel is shown in Fig. 2a and b by optical and SEM micrographs respectively. The prior austenite grain structure along with second phase precipitates distributed uniformly in the grain as well as along the prior austenite grain boundaries (PAGbs) may be seen clearly from these micrographs. The substructural details observed in TEM are shown in Fig. 3. In addition to second phase precipitates along the martensite lath boundaries, high density of dislocations may also be seen within the laths (Fig. 3b). The precipitates have been characterized as carbides in our previous investigation [12], in line with earlier findings of Choudhary et. al [13]. The mean intercept
Strain rate (s 1)
Strain amplitude (%)
Frequency (s 1)
10 2
70.25 70.375 70.50 70.25 70.31 70.375 70.50 70.375 70.50
1.0000 0.6667 0.5000 0.1000 0.0806 0.0667 0.0500 0.0067 0.0050
10 3
10 4
length of prior austenite grains was determined to be E20 μm and the width of the laths was E0.5 μm. 3.2. Low cycle fatigue 3.2.1. Cyclic stress response The variation of cyclic stress amplitude with number of cycles for the different total strain amplitudes at strain rates of 10 2 s 1, 10 3 s 1 and 10 4 s 1 is shown in Fig. 4a–c respectively. At the highest strain rate of 10 2 s 1, there was cyclic softening after the initial 20–30 cycles at the higher strain amplitudes of 70.5% and 70.375%, and after 200–300 cycles at the lowest strain amplitude of 70.25%. It may be seen that at the highest strain amplitude of 70.5% there was mild drop in the cyclic stress at the first cycle followed by mild hardening nearly up to the initial 10-20 cycles. However, at the lowest strain amplitude of 70.25% after 10 cycles there was marginal cyclic hardening up to about 200–300 cycles, and it was followed by cyclic softening till fracture. It is noteworthy that the number of cycles to peak hardening increased with decrease in strain amplitude. The degree of cyclic softening increased with strain amplitude. Similar behavior was observed also at the lower strain rate of 10 3 s 1 (Fig. 4b). The differences in the levels of the stress response curves, at different strain amplitudes were reduced with decrease in strain rate. It may be seen that the stress response curves at the lowest strain rate of 10 4 s 1, corresponding to strain amplitudes of 7 0.375% and 70.5%, were almost coincident (Fig. 4c). LCF test could not be performed at the lowest strain rate of 10 4 s 1 for the strain amplitude of 70.25% because of expected test duration of more than three months. 3.2.2. Strain-life relationship The strain-based LCF life is widely used to describe the behavior of structural materials operating at elevated temperatures and high levels of stress and strain in power generation plant during
Table 1 Chemical composition of the modified 9Cr–1Mo steel (wt%). Elements
C
Si
Mn
P
S
Cr
Mo
Ni
Al
Nb
N
V
Fe
Wt%
0.1
0.26
0.41
0.018
0.002
9.27
0.95
0.33
0.013
0.074
0.044
0.21
Balance
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20 μm
10 μm
Fig. 2. Microstructure showing PAGbs and distribution of second phase particles along the PAGbs and within the grains of normalized and tempered modified 9Cr–1Mo steel: (a) Optical micrograph (b) SEM micrograph.
their in-service period [14]. In these operations, fatigue damage is generally caused by plastic strain and is described by the Coffin– Manson relationship Δεp/2 ¼ ε′f (2Nf)c where ε′f and c are fatigue ductility coefficient and fatigue ductility exponent respectively [15]. Variation of number of reversals to failure (2Nf) with plastic strain amplitude (Δεp/2) at different strain rates of 10 2 s 1 and 10 3 s 1 is shown in Fig. 5a and linear variation of 2Nf with Δεp/2 may be seen on logarithmic scale. The LCF parameters, fatigue ductility exponent (c) and fatigue ductility coefficient ( ε′f ) are the slope and intercept on Y-axis at 2Nf ¼ 1 respectively and were determined by least square linear fit of the data in Fig. 5a. The values of LCF parameters are presented in Table 3. Both, fatigue ductility coefficient ( ε′f ) and fatigue ductility exponent (c) may be seen to increase with decrease in strain rate from 10 2 s 1 to 10 3 s 1. Effect of strain rate on fatigue life at high strain amplitude was found to be negligible, however, fatigue life was lowered at the lowest strain amplitude of 70.25% at the strain rate of 10 3 s 1 in comparison to that at the higher strain rate of 10 2 s 1. Cyclic stress–strain parameters were calculated from the half-life hysteresis loops at all the strain amplitudes at the different strain rates of 10 2 and 10 3 s 1 and are presented in the Table 4. The cyclic strain hardening exponent and cyclic strength coefficient parameters were found to increase with decrease in strain rate (Table 4).
3.2.3. Strain energy-life relationship Since LCF damage is associated with cyclic plastic strain, the dissipated strain energy has been considered for accurate prediction of fatigue life of the components. In general, fatigue life relationships may be based on stress, strain or energy parameters [16].The energy parameters have several advantages like: (a) both strain and stress parameters are included in these models, (b) these variables are independent of the direction by its scalar value, (c) the damage is easy to cumulate, and (d) more suitable to transfer the model results to the real structure. The plastic strain energy per cycle is equal to the area of the hysteresis loop. In general, the area of the hysteresis loop at halflife is considered as the average plastic strain energy per cycle (ΔWp). The LCF data were analyzed in terms of power law relationship based on energy [17], similar to the Coffin–Manson relationship.
ΔWp = Wf′(2Nf ) β where Wf′ and β are material constants and β is related to the fatigue life constant as β = b + c . The plot of ΔWp versus 2Nf is shown in Fig. 5b and the LCF parameters are presented in Table 5. In this approach both Wf0 and β were found to decrease with increase in strain rate. Similar dependency of LCF parameter on strain rate is observed in both plastic strain amplitude and energy based approach.
Fig. 3. (a) TEM micrograph of the normalized and tempered modified 9Cr–1Mo steel displaying PAGbs and M23C6 carbides along the PAGbs and fine vanadium and niobium carbides within the laths, precipitates were identified from SAD pattern, (b) high dislocation density within the lath martensite.
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Fig. 4. Variation of stress amplitude with number of cycles at different strain rates: (a) 10 2 s 1, (b) 10 3 s 1, (c) 10 4 s 1.
3.3. Masing and non-Masing behavior The stress–strain hysteresis loops were analyzed for Masing and non-Masing behavior [18]. In some metals it was observed that after matching the compressive tips, the hysteresis loops coincided with the cyclic stress–strain curve magnified by two, showing Masing behavior. However, other metals exhibited nonMasing behavior and there was coincidence only when the saturated hysteresis loops were translated downwards along the linear elastic slope. The modified 9Cr–1Mo steel was found to exhibit both Masing and non-Masing behavior based on the strain amplitude in LCF test. Fig. 6 shows the stress–strain hysteresis loops translated to a common point of maximum compressive stress of saturated hysteresis loop from the different strain amplitudes at strain rates of 10 2 s 1, 10 3 s 1 and 10 4 s 1. It is obvious that at the strain amplitudes of Z 70.375% the hysteresis loops matched with the tensile portion of the highest strain amplitude whereas the hysteresis loops of lowest strain amplitude of 7 0.25% did not match. Thus, this steel exhibits non-Masing behavior at very low strain amplitude of 70.25% and Masing behavior at the strain amplitudes Z 7 0.375%. A quite similar behavior was observed also at the lower strain rates of 10 3 s 1 and 10 4 s 1. 3.4. Dislocation substructure The tempered lath structure (Fig. 3a and b) was found to be unstable under cyclic loading and was gradually replaced by
subgrain structure. Minimizing their stored energy, the original parallel high dislocation-density martensitic laths partitioned into equiaxed subgrain structure of large size. Fig. 7 shows dislocation substructures in the specimen tested at different strain amplitudes at strain rates of 10 2 s 1. A subgrain structure with relatively low density of dislocations inside the laths and with no well-defined cell boundary may be seen in the specimen tested at the lowest strain amplitude of 7 0.25% (Fig. 7a and b). Elongated cell wall structure with high density of dislocations along cell walls may be seen in the sample tested at the higher strain amplitude of 70.375% (Fig. 7c). There was intersection of dislocations inside the laths (Fig. 7d). Similarly at the highest strain amplitude of 70.5% there was formation of elongated cell wall structure in some grains and formation of distinct subgrains (Fig. 7e and f). There was formation of distinct dislocation cell/subgrain structure also at the lowest strain rate of 10 4 s 1 (Fig. 8) and dislocation density inside the grains was high (Fig. 8b). However, no elongated cell wall structure was observed at the lowest strain rate of 10 4 s 1. It is obvious from Fig. 9 that cell size increased with increase in strain amplitude. 3.5. Fracture behavior Fracture morphology of the fatigue samples tested at 10 2 s 1 is shown in Fig. 10. It is obvious that there was initiation of multiple cracks with decrease in strain amplitude whereas a sufficiently large single crack formed at the highest strain amplitude of 70.50%. Inter striation spacing was found to increase with
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Table 5 Low cycle fatigue parameters at different strain rates, based on plastic strain energy. Strain rate (s 1) Fatigue ductility coefficient ( Fatigue ductility exponent (β) W′f ) 10 2 10 3
4.12987 4.37303
0.90446 0.9719
cracking was observed at higher magnifications at all the strain amplitudes. Similar fracture morphology was observed even at the lower strain rate of 10 3 s 1 with multiple crack initiation sites at low strain amplitudes (Fig. 11). With increase in strain amplitude to 70.5%, ratchets were seen as shown by white arrows in Fig. 11c. Ratchet lines are the lines which represent the junction surfaces between the adjacent crack origins. Different microcracks are unlikely to form on the same plane of different heights and their eventual linkage creates a vertical step on the fracture surface. Once the initial cracks link together, the ratchet lines disappear and follow the same crack propagation path. These lines are shown by arrows in Fig. 11c. Magnified view of the crack initiation site showed that in case of high strain amplitudes, striations were observed just after 50 μm depth from the surface and no striations were visible even up to the depth of 600 μm at the low strain amplitude (Fig. 12). Tire marks and distinct faceted features were observed in the specimen tested at the lowest strain amplitude of 70.25% at the strain rate of 10 3 s 1 (Fig. 13). The areas of both fatigue as well as tensile overload failure were calculated corresponding to both the strain rates and it was found that the area of fatigue region increased with increase in strain amplitude (Table 6). Fatigue fracture zone is marked by black solid lines in the fractographs shown in Figs. 10 and 11.
4. Discussion 4.1. Cyclic stress response and dislocation substructure
Fig. 5. (a) Dependence of fatigue life (as reversals to failure) with plastic strain amplitude, at strain rates of 10 2 s 1 and 10 3 s 1 and (b) Low cycle fatigue plots based on plastic strain energy and reversals to failure (2Nf) at strain rates of 10 2 s 1 and 10 3 s 1.
Table 3 Low cycle fatigue parameters at different strain rates based on plastic strain amplitude approach. Strain rate (s 1) Fatigue ductility coefficient ( εf′)
Fatigue ductility exponent (c)
10 2 10 3
0.80434 0.86978
3.6442 6.4835
Table 4 Cyclic stress–strain parameters at different strain rates. Strain rate (s 1)
n0
K0 (MPa)
10 2 10 3
0.03887 0.05333
675 715
increase in strain amplitude. Distinct fatigue striations may be seen from stage II fatigue crack propagation, however more facets may be seen at the bottom of the fractographs in Fig. 10. Secondary
It is obvious from the cyclic stress response of the modified 9Cr–1Mo steel that there was initial softening followed by stability up to 10–20 cycles, mild hardening to peak and finally cyclic softening till fracture (Fig. 4). The initial softening was essentially due to movement of free dislocations inside the laths and the subsequent hardening resulted from interaction between the precipitates (MX, X ¼C/N) and dislocations (Fig. 14). M23C6 precipitates were observed mainly at lath boundaries and prior austenite grain boundaries and had pinning influence. This steel in the normalized and tempered condition, with tempered martensite lath structure, was highly unstable under cyclic straining. The laths were gradually replaced by dislocation subgrain structure minimizing their stored energy. The relatively large extent of cyclic softening at all the strain amplitudes may be attributed mainly to formation of dislocation cell structure, in agreement with earlier observations [2,4,8]. In consequence to early onset of cyclic softening, at high strain amplitudes, there was transformation of lath martensite to subgrain structure, in the early stage. The dislocation structure was highly heterogeneous with packets of dislocation debris and ill-defined cells in it. The precipitates located along the lath boundaries imposed a pinning effect, resulting in slightly elongated cell structure. Equiaxed dislocation cells were also present. Very fine microalloy precipitates were found to interact with dislocations in dislocation-rich regions and retard the dislocation motion. It is known that the dislocations rearrange themselves during cyclic loading, into a lower energy
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high strain amplitudes. It has been reported that softening stage in 9–12%Cr steels and especially in Reduced Activation Ferritic Martensitic (RAFM) steels is clearly associated with increase in the subgrain size, regardless of the temperature [19] and softening has partially been explained from annihilation of dislocations within subgrains [20] and by lath/sub-grain boundary elimination [21]. As such there is no literature on the effect of strain amplitude and strain rate on deformation behavior and dislocation substructure of the modified 9Cr–1Mo steel, at room temperature. This steel deforms by more than one slip system. Wavy slip materials are known to attain a stable stress state and a characteristic dislocation substructure, irrespective of their initial state (hard or soft). In general, cell structure formation is observed in wavy slip materials. On the other hand planar slip materials display different cyclic stabilized stress levels depending on their initial condition and likewise different dislocation substructure. Thus, the development of a characteristic dislocation substructure i.e. cell structure in the cyclically deformed modified 9Cr–1Mo steel, a wavy slip material, was there in all the test conditions, irrespective of strain amplitude and strain rate. It may be stated that there was no change in the dislocation configuration due to change in the test condition. 4.2. Role of friction and back stress
Fig. 6. Stress–strain hysteresis loops translated to a common point of maximum compressive stress exhibiting Masing and non-Masing behavior at three different strain rates: (a) 10 2 s 1, (b) 10 3 s 1, (c) 10 4 s 1.
configuration comprising of dislocation cells, surrounded by dislocation walls, by cross-slip [1–4]. Size of the subgrains depends on the applied plastic-strain amplitude. It is obvious from Fig. 9 that cell size increased with increase in strain amplitude. Dislocation-free areas were frequently observed in the regions close to the lath boundaries at
Friction stress and back stress are well established key parameters to describe dislocation movement under constant strain control fatigue [22]. The friction stress arises from the resistance to dislocation movement in the lattice involving short-range interaction obstacles and back stress results from long-range interaction obstacles [23,24]. In the present investigation, the friction stress and back stress were determined to find out their contribution in cyclic stress response of the tempered martensitic steel. These parameters were calculated from the stress–strain hysteresis loops for all the cycles, at all the strain amplitudes, as per the procedure described elsewhere [22]. Figs. 15–17 show variation of friction stress and back stress with number of cycles at the different strain amplitudes corresponding to strain rates of 10 2, 10 3 and 10 4 s 1 respectively. It is obvious that friction stress decreased with number of cycles at all the strain amplitudes, at all the strain rates, whereas the back stress was nearly constant at the higher strain amplitudes and increased at the lowest strain amplitude. Fournier et al. [25] studied microstructural evolution and cyclic softening of this steel at 550 °C at different strain amplitudes from 70.2% to 70.5%. The softening of the steel was directly correlated to decrease in the kinematic stress (back stress) which arises from ‘directional and long-range’ obstacles to movement of dislocations. Therefore, grain and subgrain boundaries (through a dislocation pile-up mechanism) and, more generally, all microstructural heterogeneities (arrangement of dislocations, precipitates, etc.) are sources of kinematic hardening. This suggests that, during cycling the softening occurs from disappearance of microstructural heterogeneities [26]. Krishna et al. [11] have analyzed the effect of the temperature on cyclic stress response at RT, 550 and 600 °C at high strain amplitudes (7 0.7% to 71.2%), at strain rate of 10 3 s 1. They observed that decrease in the effective stress (friction stress) had a dominating effect over the decrease in internal stress (back stress) and the cyclic yield stress decreased with increase in test temperature, however both the stresses decreased with increase in test temperature [11]. Based on the results of the present investigation it is important to mention that at all the strain amplitudes the cyclic stress response was controlled primarily by friction stress.
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1 μm
0.5 μm
0.5 μm
0.5 μm
0.5 μm
0.5 μm
Fig. 7. Dislocation configurations resulting from LCF at strain rate of 10 2 s 1 at different strain amplitudes as: (a and b) 70.25%, (c and d) 70.375%, (e and f) 7 0.5%. Formation of cell structure may be seen at all the strain amplitudes.
4.3. Analysis of Masing and non-Masing behavior Effect of cyclic strain amplitude was analyzed on Masing/nonMasing behavior of this steel in the normalized & tempered condition. There was Masing behavior at high strain amplitudes (Z0.375%) and non-Masing at low strain amplitudes (o 70.375%) as shown in Fig. 6. Usually, the change from Masing to non-Masing behavior is associated with transformation of dislocation substructures to dislocation cell structures [27]. However, no such changes were observed in dislocation substructure between the low and high strain amplitude tests in the present
investigation. Irrespective of the strain amplitude, there was formation of subgrains at all the strain amplitudes. Masing and non Masing behavior in the modified 9Cr–1Mo steel was earlier studied by Krishna et al. [11] at room temperature. They found Masing behavior at strain amplitudes from 70.7% to 71.0% and non-Masing behavior at strain amplitude from 7 1.1% to 71.2% at RT. Plumree and Abdel-Raouf [27] observed Masing behavior for metals with finely dispersed particles and single phase low stacking fault metals; and non-Masing behavior in high stacking fault energy materials, in which the deformation was mainly controlled by the matrix. Depending on the strain amplitude,
P. Verma et al. / Materials Science & Engineering A 652 (2016) 30–41
1 μm
0.2 μm
1 μm
1 μm
37
Fig. 8. Dislocation configurations resulting from LCF at different strain amplitudes at the lowest strain rate of 10 4 s 1: (a and b) 7 0.375%; (c and d) 7 0.5%.
present investigation is in line with the earlier investigation [11]. However, it is noteworthy from the present investigation that there was non-Masing behavior at the very low strain amplitude of 7 0.25%. Thus, there was transition from the Masing to nonMasing behavior from high to low strain amplitude. 4.4. Fracture behavior
Fig. 9. Variation of cell size with strain amplitude, in fatigue samples tested at strain rate of 10 2 s 1.
ferritic–pearlitic AISI 1018 hot rolled steel was found to exhibit Masing behavior at low strain amplitudes and non-Masing at higher strain amplitudes. It is important to mention that all the previous investigations have been conducted at strain amplitudes above 70.5% where Masing behavior was observed. The occurrence of Masing behavior at strain amplitudes Z 7 0.375% in the
The largest portion of fatigue fracture consists of Stage II crack growth exhibiting striations on fracture surface, and is more influenced by strain amplitude and microstructure [28–30]. In general, a large portion of fatigue life is spent in crack nucleation in stage I at low strain amplitudes and stage II crack growth at high strain amplitudes. Thus, the decrease in fracture area corresponding to stage I with increase in strain amplitude from 70.25% to 70.5% and increase in the stage II area with increase in strain amplitude may be understood (Fig. 12). The microstructure and mechanical properties of the materials strongly affect the process of crack initiation and its subsequent propagation. In the ferritic– martensitic steel (EUROFER 97) lath boundaries are favorable sites for microcrack nucleation [31]. Slip irreversibility occurs in materials and plastic strain accumulates during fatigue loading. At the defect level, the irreversibility is a result of dislocation pile-up, annihilation or cross-slip. Grain boundary or inclusion-matrix phase boundary also contribute to slip irreversibility. These slip irreversibilities are considered early signs of damage during cyclic loading. The dislocations subsequently form low-energy stable structures as means to accommodate the irreversible slip processes and
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1 mm
1 mm
1 mm
15 μm
15 μm
15 μm
Fig. 10. Fracture surfaces of fatigue samples tested at room temperature, at strain rate of 10 2 s 1 at different strain amplitudes: (a, A) 7 0.25% (b, B) 7 0.375% & (c, C) 7 0.5%.In Fig. a–c the regions of fatigue fracture from surface towards interior are marked by black ink. Striations and secondary cracking are shown in the higher magnification images. Crack propagation direction is shown by white arrows.
1 mm
1 mm
1 mm
Fig. 11. Low magnification fracture surfaces of the LCF samples tested at strain rate of 10 3 s 1 at different strain amplitudes: (a) 7 0.25%, (b) 7 0.375%, (c) 7 0.5%. Fatigue regions are marked by black ink and ratchet lines are shown by white arrows.
modify the dislocation density during forward and reverse cyclic loading. Inclusions and precipitates are special defects that can initiate cracks because of different factors such as slip characteristic of the matrix, the relative strength of the matrix and inclusions, strength of the matrix inclusion interface and environmental factors. Depending upon the structure relationship between the matrix and precipitates, these interfaces could be weakest sites of a material. Matrix and precipitates may raise the mechanical stress in vicinity of the interface during cyclic loading causing, eventual interfacial crack initiation. Also faceted features were observed in the region of stage II crack growth without striation markings, prominently more at the high strain amplitudes, at the strain rate of 10 2 s 1 and even at low strain amplitudes at lower strain rate of 10 3 s 1 (Figs. 10 and 13). The occurrence of tire marks and faceted fracture with decrease in strain amplitude and strain rate may clearly be seen from
Fig. 13a. In the early stage of cracking arising from cyclic straining there were faceted features and ΔK would have been very low. As the fatigue crack started propagating distinct striation marks were visible. It may be noted that the fatigue crack propagating can occur even without formation of striations at high and low ΔK values, irrespective of the type of material [32]. Striations formed at intermediate ΔK because at high ΔK plastic blunting mechanism operates causing microvoid coalescence while at low ΔK values crystallographic orientation dependence leads to formation of cleavage like facets. Ratchet marks are another macroscopic feature that can be observed in fatigue fracture. These marks originate when multiple cracks are nucleated at different points/heights in gage section of the specimen. Since each microcrack is unlikely to form on the same plane eventual linkage of such cracks leads to formation of
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100 μm
39
100 μm
Fig. 12. Crack initiation regions resulting LCF at strain rate of 10 3 s 1 at different strain amplitudes (a) 7 0.25%, (b) 7 0.5%.
a
b
10 μm
1 μm
Fig. 13. Fractographic images of LCF sample tested at 7 0.25% at strain rate of 10 3 s 1 showing (a) tire marks, (b) faceted features. Table 6 Area of the region of fatigue crack propagation at different strain rates of 10 2 s 1 and 10 3 s 1. Strain rate (s 1) 10
2
10 3
Strain amplitude (%)
Area of fatigue region (%)
7 0.25 7 0.375 7 0.5 7 0.25 7 0.375 7 0.5
21 24 57 37 40 47
vertical step on the fracture surface. Once the initial cracks link together, the ratchet lines disappear. Therefore, the number of ratchet marks is a good indication of the number of nucleation sites. As the applied stress increases, the number of nucleation sites and associated ratchet lines increases [32]. It is obvious that crack initiation sites increased with decrease in strain rate and ratchet line formation was more prominent at the high strain amplitude of 7 0.5% at low strain rate (Fig. 11c). Thus, the decrease in fatigue life with decrease in strain may be due to increase in the crack initiation (ratchet line) sites. Area of the fatigue fracture zone was found to increase with increase in strain amplitude. Smaller area of fatigue failure at the lowest strain amplitude of 7 0.25% may be understood from the fine inter striation spacing as compared to that at high strain amplitude. It may be stated that more number of cycles can be accommodated in less area due to fine inter striation spacing.
0.2 μm Fig. 14. TEM micrograph showing interaction between precipitates (MX) and dislocations in the sample tested in LCF at strain rate of 10 3 s 1 and strain amplitude of 7 0.25%.
5. Conclusions The following investigation:
conclusions
may
be
drawn
from
this
1. In general, the modified 9Cr–1Mo steel exhibited cyclic softening at all the strain amplitudes and the strain rates
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Fig. 15. Variation of friction and back stress with number of cycles at different strain amplitudes at a strain rate of 10 2 s 1: (a) Friction stress and (b) Back stress.
Fig. 16. Variation of friction and back stress with number of cycles at different strain amplitude at strain rate of 10 3 s 1: (a) Friction stress and (b) Back stress.
Fig. 17. Variation of friction and back stress with number of cycles at different strain amplitude at strain rate of 10 4 s 1: (a) Friction stress and (b) Back stress.
investigated. There was drop in stress in the very first cycle and mild hardening during the subsequent cycles up to 20–30 cycles at the higher strain amplitudes (Z 7 0.375%) and up to 200– 300 cycles at the lowest strain amplitude of 70.25%. 2. Fatigue life based on both plastic strain amplitude as well as plastic strain energy increased linearly with decrease in these
parameters. 3. Irrespective of strain amplitude and strain rate there was transformation of unstable martensite lath structure to dislocation sub-grain structure under cyclic loading by forming dislocation cell structure. The cell size increased and density of dislocations increased with increase in strain amplitude. The
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cyclic softening in the steel may thus be attributed to formation of lower energy dislocation cell structure. 4. Both at high as well as low strain amplitude softening was controlled essentially by the friction stress which continuously decreased with number of cycles. 5. The stable hysteresis loops displayed Masing behavior at higher strain amplitudes Z 7 0.375% and non Masing behavior at lower strain amplitudes o 70.375%. There was fall in fatigue life with decrease in strain rate, which may be correlated with the more faceted nature of fracture and more crack initiation sites.
References [1] H.W. Zhou, Y.Z. He, H. Zhnag, Y.W. Ce, Int. J. Fatigue 47 (2013) 83–89. [2] V. Shankar, M. Valsan, K.B.S. Rao, R. Kannan, S.L. Manna, S.D. Pathak, Mater. Sci. Eng. A 437 (2006) 413–422. [3] B. Fournier, M. Sauzay, A. Renault, F. Barcelo, A. Pineau, J. Nucl. Mater. 386–388 (2009) 71–74. [4] A. Nagesha, R. Kannan, G.V.S. Sastry, R. Sandhya, V. Singh, K.B.S. Rao, Mater. Sci. Eng. A 554 (2012) 95–104. [5] D.W. Kim, W.S. Ryu, Proc. Eng. 10 (2011) 376–382. [6] V. Shankar, V. Bauer, R. Sandhya, M.D. Mathew, H.J. Christ, J. Nucl. Mater. 420 (2012) 23–30. [7] D. Samantaray, S. Mandal, A.K. Bhaduri, Mater. Des. 31 (2010) 981–984. [8] S. Kim, J.R. Weertman, Metall. Mater. Trans. A 19A (1988) 999–1007. [9] A.A. Saad, W. Sun, T.H. Hyde, D.W.J. Tanner, Proc. Eng. 10 (2011) 1103–1108. [10] G. Ebi, A.J. McEvily, Fatigue Fract. Eng. Mater. Struct. 17 (1984) 299–314. [11] K. Guguloth, S. Sivaprasad, D. Chakrabarti, S. Tarafder, Mater. Sci. Eng. A 604
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(2014) 196–206. [12] P. Verma, R.G. Sudhakar, P. Chellapandi, G.S. Mahobia, K. Chattopadhyay, N.C. Santhi Srinivas, V. Singh, Mater. Sci. Eng. A 621 (2015) 39–51. [13] B.K. Choudhary, J. Christopher, D.P.R. Palaparti, E. Issac Samuel, M.D. Mathew, Mater. Des. 52 (2013) 58–66. [14] Y.R. Luo., C.X. Huang, G. Yuo, Q.Y. Wang, J. Iron Steel Res. Int. 19 (2012) 47–53. [15] L.F. Coffin Jr., Met. Eng. Q. 3 (1963) 22. [16] B. Fekete, P. Trampus, J. Nucl. Mater. 464 (2015) 394–404. [17] K.V.U. Praveen, V. Singh, Mater. Sci. Eng. A 485 (2008) 352–358. [18] G. Masing, in: Proceedings of the 2nd International Congress of Applied Mechanics, Zurich 1926. [19] P. Marmy, T. Kruml, J. Nucl. Mater. 377 (2008) 52–58. [20] M.F. Giordana, I. Alvarez-Armas, A. Armas, Steel Res. Int. 83 (6) (2012) 594–599. [21] M. Sauzay, H. Brillet, I. Monnet, M. Mottot, F. Barcelo, B. Fournier, et al., Mater. Sci. Eng. A 400–401 (2005) 241–244. [22] R.G. Sudhakar, J.K. Chakravartty, N. Saibaba, G.S. Mahobia, K. Chattopadhyay, N.C. Santhi Srinivas, V. Singh, J. Nucl. Mater. 441 (2013) 455–467. [23] H.Cottrell, Oxford University Press, London 1953. [24] A. Seeger, Philos. Mag. 46 (1955) 1194–1217. [25] B. Fournier, M. Sauza, M. Caes, M. Noblecourt, M. Mottot, Mater. Sci. Eng. A 437 (2006) 183–196. [26] B. Fournier, M. Sauzay, A. Renault, F. Barcelo, A. Pineau, J. Nucl. Mater. 386–388 (2009) 71–74. [27] A. Plumtree, H.A. Abdel-Raouf, Int. J. Fatigue 23 (2001) 799–805. [28] R.O. Ritchie, Environment-sensitive fracture of engineering materials, in: Z. A. Foroulis (Ed.), The Metallurgical Society, 1979, pp. 538–564. [29] C.E. Richards, T.C. Lindley, Eng. Fract. Mech. 4 (1972) 951–978. [30] R.O. Ritchie, J.F. Knott, Mater. Sci. Eng. 14 (1974) 7–14. [31] M.N. Batista, M.C. Marinelli, S. Herenu, I. Alvarez-Armas, Int. J. Fatigue 72 (2015) 75–79. [32] Richard W. Hertzberg, Deformation and Fracture Mechanics of Engineering Materials, 4th ed., John Willey & Sons, Inc, United States, 1995.
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Materials Science & Engineering A journal homepage: www.elsevier.com/locate/msea
Low cycle fatigue behavior of modified 9Cr–1Mo steel at room temperature Preeti Verma a, N.C. Santhi Srinivas a, S.R. Singh b, Vakil Singh a,n a b
Centre of Advanced Study, Department of Metallurgical Engineering, Indian Institute of Technology (Banaras Hindu University), Varanasi, India School of Materials Science and Technology, Indian Institute of Technology (Banaras Hindu University), Varanasi, India
art ic l e i nf o
a b s t r a c t
Article history: Received 16 September 2015 Received in revised form 18 November 2015 Accepted 19 November 2015 Available online 27 November 2015
Low cycle fatigue (LCF) behavior of modified 9Cr–1Mo steel was studied in normalized and tempered condition at strain rates from 10 2 s 1 to 10 4 s 1 in the regime of low strain amplitude between 70.25% and 7 0.5% at room temperature. Cyclic softening was exhibited at the higher strain amplitudes of 7 0.375% and 7 0.50% after about 20–30 cycles and after 200–300 cycles at the lowest strain amplitude of 70.25%, at all the strain rates. There was mild tendency of hardening from 2 to 20 cycles at the highest strain amplitude of 7 0.50% and up to 200–300 cycles at the lowest strain amplitude of 7 0.25%. The rate of softening increased with increase in strain amplitude. Masing and non-Masing behavior was exhibited at the higher strain amplitudes (Z 70.375%) and lower strain amplitudes ( o 7 0.375%) respectively. Dependence of fatigue life, based on both plastic strain amplitude as well as plastic strain energy was linear and fatigue life decreased with lowering of strain rate. The unstable tempered martensitic structure was transformed into equiaxed dislocation cell structure under cyclic loading. The size of the cells and annihilation of dislocations increased with increase in strain amplitude. While the friction stress decreased with number of cycles at all the strain amplitudes, back stress was nearly constant at the high strain amplitudes and increased at the lowest strain amplitude. The observed cyclic softening was thus mainly due to decrease in friction stress, formation of low energy dislocation cell structure, and annihilation of dislocations. & 2015 Elsevier B.V. All rights reserved.
Keywords: Modified 9Cr–1Mo steel Cyclic softening Masing and non-Masing behavior Friction stress Dislocation cells Fatigue
1. Introduction Modified 9Cr–1Mo steel (with minor additions of V and Nb in conventional 9Cr–1Mo steel) is widely used for steam generator of nuclear reactors [1–7]. It is also a candidate material for future metallic fuel sodium cooled fast breeder reactor. High thermal conductivity, lower thermal expansion coefficient, high tensile and creep strength, good weldability, microstructural stability and higher resistance to stress corrosion cracking in water-steam systems of this steel compared to austenitic stainless steels are important features for its suitability in nuclear industry. Fine microalloyed precipitates of carbides, nitrides and carbonitrides of Nb and V such as Nb (C, N) and V (C, N) enhance the high temperature strength of this steel [1–6]. During service exploitation, the components of steam generators are often subjected to repeated thermal stresses as a result of temperature gradients occurring from heating and cooling during start-ups and shutdowns or thermal transients. These transient thermal stresses induce n
Corresponding author. E-mail address: [email protected] (V. Singh).
http://dx.doi.org/10.1016/j.msea.2015.11.060 0921-5093/& 2015 Elsevier B.V. All rights reserved.
cyclic strain and cause low cycle fatigue (LCF) damage in the material. There have been several studies on LCF behavior of this steel in normalized and tempered condition related to effect of strain amplitude, strain rate and temperature [2–6,8–11]. In general, there was exhibition of hardening during the initial cycles followed by continuous softening till failure at different temperatures and fatigue life was decreased with increase of temperature and it was more pronounced at the lower strain amplitudes [4]. Krishna et al. [11] studied LCF behavior of this steel at high strain amplitudes (70.7% to 71.2%) at room temperature (RT), 500 and 600 °C at strain rate of 10 3 s 1 and observed cyclic softening with rise in test temperature due to decrease in dislocation density, coarsening of martensitic laths and transformation of lath structure into dislocation cell and sub-grain structure. Cyclic softening exhibited during cyclic straining has been attributed to changes in dislocation substructure from the original lath martensite structure to subgrain and decrease in dislocation density [3,8,11]. Most of the LCF studies on this steel have been carried out at single strain rate and mostly in the regime of high strain
P. Verma et al. / Materials Science & Engineering A 652 (2016) 30–41
amplitude, at elevated temperatures. As part of evaluation of the effect of strain rate and temperature on LCF behavior of the modified 9Cr–1Mo steel for advance nuclear reactor applications, investigation was undertaken to study LCF behavior of this steel in the regime of low strain amplitude at different strain rates over a wide range of temperature from RT to 600 °C. This communication presents LCF behavior of this steel at room temperature including characterization of deformation, fracture, Masing and non-Masing behavior.
31
Fig. 1. Schematic of low cycle fatigue test specimen. Table 2 Test matrix for LCF test at room temperature.
2. Material and methods Modified 9Cr–1Mo steel of the present investigation was supplied by IGCAR Kalpakkam, India, in the form of plate, in normalized and tempered condition. It was normalized at 1060 °C for 1 h, tempered at 780 °C for 1 h and cooled in air. The chemical composition of the steel is given in Table 1. Cylindrical LCF specimens with gage section of 5.5 mm diameter, 15 mm gauge length and threaded ends of 12 mm diameter and 35 mm length, on either side and curvature radii of 25 mm were machined with length in rolling direction of the plate as per the British standard (BS 121950). Schematic of the LCF specimen with all dimensions are shown in Fig. 1. LCF tests were conducted at RT under fully reversed triangular waveform (R ¼ 1) in total-strain control mode using servo-hydraulic testing system (MTS model 810, with flex test 40 controller). Room temperature extensometer (Model: Model: 632.03C 30 MTS) was used to measure the strain during the LCF test. The test data in terms of different strain components were displayed. LCF tests were performed at RT in regime of low strain amplitude at three strain amplitudes of 70.25%, 7 0.375% and 7 0.50% and three strain rates of 10 2 s 1, 10 3 s 1 and 10 4 s 1. Test matrix for LCF tests is given in Table 2. The initial microstructure was characterized by optical, scanning electron microscope (Model: FEI Quanta 200 FEG) and TEM (Model: FEI Tecnai 20 G2). TEM foils for the study of deformation behavior under LCF were prepared from transverse section of the fatigue tested specimens by electro polishing in an electrolyte containing 6% perchloric acid, 34% n-butanol in methanol at 22 V and 40 °C, using a twinjet electropolisher (Model: Struers Tenupol 5). Deformation behavior and dislocation substructure was assessed by transmission electron microscope.
3. Results 3.1. Microstructure Microstructure of the modified 9Cr–1Mo steel is shown in Fig. 2a and b by optical and SEM micrographs respectively. The prior austenite grain structure along with second phase precipitates distributed uniformly in the grain as well as along the prior austenite grain boundaries (PAGbs) may be seen clearly from these micrographs. The substructural details observed in TEM are shown in Fig. 3. In addition to second phase precipitates along the martensite lath boundaries, high density of dislocations may also be seen within the laths (Fig. 3b). The precipitates have been characterized as carbides in our previous investigation [12], in line with earlier findings of Choudhary et. al [13]. The mean intercept
Strain rate (s 1)
Strain amplitude (%)
Frequency (s 1)
10 2
70.25 70.375 70.50 70.25 70.31 70.375 70.50 70.375 70.50
1.0000 0.6667 0.5000 0.1000 0.0806 0.0667 0.0500 0.0067 0.0050
10 3
10 4
length of prior austenite grains was determined to be E20 μm and the width of the laths was E0.5 μm. 3.2. Low cycle fatigue 3.2.1. Cyclic stress response The variation of cyclic stress amplitude with number of cycles for the different total strain amplitudes at strain rates of 10 2 s 1, 10 3 s 1 and 10 4 s 1 is shown in Fig. 4a–c respectively. At the highest strain rate of 10 2 s 1, there was cyclic softening after the initial 20–30 cycles at the higher strain amplitudes of 70.5% and 70.375%, and after 200–300 cycles at the lowest strain amplitude of 70.25%. It may be seen that at the highest strain amplitude of 70.5% there was mild drop in the cyclic stress at the first cycle followed by mild hardening nearly up to the initial 10-20 cycles. However, at the lowest strain amplitude of 70.25% after 10 cycles there was marginal cyclic hardening up to about 200–300 cycles, and it was followed by cyclic softening till fracture. It is noteworthy that the number of cycles to peak hardening increased with decrease in strain amplitude. The degree of cyclic softening increased with strain amplitude. Similar behavior was observed also at the lower strain rate of 10 3 s 1 (Fig. 4b). The differences in the levels of the stress response curves, at different strain amplitudes were reduced with decrease in strain rate. It may be seen that the stress response curves at the lowest strain rate of 10 4 s 1, corresponding to strain amplitudes of 7 0.375% and 70.5%, were almost coincident (Fig. 4c). LCF test could not be performed at the lowest strain rate of 10 4 s 1 for the strain amplitude of 70.25% because of expected test duration of more than three months. 3.2.2. Strain-life relationship The strain-based LCF life is widely used to describe the behavior of structural materials operating at elevated temperatures and high levels of stress and strain in power generation plant during
Table 1 Chemical composition of the modified 9Cr–1Mo steel (wt%). Elements
C
Si
Mn
P
S
Cr
Mo
Ni
Al
Nb
N
V
Fe
Wt%
0.1
0.26
0.41
0.018
0.002
9.27
0.95
0.33
0.013
0.074
0.044
0.21
Balance
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20 μm
10 μm
Fig. 2. Microstructure showing PAGbs and distribution of second phase particles along the PAGbs and within the grains of normalized and tempered modified 9Cr–1Mo steel: (a) Optical micrograph (b) SEM micrograph.
their in-service period [14]. In these operations, fatigue damage is generally caused by plastic strain and is described by the Coffin– Manson relationship Δεp/2 ¼ ε′f (2Nf)c where ε′f and c are fatigue ductility coefficient and fatigue ductility exponent respectively [15]. Variation of number of reversals to failure (2Nf) with plastic strain amplitude (Δεp/2) at different strain rates of 10 2 s 1 and 10 3 s 1 is shown in Fig. 5a and linear variation of 2Nf with Δεp/2 may be seen on logarithmic scale. The LCF parameters, fatigue ductility exponent (c) and fatigue ductility coefficient ( ε′f ) are the slope and intercept on Y-axis at 2Nf ¼ 1 respectively and were determined by least square linear fit of the data in Fig. 5a. The values of LCF parameters are presented in Table 3. Both, fatigue ductility coefficient ( ε′f ) and fatigue ductility exponent (c) may be seen to increase with decrease in strain rate from 10 2 s 1 to 10 3 s 1. Effect of strain rate on fatigue life at high strain amplitude was found to be negligible, however, fatigue life was lowered at the lowest strain amplitude of 70.25% at the strain rate of 10 3 s 1 in comparison to that at the higher strain rate of 10 2 s 1. Cyclic stress–strain parameters were calculated from the half-life hysteresis loops at all the strain amplitudes at the different strain rates of 10 2 and 10 3 s 1 and are presented in the Table 4. The cyclic strain hardening exponent and cyclic strength coefficient parameters were found to increase with decrease in strain rate (Table 4).
3.2.3. Strain energy-life relationship Since LCF damage is associated with cyclic plastic strain, the dissipated strain energy has been considered for accurate prediction of fatigue life of the components. In general, fatigue life relationships may be based on stress, strain or energy parameters [16].The energy parameters have several advantages like: (a) both strain and stress parameters are included in these models, (b) these variables are independent of the direction by its scalar value, (c) the damage is easy to cumulate, and (d) more suitable to transfer the model results to the real structure. The plastic strain energy per cycle is equal to the area of the hysteresis loop. In general, the area of the hysteresis loop at halflife is considered as the average plastic strain energy per cycle (ΔWp). The LCF data were analyzed in terms of power law relationship based on energy [17], similar to the Coffin–Manson relationship.
ΔWp = Wf′(2Nf ) β where Wf′ and β are material constants and β is related to the fatigue life constant as β = b + c . The plot of ΔWp versus 2Nf is shown in Fig. 5b and the LCF parameters are presented in Table 5. In this approach both Wf0 and β were found to decrease with increase in strain rate. Similar dependency of LCF parameter on strain rate is observed in both plastic strain amplitude and energy based approach.
Fig. 3. (a) TEM micrograph of the normalized and tempered modified 9Cr–1Mo steel displaying PAGbs and M23C6 carbides along the PAGbs and fine vanadium and niobium carbides within the laths, precipitates were identified from SAD pattern, (b) high dislocation density within the lath martensite.
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Fig. 4. Variation of stress amplitude with number of cycles at different strain rates: (a) 10 2 s 1, (b) 10 3 s 1, (c) 10 4 s 1.
3.3. Masing and non-Masing behavior The stress–strain hysteresis loops were analyzed for Masing and non-Masing behavior [18]. In some metals it was observed that after matching the compressive tips, the hysteresis loops coincided with the cyclic stress–strain curve magnified by two, showing Masing behavior. However, other metals exhibited nonMasing behavior and there was coincidence only when the saturated hysteresis loops were translated downwards along the linear elastic slope. The modified 9Cr–1Mo steel was found to exhibit both Masing and non-Masing behavior based on the strain amplitude in LCF test. Fig. 6 shows the stress–strain hysteresis loops translated to a common point of maximum compressive stress of saturated hysteresis loop from the different strain amplitudes at strain rates of 10 2 s 1, 10 3 s 1 and 10 4 s 1. It is obvious that at the strain amplitudes of Z 70.375% the hysteresis loops matched with the tensile portion of the highest strain amplitude whereas the hysteresis loops of lowest strain amplitude of 7 0.25% did not match. Thus, this steel exhibits non-Masing behavior at very low strain amplitude of 70.25% and Masing behavior at the strain amplitudes Z 7 0.375%. A quite similar behavior was observed also at the lower strain rates of 10 3 s 1 and 10 4 s 1. 3.4. Dislocation substructure The tempered lath structure (Fig. 3a and b) was found to be unstable under cyclic loading and was gradually replaced by
subgrain structure. Minimizing their stored energy, the original parallel high dislocation-density martensitic laths partitioned into equiaxed subgrain structure of large size. Fig. 7 shows dislocation substructures in the specimen tested at different strain amplitudes at strain rates of 10 2 s 1. A subgrain structure with relatively low density of dislocations inside the laths and with no well-defined cell boundary may be seen in the specimen tested at the lowest strain amplitude of 7 0.25% (Fig. 7a and b). Elongated cell wall structure with high density of dislocations along cell walls may be seen in the sample tested at the higher strain amplitude of 70.375% (Fig. 7c). There was intersection of dislocations inside the laths (Fig. 7d). Similarly at the highest strain amplitude of 70.5% there was formation of elongated cell wall structure in some grains and formation of distinct subgrains (Fig. 7e and f). There was formation of distinct dislocation cell/subgrain structure also at the lowest strain rate of 10 4 s 1 (Fig. 8) and dislocation density inside the grains was high (Fig. 8b). However, no elongated cell wall structure was observed at the lowest strain rate of 10 4 s 1. It is obvious from Fig. 9 that cell size increased with increase in strain amplitude. 3.5. Fracture behavior Fracture morphology of the fatigue samples tested at 10 2 s 1 is shown in Fig. 10. It is obvious that there was initiation of multiple cracks with decrease in strain amplitude whereas a sufficiently large single crack formed at the highest strain amplitude of 70.50%. Inter striation spacing was found to increase with
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Table 5 Low cycle fatigue parameters at different strain rates, based on plastic strain energy. Strain rate (s 1) Fatigue ductility coefficient ( Fatigue ductility exponent (β) W′f ) 10 2 10 3
4.12987 4.37303
0.90446 0.9719
cracking was observed at higher magnifications at all the strain amplitudes. Similar fracture morphology was observed even at the lower strain rate of 10 3 s 1 with multiple crack initiation sites at low strain amplitudes (Fig. 11). With increase in strain amplitude to 70.5%, ratchets were seen as shown by white arrows in Fig. 11c. Ratchet lines are the lines which represent the junction surfaces between the adjacent crack origins. Different microcracks are unlikely to form on the same plane of different heights and their eventual linkage creates a vertical step on the fracture surface. Once the initial cracks link together, the ratchet lines disappear and follow the same crack propagation path. These lines are shown by arrows in Fig. 11c. Magnified view of the crack initiation site showed that in case of high strain amplitudes, striations were observed just after 50 μm depth from the surface and no striations were visible even up to the depth of 600 μm at the low strain amplitude (Fig. 12). Tire marks and distinct faceted features were observed in the specimen tested at the lowest strain amplitude of 70.25% at the strain rate of 10 3 s 1 (Fig. 13). The areas of both fatigue as well as tensile overload failure were calculated corresponding to both the strain rates and it was found that the area of fatigue region increased with increase in strain amplitude (Table 6). Fatigue fracture zone is marked by black solid lines in the fractographs shown in Figs. 10 and 11.
4. Discussion 4.1. Cyclic stress response and dislocation substructure
Fig. 5. (a) Dependence of fatigue life (as reversals to failure) with plastic strain amplitude, at strain rates of 10 2 s 1 and 10 3 s 1 and (b) Low cycle fatigue plots based on plastic strain energy and reversals to failure (2Nf) at strain rates of 10 2 s 1 and 10 3 s 1.
Table 3 Low cycle fatigue parameters at different strain rates based on plastic strain amplitude approach. Strain rate (s 1) Fatigue ductility coefficient ( εf′)
Fatigue ductility exponent (c)
10 2 10 3
0.80434 0.86978
3.6442 6.4835
Table 4 Cyclic stress–strain parameters at different strain rates. Strain rate (s 1)
n0
K0 (MPa)
10 2 10 3
0.03887 0.05333
675 715
increase in strain amplitude. Distinct fatigue striations may be seen from stage II fatigue crack propagation, however more facets may be seen at the bottom of the fractographs in Fig. 10. Secondary
It is obvious from the cyclic stress response of the modified 9Cr–1Mo steel that there was initial softening followed by stability up to 10–20 cycles, mild hardening to peak and finally cyclic softening till fracture (Fig. 4). The initial softening was essentially due to movement of free dislocations inside the laths and the subsequent hardening resulted from interaction between the precipitates (MX, X ¼C/N) and dislocations (Fig. 14). M23C6 precipitates were observed mainly at lath boundaries and prior austenite grain boundaries and had pinning influence. This steel in the normalized and tempered condition, with tempered martensite lath structure, was highly unstable under cyclic straining. The laths were gradually replaced by dislocation subgrain structure minimizing their stored energy. The relatively large extent of cyclic softening at all the strain amplitudes may be attributed mainly to formation of dislocation cell structure, in agreement with earlier observations [2,4,8]. In consequence to early onset of cyclic softening, at high strain amplitudes, there was transformation of lath martensite to subgrain structure, in the early stage. The dislocation structure was highly heterogeneous with packets of dislocation debris and ill-defined cells in it. The precipitates located along the lath boundaries imposed a pinning effect, resulting in slightly elongated cell structure. Equiaxed dislocation cells were also present. Very fine microalloy precipitates were found to interact with dislocations in dislocation-rich regions and retard the dislocation motion. It is known that the dislocations rearrange themselves during cyclic loading, into a lower energy
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high strain amplitudes. It has been reported that softening stage in 9–12%Cr steels and especially in Reduced Activation Ferritic Martensitic (RAFM) steels is clearly associated with increase in the subgrain size, regardless of the temperature [19] and softening has partially been explained from annihilation of dislocations within subgrains [20] and by lath/sub-grain boundary elimination [21]. As such there is no literature on the effect of strain amplitude and strain rate on deformation behavior and dislocation substructure of the modified 9Cr–1Mo steel, at room temperature. This steel deforms by more than one slip system. Wavy slip materials are known to attain a stable stress state and a characteristic dislocation substructure, irrespective of their initial state (hard or soft). In general, cell structure formation is observed in wavy slip materials. On the other hand planar slip materials display different cyclic stabilized stress levels depending on their initial condition and likewise different dislocation substructure. Thus, the development of a characteristic dislocation substructure i.e. cell structure in the cyclically deformed modified 9Cr–1Mo steel, a wavy slip material, was there in all the test conditions, irrespective of strain amplitude and strain rate. It may be stated that there was no change in the dislocation configuration due to change in the test condition. 4.2. Role of friction and back stress
Fig. 6. Stress–strain hysteresis loops translated to a common point of maximum compressive stress exhibiting Masing and non-Masing behavior at three different strain rates: (a) 10 2 s 1, (b) 10 3 s 1, (c) 10 4 s 1.
configuration comprising of dislocation cells, surrounded by dislocation walls, by cross-slip [1–4]. Size of the subgrains depends on the applied plastic-strain amplitude. It is obvious from Fig. 9 that cell size increased with increase in strain amplitude. Dislocation-free areas were frequently observed in the regions close to the lath boundaries at
Friction stress and back stress are well established key parameters to describe dislocation movement under constant strain control fatigue [22]. The friction stress arises from the resistance to dislocation movement in the lattice involving short-range interaction obstacles and back stress results from long-range interaction obstacles [23,24]. In the present investigation, the friction stress and back stress were determined to find out their contribution in cyclic stress response of the tempered martensitic steel. These parameters were calculated from the stress–strain hysteresis loops for all the cycles, at all the strain amplitudes, as per the procedure described elsewhere [22]. Figs. 15–17 show variation of friction stress and back stress with number of cycles at the different strain amplitudes corresponding to strain rates of 10 2, 10 3 and 10 4 s 1 respectively. It is obvious that friction stress decreased with number of cycles at all the strain amplitudes, at all the strain rates, whereas the back stress was nearly constant at the higher strain amplitudes and increased at the lowest strain amplitude. Fournier et al. [25] studied microstructural evolution and cyclic softening of this steel at 550 °C at different strain amplitudes from 70.2% to 70.5%. The softening of the steel was directly correlated to decrease in the kinematic stress (back stress) which arises from ‘directional and long-range’ obstacles to movement of dislocations. Therefore, grain and subgrain boundaries (through a dislocation pile-up mechanism) and, more generally, all microstructural heterogeneities (arrangement of dislocations, precipitates, etc.) are sources of kinematic hardening. This suggests that, during cycling the softening occurs from disappearance of microstructural heterogeneities [26]. Krishna et al. [11] have analyzed the effect of the temperature on cyclic stress response at RT, 550 and 600 °C at high strain amplitudes (7 0.7% to 71.2%), at strain rate of 10 3 s 1. They observed that decrease in the effective stress (friction stress) had a dominating effect over the decrease in internal stress (back stress) and the cyclic yield stress decreased with increase in test temperature, however both the stresses decreased with increase in test temperature [11]. Based on the results of the present investigation it is important to mention that at all the strain amplitudes the cyclic stress response was controlled primarily by friction stress.
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1 μm
0.5 μm
0.5 μm
0.5 μm
0.5 μm
0.5 μm
Fig. 7. Dislocation configurations resulting from LCF at strain rate of 10 2 s 1 at different strain amplitudes as: (a and b) 70.25%, (c and d) 70.375%, (e and f) 7 0.5%. Formation of cell structure may be seen at all the strain amplitudes.
4.3. Analysis of Masing and non-Masing behavior Effect of cyclic strain amplitude was analyzed on Masing/nonMasing behavior of this steel in the normalized & tempered condition. There was Masing behavior at high strain amplitudes (Z0.375%) and non-Masing at low strain amplitudes (o 70.375%) as shown in Fig. 6. Usually, the change from Masing to non-Masing behavior is associated with transformation of dislocation substructures to dislocation cell structures [27]. However, no such changes were observed in dislocation substructure between the low and high strain amplitude tests in the present
investigation. Irrespective of the strain amplitude, there was formation of subgrains at all the strain amplitudes. Masing and non Masing behavior in the modified 9Cr–1Mo steel was earlier studied by Krishna et al. [11] at room temperature. They found Masing behavior at strain amplitudes from 70.7% to 71.0% and non-Masing behavior at strain amplitude from 7 1.1% to 71.2% at RT. Plumree and Abdel-Raouf [27] observed Masing behavior for metals with finely dispersed particles and single phase low stacking fault metals; and non-Masing behavior in high stacking fault energy materials, in which the deformation was mainly controlled by the matrix. Depending on the strain amplitude,
P. Verma et al. / Materials Science & Engineering A 652 (2016) 30–41
1 μm
0.2 μm
1 μm
1 μm
37
Fig. 8. Dislocation configurations resulting from LCF at different strain amplitudes at the lowest strain rate of 10 4 s 1: (a and b) 7 0.375%; (c and d) 7 0.5%.
present investigation is in line with the earlier investigation [11]. However, it is noteworthy from the present investigation that there was non-Masing behavior at the very low strain amplitude of 7 0.25%. Thus, there was transition from the Masing to nonMasing behavior from high to low strain amplitude. 4.4. Fracture behavior
Fig. 9. Variation of cell size with strain amplitude, in fatigue samples tested at strain rate of 10 2 s 1.
ferritic–pearlitic AISI 1018 hot rolled steel was found to exhibit Masing behavior at low strain amplitudes and non-Masing at higher strain amplitudes. It is important to mention that all the previous investigations have been conducted at strain amplitudes above 70.5% where Masing behavior was observed. The occurrence of Masing behavior at strain amplitudes Z 7 0.375% in the
The largest portion of fatigue fracture consists of Stage II crack growth exhibiting striations on fracture surface, and is more influenced by strain amplitude and microstructure [28–30]. In general, a large portion of fatigue life is spent in crack nucleation in stage I at low strain amplitudes and stage II crack growth at high strain amplitudes. Thus, the decrease in fracture area corresponding to stage I with increase in strain amplitude from 70.25% to 70.5% and increase in the stage II area with increase in strain amplitude may be understood (Fig. 12). The microstructure and mechanical properties of the materials strongly affect the process of crack initiation and its subsequent propagation. In the ferritic– martensitic steel (EUROFER 97) lath boundaries are favorable sites for microcrack nucleation [31]. Slip irreversibility occurs in materials and plastic strain accumulates during fatigue loading. At the defect level, the irreversibility is a result of dislocation pile-up, annihilation or cross-slip. Grain boundary or inclusion-matrix phase boundary also contribute to slip irreversibility. These slip irreversibilities are considered early signs of damage during cyclic loading. The dislocations subsequently form low-energy stable structures as means to accommodate the irreversible slip processes and
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1 mm
1 mm
1 mm
15 μm
15 μm
15 μm
Fig. 10. Fracture surfaces of fatigue samples tested at room temperature, at strain rate of 10 2 s 1 at different strain amplitudes: (a, A) 7 0.25% (b, B) 7 0.375% & (c, C) 7 0.5%.In Fig. a–c the regions of fatigue fracture from surface towards interior are marked by black ink. Striations and secondary cracking are shown in the higher magnification images. Crack propagation direction is shown by white arrows.
1 mm
1 mm
1 mm
Fig. 11. Low magnification fracture surfaces of the LCF samples tested at strain rate of 10 3 s 1 at different strain amplitudes: (a) 7 0.25%, (b) 7 0.375%, (c) 7 0.5%. Fatigue regions are marked by black ink and ratchet lines are shown by white arrows.
modify the dislocation density during forward and reverse cyclic loading. Inclusions and precipitates are special defects that can initiate cracks because of different factors such as slip characteristic of the matrix, the relative strength of the matrix and inclusions, strength of the matrix inclusion interface and environmental factors. Depending upon the structure relationship between the matrix and precipitates, these interfaces could be weakest sites of a material. Matrix and precipitates may raise the mechanical stress in vicinity of the interface during cyclic loading causing, eventual interfacial crack initiation. Also faceted features were observed in the region of stage II crack growth without striation markings, prominently more at the high strain amplitudes, at the strain rate of 10 2 s 1 and even at low strain amplitudes at lower strain rate of 10 3 s 1 (Figs. 10 and 13). The occurrence of tire marks and faceted fracture with decrease in strain amplitude and strain rate may clearly be seen from
Fig. 13a. In the early stage of cracking arising from cyclic straining there were faceted features and ΔK would have been very low. As the fatigue crack started propagating distinct striation marks were visible. It may be noted that the fatigue crack propagating can occur even without formation of striations at high and low ΔK values, irrespective of the type of material [32]. Striations formed at intermediate ΔK because at high ΔK plastic blunting mechanism operates causing microvoid coalescence while at low ΔK values crystallographic orientation dependence leads to formation of cleavage like facets. Ratchet marks are another macroscopic feature that can be observed in fatigue fracture. These marks originate when multiple cracks are nucleated at different points/heights in gage section of the specimen. Since each microcrack is unlikely to form on the same plane eventual linkage of such cracks leads to formation of
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100 μm
39
100 μm
Fig. 12. Crack initiation regions resulting LCF at strain rate of 10 3 s 1 at different strain amplitudes (a) 7 0.25%, (b) 7 0.5%.
a
b
10 μm
1 μm
Fig. 13. Fractographic images of LCF sample tested at 7 0.25% at strain rate of 10 3 s 1 showing (a) tire marks, (b) faceted features. Table 6 Area of the region of fatigue crack propagation at different strain rates of 10 2 s 1 and 10 3 s 1. Strain rate (s 1) 10
2
10 3
Strain amplitude (%)
Area of fatigue region (%)
7 0.25 7 0.375 7 0.5 7 0.25 7 0.375 7 0.5
21 24 57 37 40 47
vertical step on the fracture surface. Once the initial cracks link together, the ratchet lines disappear. Therefore, the number of ratchet marks is a good indication of the number of nucleation sites. As the applied stress increases, the number of nucleation sites and associated ratchet lines increases [32]. It is obvious that crack initiation sites increased with decrease in strain rate and ratchet line formation was more prominent at the high strain amplitude of 7 0.5% at low strain rate (Fig. 11c). Thus, the decrease in fatigue life with decrease in strain may be due to increase in the crack initiation (ratchet line) sites. Area of the fatigue fracture zone was found to increase with increase in strain amplitude. Smaller area of fatigue failure at the lowest strain amplitude of 7 0.25% may be understood from the fine inter striation spacing as compared to that at high strain amplitude. It may be stated that more number of cycles can be accommodated in less area due to fine inter striation spacing.
0.2 μm Fig. 14. TEM micrograph showing interaction between precipitates (MX) and dislocations in the sample tested in LCF at strain rate of 10 3 s 1 and strain amplitude of 7 0.25%.
5. Conclusions The following investigation:
conclusions
may
be
drawn
from
this
1. In general, the modified 9Cr–1Mo steel exhibited cyclic softening at all the strain amplitudes and the strain rates
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Fig. 15. Variation of friction and back stress with number of cycles at different strain amplitudes at a strain rate of 10 2 s 1: (a) Friction stress and (b) Back stress.
Fig. 16. Variation of friction and back stress with number of cycles at different strain amplitude at strain rate of 10 3 s 1: (a) Friction stress and (b) Back stress.
Fig. 17. Variation of friction and back stress with number of cycles at different strain amplitude at strain rate of 10 4 s 1: (a) Friction stress and (b) Back stress.
investigated. There was drop in stress in the very first cycle and mild hardening during the subsequent cycles up to 20–30 cycles at the higher strain amplitudes (Z 7 0.375%) and up to 200– 300 cycles at the lowest strain amplitude of 70.25%. 2. Fatigue life based on both plastic strain amplitude as well as plastic strain energy increased linearly with decrease in these
parameters. 3. Irrespective of strain amplitude and strain rate there was transformation of unstable martensite lath structure to dislocation sub-grain structure under cyclic loading by forming dislocation cell structure. The cell size increased and density of dislocations increased with increase in strain amplitude. The
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cyclic softening in the steel may thus be attributed to formation of lower energy dislocation cell structure. 4. Both at high as well as low strain amplitude softening was controlled essentially by the friction stress which continuously decreased with number of cycles. 5. The stable hysteresis loops displayed Masing behavior at higher strain amplitudes Z 7 0.375% and non Masing behavior at lower strain amplitudes o 70.375%. There was fall in fatigue life with decrease in strain rate, which may be correlated with the more faceted nature of fracture and more crack initiation sites.
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