George T. Hahn

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.

Analysis of the Rolling Contact Residual Stresses and Cyclic Plastic Deformation of SAE 52100 Steel Ball Bearings

Analyse des contraintes residuelles dans les contacts roulants et des deformations plastiques cycliques dans des roulements a billes en acier SAE 52100 (Society of automotive engineers)

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.

Elasto-Plastic Finite Element Analysis of Repeated, Two-Dimensional Rolling-Sliding Contacts

The stresses, strains, and deformations produced by repeated, two-dimensional rolling-sliding contact are analyzed using a modified finite element model developed by Bhargava et al. [1]. Rolling and sliding are simulated by translating an appropriate set of normal and tangential surface tractions across an elastic-perfectly plastic half space. The study examines a peak-pressure-to-shear strength ratio of p o /k = 4.5 and normal to tangential force ratios of T /N = 0.20 and T /N = 0.17. The calculations describe the residual stresses, displacements and the continuing cyclic radial, shear and equivalent strains generated at various depths in the rim. The results are compared with previous calculations by Johnson and Jefferis [2] of rolling-sliding contact and with pure rolling. The present work predicts much higher deformations than previously calculated.

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.

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 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.

The driving force for mode II crack growth under rolling contact

Abstract In this paper the driving force for the cyclic growth of small subsurface cracks subjected to repeated rolling contact is evaluated. Values of the mode II stress intensity range ΔKII are derived from the variations in the stress intensity factor KII with respect to the position of the contact for rolling in the absence of shear tractions and friction on the contact surface. The calculations take into account (i) the elastic contact stresses, (ii) the friction resisting the mode II sliding of the crack faces and (iii) the residual circumferential tensile and compressive stresses produced by plastic deformation close to the rim. The values of KII and ΔKII are evaluated as a function of the ratio of the peak contact pressure to the yield strength, the length of the crack, the depth of the crack below the surface, the inclination of the crack with respect to the rim surface and the coefficient of friction for the crack faces. Predictions of the cyclic crack growth rate, component life and the critical defect size, based on the ΔKII values, are illustrated.