20320140503029

International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308 (Print),
ISSN 0976 – 6316(Online) Volume 5, Issue 3, March (2014), pp. 252-260 © IAEME
252
FATIGUE LIFE ESTIMATION OF TYPE 304LN STAINLESS STEEL UNDER
STRAIN-CONTROLLED CYCLIC LOADING
S. Lincy Rubina1
, S. Vishnuvardhan2*
, G. Raghava3
, A. Sivakumar4
1
M. Tech. Student, VIT University, Vellore
2
Scientist, CSIR - Structural Engineering Research Centre, Chennai
3
Chief Scientist, CSIR - Structural Engineering Research Centre, Chennai
4
Professor, Structural Engineering Division, VIT University, Vellore
ABSTRACT
Evaluation of fatigue parameters and life of materials under cyclic strain-controlled loading
becomes important in understanding and life prediction of components and structures subjected to
large amplitude cyclic loading. Four-point correlation method, modified four-point correlation
method, universal slopes method, modified universal slopes method, uniform material law, hardness
method, median’s method and methods proposed by Mitchell et al. and Basan et al. are some of the
existing methods for strain-life fatigue prediction using monotonic tensile material properties and
hardness of the material. In the present studies, fatigue life of Type 304LN stainless steel under
strain-controlled cyclic loading has been estimated using the above methods. The results of the
studies are compared with the available results of strain-controlled constant amplitude fatigue tests
carried out earlier on Type 304LN stainless steel under six different strain amplitude values, viz,
0.20%, 0.35%, 0.50%, 0.65%, 0.80% and 0.95%. It is observed that the above methods generally
over-estimate the strain-life fatigue of the material for all strain amplitude values except the median’s
method for strain amplitude of 0.80%. Hence, relying on these methods would be unconservative.
Median’s method is found to estimate the strain-life fatigue of the material with a better accuracy.
Basan’s method, modified universal slopes method and uniform material law are found to predict
with a reasonable accuracy. Salient features of the above estimation methods including the suitability
of the methods for predicting strain-life fatigue of Type 304LN stainless steel are discussed in this
paper.
1. INTRODUCTION
Studies under strain-controlled cyclic loading are very useful in the design of components
that undergo either mechanically or thermally induced cyclic plastic strains wherein failure may
INTERNATIONAL JOURNAL OF CIVIL ENGINEERING
AND TECHNOLOGY (IJCIET)
ISSN 0976 – 6308 (Print)
ISSN 0976 – 6316(Online)
Volume 5, Issue 3, March (2014), pp. 252-260
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253
occur within relatively a few cycles, approximately less than 105
cycles, due to ‘low cycle fatigue’.
Earthquake type cyclic loading is one example which may induce stress reversals of amplitude
exceeding the elastic limit of the material leading to low cycle fatigue damage in structures.
Evaluation of fatigue parameters and life of materials under cyclic strain-controlled loading becomes
important in understanding and life prediction of components and structures subjected to large
amplitude cyclic loading. Fatigue properties of materials are characterized by the curves of strain
amplitude versus number of load reversals, obtained from strain-controlled fatigue testing of smooth
specimens. The total strain range (∆ε) is defined as the summation of elastic strain range (∆εe) and
plastic strain range (∆εp). The total strain amplitude (∆ε/2) can be expressed as:
(1)
Where, ∆εe/2 is the elastic strain amplitude, ∆εp/2 is the plastic strain amplitude. The elastic strain
amplitude can be obtained using Basquin’s law as:
(2)
Where, 2Nf is the number of reversals to failure; σf
’
is the fatigue strength coefficient and is the true
stress required to cause failure in one reversal. σf
’
is obtained as the intercept of log (∆σ/2) versus log
(2Nf) at 2Nf =1. b is the fatigue strength exponent and is the value to which the reversal must be
raised proportionate to the true stress amplitude. b is taken as the slope of the log (∆σ/2) versus log
(2Nf) plot.
The plastic strain amplitude can be obtained using Coffin-Manson’s law as:
(3)
Where, εf
’
is the fatigue ductility coefficient and is the true strain required to cause failure in one
reversal. εf
’
is obtained as the intercept of the log (∆σ/2) versus log (2Nf) plot at 2Nf =1. c is the
fatigue ductility exponent and is the value to which the number of reversals of failure must be raised
proportionate to true plastic strain amplitude.
In the present studies, fatigue life of Type 304LN stainless steel used in primary heat
transport system piping of nuclear power plants has been estimated under strain-controlled cyclic
loading. The results of the studies are compared with the available results of strain-controlled
constant amplitude fatigue tests carried out earlier on Type 304LN SS under six different strain
amplitude values, viz, 0.20%, 0.35%, 0.50%, 0.65%, 0.80% and 0.95%.
2. FATIGUE LIFE ESTIMATION METHODS
Fatigue testing requires a lot of time and effort, there have been many attempts to predict
strain-life fatigue of materials using the monotonic tensile material properties and hardness of the
material. Based on experimental results, Manson [1] first proposed two estimation methods: four-
point correlation method defined through estimates of elastic and plastic strain ranges and universal
slopes method in which the exponents b and c values are assumed to be constant for all metals for
ease of application and simplicity. Mitchell et al. [2] suggested that slope of the elastic line, b is a
function of both σf’ and σu. Ong [3] modified Manson’s four-point correlation method assuming b
and c values to be functions of both σf’ and σu. Muralidharan and Manson [4] modified the universal

254
slopes method by assigning different values to the exponents b and c and introducing σu/E to estimate
the coefficients σf’and εf’.
Baumel and Seeger [5] were the first to state the importance of grouping strain-life estimates
by alloy family and also to ignore the monotonic measure of fracture ductility. They proposed
different methods for different types of alloys in their uniform material laws. Roessle and Fatemi [6]
proposed the hardness method assuming the constant slopes as the function of Brinell hardness, HB
as σu and HB has a very good correlation for steels. Median’s method [7] was proposed by
Meggiolaro and Castro by assuming constant values for fracture strength coefficient, ductility
coefficient, fracture strength exponent and ductility exponent from a statistical evaluation of 845
different metals taking the median values of each of the four parameters. Basan et al [8] suggested
that the estimation of strain-life fatigue parameters should be made from the relationship between
chosen monotonic parameter and the strain-life relation. Salient features of these methods are
discussed below.
2.1 Original Four-point Correlation Method [1]
Total strain range is the sum of elastic and plastic strain range values. The equation in strain
amplitude form is given as:
(4)
Where, Nf is the number of cycles to failure. A, B, b, c are the coefficients whose values are to be
obtained from the points P1-P4 shown in Fig. 1.
(5)
(6)
(7)
is the strain corresponding to 104
cycles on the elastic curve and is given by:
(8)
(9)
2.2 Modified Four-point Correlation Method [3]
This method is similar to original four-point correlation method. The elastic and plastic strain
amplitudes at 104
and 106
cycles are estimated. Using these estimated strain amplitudes four points
P1'-P4' are plotted on the strain-life curve as shown in Fig. 2. The fatigue strength coefficient is

255
assumed to be equal to the true fracture stress of the material obtained by dividing the load at the
time of failure. Fatigue strength exponent is defined as the slope of the straight line joining points on
the elastic line at 106
life reversals corresponding to the ordinate equal to the elastic strain amplitude
and the second point is at one reversal with ordinate equal to true fracture stress of the material. The
fatigue ductility coefficient is taken as the logarithmic ductility. The fatigue ductility exponent is the
slope of the plastic curve between points on the plastic curve at one life reversal with ordinate equal
to logarithmic ductility and the second point is corresponding to 104
reversals.
Fig. 1: Four-point correlation by Manson Fig. 2: Modified four-point correlation by
Ong
2.3 Original Universal Slopes Method [1]
An alternative method proposed by Manson assumes that the slope of elastic (b) and plastic
(c) curves is the same for all materials, which is equal to -0.12 and -0.6 respectively. The
coefficients A and B are obtained as [ln {1/(1-RA)}]0.6
and 3.5(σu/E) by the intercept of elastic and
plastic curves at Nf=1 respectively. Representing in the widely accepted form of total strain
amplitude versus number of load reversals, the equation becomes:
(10)
2.4 Mitchell’s Method (or Socie’s Method) [2]
In this method, the fatigue parameters are evaluated using the materials monotonic properties
incorporating various approximations and assumptions. Using Basquin’s and Coffin-Manson’s laws,
the strain-life equation can be represented as:
(11)
The fatigue strength coefficient is taken as the true fracture stress of the material (σf)
corrected to the reduced area due to necking. Since the true fracture stress is not easily available, the
value is approximated to be sum of conventional ultimate tensile stress of the material and 345 MPa.
Fatigue ductility coefficient is approximated to be equal to logarithmic ductility of the material.
Fatigue strength exponent is calculated by joining a line between points corresponding to 106
cycles
in the elastic curve with ordinate 0.5σu and one reversal with ordinate equal to true fracture stress.
Fatigue ductility exponent is assumed to be equal to -0.6 for ductile materials and -0.5 for strong
materials. Therefore, the strain-life equation becomes:

256
(12)
2.5 Modified Universal Slopes Method [4]
This method was proposed to improve the original universal slopes method. This method
indicates that the tensile strength of the material also has important significance in the low cycle
fatigue behaviour of the material; hence a new term called σu/E is introduced in the coefficient of
plastic life. The modified universal slopes method for strain-life is given as:
(13)
2.6 Uniform Material Law [5]
In this method, different expressions for strain-life fatigue parameters are used for unalloyed
and low-alloyed steels and aluminium, titanium alloys. Grouping of metals was initiated in this
method. For unalloyed and low-alloy steels:
(14)
Where, ; .
2.7 Hardness Method [6]
This is a simple method proposed for estimation of strain-life, which requires hardness and
modulus of elasticity as inputs, both of which are either commonly available or easily measurable. It
was found that a relatively strong correlation was found between the transition fatigue life and
hardness.
(15)
2.8 Median’s Method [7]
This is a new estimation method which uses the medians of the individual parameters of
materials for each alloy family.
(16)
Here median values of the individual parameters of the materials in the group are taken
because median parameter is considered to be more robust especially in the case of asymmetric
distribution.
2.9 Basan’s Method [8]
This method uses Brinell hardness HB as the monotonic property from which fatigue
parameters are estimated. A total of 32 low-alloy steels having wide range of HB starting from 186
HB to 670 HB were taken for obtaining the necessary data. Using nonlinear regression analysis,
relationship between HB and log(2Nf) were established for each strain amplitude. The strain
amplitude-number of reversals relation was defined for different values of hardness, for which the
fatigue parameters were determined.

257
3. STUDIES ON TYPE 304LN STAINLESS STEEL
Fatigue life of Type 304LN stainless steel under strain-controlled cyclic loading has been
estimated using the methods discussed above based on monotonic tensile material properties and
hardness of the material. The results of the studies are compared with the available results of strain-
controlled fatigue tests carried out earlier by Bhavana Joy et al. [9] on Type 304LN stainless steel
under different strain amplitude values. The chemical composition by weight for the steel was: C,
0.03%; Mn, 1.78%; P, 0.024%; S, 0.007%; Si, 0.38%; Ni, 9.11%; Cr, 18.26%; Cu, 0.23% and the
remainder was Fe. The mechanical properties of the material were determined by carrying out
tension tests as per ASTM E 8M-04 [10]. The yield strength and ultimate tensile strength of the steel
were 315 MPa and 614 MPa, respectively. The percentage elongation was 48, the percentage
reduction in area was 80 and the Young’s modulus was 198 GPa. ASTM E 606-04 [12] was followed
in preparing the test specimens and carrying out the strain-controlled fatigue tests on Type 304LN
stainless steel. Circular specimens having uniform-gauge test section and straight sided collet-grip
end connections have been chosen for the studies. The strain-controlled tests were carried out under
constant amplitude triangular wave form loading using a ±250 kN capacity fatigue rated UTM.
Totally six specimens were tested, each at different strain amplitudes; the cyclic strain amplitude
values during the tests were ±0.20%, ±0.35%, ±0.50%, ±0.65%, ±0.80% and ±0.95%. The
corresponding number of reversals to failure (2Nf) were 117010, 11132, 5166, 2534, 1766 and 794.
4. RESULTS AND DISCUSSION
The estimation methods discussed above use either ultimate tensile strength or Brinell
hardness of the material for estimation of fatigue life. In order to evaluate the fatigue life of Type
304 LN stainless steel, ultimate tensile strength obtained from tension tests, i.e., 614 MPa and the
value of Brinell hardness of 217 for the material given in ASTM A240 [11] are used. The number of
reversals obtained for the steel using different estimation methods are given in Table 1.
Table 1: Number of reversals to failure
Strain
Amplitude
(%)
Number of reversals to failure (2Nf)
Original
four-point
correlation
method
Modified
four-point
correlation
method
Original
universal
slopes
method
Modified
universal
slopes
method
Mitchell's
method
Uniform
material
law
Hardness
method
Median's
method
Basan's
method
±0.20 189038 297676 213660 322000 906345 255492 690545 145430 203103
±0.35 35734 34072 37675 27713 101529 26532 43335 15047 17645
±0.50 14804 12759 15342 9031 37352 9337 12913 5317 6470
±0.65 8204 6892 8423 4428 19693 4783 6080 2736 3488
±0.80 5278 4419 5381 2634 12323 2932 3535 1684 2238
±0.95 3715 3125 3765 1753 8520 1995 2318 1150 1585
Figure 3 shows strain amplitude versus number of reversals curves obtained using different
estimation methods. It is observed that the estimation methods are generally non-conservative in

258
predicting the strain-life fatigue of the material for all strain amplitude values except the median’s
method for strain amplitude of 0.80%. Median’s method is found to estimate the strain-life fatigue
of the material with a better accuracy, with a deviation of less than 20%. Such accurate prediction is
possible because the method was formulated by grouping of metals based on their properties and
values for fatigue parameters are proposed based on the median value obtained for each group of
metals. Basan’s method, modified universal slopes method and uniform material law are found to
predict the strain-life fatigue with a reasonable accuracy. In Basan’s method, the fatigue parameters
are defined according to the hardness value of the material. In view of the fact that materials
distributed across a wide range of hardness were analysed and that values of 2Nf for very different
strain amplitudes ∆ε/2 were considered, prediction by Basan’s method is closer to the experimental
values.
Fig. 3: Comparison of strain amplitude versus number of reversals curves
obtained using different estimation methods
Due to the poor correlation between fatigue ductility coefficient εf' and true fracture ductility
εf, as well as εf
’
and σu /E, it is observed that the estimation of fatigue ductility coefficient εf' is
unsatisfactory in the original four-point correlation method, original universal slopes method and
modified four-point correlation method. A very weak correlation is also noted between b and σu, c
and σu, as well as between b and εf. This effectively brings into question the validity of four-point
correlation method, modified four-point correlation method and partly, Mitchell’s method.
Prediction by the modified universal slopes method was more accurate compared to the original
universal slopes method because the parameter σu/E was introduced in the estimation of both fracture
strength and fracture ductility coefficient in the modified uniform slopes method. The strain-life
fatigue predicted by Mitchell’s method is highly non-conservative compared with the other methods
for the material. Figure 4 shows the ratio between the fatigue life estimated by different methods and
experimental fatigue life for Type 304LN stainless steel at various strain amplitudes.

259
Fig. 4: Ratio between the fatigue life estimated by
different methods and experimental fatigue life
5. SUMMARY AND CONCLUSIONS
Fatigue life of Type 304LN stainless steel under strain-controlled cyclic loading has been
estimated using some of the existing methods based on monotonic tensile material properties and
hardness of the material. The results of the studies are compared with the available results of strain-
controlled fatigue tests carried out earlier on Type 304LN stainless steel under six different strain
amplitude values, viz, 0.20%, 0.35%, 0.50%, 0.65%, 0.80% and 0.95%. Salient features of some of
the existing methods for strain-life fatigue prediction using monotonic tensile material properties and
hardness of the material are also discussed. On comparison with the experimental values, it is
observed that the estimation methods generally predict higher values of the strain-life fatigue of the
material for all strain amplitude values except the median’s method for strain amplitude of 0.80%.
Hence, use of these methods would result in unconservative values. The strain-life fatigue predicted
by Mitchell’s method is highly non-conservative compared with the other methods for the material.
Median’s method is found to estimate the strain-life fatigue of the material with a better accuracy.
Estimations by original and modified four-point correlation methods, original universal slopes
method and hardness method are found to be non-conservative to an extent of 1.5 to 4.5 times of the
observed strain-life fatigue.
6. ACKNOWLEDGEMENTS
The first author thanks the Director, CSIR-SERC, Chennai for permitting her to carry out her
M.Tech. project work at CSIR-SERC based on which this paper has been prepared. The authors
from CSIR-SERC thank Dr Nagesh R. Iyer, Director and Dr K. Ravisankar, Chief Scientist and
Advisor (Management), CSIR-SERC for the constant support and encouragement extended to them
in their R&D activities. This paper is published with the kind permission of the Director, CSIR-
SERC, Chennai.

260
7. REFERENCES
[1] Manson S.S., “Fatigue: a complex subject - some simple approximations”, Experimental
Mechanics - Journal of the SESA, 1965, Vol. 5, pp. 193-226.
[2] Mitchell M.R., Socie, D.F. and Caulfleld, E.M, “Fundamentals of modern fatigue analysis”,
Fracture Control Program Report No. 26”, University of Illinois, USA, 1977, pp. 385-410.
[3] Ong J.H, “An improved technique for the prediction of axial fatigue life from tensile data”,
International Journal of Fatigue, 1993, Vol. 15, No. 3, pp. 213-219.
[4] Muralidharan U. and Manson S.S., “Modified universal slopes equation for estimation of
fatigue characteristics”, Journal of Engineering Materials and Technology: Transactions of
the ASME, 1988, Vol. 110, pp.55-58.
[5] Baumel A. Jr. and Seeger T., Materials Data for Cyclic Loading - Supplement I, Elsevier
Science Publishers, Amsterdam, 1990.
[6] Roessle M.L. and Fatemi A., “Strain-controlled fatigue properties of steels and some simple
approximation”, International Journal of Fatigue, 2000, Vol. 22, pp. 495-511.
[7] Meggiolaro. M.A. and Castro. J.T.P., “Statistical evaluation of strain-life fatigue crack
initiation prediction”, International Journal of Fatigue, 2004, Vol. 26, pp. 463-476.
[8] Robert Basan, Domagoj Rubeša, Marina Franulovic and Božidar Križan, “A novel approach
to the estimation of strain life fatigue parameters”, Procedia Engineering, Vol. 2, 2010,
pp. 417-426.
[9] Bhavana Joy, Vishnuvardhan S., Raghava G., Gandhi P. and Mathews M. Paul, “Low cycle
fatigue characteristics of SS304LN stainless steel”, Proceedings of the 2nd
International
Conference on Materials for the Future, Thrissur, February 23-25, 2011.
[10] ASTM E 8M - 2004, “Standard test methods for tension testing of metallic materials
[Metric]”, ASTM International, USA.
[11] ASTM A 312/A 312M - 09, “Standard specification for seamless, welded and heavily cold
worked austenitic stainless steel pipes, ASTM International, USA.
[12] ASTM E 606 - 04, “Standard practice for strain-controlled fatigue testing”, ASTM
International, USA.
[13] ASTM A240/A240M-13, “Standard specification for Chromium and Chromium-Nickel
stainless steel plate, sheet, and strip for pressure vessels and for general Applications, ASTM
International, USA.
[14] Park J. and Song J., “Detailed evaluation of methods for estimation of fatigue properties”,
International Journal of Fatigue, 1995, Vol. 17, pp. 365-373.
[15] Ong J.H., “An evaluation of existing methods for the prediction of axial fatigue life from
tensile data”, International Journal of Fatigue, 1993, Vol. 15, No. 1, pp. 13-19.
[16] Robert Basan, Domagoj Rubeša, Marina Franulovic and Božidar Križan, “Analysis of strain-
life fatigue parameters and behaviour of different groups of metallic materials”, International
Journal of Fatigue, 2011, Vol. 33, pp. 484-491.
[17] Ong J.H., “An evaluation of existing methods for the prediction of axial fatigue life from
tensile data”, International Journal of Fatigue, 1993, Vol. 15, No 1, pp 13-19.
[18] Ram Ranjan Sahu, Dr. Pramod Kumar Gupta b, “Studies on Geometrical Featured Metallic
Shell Structures for Inward Inversion”, International Journal of Civil Engineering &
Technology (IJCIET), Volume 3, Issue 2, 2012, pp. 251 - 264, ISSN Print: 0976 – 6308,
ISSN Online: 0976 – 6316.
[19] Muthuraj.M.P and Subramanian. K, “Experimental Investigation on Glass Fibre Reinforced
Plasticbridge Decks Subjected to Static and Fatigue Loading”, International Journal of Civil
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