A probabilistic fatigue crack growth life approach to the definition of inspection intervals for railway axles

Different options that rely on fracture mechanics are currently used in engineering during the design and assessment of components. One of the most important aspects is the time taken for a crack to extend to its critical size. If this time is long enough, a design concept based on inspection intervals can be applied, as is it the case of a railway axle component. To define inspection intervals that ensure the continuous and safe operation of a damage-tolerant railway axle, a reliable estimation of its fatigue crack growth life is required. Due to the uncertainties involved in the fatigue process, inspections must be devised not only considering the uncertainties in the performance of the inspection technique, but also based on a probabilistic lifespan prediction. From this premise, this paper presents a procedure for determination of inspection intervals that uses a conservative fatigue crack growth life estimation based on the lifespan probability distribution. A practical example to illustrate the reliability-based inspection planning methodology in a railway axle under random bending loading is given. The inspection intervals are further assessed in terms of overall probability of detecting cracks in successive inspections and in terms of probability of failure, considering the probability of detection curve of the non-destructive testing technique. The procedure developed provides recommendation for the definition of inspection intervals and associated inspection techniques.

A Novel Methodology for Calculating Crack Opening Stress under Tension-Compression Cyclic Load

Crack closure model has been used in several applications on the prediction of fatigue crack growth life, with expression of crack opening stress often serving as milestones. A typical difficulty in calculating the crack opening stress is the phenomenon of crack closure caused by the compressive load effect. Compressive load effect, resulting in the change of residual stress status at the unloading stage and the decrease of crack opening stress, is a long-term challenge for predicting fatigue crack growth life. We propose the expression of crack opening stress to predict fatigue crack growth life based on the analysis of compact tensile specimen with elastoplastic element method. It combines the characteristics of material and load to deal with the phenomenon of crack closure and uses stress ratio and normalized maximum applied load variable to construct the expression of crack opening stress. In the study of tensile-compression fatigue crack growth experiments, the proposed expression is proved to improve, by comparative analysis, the predictive ability on the whole range of experiment data. The novel expression is accurate and simple. Consequently, it is conducive to calculate the crack opening stress under tension-compression load.

MODELING AND CALCULATION OF FATIGUE CRACK GROWTH LIFE IN STEELS

In this work, we studied the kinetics of fatigue crack growth on compact steel tensile specimens (C (T)-type), in the middle section of crack growth diagram under regular and irregular loading with different asymmetries and maximum load. The crack growth kinetics was obtained by the authors experimentally on modern servo-hydraulic testing machine. Irregular loading was carried out using samples of standard loading spectra characteristic of various technical objects experiencing variable loading during operation. The values of the crack growth rate were obtained. Parameters that evaluate the character of irregular loading and crack closure, namely, irregularity factor and crack closure ratio were suggested. When calculating the effective value of the magnitude of the stress intensity factor (SIF) at the crack mouth, it is proposed to consider in addition to the closure coefficient and cracks also measure irregular loading. The fatigue crack growth life was predicted taking into account its “closure” and the nature of loading according to the approach proposed by the authors and the cyclic calculation method (cycle-by-cycle), all the data obtained are tabulated and distributed according to the type of loading. The results obtained showed good convergence of the calculated and experimental data, which confirms the high values of the correlation.

Modeling and calculation of the fatigue crack growth life in structural steels

The kinetics of fatigue crack growth has been studied in tensile testing of compact steel tensile specimens (S(T)-type) in the middle section of the kinetic diagram of fatigue fracture (fatigue crack growth diagram) under regular and irregular loading with different asymmetry and maximum load values. The samples were tested on a BISS Nano-25kN servo-hydraulic machine. Standard loading spectra typical for different technical objects exposed to alternating loading during operation were used. The values of the crack growth rate per cycle in the loading block were obtained. Parameters for assessing the character of irregular loading and crack closure, namely, the irregularity factor and crack closure coefficient were proposed. When calculating the effective value of the range of the stress intensity factor (SIF) at the crack mouth, we propose also to take into account the loading irregularity in addition to the closure coefficient. With this approach, the obtained fatigue crack growth diagrams can be grouped into one equivalent curve, which is characteristic of regular loading with R = 0. Moreover, grouping of the fatigue crack growth diagrams provided the use of unified parameters when calculating the crack growth kinetics, regardless of the type and parameters of loading, which rather simplified the crack growth determination. The fatigue crack growth life was predicted taking into account the crack «closure» and the nature of loading according both to the approach developed by the authors and by cyclic calculation method (cycle-by-cycle). All the data obtained are tabulated and classed according to the type of loading. The calculation results and experimental data showed good convergence, which was confirmed by the high values of the correlation coefficient.