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

1987 ◽  
Vol 109 (4) ◽  
pp. 618-626 ◽  
Author(s):  
G. T. Hahn ◽  
V. Bhargava ◽  
C. A. Rubin ◽  
Q. Chen ◽  
K. Kim
Keyword(s):  
Residual Stresses ◽  
Kinematic Hardening ◽  
Cyclic Strain ◽  
Later Life ◽  
Element Model ◽  
Cyclic Stress ◽  
Bearing Steel ◽  
Rolling Contact ◽  
Cyclic Plasticity ◽  
Ball Bearings

Measurements of the cyclic stress-strain hysteresis loop shapes of hardened, HRC-62, SAE 52100 bearing steel, derived from torsion tests are presented. These are reduced to 3-parameter, elastic-linear-kinematic hardening-plastic (ELKP) representations. The ELKP behavior and properties of the steel are employed in an elastic-plastic finite element model of two dimensional, rolling contact. The distortion of the rim and the distribution and magnitude of the residual stresses and cyclic plasticity for repeated contacts at a Hertzian pressure of p0 = 3636 MPa (528 ksi), are calculated. The results are compared with the residual stresses and other features observed in the inner raceway of SAE 52100 steel, deep grooved ball bearings. The calculations predict the modest residual stresses observed in the early life: N ≲ 106 contacts. The much higher levels of residual stress that develop in later life: 108 ≲ N ≲ 1010, are shown to be connected with metallurgical changes and an attending volume expansion that are cyclic strain induced. The origins of these stresses and their effect on bearing life are discussed.

Finite Element Analysis of Rolling Contact for Nonlinear Kinematic Hardening Bearing Steel

1995 ◽  
Vol 117 (4) ◽  
pp. 729-736 ◽  
Author(s):  
M. Howell ◽  
G. T. Hahn ◽  
C. A. Rubin ◽  
D. L. McDowell
Keyword(s):  
Finite Element ◽  
Kinematic Hardening ◽  
Element Model ◽  
Bearing Steel ◽  
Rolling Contact ◽  
Image Point ◽  
Element Analysis ◽  
Transient Region ◽  
Pure Rolling ◽  
Constitutive Properties

A Mroz image point, two surface, nonlinear-kinematic-hardening-plastic (MNKP) representation of bearing steel is inserted into a finite element model of 2-dimensional, line contact for pure rolling. The calculations are compared with previous results for the same contact pressure derived for elastic-linear-kinematic-hardening-plastic (ELKP) behavior. The residual stress, deformation, and the connection between continuing cyclic deformation, etching bands, and cracks are analyzed. Unlike the ELKP constitutive properties, the MNKP behavior displays a distinct transient region which results in higher residual stresses.

scholarly journals Micromechanical Modelling of the Cyclic Deformation Behavior of Martensitic SAE 4150—A Comparison of Different Kinematic Hardening Models

Metals ◽  
2019 ◽  
Vol 9 (3) ◽  
pp. 368 ◽  
Author(s):  
Benjamin Schäfer ◽  
Xiaochen Song ◽  
Petra Sonnweber-Ribic ◽  
Hamad ul Hassan ◽  
Alexander Hartmaier
Keyword(s):  
Kinematic Hardening ◽  
Three Dimensional ◽  
High Strength ◽  
Element Model ◽  
Calibration Procedure ◽  
Cyclic Stress ◽  
System Level ◽  
Strain Behavior ◽  
Hardening Models ◽  
Mean Stress Relaxation

A fundamental prerequisite for the micromechanical simulation of fatigue is the appropriate modelling of the effective cyclic properties of the considered material. Therefore, kinematic hardening formulations on the slip system level are of crucial importance due to their fundamental relevance in cyclic material modelling. The focus of this study is the comparison of three different kinematic hardening models (Armstrong Frederick, Chaboche, and Ohno–Wang). In this work, investigations are performed on the modelling and prediction of the cyclic stress-strain behavior of the martensitic high-strength steel SAE 4150 for two different total strain ratios (R ε = −1 and R ε = 0). In the first step, a three-dimensional martensitic microstructure model is developed by using multiscale Voronoi tessellations. Based on this martensitic representative volume element, micromechanical simulations are performed by a crystal plasticity finite element model. For the constitutive model calibration, a new multi-objective calibration procedure incorporating a sensitivity analysis as well as an evolutionary algorithm is presented. The numerical results of different kinematic hardening models are compared to experimental data with respect to the appropriate modelling of the Bauschinger effect and the mean stress relaxation behavior at R ε = 0. It is concluded that the Ohno–Wang model is superior to the Armstrong Frederick and Chaboche kinematic hardening model at R ε = −1 as well as at R ε = 0.

An Analytical Approach to Elastic-Plastic Stress Analysis of Rolling Contact

1994 ◽  
Vol 116 (3) ◽  
pp. 577-587 ◽  
Author(s):  
Yanyao Jiang ◽  
Huseyin Sehitoglu
Keyword(s):  
Residual Stresses ◽  
Stress Analysis ◽  
Analytical Approach ◽  
Kinematic Hardening ◽  
Tangential Force ◽  
Rolling Contact ◽  
Approximate Determination ◽  
Elastic Plastic ◽  
Surface Plasticity ◽  
Plastic Stress

Based on a stress invariant hypothesis and a stress/strain relaxation procedure, an analytical approach is forwarded for approximate determination of residual stresses and strain accumulation in elastic-plastic stress analysis of rolling contact. For line rolling contact problems, the proposed method produces residual stress distributions in favorable agreement with the existing finite element findings. It constitutes a significant improvement over the Merwin-Johnson and the McDowell-Moyar methods established earlier. The proposed approach is employed to study combined rolling and sliding for selected materials, with special attention devoted to 1070 steel behavior. Normal load determines the subsurface residual stresses and the size of the subsurface plastic zone. On the other hand, the influence of tangential force penetrates to a depth of 0.3a, where a is the half width of the contact area, and has diminishing influence on the residual stresses beyond this thin layer. A two-surface plasticity model, commensurate with nonlinear kinematic hardening, is utilized in solution of incremental surface displacements with repeated rolling. It is demonstrated that a driven wheel undergoes greater plastic deformation than the driving wheel, suggesting that the driven wheel experiences enhanced fatigue damage. Furthermore, the calculated residual stresses are compared with the existing experimental data from the literature with exceptional agreements.

Residual Stresses in 3D Sheet Metal Guillotining Using a Coupled Finite Elastoplastic Damage Model

2006 ◽  
Vol 524-525 ◽  
pp. 89-94
Author(s):  
Abel Cherouat ◽  
N. Belamri ◽  
Khemais Saanouni ◽  
P. Autesserre
Keyword(s):  
Numerical Simulation ◽  
Residual Stresses ◽  
Sheet Metal ◽  
Kinematic Hardening ◽  
Damage Model ◽  
Element Model ◽  
Elastoplastic Model ◽  
Dynamic Resolution ◽  
Explicit Dynamic ◽  
Fully Coupled

This work deals with the numerical simulation of 3D guillotining of sheet metal using anisotropic elastoplastic model accounting for non-linear isotropic and kinematic hardening fully coupled with isotropic ductile damage and initial residual stresses. Both theoretical and numerical aspects are presented. A 3D finite element model is developed for the numerical simulation of the study state guillotining process. An explicit dynamic resolution strategy is used to solve the associated initial and boundary value problem. Results from the simulation of the guillotining process are given and the influence of residual stresses is investigated.

Compressive Residual Stresses Effect on Fatigue Life of Rolling Bearings

2007 ◽  
Author(s):  
Spiridon S. Cretu ◽  
Marcelin I. Benchea ◽  
Ovidiu S. Cretu
Keyword(s):  
Fatigue Life ◽  
Residual Stresses ◽  
Equivalent Stress ◽  
Rolling Contact ◽  
Deformation Analysis ◽  
Ball Bearings ◽  
Analysis Model ◽  
Loading Cycle ◽  
Von Mises ◽  
Compressive Residual Stresses

The fatigue life tests carried out on two groups of ball bearings confirm the positive influence of the compressive residual stresses induced by a previous loading in the elastic-plastic domain. The values of residual stresses are numerically evaluated by employing a three-dimensional strain deformation analysis model. The model is developed in the frame of the incremental theory of plasticity by using the von Mises yield criterion and Prandtl-Reuss equations. To consider the material behaviour the Ramberg-Osgood stress-strain equation is involved and a nonlinear equation is considered to model the influence of the retained austenite. To attain the final load of each loading cycle the two bodies are brought into contact incrementally, so that for each new load increment the new pressure distribution is obtained as the solution of a constrained system of equation. Conjugate gradients method in conjunction with discrete convolution fast Fourier transform is used to solve the huge system of equations. Both the new contact geometry and residual stresses distributions, are further considered as initial values for the next loading cycle, the incremental technique being reiterated. The cyclic evaluation process of both plastic strains and residual stresses is performed until the material shakedowns. Comparisons of the computed residual stresses and deformed profiles with corresponding measured values reveal a good agreement and validate the analysis model. The von Mises equivalent stress, able to include both elastic and residual stresses, is considered in Ioannides-Harris rolling contact fatigue model to obtain theoretical lives of the ball bearings groups. The theoretical analysis reveals also greater fatigue lives for the ball bearings groups with induced residual stresses than the fatigue lives of the group without induced residual stresses.

Modeling of Surface Modified Layers in the Presence of Surface Irregularities

1996 ◽  
Vol 118 (4) ◽  
pp. 753-758 ◽  
Author(s):  
Vikas Gupta ◽  
George T. Hahn ◽  
Pedro Bastias ◽  
Carol A. Rubin
Keyword(s):  
Surface Modification ◽  
Half Space ◽  
Kinematic Hardening ◽  
Bearing Steel ◽  
Rolling Contact ◽  
Body Model ◽  
Altered Layer ◽  
Surface Irregularities ◽  
Modified Layer ◽  
Surface Modified

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).

Microstructural Alterations of Rolling—Bearing Steel Undergoing Cyclic Stressing

1966 ◽  
Vol 88 (3) ◽  
pp. 555-565 ◽  
Author(s):  
J. A. Martin ◽  
S. F. Borgese ◽  
A. D. Eberhardt
Keyword(s):  
Shear Stress ◽  
Fatigue Cracking ◽  
Rolling Bearing ◽  
Cyclic Stress ◽  
Bearing Steel ◽  
Rolling Contact ◽  
Microstructural Alterations ◽  
Transmission Electron ◽  
Aisi 52100 ◽  
A Cell

After prolonged cyclic stressing in rolling contact, AISI 52100 bearing steel parts develop extensive regions of microstructural alteration, designated as white etching areas. These are oriented in predictable directions relative to the rolling track. Lenticular carbides are always associated with these areas. Evidence is presented indicating that the boundaries of lenticular carbides constitute planes of weakness which may be preferred planes of fatigue cracking. In the transmission electron microscope the martensitic structure appears gradually transformed into a cell like structure by the action of cyclic stress. The size of crystallites is greatly reduced in this process. The density of microstructural change is found increased with cycling and is distributed in depth along a curve resembling that of the calculated maximum unidirectional shear stress with little or no visible change in the region of maximum orthogonal (alternating) shear stress.

Improvement of Rolling Contact Fatigue Life by a Preliminary Loading in Elastic-Plastic Domain

2008 ◽  
Author(s):  
Spiridon Cretu
Keyword(s):  
Fatigue Life ◽  
Residual Stresses ◽  
Rolling Contact Fatigue ◽  
Contact Fatigue ◽  
Rolling Contact ◽  
Ball Bearings ◽  
Loading Cycle ◽  
Elastic Plastic ◽  
Plastic Domain ◽  
Von Mises

An analysis model has been developed to model the nonlinear strain rate dependent deformation of rolling bearing steel stressed in the elastic-plastic domain. The model is developed in the frame of the incremental theory of plasticity by using the von Mises yield criterion and Prandtl-Reuss equations. By considering the isotropic and non-linear kinematic hardening laws of Lemaitre-Caboche, the model accounts for the cyclic hardening phenomena. To attain the final load of each loading cycle, the two bodies are brought into contact incrementally. For each new load increment new increments for the components of stress and strain tensors, but also increments of residual stresses, are computed for each point of the 3D mesh. Both, the new contact geometry and residual stresses distributions, are further considered as initial values for the next loading cycle, the incremental technique being reiterated. The cyclic evaluation process of both, plastic strains and residual stresses is performed until the material shakedowns. The experimental part of the paper regards to the rolling contact fatigue tests carried out on two groups of line contact test specimens and on two groups of deep groove ball bearings. In both cases, the experimental data reveal more than two times greater fatigue life for the group with induced residual stresses versus the life of the reference group. The von Mises equivalent stress is considered in Ioannides-Harris rolling contact fatigue model to obtain theoretical lives. The theoretical analysis revealed greater fatigue lives for the test specimens and for the ball bearings groups with induced residual stresses than the fatigue lives of the corresponding reference groups.

Elasto-Plastic Finite Element Analysis of Repeated Three-Dimensional, Elliptical Rolling Contact With Rail Wheel Properties

1991 ◽  
Vol 113 (3) ◽  
pp. 434-441 ◽  
Author(s):  
S. M. Kulkarni ◽  
G. T. Hahn ◽  
C. A. Rubin ◽  
V. Bhargava
Keyword(s):  
Finite Element ◽  
Plastic Strain ◽  
Half Space ◽  
Kinematic Hardening ◽  
Rolling Direction ◽  
Three Dimensional ◽  
Rolling Contact ◽  
Cyclic Plasticity ◽  
Wheel Load ◽  
Stress Strain

This paper presents an elasto-plastic analysis of the repeated, frictionless, three-dimensional rolling contact similar to the ones produced by the rail-wheel geometry. This paper treats an elliptical contact rolling across a semi-infinite half space. The contact shape and loading: semi-major axis (in the rolling direction), w1 = 8 mm, and semi-minor axis, w2 = 5.88 mm, reflect standard rail and wheel curvatures and a wheel load of 149 KN (33,000 lb). A three-dimensional, elasto-plastic finite element model, developed earlier, is employed together with the elastic-linear-kinematic-hardening-plastic (ELKP) idealization of the cyclic plastic behaviour of a material similar to rail and wheel steels. The calculations present the displacements, the stress-strain distributions, stress-plastic strain histories and the plastic strain ranges in the half-space. The cyclic plasticity approaches a steady state after one contact with further contacts producing open but fully reversed stress-strain hysteresis loops, i.e., plastic shakedown.

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

1991 ◽  
Vol 58 (2) ◽  
pp. 347-353 ◽  
Author(s):  
S. M. Kulkarni ◽  
G. T. Hahn ◽  
C. A. Rubin ◽  
V. Bhargava
Keyword(s):  
Finite Element ◽  
Half Space ◽  
Kinematic Hardening ◽  
Three Dimensional ◽  
Bearing Steel ◽  
Complex Stress State ◽  
Rolling Contact ◽  
Stress Strain ◽  
Element Analysis ◽  
Shakedown Limit

This paper describes calculations for repeated, frictionless, three-dimensional rolling contact, for a relative peak pressure (po/k) of 6.0 (above the shakedown limit) for a circular contact patch. This analysis was carried out for two material responses, elastic-perfectly plastic (EPP) and elastic-linear-kinematic-hardening plastic (ELKP), using the elasto-plastic finite element model developed earlier. The ELKP material parameters are those appropriate for hardened bearing steel. Frictionless three-dimensional rolling contact is simulated by repeatedly translating a Hertzian pressure distribution across the surface of an elasto-plastic half space. The half space is represented by a finite mesh with elastic boundaries. The paper describes the complex stress state existing in the half space and the attending plasticity, as the load translates. The calculations present the distortion of the rim, the residual stress-strain distributions, stress-strain histories, and the cyclic plastic strain increments in the vicinity of the contact. Compared with the analyses at the shakedown limit, higher residual stresses and strains are observed.

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