RICERCA ITALIANA     

Numerical models for the analysis of Rolling Contact Fatigue (RCF) life

Politecnico di Bari

Abstract

The research plan will be developed on various themes, coordinated by Proff. Demelio and Ciavarella, and as a continuation of activities undertaken at PoliBA in the last 5 years, also in collaboration with excellence centres in Europe such as Sheffield, Ecole Polytechnique, Leicester, etc.

The research program of Prof. Demelio will examine the mechanism due to defect and inclusions subsurface. This will study the stress concentration with semi-analytical methods extending the work of Greenwood, and validated with more sophisticated methods due to Kelly et al., as well as a FEM investigation.

A second part of the research plan will be an experimental plan, which will allow to consider existing correlations between fatigue limits under standard tension/compression or rotating bending, with that under RCF, with and without a calibrated hole in the specimen, with typical rail steels. The experimental plan will make use of the testing machine developed at DIMeG.

A second part of the research plan will be devoted to the analysis of the plastic deformation damage mechanism, in terms of residual stresses, as well as standard multiaxial fatigue criteria, and finally of ratchetting plastic deformations. <<<

Principal Investigator

Giuseppe Pompeo DEMELIO Politecnico di BARI

Research Objectives

Rolling contact fatigue affects various important engineering applications, such as rolling bearings, gears and rail-wheel contacts. In the latter case, failure may be of interest for both the wheel and the rail, without having particularly evident alerting signs and producing serious consequences in terms of damage, casualities and injuries.
The three mentioned applications can be reconducted to surface fatigue, but are tradizionally studied and treated in different manners and with different approaches, neglecting a deeper understanding of the damage phenomena at the origin of such differences.
There is, therefore, the necessity of having a better and more reliable predicting tool, as a consequence of scientific understanding of the various damage phenomena and consenting of better distillating differencies or analogies between the various applications.
In the case of rail-wheel contact, we have isolated in the literature a few major failure mechanisms, i.e.: surface fatigue (ratchetting and wear), sub-surface fatigue (high cycle fatigue), and fatigue from subsurface defects.
In the former case, it is not possible to neglect large incremental and cyclic plastic deformations, leading to failure (crack initiation) or wear, of low-cycle fatigue. In sub-surface fatigue, at depth around 3-10 mm, the predictive models refer to standard multiaxial fatigue criteria. Finally, for subsurface fatigue originated from defects or inclusions, at depths below 10 mm, contact geometry has a minor effect, whereas the value of the load has a first order effect.
The objective of the research plan is to compare the various damage mechanism criteria, in the ligth of the most recent studies on crack initiation for cylic plastic deformation cumulation, as well as specific multiaxial fatigue criteria, and fatigue limit in the presence of defects. <<<

First Results

Research unit coordinated by Prof. Demelio:

1) Diagrams of stress concentrations in presence of the hole/inclusion as a function of loading conditions, geometry, materials combinations

2) Determination of stress cycles (possibly multiaxial) for hole/inclusion subsurface

3) Atzori-Lazzarin diagram for Hertzian loading and crack or e cricca or hole/inclusion subsurface

Research unit coordinated by Prof. Ciavarella:

1) Residual stresses for perfect plasticity model (in particular, hydrostatic component as required for DangVan's criterion)
2) Same as 1, but linear kinematic,
3) Same as 1, but Bower's non-linear kinematic
4) Same as 1, but with Chaboche model

Multiaxial fatigue parameters
5) DangVan's criterion
6) Papadopoulos' criterion
7) Susmel-Lazzarin's criterion
8) Comparison will older criteria

Geometries
1) 2D Hertzian contact (Carter type tractions)
2) Axisymmetric or 3D Hertzian contact (‘lemon like' tractions)

Loads (Q is tangential load, P is normal load):
1) Pure rolling,
2) rolling with Q/P>0 (traction), up to full sliding Q/P=f;
3) rolling with Q/P<0 (braking), up to full sliding Q/P=-f;Experimental plan
1) fatigue test results on rail steel specimen with calibrated drilled hole
2) RCF test results

Overall conclusions
3) Atzori-Lazzarin diagrams
4) multiparametric criterion for different damage mechanisms. <<<

Timescale

24 months

National and international background

Rolling Contact Fatigue (RCF) is one of the most complex areas of fatigue, at the boundary between fatigue, crack propagation and wear, with presently a lack of true quantitative models. The development of rail materials has been constant from the early 1820s to date from iron to Bessemer steel, and finally to the modern pearlitic rail steels of high carbon content (0.5%), and low level of phosphorus and other impurities (however, for switch and other crossing components under more severe operational conditions, bainitic and Hadfield's manganese steels are used). These metallurgical improvements have solved many technical problems and permitted the progress in the railways, but have largely progressed independently on RCF understanding, Indeed, despite the critical nature of the components involved, there is lack of extensive prototypical testing with respect to, for example, car manufacturing and aeronautical industries where ultimately fatigue testing in service is conducted on a large number of vehicles (Smith, [1]).
As surface RCF fatigue and wear seem related by the common mechanism of RF (Ratchetting Failure), i.e. the progressive cumulative process of shear strain increase up to very large values, it is to be expected that, as in wear, many factors other than standard and more easily established material properties affect the performance of a given system and make difficult to make a priori even rough quantitative estimates. Generally, in wear empirical models are used such as the Archard's law whose coefficient needs to be measured experimentally as it varies few order of magnitudes in dry friction tests, and is very sensitive to surface conditions (roughness, lubrication etc.) rather than just material properties. In the classical approach to fatigue, the behavior of the material is largely clearer, and the typical situation where cycles of elastic and plastic strains (the latter generally in a form of cyclic plasticity), can be dealt satisfactorily with the celebrated Basquin-Coffin-Manson law: at high levels of strains, Low Cycle Fatigue results and elastic strains can be neglected; conversely for low levels of strains, High Cycle Fatigue is obtained and indeed sometimes a distinct fatigue limit. However, in the case of RCF, the stress field is multiaxial, the stress components vary out-of-phase, there is a large compressive hydrostatic component, and residual stresses as well as size effects may have a large effect. Moreover, RCF initiation depends at high loads additionally on ratchetting plastic strains, for which very little is known on its correlation with cyclic hardening material properties over large number of cycles.

In other words, it comes with no surprise that with so many difficulties, relatively little progress has been made. It is generally not possible to separate wear and RCF which act at the same time (and notice that wear may be beneficial when is large enough to remove the initiated embryo cracks), especially asboth resistances increases with hardness but their reciprocal role is unclear. For example while in standard pearlitic steels, increased hardness improves both RCF fatigue deformation and wear, in bainitic steels, wear rate doesn't decrease significantly at higher hardnesses (Clayton & Su, [2]).

Merwin [3] and Merwin & Johnson [4], see also Johnson's book [5], firstly showed the mechanics of shakedown and excess of shakedown in rolling contact. With a simple elastic-perfectly plastic material model, the shakedown limit in a plane contact for frictionless contact was shown to correspond to peak pressure being 4 times the yield strength in shear. For higher loads, Merwin solved the plasticity problem with a simplified approximate method; however, later refined FEM analysis (Bhargava et al, [6]) found much higher ratchet rates than Merwin's, which were also corrected by an improved elastic-perfectly plastic solution (Hearle & Johnson [7]). In a recent paper (Ponter Afferrante and Ciavarella, [8]), another aspect of Merwin's experimental results was noticed, i.e. that he had used a yield limit corresponding to nearly 1% of plastic deformation in the monotonic curve for Dural and for his steel, but to a much higher deformation (25%) for copper. Also, as proved by Bower & Johnson [9] even with a quite complex non linear kinematic hardening plasticity model, it is not easy to model the ratchet rate decay in rail steel, partly because of earlier fatigue failure in biaxial tests, with respect to RCF tests. The strategy based only on plasticity models therefore seems prohibitively complex, and particularly in the case of RF (Ratchetting Failure) suggested by [Kapoor, 10].

It is generally known that shakedown and fatigue limits are not directly connected, as they involve processes occurring at different scales. Therefore, generally fatigue limit properties of materials are directly measured from experiments, and DangVan's criterion [11] permits to use shakedown theories to examine the effect of multiaxiality by making the additional assumption that shakedown occurs at the mesoscopic scale, and that it is possible to find a simple link to the macroscopic scale. As a general rule (see Fleck et al, [12]) very soft metals and alloys show cyclic hardening and a large fatigue ratio whereas when they are heavily work-hardened tend to cyclically soften and have low fatigue ratios. The latter is the common case in rail materials. There is perhaps a better correlation of fatigue limit with cyclic yield strength, and fatigue limit is often close to correspond to cyclic strain amplitudes of 0.2-0.35%, but if the multiaxiality of RCF doesn't change this picture, then we would expect the fatigue limit to be lower than the shakedown limits.

In frictionless line contact, elastic and plastic shakedown (as well as ratchetting limit) all coincide. The Dang Van criterion leads to a HCF fatigue limit of peak pressure equal to 4.55 times the fatigue limit in pure torsion [Ekberg, 13]. However, RCF experimental results by Clayton & Su [2] show a fatigue limit well below the shakedown limit, and for peak pressures around 3 times the Brinell Hardness number. Juvinall & Marshek [14] report a table for various materials, and for steel a fatigue limit at 10^7 cycles of nearly 2.8 times the Brinell Hardness number, suggesting also a certain curve for the entire life. Preliminary calculations show application of the HCF Dang Van criterion may improve the prediction of the bainitic steels (but the conclusion here are very qualitative being the exact data on fatigue limit unavailable), but most likely does not solve the puzzle regarding the more standard pearlitic steels such as BS11 and STD, which show a fatigue limit being almost half of what predicted by both HCF fatigue criterion and shakedown principles. <<<