A note on Merwin’s measurements of forward flow in rolling contact

The first quantitative analysis of the forward flow in frictionless rolling contact, firstly discovered experimentally by Crook [Proc. Inst. Mech. Eng. London 171 (1957) 187], was conducted by Merwin [Plastic deformation of surfaces in rolling, Ph.D. Dissertation, Cambridge University, UK, 1962] who attempted to model the ratchetting phenomenon in excess of shakedown (the cumulative forward flow due to continuous shear strain increase observed in experiments) as a function of load using a simple perfect plasticity model and a simplified solution to the elasto-plastic problem. However, later FEM analysis [J. Appl. Mech., Trans. ASME 52 (1985) 67, 75] and more refined calculations still based on perfect plasticity but using distributed dislocations [J. Mech. Phys. Solids 33 (1987) 61], found that the ratchet rate was much higher than what measured in experiments, showing the Merwin's approximate solution method was not effective. However, later analysis have concentrated on sophisticated non-linear hardening laws, also because the ratchetting strain rate was found to slowly decay in rail steel materials. This note is focused on another, less known, aspect of the original Merwin's analysis: his material data were limited to monotonic curves, but his yield limit choice corresponds for around 1% for mild steel and Dural, but to nearly 25% deformation in copper, indicating that hardening plays a significant role into the mechanics of the problem, and that Merwin had taken this into account a posteriori by looking at the load where ratchetting begins. The paper suggests that the cyclic strain growth can be divided into two sequential phenomena: the first, assuming there is no long term material ratchetting (MR), i.e. a calculation based upon elastic properties and a monotonic stress-plastic strain curve, and a second, steady state, for a hardened structure, depending only on MR. In the first phase, we assume the plastic flow is dominated by structural ratchetting (SR), i.e. assuming the ratchetting is well described by the perfectly plastic prediction, where the yield limit is increased according to the level of deformation. This process leads to a quick saturation and the following deformation is attributed to the steady-state material response which we denominate MR. Further, it is shown that experimental measurements of Merwin have more to do with MR than SR