Assessment of lifetime of railway axle
Highlights
► Stress intensity factor for commuter train axle was calculated by the finite element method. ► Main laws of stress ratio influence on fatigue crack growth rate were revealed. ► Probabilistic analysis of axle’s lifetime with an initial defect was performed. ► Distribution functions for final crack depth in axle after 106 cycles of block loading were obtained.
Introduction
Railway axles are designed for a long term of operation. However, there are known cases of their failure, which are caused by defects that arise during the operation and serve as a source of origin and development of cracks to critical size [1], [2], [3], [4], [5]. This requires further study and improvement of the reliability of fatigue lifetime assessment and durability of axles, as well as determination of intervals between inspections.
To evaluate the residual lifetime of wheelset axles, the approaches of linear fracture mechanics are often used [5], [6], [7]. A methodology for prediction the residual lifetime of bogies axle were proposed [4], [5], [8], [9], [10], based on different models of crack growth, taking into account an actual load spectrum [5], [7], [8], defects in the form of surface cracks [1], [5], [6], [8] or dints during operation [5]. Also, a variety of deterministic approaches were suggested for the study of multiple cracks in structural elements and related problems, see e.g. [11], [12], [13], [14], [15], [16].
It is known that in-service defects in the cylindrical bodies, especially in the axles of railway transport, often take the form of semi-elliptical surface cracks [1], [5], [8]. One of the main parameters that characterize the fatigue crack growth (FCG) is the stress intensity factor (SIF).
To predict the residual lifetime of these structures with cracks, one needs to assess correctly the SIF with respect to real loading scheme. For each case of the stepped axle of cylindrical shape with cracks, it is necessary to determine SIF [7], [8], [10], [17]. Three-dimensional finite-element modelling is the most suitable method for evaluation of stress–strain state of such structures [7], [17].
The uncertainty of operating loading, characteristics of mechanical properties of the material and the local geometry of the structural element can also affect significantly the limit state and residual lifetime of the component [7], [18], [19].
To describe the dependencies of the strength and durability of structural elements on the scatter of material properties, probability distribution functions are most commonly employed. These functions are presented in Table 1. These functions were used as input parameters for modelling of FCG resistance, as well as for modelling of the final crack depth after preset number of cycles and lifetime for which crack size will reach final value.
The present study is concerned with the probabilistic analysis of lifetime of railway axle with an initial defect in the form of surface semi-elliptical crack based on assessed stress–strain state, the operational loading sequence taking into account the scatter of characteristics of FCG resistance.
Section snippets
Crack geometry and finite element modelling
The draft of railway axle and fillet dimensions are shown in Fig. 1a and b. Stress–strain state and SIF were assessed by finite element method (FEM) in the elastic formulation using ANSYS© software package.
The load P on axle-box was taken equal to 260 kN. Young’s modulus was E = 2 × 105 MPa, Poisson’s ratio was ν = 0.3. Semi-elliptical crack with ratio of a/c = 0.4 was considered (Fig. 2a).
Crack depth a was chosen equal to 0.5 mm, 1.0 mm, 3.0 mm, 8.0 mm, 16.0 mm and 32.0 mm. Axle diameter D in the place of
Stress analysis
The normal stresses on the surface of axle fillet under the load on axle-box of 260 kN in the most dangerous cross-section (where the crack appears during the service) are 152 MPa (Fig. 3).
Fig. 4 shows the distribution of normal stress in the vicinity of the crack with a depth of 16 mm at the deepest point (point A, Fig. 2a).
The dimensionless SIF Y was calculated by a formula:where σ are normal stresses on the surface of fillet in the most dangerous cross-section. The dependence of
The influence of stress ratio on fatigue crack growth rate in 0.45% С steel
During the operation, an axle undergoes static and cyclic loading, including random loading, bending, as well as corrosive action of environment and climate temperatures. The influence of stress ratio on FCG rate in axle steel with 0.45% C was studied.
The characteristics of mechanical properties of axle steel under static tension at room temperature: yield strength σ0.2 = 360 MPa, ultimate tensile strength σu = 610 MPa, relative elongation δ = 16%, relative reduction ψ = 40%.
Middle crack tension
Conclusions
Stress intensity factor for railway axle under the operating loading with surface semi-elliptical crack with relative depth from 0.004 to 0.25 at the transition region from cylindrical surface to fillet were assessed by the finite element method.
It was found out that, with increasing of crack depth to axle diameter ratio a/D from 0.004 to 0.25, the dimensionless SIF YA at the deepest point monotonously decreases from 0.830 to 0.359, and the YC for a surface point decreases at first (to a/D =
Acknowledgement
These studies were supported by the Fundamental Research State Fund of Ukraine, Number of state registration 0109U002297.
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