Modeling and experimental characterization of large biaxial strains and induced anisotropy in pearlitic rail steel
Doctoral thesis, 2019

Large shear strains accumulate in the near-surface region under the running band of railway rails. In this region, rolling contact fatigue cracks often initiate, causing major problems for the railway industry. However, characterization of the constitutive and fatigue behavior of the material in this region is difficult due to the high strain gradient. The solution proposed in this thesis is to produce highly deformed cylindrical test bars: An axial-torsion test rig is used to predeform the bars in torsion while subjected to axial compressive loading. The obtained material state is found to be similar to that of field samples of rails at a depth between 50 and 100 μm. Using this predeformation method, the evolution of the yielding behavior is evaluated. The predeformed test bars are re-turned and drilled out to form thin-walled test bars, which can be used to measure yield surfaces. It is found that the degree of anisotropy quickly evolves with increasing predeformation and then saturates. Furthermore, the quadratic Hill yield criterion describes the anisotropic yield surfaces well.

To better optimize rail maintenance and material selection, there is an industrial need for a model capable of predicting rail deterioration. An important component of such a model is an accurate material model that captures the relevant physical phenomena. A hyperelasto-plastic framework for finite strain material models is adopted in this thesis. As a first study, the predeformation method was simulated using 2D axisymmetric elements. It is shown that very good results can be achieved by using material models with advanced kinematic hardening laws. Next, an improved simulation methodology for axial, torsional and pressure loading is developed, resulting in an efficient 1D formulation. This methodology includes material removal to simulate the re-machining of the test bars into tubular bars. Using this methodology, 3 different distortional hardening models are evaluated in terms of how well they fit and predict the experimental data. The two phenomenological models perform better than the crystal plasticity model. However, these models should be further developed to improve their predictive abilities.

Pearlitic steel

yield criteria

distortional hardening


kinematic hardening

biaxial loading


VDL, Chalmers Tvärgata 4C
Opponent: Professor Odd Sture Hopperstad, NTNU, Norway


Knut Andreas Meyer

Chalmers, Industrial and Materials Science, Material and Computational Mechanics

A comparison of two frameworks for kinematic hardening in hyperelasto-plasticity

Proceedings of the 14th International Conference on Computational Plasticity - Fundamentals and Applications, COMPLAS 2017,; (2017)p. 342-350

Paper in proceeding

Modeling of kinematic hardening at large biaxial deformations in pearlitic rail steel

International Journal of Solids and Structures,; Vol. 130(2018)p. 122-132

Journal article

Material model calibration against axial-torsion-pressure experiments accounting for the non-uniform stress distribution

Finite Elements in Analysis and Design,; Vol. 163(2019)p. 1-13

Journal article

Have you ever noticed how hard it is to bike with soft tires? What about how different it feels after you inflate them? The bike may roll more easily, but the bumps on the road are also more noticeable. The same happens for railway wheels: A steel wheel rolling over a steel rail has a very low rolling resistance. This makes trains very eco-friendly. The drawback, however, is a very high contact loading equivalent to the weight of 100 bikers on an area the size of a coin. This, together with forces from acceleration and braking, cause the surface layer of the rail to deform. As the deformations increase, the properties of the rail material change, and cracks appear. When the cracks become too large they need to be removed by maintenance grinding. This is a costly and slow operation that requires planning well in advance to avoid delayed trains.

In this thesis, a new experimental method is presented. It is used to investigate how a material's properties are affected by large deformations. One important property is the yield limit. This is the maximum stress a material can withstand without permanently deforming. It is found that the yield limit is initially the same in all loading directions. After the deformations have accumulated, however, the yield limit depends on the loading direction. This effect is typically not accounted for when modeling the behavior of the rail material. Models that are capable of capturing this effect are therefore evaluated in this thesis. Such models can be used to optimize maintenance planning. Ultimately, our research should lead to smoother railway operations with fewer delayed trains.

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.

Research into enhanced track and switch and crossing system 2 (In2Track-2)

Swedish Transport Administration, 2018-11-01 -- 2021-10-31.

European Commission (EC) (EC/H2020/826255), 2018-11-01 -- 2021-10-31.

Areas of Advance


Materials Science

Subject Categories

Applied Mechanics

Computational Mathematics

Metallurgy and Metallic Materials


C3SE (Chalmers Centre for Computational Science and Engineering)



Doktorsavhandlingar vid Chalmers tekniska högskola. Ny serie: 4622



VDL, Chalmers Tvärgata 4C

Opponent: Professor Odd Sture Hopperstad, NTNU, Norway

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3/2/2022 2