Low Cycle Fatigue and Ratcheting Behavior of SA333 Gr-6 Steel at 300[degrees]C Temperature.
SA333 Gr-6 C-Mn steel is used in engineering structures due to its favorable properties like higher thermal conductivity and lower thermal expansion. This is commonly available material and can be fabricated by welding and bending process. In nuclear power plants, this material is used as a primary heat transport piping system for pressurized heavy water reactor (PHWR). The piping structures consist of T joints, curved elbow joint, and straight pipes . The cyclic plastic deformation can occur during start-up and shutdown as well as variation in operating condition or during a seismic event. The cyclic loading is not restricted to continuous symmetric strain cycling. It may be symmetric/asymmetric, stress-/strain-controlled, uniaxial/multiaxial, or continuous/stepped/random . One such strain-controlled cyclic plastic excursion is generally termed as low cycle fatigue (LCF), while a stress-controlled asymmetric cyclic loading is termed as ratcheting. Ratcheting leads to permanent accumulation of plastic strain and consequence to early damage to the material. To overcome these problems, knowledge of the resistance of materials to damage accumulation and failure under symmetric and asymmetric type fatigue loading is important for the efficient design of piping material.
Several investigations have been carried out on SA333 Gr-6 steel to understand the deformation behavior. LCF studies were carried out by Samuel et al.  and Siva et al.  at elevated temperatures and at ambient temperature respectively. Hong et al.  and Huang et al.  describe the metallurgical aspects of dynamic strain aging (DSA) in C-Mn steel. These deformation studies are important to understand the fatigue behavior of C-Mn steel. The ratcheting tests on SA333 Gr-6 steel have been studied by various authors [2, 7, 8] at ambient temperature. There is limited literature on ratcheting and LCF of SA333 Gr-6 steel at elevated temperatures.
In this article, an experimental analysis of LCF and ratcheting behavior of the material SA333 Gr-6 steel has been carried out at a temperature of 300[degrees]C, which is the common working temperature of this material. In LCF experiments, various aspects of analysis like cyclic stress response curve, hardening behavior, and Masing and non-Masing characteristic were carried out, whereas ratcheting behavior of the material has been described in terms of ratcheting strain accumulation response curve, hysteresis loop area, ratcheting strain rate, and plastic strain amplitude with a variation of mean stress and stress amplitudes. These all are the important aspects to understand the deformation behavior of the material.
2. Materials and Methods
The raw material for this investigation was SA333 Gr-6 C-Mn steel cylindrical pipe with an outer diameter of 320 mm and a wall thickness of 55 mm. The chemical composition
(in wt. %) of the investigated material is as follows: C 0.18%, Mn 0.9%, Si 0.02%, P 0.02%, and balance Fe. The as-received microstructure of the material consists of ferrite-pearlite banded structure, shown in Figure 1. The width of ferrite and pearlite band was 19 um and 15 um, respectively. LCF specimens were fabricated from the pipe stock along the longitudinal axis. The specimen having a gauge diameter of 8 mm and a gauge length of 15 mm was selected for various studies and is shown in Figure 2. The tensile tests were carried out at room temperature (RT) and 300[degrees]C at a strain rate of 1 x [10-.sup.3] [s.sup.-1]. Each test was repeated using two samples and results are listed in Table 1.
LCF tests were conducted at strain amplitudes (i.e., half of total strain ranges) of [+ or -]0.35% to [+ or -]1.25% at 300[degrees]C temperature. A constant strain rate of 1 x [10-.sup.3] [s.sup.-1] was maintained for all the tests and frequencies were varied accordingly.
Asymmetric stress-controlled ratcheting tests have been carried out at 300[degrees]C with various combination of mean stress and stress amplitude. For a fixed stress amplitude of 400 MPa, mean stress varies between 0 and 75 MPa, and for the fixed mean stress of 100 MPa, stress amplitude varies between 300 and 400 MPa. For ratcheting tests, 115 MPa [s.sup.-1] stress rate was maintained.
The triangular waveform was employed for both the tests on 100 kN closed-loop servo electric universal testing machine (Instron 8862). An extensometer of 12.5 mm gauge length with 20% and 100% travel was employed for LCF and ratcheting tests, respectively. A three-zone-resistant heating furnace with temperature controller was used to maintain the test temperature. To measure the temperature of the specimen, an R-type thermocouple was employed and the test temperature was maintained within [+ or -]3[degrees]C. LCF tests were stopped after a 20% decrease in maximum load, whereas ratcheting tests were continued till failure of the specimen. All tests data were saved to the computer by the data acquisition system and its storage is in Excel and DAT file. In each cycle, 200 data points were recorded.
5. Results and Discussion
3.1. Strain-Controlled Low Cycle Fatigue Behavior
3.1.1. Cyclic Stress Response Curve Figure 3 shows the cyclic stress response curves of SA333 Gr-6 steel obtained from LCF tests at various strain amplitudes ranging from [+ or -]0.35% to [+ or -]1.25%. Cyclic stress response curve represents the cyclic hardening and softening characteristic of the material during symmetric strain cycling. From Figure 3 it can be seen that the material displays cyclic hardening throughout its fatigue life at all the strain amplitudes, but the rate of cyclic hardening alters with strain amplitude. The peak stress increases with an increase in strain amplitude. It may be noted that the saturated state of hardening was not exhibited at any of the strain amplitude. The hardening of the material is due to the interaction of mobile dislocations with the solute atoms (carbon and nitrogen) [9, 10] is termed DSA phenomena. Samuel et al.  reveal that 300[degrees]C temperature is a DSA regime for this material. Similar stress response curves have been reported by Paul et al.  and Siva et al.  at ambient temperature; however, the extent of hardening at 300[degrees]C is found greater.
The degree of hardening (DOH) is defined as the difference between the first cycle stress and peak stress which is represented as follows:
DOH = ([[sigma].sub.p] - [[sigma].sub.i])/[[sigma].sub.i] Eq. (1)
where [[sigma].sub.p] and [[sigma].sub.i] represent the peak stress and initial stress amplitudes, respectively, for given strain amplitude. Figure 4 shows the DOH versus strain amplitude. It can be observed that the DOH increases up to [+ or -]0.75% strain amplitude after that decreasing trend was observed. The hardening-softening behavior is governed by dislocation generation and temperature effect. The initial hardening of material is depending upon the generation of dislocations and their mutual interaction within self and secondary hardening is due to DSA effect . In DSA phenomena, interaction of dislocation with solute atoms during deformation leads to an increase in stress required for dislocation movement due to obstruction made by solute atoms [9, 10].
3.1.2. Fatigue Life Study The life of the material decreases with the increase of strain amplitude. The material at elevated temperature shows lower fatigue life in comparison to ambient temperature . The usual way of representing LCF life is to plot the variation of plastic strain amplitude, ([A[epsilon].sub.p]/2) versus a number of reversals to failure, (2Nf). The strain-life relationship is derived from the relationship proposed by Basquin  and Coffin and Manson [12, 13]. The strain-life relationship is presented as follows:
[mathematical expression not reproducible] Eq. (2)
where ([[DELTA][[epsilon].sub.t]/2) is the total strain amplitude, ([[DELTA][[epsilon].sub.e]/2) is the elastic strain amplitude, [[epsilon].sub.f] is the fatigue ductility coefficient, c is the fatigue ductility exponent, [sigma]f is the fatigue strength coefficient, b is the fatigue strength exponent, and E is the modulus of elasticity. Figure 5 shows the Coffin-Manson plot for 300[degrees]C LCF test. In strain-life plot curve, plastic strain amplitude versus a number of reversals to failure represents the Coffin-Manson plot. The values of different parameter evaluated from Equation 2 are listed in Table 2.
The slope of Coffin-Manson plot signifies the fatigue ductility exponent c which shows more negative value at 300[degrees]C in comparison to the c value obtained by Samuel et al.  at RT. The reduction in life at a higher temperature and negative increase in c value has been attributed to the effect of increase in inelastic deformation in a cycle, creep damage, and oxidation . The more negative value of c obtained with increasing temperature correlates well with the influence of DSA .
3.1.3. Hysteresis Loop Analysis In this study saturated stress-strain hysteresis loops for different strain amplitudes with common compressive tips of LCF tested at 300[degrees]C are plotted in Figure 6. It shows that the loading path of the saturated (taken at half-life) hysteresis loops follows the common loading curve at strain amplitudes [+ or -]0.35% and [+ or -]0.5% representing the Masing behavior of the material, which is shown in Figure 6. Other strain amplitude curves do not follow the common path. Overall it can be concluded that SA333 Gr-6 steel exhibits non-Masing behavior. Paul et al.  and Siva et al.  show the non-Masing behavior of this material at RT. The material shows non-Masing characteristic at other cycles also. However, the shape and size of the loops may vary with the number of cycles. Non-Masing behavior has also been reported by Siva et al.  for the various design of specimens like axial hollow and shear hollow.
The cyclic stress-strain curves of a material showing Masing or non-Masing behavior depend on its microstructure and the loading conditions. If material shows Masing behavior, then it implies that deformation structure remains the same irrespective of the strain amplitudes or in terms of mobility of dislocations . However, Masing behavior is not a universal phenomenon in engineering materials. Plumtree et al.  have shown that some materials show Masing behavior, while others do not. Maier et al.  observed Masing behavior in ultrafine-grained copper. Fan and Jiang  noted Masing behavior in pressure vessel steel at 300[degrees]C and 420[degrees]C.
In order to quantify the deviation from Masing behavior, all the hysteresis loops represented in Figure 6 shifted to common linear elastic portion in such a way that loading portion of all the hysteresis loops forms a common envelope curve. This plot is shown in Figure 7. The common curve is known as a master curve which has been indicated in Figure 7. The deviation from Masing is the measure of the difference [delta][[sigma].sub.0] between the smallest strain amplitude loop and the succeeding higher strain amplitude loops on the translated axis. The deviation from Masing behavior can be measured from Figure 7 and the same is plotted in Figure 8. It can be seen that with the increase of strain amplitude, deviation ([delta][[sigma].sub.0]) from Masing behavior increases. It is observed that the magnitude of [delta][[sigma].sub.0] is considerably higher at strain amplitudes [+ or -]1.0% and [+ or -]1.25%. The magnitude of deviation ([delta][[sigma].sub.0]) also signifies the expansion in proportional limit with respect to the inner most hysteresis loop. Therefore, we can say that non-Masing behavior is the manifestation of a change in the proportional limit. The proportional limit for this material is nothing but the linear region of the loading curve of the hysteresis loop.
The cyclic hardening or softening behavior can be characterized by comparing the cyclic stress-strain curve and tensile stress-strain curve. The cyclic stress-strain curve can be determined by the following equation:
[mathematical expression not reproducible] E q. (3)
where [[sigma].sub.a] is the stress amplitude at half-life, [[epsilon].sub.a] is the strain amplitude, E is the modulus of elasticity, K' is the cyclic strain hardening coefficient, and n' is the hardening exponent. For SA333 Gr-6 steel, the constant values are calculated as K' = 756 and n' = 0.083. Now put these values in Equation 3 to get [[epsilon].sub.a] and then plot cyclic stress-strain curves matching the peaks of stable hysteresis loops. The same is shown in Figure 9. It can be seen that the cyclic stress-strain curve lies above the tensile monotonic curve signifies the cyclic hardening characteristic of the material.
3.2. Stress-Controlled Ratcheting Behavior
3.2.1. Influence of Mean Stress ([[sigma].sub.m]) and Stress Amplitude ([[sigma].sub.a]) on Ratcheting Behavior The influence of [[sigma].sub.m] and [[sigma].sub.a] on ratcheting behavior of SA333 Gr-6 C-Mn steel has been studied at 300[degrees]C. The initial ten cycles of stress-strain loops at different mean stress and stress amplitude show the shifting of the hysteresis loop along the strain axis with an increase in [[sigma].sub.m] and [[sigma].sub.a] shown in Figure 10. The movement of the hysteresis loop along the strain axis represents the quantity of strain accumulation. Larger the opening of hysteresis loop, greater will be the strain. It can be seen that at mean stress of 0 MPa and 400 MPa stress amplitude the stress-strain loop remains constant in one place means there was no increment in strain.
Figure 11 represents the ratcheting response curves at a various combination of [[sigma].sub.m] and [[sigma].sub.a]. It was observed that initial ratcheting strain increases with an increase in mean stress or stress amplitude. Initially ratcheting strain curves were stable up to a few cycles after that there was a slow increase in strain accumulation and, finally, a rapid increment was observed until the failure of the material. Some ratcheting strain curves remain constant until the termination of tests at the other load conditions. For fixed [[sigma].sub.a], with an increase in [[sigma].sub.m], [[sigma].sub.max] increases which lead to increase in ratcheting strain accumulation ([[epsilon].sub.r]). Ratcheting strain accumulation can be calculated as the average of maximum strain and minimum strain of that particular loop.
Figure 11 also shows that ratcheting fatigue life decreases with an increase in [[sigma].sub.m] and [[sigma].sub.a], whereas ratcheting strain accumulation increases. The decrease in life with increasing [[sigma].sub.m] and [[sigma].sub.a] can be explained in terms of increase in plastic strain amplitude as well as the hysteresis loop area given in Table 3. The results reported for carbon steel 1026 , Stainless Steel SS304 [19, 20], and SA333 Gr-6 C-Mn steel  under engineering stress-controlled show similar behavior, whereas Sarkar et al.  for 316LN stainless steel under engineering stress-controlled, Paul et al.  for Stainless Steel SS304, and Paul et al. [2, 23] for SA333 Gr-6 steel under true stress-controlled have shown an increase in ratcheting life with an increase in [[sigma].sub.m]. Paul et al.  have shown a decrease in life even when plastic strain amplitude decreases. In the present investigation, the decrease in ratcheting life is associated with the increase in plastic strain amplitude.
Resistance to ratcheting strain accumulation due to DSA is a consequence of locking-unlocking of mobile dislocations by solute atoms like carbon and nitrogen [9, 10]. At 300 and 350 MPa stress amplitudes with the mean stress of 100 MPa, it was observed that no strain get accumulated after the first cycle. Due to non-ratcheting of the material at 100 MPa [[sigma].sub.m] and 300 MPa [[sigma].sub.a], the test was stopped. Sarkar et al.  have been reported a similar response for material 316LN SS at 550[degrees]C; this may be due to an elastic shake down as the locking of mobile dislocation by the solute atoms (carbon or nitrogen) associated with DSA, which was highly prominent in this load combination. It was also observed that in this load combination plastic strain amplitude reduces almost to zero. The observation of the fracture surface reveals that fracture mode was transgranular with secondary cracks at 100 MPa mean stress and 350 MPa stress amplitude. Figure 11 also indicates that lowest ratcheting life was observed at a mean stress of 100 MPa and 400 MPa stress amplitude, because of rapid strain accumulation in the material as [[sigma].sub.max] was near about ultimate tensile strength (UTS) of the material 512 MPa. The failure of the material was ductile in nature. The results of ratcheting tests at 300[degrees]C are shown in Table 3.
3.2.2. Ratcheting Strain Rate with Mean Stress and Stress Amplitude The ratcheting strain rate response curve represents the hardening-softening characteristic of the material. If ratcheting rate increases or decreases, then this signifies the softening and hardening behavior of the material, respectively. The ratcheting rate can be defined as the difference in ratcheting strain between two consecutive cycles [8, 21]. Figure 12 shows the three regimes in ratcheting rate curve. In regime I, the ratcheting rate decreases gradually with number of cycle (N): termed as primary ratcheting. In regime II, ratcheting rate remains constant: known as secondary ratcheting. While in regime III, ratcheting rate increases rapidly with the increase in number of cycles, called tertiary ratcheting, and results in large ratcheting strain in limited cycles . The ratcheting rate curve is similar to conventional creep curve, but the deformation mechanism is different. The ratcheting is governed by the movement of dislocations, their interaction and cell formation , whereas creep is related to dislocation glide, diffusion, and grain boundary sliding [8, 26].
The ratcheting strain rate versus a number of cycle curves with the variation of mean stress and stress amplitude has been shown in Figure 13 (a) and 13 (b), respectively.
It can be seen that in the initial cycles, ratcheting rate increases with the increase of mean stress and stress amplitude. The decrease in ratcheting rate with a number of cycles signifies the cyclically hardening characteristic of the material. The ratcheting rate at half-life shows an increasing trend with the increase of mean stress and stress amplitude. However, the ratcheting rate remains constant (almost zero) throughout the ratcheting life at the fixed mean stress of 100 MPa, at 300 and 350 MPa stress amplitude, shown in Figure 13 (b). The lower ratcheting rate may be due to pronounced hardening induced by DSA which lead to very slow ratcheting strain accumulation. Here, no strain burst was observed on ratcheting strain rate curves. Sarkar et al.  have shown the strain burst phenomena indicating the release of dislocations from the solute atoms.
From the above mentioned experimental analysis, the following conclusions are derived from strain-controlled LCF and stress-controlled ratcheting behavior of SA333 Gr-6 C-Mn steel at 300[degrees]C.
* The material shows cyclic hardening throughout its fatigue life at all the strain amplitudes. The initial and half-life stress amplitudes increases with an increase in strain amplitude. The extent of cyclic hardening at elevated temperature (300[degrees]C) is found greater than that of the ambient temperature.
* The plastic strain-life plot signifies that fatigue life of the material decreases with an increase in plastic strain amplitude. Higher the plastic strain amplitude, lower is the fatigue life.
* The DSA phenomena lead to the hardening of the material. The DOH increases with an increase in strain amplitude up to [+ or -]0.75%. Further decreases due to early damage of the material because of the greater plastic strain amplitude.
* The material shows non-Masing behavior and deviation ([delta][[sigma].sub.o]) from Masing behavior increase with the increase in strain amplitudes. However, Masing behavior was observed at lower strain amplitudes.
* Ratcheting strain accumulation increases, whereas ratcheting fatigue life decreases with an increase in mean stress or stress amplitude. Increase in plastic strain amplitude from stress amplitude 300 MPa to 400 MPa leads to early damage to the material, that is, decrease in life from 35000 to 150 cycles.
* Ratcheting strain rate increases with an increase in mean stress and stress amplitude. The decrease in ratcheting strain rate signifies the hardening characteristic of the material due to the interaction of mobile dislocation with the solute atoms.
LCF - Low cycle fatigue
DSA - Dynamic strain aging
RT - Room temperature
DOH - Degree of hardening
YS - Yield strength
UTS - Ultimate tensile strength
EI - Total elongation
RA - Reduction in area
Nf - Number of cycles
[[sigma]'.sub.f] - Fatigue strength coefficient
b - Fatigue strength exponent
[[DELTA][[epsilon].sub.t]/2 - Total strain amplitude
[[DELTA][[epsilon].sub.e]/2 - Elastic strain amplitude
[[DELTA][[epsilon].sub.p]/2 - Plastic strain amplitude
[[epsilon].sub.f] - Fatigue ductility coefficient
c - Fatigue ductility exponent
[[sigma].sub.i] - Initial stress amplitude
[[sigma].sub.p] - Peak stress amplitude
[[epsilon].sub.a] - Strain amplitude
E - Modulus of elasticity
K' - Cyclic strain hardening coefficient
n' - Hardening exponent
[delta][[sigma].sub.o] - Deviation from Masing behavior
[[sigma].sub.m] - Mean stress
[[sigma].sub.a] - Stress amplitude
[[sigma].sub.max] - Maximum stress
[[epsilon].sub.r] - Ratcheting strain
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Girendra Kumar and Ashok Kumar, National Institute of Technology Jamshedpur, India
H.N. Bar, National Metallurgical Laboratory, Jamshedpur, India
[C] 2019 SAE International. All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without the prior written permission of SAE International.
Positions and opinions advanced in this work are those of the author(s) and not necessarily those of SAE International. Responsibility for the content of the work lies solely with the author(s).
Received: 17 Sep 2018
Revised: 26 Nov 2018
Accepted: 07 Jan 2019
e-Available: 23 Jan 2019
Ratcheting, Low cycle fatigue, Cyclic hardening, Ratcheting rate, Dynamic strain aging (DSA)
Kumar, G., Kumar, A., and Bar, H., "Low Cycle Fatigue and Ratcheting Behavior of SA333 Gr-6 Steel at 300[degrees]C Temperature," SAE Int. J.
TABLE 1 Mechanical properties of SA333 Gr-6 C-Mn steel at RT and 300[degrees]C temperature. Temp. YS, MPa UTS, MPa % EI % RA RT 324.8 523.2 53.5 72.09 300[degrees]C 230.9 512.3 48.6 68.6 [C] 2019 SAE International. All Rights Reserved TABLE 2 Low cycle fatigue parameters of SA333 Gr-6 steel at 300[degrees]C. MPa b % c 704.2 -0.056 0.456 -0.675 [C] 2019 SAE International. All Rights Reserved TABLE 3 Ratcheting test result at 300[degrees]C for different [[sigma].sub.m] and [[sigma].sub.a] combinations. Plastic [[sigma].sub.a] [sigma]m Number of Ratcheting strain at (MPa) (MPa) cycles (Nf) strain (%) half-life (%) 400 0 7000 (Test 0.5 0.069 stopped) 400 50 1795 20.7 0.186 400 75 950 40.5 0.201 300 100 35000 1.49 0.0023 (Test stopped) 350 100 7386 4.39 0.022 400 100 150 19.6 0.145 Loop area [[sigma].sub.a] at half-life (MPa) (MJ/[m.sup.3]) 400 1.521 400 4.207 400 4.56 300 0.743 350 0.937 400 2.88
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|Author:||Kumar, Girendra; Kumar, Ashok; Bar, H .N.|
|Publication:||SAE International Journal of Materials and Manufacturing|
|Article Type:||Technical report|
|Date:||Mar 1, 2019|
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