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Estimation Methods for Fatigue Properties of Steels Under Axial and Torsional Loading

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International Journal of Fatigue 24 (2002) 783–793www.elsevier.com/locate/ijfatigue
Estimation methods for fatigue properties of steels under axial andtorsional loading
K.S. Kim
a,*
, X. Chen
b
, C. Han
a
, H.W. Lee
c
a
Department of Mechanical Engineering, Pohang University of Science and Technology, South Korea 790784
b
School of Chemical Engineering, Tianjin University, People’s Republic of China, 300072
c
Department of Mechanical Engineering, Pusan National University, Pusan, South Korea
Received 7 June 2001; received in revised form 6 August 2001; accepted 27 September 2001
Abstract
Uniaxial and torsional fatigue tests have been conducted on eight steels. The cyclic equivalent stress and strain amplitudes canbe ﬁtted by the Ramberg-Osgood relationship. Fatigue lives are found correlated with the equivalent strain amplitude. Seven methodsfor estimating uniaxial fatigue properties from tensile properties or hardness have been evaluated. The modiﬁed universal slopesmethod by Muralidharan and Manson, the uniform material law by Ba¨umel and Seeger and the hardness method by Roessle andFatemi predicted over 93% of test cases within the factor of 3 compared with observed lives. These methods are also foundapplicable to torsional fatigue with fatigue properties estimated from uniaxial fatigue properties based on the equivalent straincriterion.
©
2002 Elsevier Science Ltd. All rights reserved.
Keywords:
Uniaxial fatigue; Torsional fatigue; Fatigue properties
1. Introduction
The strain-based fatigue life analysis is routinely per-formed to assess the fatigue resistance of structuralcomponents [1]. The characterization of fatigue endur-ance of engineering materials is usually made throughuniaxial fatigue tests, and fatigue properties under suchloading are available for a large body of materials. Often,however, circumstances are encountered in servicewhere the fatigue resistance of a component needs to beanswered within a short timeframe but fatigue data forthe material are not available. The situation becomeseven more difﬁcult if the loading condition is multiaxial.Some multiaxial fatigue criteria [2,3] require torsionalfatigue data to determine all material constants. How-ever, torsional fatigue data can be found only for a lim-ited number of materials. Therefore, it would be desir-able to have an estimation scheme for torsional fatigueproperties from readily available material properties.
* Corresponding author. Tel.:
+
82-54-279-2182; fax:
+
82-54-279-5899.
E-mail address:
illini@postech.ac.kr (K.S. Kim).
0142-1123/02/$ - see front matter
©
2002 Elsevier Science Ltd. All rights reserved.PII: S0142-1123(01)00190-6
Over the last few decades, many researchers haveattempted to develop relations between monotonic ten-sile properties and uniaxial fatigue properties of engin-eering materials. If reliable relations with reasonableaccuracy can be established, they can serve to providefast solutions to fatigue problems without time and costinvolved in fatigue testing. Manson [4] ﬁrst proposedtwo methods; the four-point correlation method and theuniversal slopes method, to estimate the strain-life curveusing monotonic tensile data. Mitchell [5] proposed amethod suitable for steels. Ba¨umel and Seeger [6] pro-posed the uniform material law for metals. Muralidharanand Manson [7] proposed a modiﬁed universal slopesmethod, and Ong [8] suggested a modiﬁed four-pointcorrelation method. Roessle and Fatemi [9] recently pro-posed a method requiring only hardness and the modulusof elasticity to estimate uniaxial fatigue properties of steels. In a study conducted by Park and Song [10], sixmethods [4–8] were evaluated for a total of 138 ferrousand nonferrous metallic materials. They reported thatthose proposed by Ba¨umel and Seeger [6], Muralidharanand Manson [7], and Ong [8] yielded better predictionsover others. Another assessment of different methodswas carried by Ong [11], in which the ASM data for 49
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K.S. Kim et al. / International Journal of Fatigue 24 (2002) 783
–
793
Nomenclature
e
Strain range in axial fatigue test
s
Stress range in axial fatigue test
t
Shear stress range in torsional fatigue test
g
Shear strain range in torsional fatigue test
N
f
Cycles to failure
s
f
Axial fatigue strength coef
ﬁ
cient
e
f
Axial fatigue ductility coef
ﬁ
cient
b
Axial fatigue strength exponent
c
Axial fatigue ductility exponent
t
f
Shear fatigue strength coef
ﬁ
cient
g
f
Shear fatigue ductility coef
ﬁ
cient
b
o
Shear fatigue strength exponent
c
o
Shear fatigue ductility exponent
K
Cyclic strain hardening coef
ﬁ
cient
n
Cyclic strain hardening exponent
K
0
Cyclic shear strain hardening coef
ﬁ
cient
n
0
Cyclic shear strain hardening exponent
s
¯
Equivalent stress
e
¯
Equivalent strain
E
Young
’
s modulus
G
Shear modulus
n
Poisson ratio
e
f
True fracture ductility
s
u
Ultimate tensile strength
s
y
Yield strength (0.2%)
RA
Reduction in area (%)
EL
Elongation
HB
Brinell hardnesssteels were used with the modi
ﬁ
ed and srcinal versionsof the four-point correlation method [4,8] and the univer-sal slopes method [4,7] and Mitchell
’
s method [5]. It wasconcluded in [11] that the modi
ﬁ
ed four-point corre-lation method and the modi
ﬁ
ed universal slopes methodgave a satisfactory agreement between predicted andexperimental fatigue lives.In this paper, the results of strain controlled axialfatigue tests and torsional fatigue tests on eight steelsare presented. Seven aforementioned methods are evalu-ated for estimating uniaxial fatigue properties from ten-sile properties or hardness. Also, the approaches basedon the equivalent strain criterion and the maximum shearstrain criterion will be investigated for estimating tor-sional fatigue properties from uniaxial fatigue properties.
2. Experiment
The test materials used in this investigation are eightsteels purchased in the form of wrought bars. The chemi-cal compositions of the materials are given in Table 1.The monotonic tensile properties obtained from solidspecimens with a diameter of 6 mm are listed in Table 2.The geometry of the fatigue specimen is shown inFig. 1. The specimen was gun-drilled and honed throughthe center. The gage section of the outside contour wasmachined, ground and polished with alumina powder(0.3
µ
m). The effect of residual stresses that could havebeen introduced in the machining process has been ignoredin this study.Fatigue tests were conducted on a servo-hydraulicMTS axial-torsional materials testing system. All testswere carried out under strain control. A tension-torsionextensometer with an axial gage length of 20 mm anda diameter of 12.5 mm was used to control the strain.Triangular waveforms were used for both axial and tor-sional fatigue. Tests were carried out under fullyreversed strain cycling with frequencies in the range of 0.5
1Hz. The lower frequency was applied to higheramplitude tests. Failure was de
ﬁ
ned as a drop of 10%in load for axial tests, and a drop of 10% in torque for
785
K.S. Kim et al. / International Journal of Fatigue 24 (2002) 783
–
793
Table 1Chemical composition of test materials (wt.%)Material C Si Mn P S Cu Ni Cr MoSNCM630 0.32 0.25 0.45 0.013 0.017 0.18 2.52 2.54 0.51SNCM439 0.39 0.24 0.72 0.09 0.018 0.13 1.65 0.67 0.16SCM440 0.42 0.22 0.71 0.01 0.01 0.13 0.08 1.01 0.22SCM435 0.38 0.21 0.7 0.015 0.018 0.11 0.09 0.83 0.16SFNCM85S 0.2 0.25 0.8 0.017 0.008
–
0.49 0.55 0.19SF60 0.43 0.18 0.69 0.023 0.007
– – – –
S45C 0.43 0.18 0.69 0.023 0.007
– – – –
S25C 0.27 0.24 0.53 0.019 0.002
– – – –
Table 2Mechanical properties of test materials.Material
E
(GPa)
G
(GPa)
n s
y
(MPa)
t
y
(MPa)
s
u
(MPa)
EL
(%)
RA
(%)
HB
SNCM630 196 77 0.273 951 581 1100 19 49 327SNCM439 208 80 0.296 950 560 1050 13 37 323SCM440 204 80 0.283 846 440 1000 13 36 319SCM435 210 81 0.3 795 460 951 18 66 300SFNCM85S 201 80 0.26 565 340 825 21 66 241SF60 208 79 0.311 580 274 820 19 53 167S45C 206 79 0.298 590 341 798 17 39 234S25C 209 80 0.29 280 182 508 19 52 153Fig. 1. Specimen geometry (unit: mm).
torsional tests. The stress amplitude was measured in apreset interval of cycles. The stress amplitude at approxi-mately half-life, where the stress-strain response wasstable, was used for the cyclic stress-strain curve. Atleast seven tests were conducted for each type of axialand torsional loading at strain amplitudes ranging from0.2% to 2%.
3. Methods for estimating uniaxial fatigueproperties
The relationship between the applied strain amplitudeand fatigue life under uniaxial loading and torsionalloading can be expressed by Basquin-Cof
ﬁ
n-Mansonequations:
e
2
s
f
E
(2
N
f
)
b
e
f
(2
N
f
)
c
for uniaxial fatigue, (1)
g
2
t
f
G
(2
N
f
)
b
0
g
f
(2
N
f
)
c
0
for torsional fatigue, (2)The material constants
s
f
,
e
f
,
b
and
c
are the uniaxialfatigue properties, and
t
f
,
g
f
,
b
o
, and
c
o
are the torsionalfatigue properties. The strain amplitudes of Eq. (1) andEq. (2) can be split into elastic and plastic components,and they can be individually related to life by equatingto the
ﬁ
rst and second terms, respectively, on the right.An outline is given in the following section for esti-mating uniaxial fatigue properties that are examined inthis study. The equations in the original papers havebeen rewritten in the nomenclature of the present paper.The details how these equations were obtained can befound not only in the srcinal paper for each method butalso in review papers [10,11]. It is also noted that thetrue fracture ductility
e
f
in some of the equations maybe obtained from
e
f
ln[100/(100
RA
)].
3.1. Four-point correlation method
Manson [4] proposed the four-point correlationmethod to estimate the strain-life curve using monotonictensile properties. The four points here include twopoints on the elastic strain-life curve and two points on
786
K.S. Kim et al. / International Journal of Fatigue 24 (2002) 783
–
793
the plastic strain-life curve. The fatigue properties arerelated to monotonic tensile properties as follows:
s
f
E
2
10
b
log 2+ log
2.5
s
u
(1+
e
f
)
E
, (3a)
b
log
2.5(1+
e
f
)0.9
log[1/(4
×
10
5
)], (3b)
e
f
12
10
c
log120+ log
14
e
3/4
f
, (3c)
c
13 log
0.0132
−
e
∗
1.91
13 log
14
e
3/4
f
, (3d)where
e
∗
is the elastic strain range at 10
4
cycles andis estimated by
e
∗
10
b
log(4
×
10
4
)+ log
2.5
s
u
(1+
e
f
)
E
(3e)
3.2. Universal slopes method
An alternative approach was also proposed by Manson[4], in which it was assumed that the slopes of the elasticstrain-life and plastic strain-life curves do not vary withmaterials. The fatigue properties are estimated by
s
f
1.9018
s
u
, (4a)
b
0.12, (4b)
e
f
0.7579
e
0.6
f
, (4c)
c
0.6. (4d)
3.3. Mitchell
’
s method
Mitchell [5] suggested the following equations forsteels with hardness below 500 HB:
s
f
s
u
345(
MPa
), (5a)
b
16 log
2(
s
u
+345)
s
u
, (5b)
e
f
e
f
, (5c)
c
0.6. (5d)
3.4. Modiﬁed four-point correlation method
Ong [8] proposed a modi
ﬁ
ed four-point correlationmethod. The estimation equations are given as
s
f
s
u
(1
e
f
), (6a)
b
16
log
0.16
s
u
E
0.81
log
s
u
E
, (6b)
e
f
e
f
, (6c)
c
14 log
0.00737
−
e
∗
e
/22.074
log
e
f
, (6d)where
e
∗
e
is the elastic strain range at 10
4
cycles andis given by
e
∗
e
2
s
f
E
[10
23
log[0.16(
s
u
/
E
)
0.81
]
−
log(
s
f
/
E
)
], (6e)where
s
f
s
f
.
3.5. Modiﬁed universal slopes method
The universal slopes method [4] was modi
ﬁ
ed byMuralidharan and Manson [7], and the following equa-tions were proposed:
s
f
E
0.623
s
u
E
0.832
, (7a)
b
0.09, (7b)
e
f
0.0196
e
0.155
f
s
u
E
−
0.53
, (7c)
c
0.56. (7d)
3.6. Uniform material law
This method, proposed by Ba
¨
umel and Seeger [9],may be considered as a universal slopes method. How-ever, it assigns different slopes to the unalloyed and low-alloy steels, and to aluminium and titanium alloys. Onlythe elastic modulus and tensile strength of the materialare needed for estimation of fatigue properties. For unal-loyed and low-alloy steels, the equations are given by
s
f
1.5
s
u
, (8a)
b
0.087, (8b)
e
f
0.59
y
, (8c)
c
0.58.where
y
1
for
s
u
E
0.003, (8e)
y
1.375
125.0
s
u
E
for
s
u
E
0.003. (8f)Notice that
b
and
c
are very close to those of the modi-
ﬁ
ed universal slopes method.

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