AbstractLow cycle fatigue tests were carried out on 316 L(N) stainless steel at room temperature employing strain amplitudes ranging from ± 0.3 to ±1.0% and a strain rate of 3×10−3s−1. The material showed initial hardening for a few cycles followed by prolonged softening, saturation and final failure. The fatigue life was found to decrease with increase in strain amplitude. The analysis of stable hysteresis loops showed non-Masing behaviour for this material. The elasto-plastic response of the material under cyclic loading was characterized taking into account isotropic and kinematic hardening occurring during cycling. The material parameters were obtained from the experimental hysteresis loops and cyclic stress response of the material. Finite element analysis of elasto-plastic deformation was carried out to obtain the stabilized hysteresis loop and cyclic stress response of the material. The predicted hysteresis loops showed good agreement with experimental results. The low cycle fatigue life prediction was carried out based on plastic strain energy dissipation with cycling

Goyal, Sunil

Ray, S.K.

Roy, Samir Chandra

Sandhya, R.

Elsevier - Publisher Connector 

 Procedia Engineering  55 ( 2013 )  165 – 170 
1877-7058 © 2013 The Authors. Published by Elsevier Ltd.
Selection and peer-review under responsibility of the Indira Gandhi Centre for Atomic Research.
doi: 10.1016/j.proeng.2013.03.237 
6th International Conference on Cree
Analysis of Hysteresis Loo
Low Cycle Fati
Samir Chandra Roya, Su
aMetallurgical and Material Engin
bIndira Gandhi Centre for 
Abstract 
Low cycle fatigue tests were carried out on 316 L
ranging from ± 0.3 to ±1.0 % and a strain rate of 3×1
by prolonged softening, saturation and final failure. T
The analysis of stable hysteresis loops showed non-M
material under cyclic loading was characterized tak
cycling. The material parameters were obtained from
material. Finite element analysis of elasto-plastic de
cyclic stress response of the material. The predicted h
low cycle fatigue life prediction was carried out based
 
© 2013 The Authors. Published by Elsevier Ltd
Gandhi Centre for Atomic Research. 
 
Keywords: Low cycle fatigue; non-Masing behavior; isotrop
1. Introduction 
In liquid metal cooled fast breeder reactors
cyclic thermal stresses as a result of temperatu
during transients. Therefore, low cycle fatigu
significant consideration in the design and life a
Masing or non-Masing behavior under fatigue
conditions. For materials showing Masing beha
coincide with the cyclic stress-strain curve ma
behavior, coincidence occurs only when the sa
slope to match the loading branches [3-7]. 
 
 
∗
 Corresponding Author:  
 E-mail address: goyal@igcar.gov.in 
p, Fatigue and Creep-Fatigue Interaction [CF-6
 
ps of 316L(N) Stainless Steel und
gue Loading Conditions 
nil Goyalb∗, R. Sandhyab, S. K. Raya 
eering, Jadavpur University, Kolkata- 700 032, India 
Atomic Research, Kalpakkam- 603 102, India 
(N) stainless steel at room temperature employing strain amp
0-3s-1. The material showed initial hardening for a few cycles fo
he fatigue life was found to decrease with increase in strain am
asing behaviour for this material. The elasto-plastic response
ing into account isotropic and kinematic hardening occurring
 the experimental hysteresis loops and cyclic stress response
formation was carried out to obtain the stabilized hysteresis lo
ysteresis loops showed good agreement with experimental resu
 on plastic strain energy dissipation with cycling. 
. Selection and/or peer-review under responsibility of the 
ic hardening; kinematic hardening; plastic strain energy dissipation. 
 (LMFBRs), the components are often subjected to re
re gradients which occur during start-ups and shut-dow
e (LCF) represents a predominant failure mode, req
nalysis of LMFBR components [1, 2]. The material may e
 loading depending on the microstructure and experi
vior, the matching of compressive tips of the hysteresis
gnified by two. Whereas, for materials that show non-M
turated hysteresis loops are translated along the linear 
] 
er 
litudes 
llowed 
plitude. 
 of the 
 during 
 of the 
op and 
lts. The 
Indira 
peated 
ns or 
uiring 
xhibit 
mental 
 loops 
asing 
elastic 
Available online at www.sciencedirect.com
 2013 The Authors. Published by Elsevier Ltd.
Selection and peer-review under responsibility of the Indira Gandhi Centre for Atomic Research.
Open access under CC BY-NC-ND license. 
Open access under CC BY-NC-ND license. 
166   Samir Chandra Roy et al. /  Procedia Engineering  55 ( 2013 )  165 – 170 
For accurate LCF life prediction using hysteresis loop energy, it is very important to predict the hysteresis 
loop accurately. The prediction of hysteresis loop depends on the hardening models that characterize the 
hysteresis loop. Among the various hardening models available in literature [8] the most widely used are 
Armstrong and Frederick for non-linear kinematic hardening. In the present investigation, the analysis of 
hysteresis loop energy is used for the low cycle fatigue life prediction. The saturated hysteresis loops obtained 
from experiments are compared with the hysteresis loops predicted with finite element analysis by 
incorporating the combined kinematic and isotropic hardening. The low cycle fatigue life is predicted based on 
non-Masing analysis of stabilized hysteresis loops obtained at various strain amplitudes in experiments. 
2. Experimental 
316L(N) SS material used in the present study has the following chemical composition (in wt.%): C: 0.027, 
Mn: 1.7, Ni: 12.2, Cr: 17.53, Mo: 2.49, N: 0.07, Si: 0.22, S: 0.0055, P: 0.013, Fe: balance. The material was 
subjected to a solution annealing treatment at 1373 K for 1 h followed by water quenching. LCF experiments 
were carried out on  cylindrical specimens of gauge length 25 mm and diameter 10 mm employing a constant 
strain rate of 3×10−3 s−1 at different strain amplitudes (± 0.30 % to ± 1.0 %) at room temperature. All the tests 
were carried out in air under fully reversed, total axial strain control mode employing a symmetrical triangular 
strain-time waveform using DARTEC servo hydraulic fatigue testing system. 
3. Computations 
Finite element analysis (FEA) of low cycle fatigue behavior was carried out using ABAQUS finite element 
software. The elasto-plastic response of the material under low cycle fatigue loading was modeled using 
combined nonlinear kinematic and exponential isotropic hardening laws [9]. 
In case of nonlinear kinematic hardening, the back stress (x) is defined by the following expression: 
( )pecx γε
γ
−
−= 1   (1) 
where εp is plastic strain, Ȗ and c are the kinematic hardening material constants and Ȗ determines the rate at 
which the saturation of back stress c/Ȗ is reached. Kinematic hardening coefficients were obtained from the 
experimental tensile part of saturated hysteresis loops obtained from experiments. 
In case of isotropic hardening, the isotropic function (r(p)) is defined by the following equation,   
( ) ( )bpeQpr −−= 1   (2) 
in which p is accumulated plastic strain, b and Q are material constants and b determines the rate at which r(p) 
reaches saturation (Q). Isotropic hardening coefficients were obtained from the stress-strain hysteresis loop of 
experimental data. 
4. Results and discussions 
4.1. Cyclic stress response 
The dependency of peak tensile stress on number of cycles and strain amplitude is depicted in Fig. 1. The 
material showed initial hardening followed by gradual prolonged softening, saturation and final failure.  
The cyclic stress-strain curve and the variation of low cycle fatigue life with total, elastic and plastic strain 
amplitudes is represented by the following relationship respectively: 
167 Samir Chandra Roy et al. /  Procedia Engineering  55 ( 2013 )  165 – 170 
( )npK ′Δ′=Δ 22/ εσ   (3) 
 
( ) ( )cffbfft NNE 222 ε
σε
′+
′
=
Δ
    (4) 
Where Δσ, Δεp, Δεt, Nf, E, K′, n′ , σf′, b, εf′, c are stress range, strain range, total strain range, no of cycle to 
failure, Young’s modulus, cyclic strength coefficient, cyclic strain hardening exponent, fatigue strength 
coefficient, fatigue strength exponent,  fatigue ductility coefficient and fatigue ductility exponent respectively. 
LCF parameters obtained from experimental data are shown in Table 1. 
 
 
Fig. 1. Cyclic stress response curve of 316 L(N) SS. 
Table. 1. Values of coefficients of strain-life relation for 316 L(N) SS 
 
Cyclic stress strain curve coefficients Basquin relation coefficients Coffin-Manson relation coefficients 
K′ n′ σf′ b εf′ c 
2854 MPa 0.378 1444 MPa -0.159 0.294 -0.494 
4.2. Comparison of cyclic behaviour 
Combined isotropic and kinematic hardening model was employed in cyclic elasto-plastic finite element 
analysis to predict the hysteresis loop and cyclic stress response of the material, Table 2.  
Table. 2. Elastic and hardening properties of 316 L(N) 
Young’s 
Modulus Yield stress Kinematic hardening parameters Isotropic hardening parameters 
E: 200 GPa ı0: 211 MPa C: 57805 MPa γ : 619.04 Q: 42.30 MPa b: 21.60 
 
The coefficients were obtained from the experimental hysteresis loops at a total strain amplitude ± 0.5 % and 
were incorporated in the material model defined in FEA. Fig. 2 and Fig. 3 show the comparison of the 
simulated hysteresis loop obtained from ABAQUS and experimental for ± 0.4 % and ± 0.5 % strain amplitudes 
respectively. The results showed good agreement between the numerical simulation and the experimental 
results. However, at higher strain amplitudes the extent of hardening was lower in simulated first cycle. 
168   Samir Chandra Roy et al. /  Procedia Engineering  55 ( 2013 )  165 – 170 
 
Fig. 2. Comparison of first cycle hysteresis loop obtained from 
experiment and simulation, ± 0.4 % strain amplitude 
Fig. 3. Comparison of first cycle hysteresis loop obtained from 
experiment and simulation, ± 0.5 % strain amplitude. 
Initial few cycles were predicted by finite element analysis. Fig. 4 and Fig. 5 show the comparison of the 
tensile stress amplitude with number of cycles for experiments and simulation at strain amplitudes of ± 0.4 % 
and ± 0.5 % respectively.  
 
 
Fig. 4. Comparison of cyclic stress response from experiment 
and simulation, ± 0.4% strain amplitude. 
Fig. 5. Comparison of cyclic stress response from experiment and 
simulation, ± 0.5% strain amplitude. 
Good correlation was obtained between the responses simulated using the determined parameters and the 
experimental observations. However, higher cyclic stress response obtained from experiments than by 
simulation could be due to non-Masing behavior exhibited by the material above ±0.5% strain amplitude. 
4.3. Hysteresis loop analysis and fatigue life prediction 
The cyclic stress response showed the saturation after few cycles as shown in the Fig. 1. Saturated hysteresis 
loops with common compressive tips for various strain amplitudes are plotted in Fig. 6.  
The figure shows that loading part of the saturated hysteresis loops follow the common loading curve, 
representing the Masing behavior [3] at low strain amplitudes (± 0.3 % to ± 0.5 %). At higher strain amplitudes 
(± 0.6 % to ± 1.0 %), saturated hysteresis loops do not follow the common loading curve and depicts the non-
Masing behavior [4]. Detailed microstructural investigation of 304LN SS carried out by Sivaprasad et al. 
showed that the non-Masing in the material was due to the phase instability and transient dislocation 
substructure [6].  
169 Samir Chandra Roy et al. /  Procedia Engineering  55 ( 2013 )  165 – 170 
In order to determine the total plastic strain energy dissipated till failure, accurate measurement of hysteresis 
loops and cyclic properties of the material is essential. To calculate the hysteresis loop area, a Master curve is 
generated for stable hysteresis loops at different strain amplitudes. The Master curve is obtained by matching 
the loading branches of stable hysteresis loops of different strain amplitudes and by translating each loop along 
the linear elastic portions as shown in Fig. 7. 
 
Fig. 6. Stable hysteresis loops common compressive tips.  Fig. 7. Construction of Master curve for non-Masing analysis. 
The total strain energy released during fatigue (WT) is calculated by multiplication of no of cycles to failure 
(Nf) and area under the stable hysteresis loop (¨W), Eq. (5) [3, 6]. 
fT NWW .Δ=   (5)  
pp
n
n
n
nW εδσεσ Δ¹¸
·
©¨
§
+
+ΔΔ¹¸
·
©¨
§
+
−
=Δ .
1
2
.
1
1
0   (6) 
where n is the strain hardening exponent of Master curve, δı0 is the change in proportional limit of stable loops 
for different strain amplitude. 
In case of Masing behaviour the second term of Eq. (6) is to be omitted and n was found to be different for 
Masing and non-Masing behavior. Parameter n obtained from the Master curve was found to be 0.152. The 
predicted fatigue life shows good agreement with the experimental fatigue lives, as shown in Fig. 8. 
 
 
Fig. 8. LCF life prediction based on plastic strain energy dissipation by non-Masing analysis. 
170   Samir Chandra Roy et al. /  Procedia Engineering  55 ( 2013 )  165 – 170 
5. Conclusions 
• Cyclic stress response of the material was characterized by initial hardening followed by prolonged 
softening, saturation and final failure. 
• The material showed Masing behavior at low strain amplitudes and non-Masing behavior at higher strain 
amplitudes.  
• Predicted first cycle hysteresis loops from simulation showed good correlation with the experimental results 
and fatigue life predicted by non-Masing analysis was found to be close to the actual fatigue life. 
Acknowledgement 
The authors are grateful to Shri S. C. Chetal, Director, IGCAR and Dr. T. Jayakumar, Director, Metallurgy and 
Materials Group, IGCAR for their constant encouragement and support. The authors are also thankful to Dr. A. 
K. Bhaduri, AD, MDTG and Dr. M. D. Mathew, Head, MMD for their keen interest in this work. Help 
rendered by Mr. K. Mariappan during the course of experimental work is greatly acknowledged. 
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[6]  S.Sivaprasad, S.K.Paul, A.Das, N.Narasiah, S.Tarafder, Cyclic plastic behaviour of primary heat transport piping materials: Influence 
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[7]  L.P.Borrego, L.M.Abreu, J.M.Costa and J.M.Ferreira. Analysis of low cycle fatigue in AlMgSi aluminium alloys. Anales De Mecánica 
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Analysis of Hysteresis Loops of 316L(N) Stainless Steel under Low Cycle Fatigue Loading Conditions 

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Analysis of Hysteresis Loops of 316L(N) Stainless Steel under Low Cycle Fatigue Loading Conditions

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