V. Bhargava

Elasto-Plastic Finite Element Analysis of Three-Dimensional Pure Rolling Contact Above the Shakedown Limit

This paper describes elasto-plastic finite element calculations of repeated, three-dimensional, pure rolling contact above shakedown. The calculations are for a sphere in contact with a flat, elastic-perfectly plastic half space at a relative peak pressure, po/k = 6.0. The contact is simulated by repeatedly translating a semiellipsoidal (Hertzian) pressure distribution across a 3-D mesh whose boundaries are appropriately displaced. The calculations describe the distortion of the rim, the residual stresses and strains and the incremental cyclic plastic strains.

The Cyclic Stress-Strain Properties, Hysteresis Loop Shape, and Kinematic Hardening of Two High-Strength Bearing Steels

Measurements of the shapes of the cyclic, stress-strain hysteresis loops obtained from AISI 1070 (HRC 60) and AISI 52100 (HRC 62) steels subjected to constant stress and constant plastic strain amplitude cycles in torsion are presented. The study examines plastic strain amplitudes in the range of 0.0002 ≤ Δεp/2≤ 0.0015, which are similar to the strain amplitudes produced by rolling contact. The effects of a mean stress are also evaluated. The cyclic hardening of the two steels and other changes in the character of the loops during the cyclic life, 34 ≤Nf≤ 2156, are defined. A three-parameter, bilinear, elastic-linear-kinematic-hardening-plastic (ELKP) model is shown to describe the multivalued cyclic stress-strain relations of these steels. The principal material properties of the model, in addition to the elastic modulus, the kinematic yield strength, and the plastic modulus, are evaluated. The ELKP properties define the material’s resistance to cyclic plasticity, the loop shape and area (plastic energy dissipation), the conventional cyclic stress-strain curve, the endurance limit, and the rolling contact shakedown pressure. The implications for rolling contact are discussed.

Rolling contact deformation, etching effects, and failure of high-strength bearing steel

This paper examines the connections between the continuing cyclic plastic deformation, the etching effects, and the fatigue life of a high-strength bearing steel under rolling contact. Etching effects, called the “dark etching regions” and the “white etching bands,” are observed after several million cycles. The inclinations of the white etching bands vary between 20 to 30 deg and 70 to 80 deg to the rolling direction, depending on the loading conditions and geometry of the rolling elements. The principal axes of stress and plastic strain rotate continuously as the rolling element translates over a fixed point below the running surface. At the same time, the cyclic plastic activity varies. A finite element model is used to calculate the inclinations and amounts of cyclic plastic strain as the roller translates over the running surface. The calculations are performed for both elastic linear kinematic-hardening plastic (ELKP) and elastic perfectlyplastic (EPP) material behaviors. Inclinations of concentrated plastic strain activity combined with low hydrostatic pressure are identified. There is a good correlation between the inclinations of the white etching bands and the inclinations of concentrated plastic activity calculated for the ELKP material behavior. No such correlation is obtained for the EPP behavior. Strain concentrations are intensified by the hydrostatic pressure dependence of the kinematic yield strength. While an equal amount of plastic strain activity occurs in the conjugate directions, no etching bands are observed at these inclinations. The reasons for this are not clear. The shakedown limit obtained for the two models is essentially the same. The fatigue lives under rolling contact are compared with the lives obtained in simple cyclic torsion experiments with the same cyclic plastic strain amplitudes. The rotation of the principal shear direction and the high hydrostatic pressure attending rolling contact may be responsible for the seven orders-of-magnitude longer contact lives.

Elastoplastic Finite Element Analysis of Three-Dimensional, Pure Rolling Contact at the Shakedown Limit

This paper describes a three-dimensional elastoplastic finite element model of repeated, frictionless rolling contact. The model treats a sphere rolling on an elastic-perfectly plastic and an elastic-linear-kinematic-hardening plastic, semi-infinite half space. The calculations are for a relative peak pressure (po /k ) = 4.68 (the theoretical shakedown limit for perfect plasticity). Three-dimensional rolling contact is simulated by repeatedly translating a hemispherical (Hertzian) pressure distribution across an elastoplastic semi-infinite half space. The semi-infinite half space is represented by a finite mesh with elastic boundaries. The calculations describe the distortion of the rim, the residual stress-strain distributions, stress-strain histories, and the cyclic plastic strain ranges in the vicinity of the contact.

Analysis of rolling contact with kinematic hardening for rail steel properties

Abstract This study presents calculations of two-dimensional rolling contact deformation for rail steel properties. Finite element analyses, previously carried out for perfect plasticity, are extended to the kinematic hardening behavior of rail steel. A three-parameter elastic-linear-kinematic-hardeningplastic description of the cyclic stress-strain behavior of rail steel is inserted in the finite element model. Steady state results are obtained after two translations. The effects of the kinematic hardening at three relative peak pressures p o k k = 4.0, 4.5 and 5.0 are examined. The calculations evaluate the rim distortion, the cyclic plastic strains and the residual stresses, the shakedown limit for kinematic hardening and the effects of strain-amplitudedependent kinematic properties. The calculations reveal that the kinematic hardening of rail steel produces substantial alterations relative to the deformation and residual stresses associated with perfect plasticity. Cyclic strains are an order of magnitude smaller and the residual stresses are about half the value of comparable relative contact pressures. While the relative elastic shakedown limit, p o k k = 4 , is the same as for perfect plasticity, absolute values of wheel load at shakedown are modest because of the relatively low value of the kinematic yield strength of rail steel. Accordingly, a 33000 lbf (146.7 KN) wheel load applied to a new rail produces a relative peak contact pressure p o k k = 6.2 which exceeds the corresponding shakedown limit.

The influence of residual stresses on rolling contact mode II driving force in bearing raceways

Abstract This paper evaluates the effects of rolling-contact-generated residual stresses on the mode II cyclic stress intensity range ΔK II that drives subsurface crack growth in a rim subjected to repeated rolling contacts. It treats the circumferential residual stresses generated in high strength bearing steels in the early life (2 ⩽ N ⩽ 10 7 contacts ) and the higher levels existing in the later life (10 8 ⩽ N ⩽ 10 10 contacts ). ΔK II is evaluated for repeated, two-dimensional, frictionless rolling contact, for small, planar, subsurface cracks under linear elastic fracture mechanics conditions. The calculations are performed as a function of hertzian pressure, relative crack depth, crack inclination, and crack face friction for the two sets of residual stress fields. The results are compared with observations of crack growth and spalling. The work shows that the later life residual stresses substantially reduce the ΔK II values for rough cracks at all but the smallest inclinations, favoring the formation of shells.

Finite Element Analysis of the Influence of Kinematic Hardening in Two-Dimensional, Repeated, Rolling-Sliding Contact

A study was performed wing a finite element model to compare the stresses, strains and deformations of repeated, two-dimensional, rolling-sliding contact for an elastic-kinematic-hardening-plastic (ELKP) representation of rail steel with those produced by elastic-perfectly plastic (EPP) material behavior. Kinematic-hardening produces fully reversed stress-strain hysteresis loops, and thus, no forward flow. Stresses, strain increments, and displacements are drastically reduced by the kinematic-hardening plasticity. Presented at the 43rd Annual Meeting in Cleveland, Ohio May 9–12, 1988

Analysis of cyclic crack growth in high strength roller bearings

Abstract The lives of ball and roller bearings and raceways depend on the number of rolling contacts consumed by 3 stages of the failure process: (i) the preinitiation; (ii) crack initiation, and (iii) crack growth stages. This paper employs fracture mechanics analyses to estimate the portion of the bearing life residing in the crack growth stage. Rough estimates of: (a) the Mode II, ΔK II driving force for small cracks below the rim surface subjected to repeated 2-dimensional, pure rolling contacts, (b) the corresponding crack growth rates, and (c) the number of contacts to failure, are obtained as a function of the peak contact pressure, initial flaw size and other variables. Factors influential to the growth stage are identified. Finally, the comparisons with measured total lives provide insights into the validity of the analysis and the importance of growth relative to the preinitiation and crack initiation stages.

Rolling contact deformation and microstructural changes in high strength bearing steel

Abstract This paper examines the connections between the continuing cyclic plastic deformation, the etching effects and the fatigue life of high strength bearing steel under rolling contact. A finite element model is used to calculate the increments of cyclic plastic strain as the roller translates over the running surface. The cyclic plastic strain is related to the plasticity-induced microstructural changes observed in bearings. The calculations are performed for both elastic linear kinematic hardening plastic and elastic-perfectly plastic material behaviors. Observed fatigue lives under rolling contact are compared with the lives obtained in simple cyclic torsion experiments with the same cyclic plastic strain amplitudes. The rotation of the principal shear direction, the smaller strained volume, and the high hydrostatic pressure attending rolling contact may be responsible for the contact lives, which are seven orders of magnitude longer.

Elastic-plastic analysis of hardened layers in rims subjected to repeated rolling contacts

This paper examines the effects of shallow, surface, and subsurface hardened layers on the response of rims to repeated, 2-dimensional (plane strain) rolling contacts. The rolling is simulated by translating a Hertzian pressure distribution across a finite element model of an elastic-plastic half-space. Four cases are examined: (1) a homogeneous rim, (2) and (3) rims with 0.2w-deep and 0.4w-deep (2w is the Hertzian contact width) hardened surface layers, and (4) a rim with a 0.4w-deep subsurface layer. The dimension 2w can be viewed as either the macrocontact width or the microasperity contact width. The calculations treat elastic-perfectly plastic, cycle and amplitude independent, Von Mises material behavior with the yield strength of the hardened layers twice the value of the surrounding material. The effects of pure rolling at a peak contact pressure-to-shear yield strength ratiop0/k = 5 are examined. The calculations describe the effects of the layers on the displacements of the rim surface, the extent of the plastic zone, the residual stresses, and incremental plastic strains. The results indicate that the response of the material at different depths is weakly coupled. Cyclic plasticity is eliminated in the hardened layers, but is not substantially altered in the adjacent material. The hardened layer must occupy a large part of the respective active plastic zones of the macrocontact and microasperity contact to prevent continuing cyclic plastic deformation in the two regions.