Fredrik Larsson

A study of multiple crack interaction at rolling contact fatigue loading of rails

Abstract The objective of this paper is to investigate geometric and material parameters that affect the interaction of multiple pre-existing (initiated) cracks due to rolling contact fatigue (RCF) loading conditions. In particular, the behaviour of short cracks (head checks) in railway rail is studied. Parameters of interest are initial crack angle and spacing, distribution of initial crack lengths, width of the load/contact zone, and the material properties (in particular, the friction coefficient). Furthermore, the sensitivity of the finite element (FE)-mesh density is investigated. An open question of particular interest is the effect of crack interaction, e.g. shielding, on the prevailing crack spacing. In view of all uncertainties of the material model as well as the three-dimensional geometric complexity of the RCF problem, it is important to obtain a good understanding of the sensitivity of parameter changes. This is achieved in the presented investigation, although it is carried out using simplifying assumptions such as plane strain, linear elasticity, and Hertzian pressure distribution.

An Efficient Approach to the Analysis of Rail Surface Irregularities Accounting for Dynamic Train–Track Interaction and Inelastic Deformations

A two-dimensional computational model for assessment of rolling contact fatigue induced by discrete rail surface irregularities, especially in the context of so-called squats, is presented. Dynamic excitation in a wide frequency range is considered in computationally efficient time-domain simulations of high-frequency dynamic vehicle–track interaction accounting for transient non-Hertzian wheel–rail contact. Results from dynamic simulations are mapped onto a finite element model to resolve the cyclic, elastoplastic stress response in the rail. Ratcheting under multiple wheel passages is quantified. In addition, low cycle fatigue impact is quantified using the Jiang–Sehitoglu fatigue parameter. The functionality of the model is demonstrated by numerical examples.

Numerical evaluation of the transient response due to non-smooth rolling contact using an arbitrary Lagrangian–Eulerian formulation

A theoretical and numerical framework to evaluate rolling contact using an arbitrary Lagrangian–Eulerian (ALE) formulation is established. A finite element formulation is implemented featuring cylinder–plate contact, automated mesh refinement, non-reflecting boundary conditions, and the ability to incorporate surface roughness through user-defined gap functions. Presented examples include rolling contact on a corrugated surface and negotiation of a surface discontinuity. Sensitivity and validation analyses are presented and show the model to be robust and the trends in parametric responses to be reasonable as compared to results in literature. Owing to the ALE formulation, the model can be kept very compact and the computational demands very modest.

The influence of rail surface irregularities on contact forces and local stresses

The effect of initial rail surface irregularities on promoting further surface degradation is investigated. The study concerns rolling contact fatigue formation, in particular in the form of the so-called squats. The impact of surface irregularities in the form of dimples is quantified by peak magnitudes of dynamic contact stresses and contact forces. To this end simulations of two-dimensional (later extended to three-dimensional) vertical dynamic vehicle–track interaction are employed. The most influencing parameters are identified. It is shown that even very shallow dimples might have a large impact on local contact stresses. Peak magnitudes of contact forces and stresses due to the influence of rail dimples are shown to exceed those due to rail corrugation.

A 3D/2D Comparison between Heterogeneous Mesoscale Models of Concrete

A model for 3D Statistical Volume Elements (SVEs) of mesoscale concrete is presented and employed in the context of computational homogenization. The model is based on voxelization where the SVE is subdivided into a number of voxels (cubes) which are treated as solid finite elements. The homogenized response is compared between 3D and 2D SVEs to study how the third spatial dimension influence the over-all results. The computational results show that the effective diffusivity of the 3D model is about 1.4 times that of the 2D model.

Finite element modelling of frictional thermomechanical rolling/sliding contact using an arbitrary Lagrangian–Eulerian formulation

A theoretical and computational framework for the analysis of thermomechanically coupled, frictional, stationary (steady-state) rolling contact based on an Arbitrary Lagrangian–Eulerian (ALE) kinematical description is presented. The finite element method is employed in a numerical implementation featuring two-dimensional cylinder–plate rolling contact, with a contact formulation incorporating mechanical and thermal frictional interaction. The ALE formulation is noted to allow for linearization of the governing equations, localized mesh refinement, a time-independent description of stationary dynamics, velocity-independent contact interface modelling and so on. Numerical simulations show the model to be able to capture, for example, stick/slip behaviour and a range of thermal phenomena, including the effect of convective cooling of the cylinder due to the contact with the plate.

Identification of wheel–rail contact forces based on strain measurements, an inverse scheme and a finite-element model of the wheel

The wheel–rail contact force is an essential parameter in many aspects in railway mechanics, for instance, in rolling contact fatigue analysis. Since the wheel–rail contact force cannot be measured directly, instrumented wheelsets have been developed to collect the radial strains at certain positions on the wheel web. In this paper, an inverse method to estimate the wheel–rail contact force history based on strain measurements is discussed. In the proposed method, the contact force is determined by minimizing the least-squares discrepancy between measured radial strains and corresponding computed strains from a three-dimensional finite-element model of the wheel. The inverse method is compared with the existing method based on direct extraction of the contact force from combinations of measured strains using Wheatstone bridges. Using synthetic data, it is found that the proposed inverse method is insensitive to the eigenmodes of the wheel, as opposed to the existing method. In addition, noise reduction by using Tikhonov regularization and by choosing proper sampling rates are discussed.

Identification of Wheel-Rail Contact Forces Based on Strain Measurement and Finite Element Model of the Rolling Wheel

In railway mechanics, the wheel-rail contact force is an important measure in the analysis of different kinds of rolling contact fatigue as well as being used for track condition monitoring. As the contact force cannot be measured directly in the field, one approach is to measure the strain at certain points on an instrumented wheel and upon employing signal processing techniques, extract an estimation of the contact force. However, the obtained force is restricted in terms of frequency content, i.e. the results are not accurate close to certain resonance frequencies of the wheel, [2]. In order to investigate and overcome the experienced problems, a 3-D Finite Element model of the wheel is used in an inverse identification procedure [7], whereby the proper dynamics of the system is taken into account. The method of signal processing using two Wheatstone bridges is compared with the inverse identification scheme by means of synthetic data.

Assessment of homogenization errors in transient problems

Model-based 1st order homogenization for stationary problems was recently extended to transient problems. Along with the classical averages, a higher order conservation quantity in the macroscale problem is then obtained. This effect depends on the size of the “subscale computational cell” (denoted RVE) that is subjected to different prolongation conditions (Dirichlet, Neumann). The issue addressed in this paper is how to choose the optimal size of the RVE in order to obtain the best possible fit to the single-scale solution. It turns out that there is a trade-off between the RVE-size and the macroscale mesh diameter.

Author Correction: Toxic fluoride gas emissions from lithium-ion battery fires

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