Finite element procedures for crack path prediction in multi-axial fatigue
Doctoral thesis, 2018

Rolling Contact Fatigue (RCF) cracks in rails are among the most detrimental railway track defects regarding reliability and cost. The cracks typically grow in shear mode up to a certain length at which they might arrest or kink into a more tensile-driven growth. This growth scheme appears as a result of non-proportional loading, large plastic deformations at the rail surface and primary compression with crack-face friction. In contrast, most existing crack growth criteria in the literature feature quantities that are susceptible to the limitations of small-scale yielding, e.g. Stress Intensity Factors (SIFs),
tensile-mode growth and unloaded crack-faces. Consequently, the range of validity of the existing criteria may be questioned in the non-linear crack growth setting of RCF.

In a study of the role of inelastic deformation on the crack loading, elastic–plastic simulations are carried out in pre-cracked tubular specimens subjected to mixed-mode cyclic loading. The crack loading is quantified via the Crack-Tip Displacements (CTDs) in modes I and II. Shakedown and ratcheting effects in the ranges of the CTDs are compared to trends of crack growth curves from experiments in the literature. It is concluded that the ranges of the CTDs can be used for qualitative crack growth assessment in the examined load cases. In addition, a gradient-enhanced mixed variational formulation is
developed for overcoming the numerical difficulties associated with the computation of Configurational Forces (CFs) for inelasticity. The mesh sensitivity of the CFs acting on an embedded discrete singularity is investigated. Results highlight that the proposed formulation provides sufficient regularity for the computation of CFs, which may then be used in the formulation of criteria for RCF crack propagation.

Predictions of the multi-axial fatigue crack path are performed based on instantaneous crack growth direction criteria. To this end, a generic model for load cycle evaluation is proposed and implemented on criteria based on CFs and CTDs. The predicted directions are compared towards mixed-mode fatigue crack growth experiments from the literature. Of the evaluated criteria, the ones based on CFs and CTDs accurately predict the tensile-mode growth. Classical SIF-based criteria seem to handle tensile-mode growth under moderate shear-mode loading. Moreover, the criterion based on CTDs captures the shear-mode growth and the tensile-mode growth as well as the transition between them. The latter growth schemes essentially resemble the RCF crack growth.

In an investigation of the influence of various railway operational parameters on predicted RCF crack growth directions, the coefficient of friction at the wheel–rail interface was found the most influential as compared to the wheel tonnage and crack-face friction. The latter had no effect on predicted directions, due to crack-tip opening at the instances of maximum shear CTDs.

Fracture mechanics

Configurational forces


Numerical simulation

Rolling contact fatigue


room VDL, Chalmers Tvärgata 4C, Gothenburg
Opponent: Prof. Bo Alfredsson, Department of Solid Mechanics, Royal Institute of Technology, KTH, Sweden


Dimosthenis Floros

Chalmers, Industrial and Materials Science, Material and Computational Mechanics

On configurational forces for gradient-enhanced inelasticity

Computational Mechanics,; Vol. 61(2018)p. 409-432

Journal article

Floros, D, Ekberg, A, Larsson F. Evaluation of crack growth direction criteria on mixed-mode fatigue crack growth experiments

Floros, D, Ekberg, A, Larsson, F. Evaluation of mixed-mode crack growth criteria under rolling contact conditions

Floros, D. Evaluation of rolling contact fatigue crack growth directions in rails under varying operational conditions


The railway was established as a widely used means of transportation already by the early 1800’s. In the last decades, an increasing number of passengers and goods are being transported by the railway. Railway traffic presents several advantages compared to other means of transport such as very high capacity, punctuality, reduced CO 2 footprint and remarkable passage safety.

A key ingredient is the steel-to-steel contact between wheel and rail which reduces the frictional losses in rolling. However, the steel material of the components is subjected to severe mechanical loads. Defects such as cracks on the surface of rails and wheels greatly affect railway traffic in terms of reliability and cost. To mitigate such defects, preventive and corrective maintenance actions are often necessary. Traffic delays is an immediate
outcome especially of corrective maintenance operations, such as unscheduled replacement of a defective rail or wheel. To avoid such unplanned operations, preventive maintenance is opted for by railway infrastructure managers and operators. In such maintenance operations, existing defects on the surface of the rails and wheels are removed by grinding, milling or turning. These are operations in which the surface layer that contains the defects is removed before the cracks reach a depth below which they tend to become critical and propagate abruptly towards complete rupture of the rail. Thereby, knowledge of the direction and speed of propagation of early detected cracks is crucial information that essentially guides railway technicians on how much rail material should be removed from the rail surface and when.

Knowledge of the propagation behaviour of surface cracks in rails is limited and in current practice stems primarily from empirical knowledge. Once sufficiently severe cracks are detected in field, a small fraction of a millimetre from the surface of the rails is removed. This operation is repeated with varying intervals in different railway track sections where cracks are expected to form. These empirical methods allow for scheduling and are well suited for constant railway operational conditions. However, variation in e.g. climate conditions, the increasing number of passengers and increased amount of
transported goods over the years continuously alter railway operational conditions.

The work described in this thesis aims to contribute in exactly the information of the propagation behaviour of surface cracks in rails. To this end, theoretical and numerical simulation frameworks are developed that are based on (computational) mechanics and other engineering tools. These tools are used to develop models able to predict the propagation behaviour of cracks under arbitrary railway operational conditions. The validity of the theoretical models has been tested against crack propagation experiments from the literature and “real” data from field observations. Results indicate the great potential regarding prediction of crack propagation in rails via numerical simulations. Advances in crack growth predictive methods reported here are expected to contribute to a more sustainable railway and to optimization of the maintenance process of railway tracks. This is achieved through more targeted inspection intervals, reduced disturbance of traffic for maintenance work and more efficient use of resources.

Research into enhanced tracks, switches and structures (In2Track)

Swedish Transport Administration (TRV2016/50535), 2016-09-01 -- 2019-06-30.

European Commission (EC) (EC/H2020/730841), 2016-12-01 -- 2020-12-31.

Areas of Advance


Materials Science

Subject Categories

Applied Mechanics

Infrastructure Engineering

Other Materials Engineering


C3SE (Chalmers Centre for Computational Science and Engineering)



Doktorsavhandlingar vid Chalmers tekniska högskola. Ny serie: 4530



room VDL, Chalmers Tvärgata 4C, Gothenburg

Opponent: Prof. Bo Alfredsson, Department of Solid Mechanics, Royal Institute of Technology, KTH, Sweden

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3/2/2022 2