Rail fatigue crack propagation in high-speed wheel/rail rolling contact
J. Mod. Transport.
DOI 10.1007/s40534-017-0138-6
Rail fatigue crack propagation in high-speed
wheel/rail rolling contact
Xiaoyu Jiang1 • Xiaotao Li1 • Xu Li1 • Shihao Cao2
Received: 11 January 2017 / Revised: 5 July 2017 / Accepted: 6 July 2017
Ó The Author(s) 2017. This article is an open access publication
Abstract To study the wheel/rail rolling contact fatigue of
high-speed trains, we obtain the distribution of contact forces
between wheel and rail by introducing the strain-rate effect.
Based on the finite element simulation, a two-dimensional
finite element model is established, and the process of a
wheel rolling over a crack is analyzed to predict the crack
propagation direction. The statistics of possible crack propagation angles are calculated by the maximum circumferential stress criterion. The crack path is then obtained by
using the average crack propagation angle as the crack
propagation direction according to Weibull distribution.
Results show that the rail crack mode of low-speed trains is
different from that of high-speed trains. The rail crack
propagation experiences a migration from opening mode to
sliding mode under the low-speed trains; however, the rail
crack mainly propagates in the opening mode under highspeed trains. Furthermore, the crack propagation rate for
high-speed trains is faster than that for low-speed trains. The
simulated crack paths are consistent with the experimental
ones, which proves that it is reasonable to use the average
value of possible crack propagation directions as the actual
crack propagation direction.
Keywords Rolling contact fatigue Finite element Crack
propagation Weibull distribution
The Chinese version of this paper was published in Journal of
Southwest Jiaotong University (2016)51(2).
& Xiaoyu Jiang
1
School of Mechanics and Engineering, Southwest Jiaotong
University, Chengdu 610031, China
2
School of Civil Engineering, Southwest Jiaotong University,
Chengdu 610031, China
1 Introduction
Wheel/rail contact fatigue is always a serious problem for
railways, especially for high-speed railways, but it is difficult
to solve so far [1]. Wheel/rail contact fatigue increases the
operating costs and endangers the safety of trains. The failure
mechanism in wheel/rail contacts is very complicated, and
many vague aspects remain to be studied. The main damage
form of high-speed rails is governed by fatigue crack growth
[2]. Plastic deformation layers will form and accumulate in
rails after repeated rolling compaction. When the plastic
deformation reaches a threshold value, micro-cracks are
generated, which may further grow into macro-cracks [3].
The crack propagation rate of rail surface would become
smaller when the crack propagated to a certain level [4].
The crack propagation of rails has been an important
research direction in the field of wheel/rail contact fatigue.
Criterions to predict crack propagation direction were
proposed by many previous works, such as the maximum
circumferential tensile stress criterion [5], the minimum
strain energy density factor criterion [6], the maximum
energy release rate criterion [7] and an empirical formula
[8]. These criterions can be used to predict crack propagation direction under proportional monotonic loads, but
they cannot be applied to random loads. For the crack
propagation problem under complex loads, an infinitesimal
branch crack needs to be established at the tip of the main
crack, and the crack propagation direction can be determined by the stress intensity factor or the propagation rate
of the branch crack. This method was applied to predict
crack propagation direction under complex loads by some
researchers [9–14]. However, the applicable conditions of
this method remain disputable and unclear. Hence, it is not
a mature method for predicting crack propagations.
123
X. Jiang et al.
The load paths of the rail crack in wheel/rail contact are
different from conventional experimental load paths in that
the crack propagation direction under wheel/rail contact is
uncertain. In this paper, the probabilistic method is applied
to predict the crack propagation direction. The results
preliminarily demonstrate that it is reasonable to use the
average value of possible crack propagation directions as
the crack propagation direction.
e_eq1 ¼ 300 s1 ; rs2 = 738 MPa is the yield stress at the
strain rate e_eq1 ¼ 450 s1 ; e_eq is the total strain rate of the
material deformation, and it can be expressed as
1
½ðe_x e_y Þ2 þ ðe_y e_z Þ2
e_eq ¼ pffiffiffi
2ð1 þ mÞ
1
3
þ ðe_z e_x Þ2 þ ðc_2xy þ c_2yz þ c_2zx Þ2 ;
2
ð2Þ
where e_x , e_y and e_z are components of the linear strain rate;
c_xy , c_yz and c_zx are components of the shear strain rate; and
v is Poisson’s ratio of the material.
2 Methodology
2.1 Research model
A research model of wheel/rail contact as shown in Fig. 1 is
built. In this model, the wheel rolls forward with a speed of
v and without acceleration. Although there is no whole
sliding between wheel and rail, the local sliding and adhesion
still exist in the contact zone. G is the weight of the wheel. Me
is the driving moment. Fw is wind resistance. The rail surface
contains a micro-crack before the wheel rolls over the rail.
The contact pressure is p, and the contact friction is f.
2.2 Strain-rate effect of wheel/rail contact
The strain rate in the contact zone is relatively large
because the wheel rolls on the rail at a high speed. The
U71Mn steel, as the rail material, shows an obvious strainrate effect when the strain rate is relatively large. The
strain-rate characteristics of U71Mn steel can be given as
follows [15, 16]:
8
when e_eq 1 s1 ;
rs0
>
>
>
>
>
< r þ ðrs1 rs0 Þlg e_eq when 1 s1 e_ 300 s1 ;
s0
eq
rs ¼
lg e_eq1
>
>
>
ðr rs1 Þlg e_eq
>
>
: rs1 þ s2
when 300 s1 e_eq 450 s1 ;
ðlg e_eq2 lg e_eq1 Þ
ð1Þ
where rs is the yield stress at the strain rate e_eq ;
rs0 = 550 MPa is the yield stress in quasi-static state;
rs1 = 637 MPa is the yield stress at the strain rate
Fig. 1 Model for wheel/rail in rolling contact
123
2.3 Maximum circumferential tensile stress
criterion
Erdogan and Sih [5] proposed the maximum circumferential tensile stress criterion in 1963. Based on the criterion,
the crack propagation direction can be given by
2
3
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
9
2
>
1
K
1
K
>
I
I
>
h ¼ 2 tan1 4
þ85; KII [ 0 >
>
>
4 KII 4
KII
=
2
3
;
ð3Þ
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
2
>
>
>
1
K
1
K
I
I
>
þ
þ85; KII \0 >
h ¼ 2 tan1 4
>
;
4 KII 4
KII
where h is the crack propagation direction defined with a
positive value in the counterclockwise direction and a
negative value in the clockwise direction; KI and KII are
stress intensity factors of types I and II, respectively. The
singular element is employed in the crack tip, as shown
in Fig. 2. The stress intensity factors at the crack tip can
be obtained by the displacement extrapolation method
[17]:
9
rffiffiffiffiffiffi
>
l
2p
>
KI ¼
½4ðvb vd Þ þ ve vc >
=
jþ1 L
;
ð4Þ
rffiffiffiffiffiffi
>
>
l
2p
>
½4ðub ud Þ þ (...truncated)
