Letter to the Editor On the Ekberg, Kabo and Andersson calculation of the Dang Van high cycle fatigue limit for rolling contact fatigue

A B S T R A C T Recently, various methods have been proposed to assess the risk of rolling contact fatigue failure by Ekberg, Kabo and Andersson, and in particular, the Dang Van multiaxial fatigue criterion has been suggested in a simple approximate formulation. In this note, it is found that the approximation implied can be very significant; the calculation is improved and corrected, and focused on the study of plane problems but for a complete range of possible friction coefficients. It is found that predicted fatigue limit could be much higher than that under standard uniaxial tension/compression for 'hard materials' than for 'ductile materials.' This is in qualitative agreement, for example, with gears' design standards, but in quantitative terms, particularly for frictionless condition, the predicted limit seems possibly too high, indicating the need for careful comparison with experimental results. Some comments are devoted to the interplay of shakedown and fatigue. Rolling contact fatigue (RCF) occurs in railways, but also in gears and rolling bearings, and many other mechanical applications. It has various forms (plastic deformations , macro-and micro-pitting, spalling, crack initiation from inclusions, etc.) and is generally interacting with other forms of surface damage, and in particular wear. Both phenomena (RCF and wear) strongly depend on surface roughness and lubrication conditions, and therefore it is not surprising that a general understanding or design methodology has so far been lacking. Recently, Ek-berg, Kabo and Andersson (EKA), 1 have suggested an approach to the problem with independent consideration of various mechanisms at play, corresponding to various indexes. The first (surface-initiated fatigue) derives from the classical approach based on plasticity theory, shakedown and ratcheting, as described, for example, in Chapter 9 of Johnson's book. 2 Ratcheting in particular would seem to dominate the process at sufficiently large pressures, and its modelling was initially apparently successful with simple analyses using elastic–perfectly plastic constitutive equations. More recent FEM plasticity models quite efficiently take account of more complex constitutive laws and also can compute the steady-state response (if there is one) directly , 3–5 but the ratcheting response modelling remains today one of the most complex in plasticity theory. For example, in the celebrated RCF experiments by Merwin 6 also reported in Merwin and Johnson, 7 the choice of yield limit was quite arbitrary (1% of permanent strain in the monotonic curves for dural and mild steel, but 25% for copper) and probably motivated …