Calculation of minimum crack size for growth under rolling contact between wheel and rail

• We present a procedure to model the interaction between wear and fatigue crack growth.
• We examine the smallest crack size for growth under contact, wear and grinding conditions.
• The residual stress affects most on the crack growth.
• Periodic grinding help to stop crack growth in small sized crack, but it cannot stop the growth any more for large sized crack.

The minimum crack size for growth amin, which is defined as the smallest sized crack that grows fast enough to stay ahead of removal by wear and periodic grinding, was studied by employing Archard׳s wear model and Fletcher and Kapoor׳s “2.5D” fatigue crack growth model. For this purpose, a numerical analysis process was proposed by modeling the real railway operation conditions: typical crack driving forces, including bending, contact, thermal and residual stresses, and crack truncation, including contact wear and periodic grinding. A series of parametric studies was then conducted to predict amin by varying the dominant crack growth contributors, such as the tractive coefficient (tc=0.1, 0.2, 0.3 and 0.4), creepage coefficient (γ=0.1%, 0.2%, 0.3%, 0.4% and 0.5%) and temperature difference (ΔT=−20, 0 and 20 °C). From the analysis results, we found that the tractive coefficient is the most influencing parameter in the determination of amin, while the creepage coefficient has a large effect on amin under a low tractive coefficient, but the effect is diminished as the tractive coefficient is increased. The sizes of amin vary from 0.106 (tc=0.4, γ=0.1%) to 5.730 mm (tc=0.1, γ=0.5%) without the application of a periodic grinding condition, but they are increased by approximately 24% on average with the application of periodic grinding. This means that even though a larger crack can be worn out with the implementation of grinding, once a crack grows over a certain size, the periodic grinding does not stop its growth.