P.C. Bastias

Determination of monotonic stress-strain curve of hard materials from ultra-low-load indentation tests

Abstract A method has been proposed to determine the stress-strain curve of hard materials from ultra-low-load indentation tests using geometrically similar indenters. The hardness-flow stress, and characteristic plastic strain-cone angle correlations, for conical indenters, were obtained from a number of calculations with different stress-strain curves using the finite element code ABAQUS. The flow stress values thus obtained, lie between that predicted by the slip line field theory and the spherical cavity expansion model. These correlations do not assume any deformation mode, and are thus valid for a wide range of hardness to elastic modulus ratio. The validity of the proposed method was checked by determining the monotonic stress-strain curve of 1070 steel from ultra-low-load indentation tests performed in the present study. Also, the stress-strain curves of copper and steel were obtained from macroscopic hardness values reported by Atkins and Tabor (Atkins, A.G. and Tabor, D. (1965) Plastic indentation in metals with cones. Journal of the Mechanics and Physics of Solids 13 , 149–164.). The predicted stress-strain curves agree well with the known properties of these materials. These correlations were then used to determine the monotonic stress-strain curve of silicon nitride.

Rolling Contact Fatigue (RCF) resistance of Austempered Ductile Iron (ADI)

Abstract The present work reports on the Rolling Contact Fatigue (RCF) resistance of Austempered Ductile Iron (ADI) as evaluated by using a ball–rod rolling contact fatigue tester. The tests were carried out until a spall was detected with a load ratio p0/kk=6, where p0 is the maximum Hertz stress and kk the kinematic shear yield stress. The results obtained for the RCF tests were compared with the properties of AISI 440C and SAE 52100 bearing steels. The spalls were observed using optical and electron scanning microscopy. The microstructure was found to have a strong influence in RCF results. It is concluded that ADI has good resistance to crack propagation but low resistance to crack nucleation. The RCF resistance of ADI under the present experimental conditions is not satisfactory.

Analysis of rolling contact spall life in 440C bearing steel

Abstract This paper describes calculations and measurements aimed at resolving and analysing the nucleation and growth components of the near-surface mode of rolling contact failure of 440C steel. Preliminary results of two-body, finite element calculations of repeated rolling contact with a dent in the running surface are described. Measurements of the nucleation and growth components of the life are derived from observations of cracks nucleated at small dents. The three-dimensional character of the spalls is examined. Calculations of the fracture mechanics driving force for surface breaking cracks are reviewed and compared with the measurements. The agreements provide support for the view that surface irregularities and the hydrostatic pressure of fluid in the crack cavity play a role in the nucleation and growth of the spall and that there is a threshold contact pressure for spall growth.

Calculations of the frictional heating of a locomotive wheel attending rolling plus sliding

Abstract Three-dimensional and two-dimensional finite element analyses of frictional wheel heating are combined with a simplified analysis of the heat conducted across the contact patch to produce estimates of the variation of the maximum wheel temperature with time for different combinations of creep and adhesion. These analyses can be used to evaluate the wheel temperature for up to 1 h periods of rolling-sliding. After 13 min of contact at a velocity of 22.2 m s −1 , average maximum temperatures on the surface of the wheel exceed 600°C for creepadhesion products CA > 0.054. Temperature spikes of about 100°C for durations of about 10 ms are superimposed on the average maximum. The calculations show that 29% of the frictional heat deposited on the wheel surface is conducted to the rail. This corresponds with a heat flow rate partitioning factor, δ = 0.36.

Elasto-plastic finite-element analysis of 2-D rolling-plus-sliding contact with temperature-dependent bearing steel material properties

Abstract A coupled thermo-mechanical finite-element model developed to study 2-D rolling-plus-sliding contact on a kinematically hardening substrate is described. Such a contact condition is simulated by repeatedly translating a thermo-mechanical load across the surface of the substrate. The substrate is modeled as a semi-infinite half-space represented by a 2-D finite-element mesh with appropriate boundary condition on the displacements and temperature gradients. Elastic-linear-kinematic-hardening-plastic (ELKP) material constitutive relations are used to model the material behavior of 52100 bearing steel. Effects of frictional heating and temperature-dependent material and thermo-physical properties on the substrate are studied. The stress and strain distributions developed are reported.

Analysis of fretting conditions in pinned connections

A 2-dimensional, finite element model of a pinned connection, involving AA7075-T6 aluminum alloy sheet and aluminum and steel pins, is used to evaluate the local mechanical parameters that control fretting wear damage. These include the contact pressure, the slip amplitude, the tensile stress parallel to the hole interface and a fretting wear (F1) and fretting fatigue (F2) parameter. The connection is subjected to cyclic loading with a peak nominal stress of σ = 125 MPa and R = 0.1. The dimensions and constraints of the model approximate those of multi-riveted panels. Values of interference in the range 0–2% interference, and 2 values of the coefficient of friction, μ=0.2 and μ = 0.5, are examined. The variations of the mechanical parameters with angular position about the hole are defined. Peak contact pressures in the range p = 500–600 MPa are obtained at the pin-bore interface. The slip amplitudes in the range 2 μm < δ < 20 μm, and circumferential tensile stresses as high as σ ≈100 MPa, are produced in regions where the contact pressure is generally above p = 400 MPa. The peak values of the fretting wear parameter, 0.3 kPa m < F1 < 3 kPa m, coupled with small slip amplitudes and specific wear rates cannot account for significant material loss in the stiff model connection examined here. However, the relatively large fretting fatigue parameter values, 6 × 1010 Pa m < F2 < 70 × 1010 Pa m, could promote early fretting fatigue failure in the absence of interference.

Finite element modelling of subsurface mode II cracks under contact loads

Abstract A finite element model for simulating cracks in an elastic half space subjected to two dimensional rolling contact is introduced. The mode II stress intensity range δ k 11 is evaluated for both a point load and a Hertzian pressure distribution. The results agree with closed form solutions. The model makes it possible to study both long as well as short cracks of any inclination. Although only the frictionless crack case and linear elastic material behavior are treated here, the model may be extended to treat both friction and elastic-plastic behavior. Crack Tip Shear Displacement Δ(CTSD)c obtained from the finite element analysis could be used in place of K 11 or the J- integral as the crack tip controlling parameter thus avoiding difficulties produced by friction and unloading.

Influence of indent geometry on repeated two-dimensional rolling contact

A two-body, elasto-plastic finite element model is employed to simulate repeated rolling contact in the presence ofa surface irregularity. It is shown that the maximum Mises stress and equivalent plastic strain values in the substrate are related to the height of the pressure spikes. The results of the finite element calculations are used to derive generalizations about the influence of the indent geometry on the pressure spikes, peak cyclic plastic strains and their location below the surface. These relations can serve as guidelines for designing the depth and properties of surface coatings and modified layers.

Contribution of Surface Irregularities to Rolling Contact Plasticity in Bearing Steels

A “two-body” elasto-plastic finite element model of two-dimensional rolling and rolling-plus-sliding has been developed to treat the effect of surface irregularities. The model consists of a smooth cylinder in contact with a semi-infinite half-space that is either smooth or fitted with one of two irregularities: a 0.4 μm deep groove, or a 7 μm deep groove. The model incorporates elastic-linear-kinematic-hardening-plastic (ELKP) and nonlinear-kinematic-hardening-plastic (NLKP) material constitutive relations appropriate for hardened bearing steel and the 440C grade. The calculated contact pressure distribution is Hertzian for smooth body contact, and it displays intense, stationary, pressure spikes superposed on the Hertzian pressure for contact with the grooved and ridged surface. The results obtained for the 0.4 μm deep groove are consistent with those reported by Elsharkawy and Hamrock (1991) for an EHD lubricated contact. The effect of translating the counterface on the half space, as opposed to indenting the counterface on the half-space with no translation, is studied. The stress and strain values near the surface are found to be similar for the two cases, whereas they are significantly different in the subsurface. Efforts have been made to identify the material constitutive relations which best describe the deformation characteristics of the bearing steels in the initial few cycles. ELKP material constitutive relations produce less net plastic deformation in the initial stages, for a given stress, than seen in experiments. NLKP model produces more plasticity than the ELKP model and shows promise for treating the net distortions in the early stages. Artificial indents were inserted on the running track of the cylindrical rolling elements and profilometer measurements of these indents were made, before and after rolling. These preliminary measurements show that substantial plastic deformation takes place in the process of rolling. The deformations of the groove calculated with the finite element model are compared to those measured experimentally.

Modeling of Surface Modified Layers in the Presence of Surface Irregularities

Finite element calculations that examine the effects of surface modification on the deformation produced by pure rolling contact are presented. The model simulates the repeated, two-dimensional (line) contact of a cylinder that is rolling over a semi-infinite half space. The half space is treated as an elastic-linear-kinematic-hardening-plastic (ELKP) material with the cyclic flow properties of a hardened, HRC-62, bearing steel. Two different cases are examined : (i) a smooth half space is studied using a one-body model, and (ii) a half space with a 100 μm wide and 7 μm deep surface asperity is studied using a two-body model. In both cases, calculations are performed for a homogeneous body and a body with a shallow, surface modified layer. The surface modified layer is alternately : (a) stiffer, (b) harder, (c) softer, and (d) harder and stiffer as compared to the substrate. Consistent with the earlier studies of surface modification (Bhargava, 1987), the present findings indicate that the benefits of the mechanical property modifications are confined to the altered layer itself. This may explain the improvement in performance realized by relatively thin modified layers (5 μm).