An Analytical Solution for Three-Dimensional Elliptical Elastic-Plastic Rolling Contact

2014 ◽  
Vol 658 ◽  
pp. 207-212
Author(s):  
Gabriel Popescu
Keyword(s):  
Residual Stresses ◽  
Yield Criterion ◽  
Tangential Force ◽  
Rolling Direction ◽  
Three Dimensional ◽  
Rolling Contact ◽  
Material Behavior ◽  
Hertzian Contact ◽  
Plastic Behavior ◽  
Elastic Plastic

An analytical three-dimensional elastic-plastic over-rolling solution is used to evaluate the plastic strains and residual stresses. Central to this plastic contact formulation is the incremental approach to deal with non-linear material behavior. The Prandtl-Reuss constitutive equations in conjunction with Huber-Mises-Hencky yield criterion and Ramberg-Osgood strain-hardening relationships are applied to describe the plastic behavior of common hardened bearing steel. The model was extended to include the tangential force in the rolling direction, assumed to be proportional to the hertzian contact pressure. Comparisons of three-dimensional pure rolling and rolling/sliding contact results were provided to elucidate the differences in residual stresses and residual profiles in case of kinematic and work-hardening materials.

Three-Dimensional Elastic-Plastic Stress Analysis of Rolling Contact

2002 ◽  
Vol 124 (4) ◽  
pp. 699-708 ◽  
Author(s):  
Yanyao Jiang ◽  
Biqiang Xu ◽  
Huseyin Sehitoglu
Keyword(s):  
Finite Element ◽  
Residual Stresses ◽  
Stress Analysis ◽  
Tangential Force ◽  
Three Dimensional ◽  
Rolling Contact ◽  
Normal Surface ◽  
Elastic Plastic ◽  
Residual Strains ◽  
Plastic Shakedown

Three-dimensional elastic-plastic rolling contact stress analysis was conducted incorporating elastic and plastic shakedown concepts. The Hertzian distribution was assumed for the normal surface contact load over a circular contact area. The tangential forces in both the rolling and lateral directions were considered and were assumed to be proportional to the Hertzian pressure. The elastic and plastic shakedown limits obtained for the three-dimensional contact problem revealed the role of both longitudinal and lateral shear traction on the shakedown results. An advanced cyclic plasticity model was implemented into a finite element code via the material subroutine. Finite element simulations were conducted to study the influences of the tangential surface forces in the two shear directions on residual stresses and residual strains. For all the cases simulated, the p0/k ratio (p0 is the maximum Hertzian pressure and k is the yield stress in shear) was 6.0. The Qx/P ratio, where Qx is the total tangential force on the contact surface in the rolling direction and P is the total normal surface pressure, ranged from 0 to 0.6. The Qy/P ratio (Qy is the total tangential force in the lateral direction) was either zero or 0.25. Residual stresses increase with increasing rolling passes but tend to stabilize. Residual strains also increase but the increase in residual strain per rolling pass (ratchetting rate) decays with rolling cycles. Residual stress levels can be as high as 2k when the Qx/P ratio is 0.6. Local accumulated shear strains can exceed 20 times the yield strain in shear after six rolling passes under extreme conditions. Comparisons of the two-dimensional and three-dimensional rolling contact results were provided to elucidate the differences in residual stresses and ratchetting strain predictions.

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.

Simulation of Plasto-Elastohydrodynamic Lubrication in a Rolling Contact

2016 ◽  
Vol 138 (3) ◽  
Author(s):  
Tao He ◽  
Dong Zhu ◽  
Jiaxu Wang
Keyword(s):  
Plastic Deformation ◽  
Plastic Strain ◽  
Rolling Direction ◽  
Three Dimensional ◽  
Elastohydrodynamic Lubrication ◽  
Surface Plastic Deformation ◽  
Rolling Contact ◽  
Surface Plastic ◽  
Contact Center ◽  
Elastic Plastic

Surface plastic deformation due to contact (lubricated or dry) widely exists in many mechanical components, as subsurface stress caused by high-pressure concentrated in the contact zone often exceeds the material yielding limit, and the plastic strain accumulates when the load is increased and/or repeatedly applied to the surface in a rolling contact. However, previous plasto-elastohydrodynamic lubrication (PEHL) studies were mainly for the preliminary case of having a rigid ball (or roller) rotating on a stationary elastic–plastic flat with a fixed contact center, for which the numerical simulation is relatively simple. This paper presents an efficient method for simulating PEHL in a rolling contact. The von Mises yield criteria are used for determining the plastic zone, and the total computation domain is discretized into a number of cuboidal elements underneath the contacting surface, each one is considered as a cuboid with uniform plastic strain inside. The residual stress and surface plastic deformation resulted from the plastic strain can be solved as a half-space eigenstrain–eigenstress problem. A combination of three-dimensional (3D) and two-dimensional (2D) discrete convolution and fast Fourier transform (DC-FFT) techniques is used for accelerating the computation. It is observed that if a rigid ball rolls on an elastic–plastic surface, the characteristics of PEHL lubricant film thickness and pressure distribution are different from those of PEHL in the preliminary cases previously investigated. It is also found that with the increase of rolling cycles, the increment of plastic strain accumulation gradually approaches a stable value or drops down to zero, determined by the applied load and the material hardening properties, eventually causing a groove along the rolling direction. Simulation results for different material hardening properties are also compared to reveal the effect of body materials on the PEHL behaviors.

Three-Dimensional Finite Element Elastic–Plastic Model for Subsurface Initiated Spalling in Rolling Contacts

2013 ◽  
Vol 136 (1) ◽  
Author(s):  
John A. R. Bomidi ◽  
Farshid Sadeghi
Keyword(s):  
Finite Element ◽  
Plastic Strain ◽  
Fatigue Damage ◽  
Three Dimensional ◽  
Rolling Contact ◽  
Material Behavior ◽  
Lower Percentage ◽  
Fe Model ◽  
Plastic Model ◽  
Elastic Plastic

In this investigation, a three-dimensional (3D) finite element (FE) model was developed to study subsurface initiated spalling observed in rolling line contact of tribo components such as bearings. An elastic–kinematic hardening–plastic material model is employed to capture the material behavior of bearing steel and is coupled with the continuum damage mechanics (CDM) approach to capture the material degradation due to fatigue. The fatigue damage model employs both stress and accumulated plastic strain based damage evolution laws for fatigue failure initiation and propagation. Failure is modeled by mesh partitioning along unstructured, nonplanar, intergranular paths of the microstructure topology represented by randomly generated Voronoi tessellations. The elastic–plastic model coupled with CDM was used to predict both ratcheting behavior and fatigue damage in heavily loaded contacts. Fatigue damage induced due to the accumulated plastic strains around broken intergranular joints drive the majority of the crack propagation stage, resulting in a lower percentage of life spent in propagation. The 3D FE model was used to determine fatigue life at different contact pressures ranging from 2 to 4.5 GPa for 33 different randomly generated microstructure topology models. The effect of change in contact pressure due to subsurface damage and plastic strain accumulation was also captured by explicitly modeling the rolling contact geometry and the results were compared to those generated assuming a Hertzian pressure profile. The spall shape, fatigue lives, and their dispersion characterized by Weibull slopes obtained from the model correlate well with the previously published experimental results.

Cyclic Deformation Caused by Repeatedly Contact Loading

2018 ◽  
Vol 883 ◽  
pp. 8-15 ◽  
Author(s):  
Chang Hung Kuo ◽  
Siew Fern Lim ◽  
Hung Ru Ho
Keyword(s):  
Plastic Deformation ◽  
Residual Stresses ◽  
Rolling Contact ◽  
Plastic Behavior ◽  
Plastic Strains ◽  
Contact Loading ◽  
Mapping Algorithm ◽  
Cyclic Plastic ◽  
Elastic Plastic ◽  
Shakedown Limit

An elastic-plastic contact stress analysis is presented to study cyclic plastic deformation of rolling elements under repeatedly contact loadings. The rolling contact is simulated by a Hertzian line contact loading translating over the surface of an elastic-plastic half-space, and the Chaboche nonlinear hardening rule is used to model the cyclic plastic behavior of contact components. A finite element procedure based on the return mapping algorithm is implemented to analyze the evolution plastic strains and residual stresses versus contact cycles. For the contact loading below the shakedown limit, p0/k=4, the plastic deformation occur only at first few contact cycles and become pure elastic in the subsequent cycles due to the existing residual stresses and material hardening. For the contact loading exceeding the shakedown limit, p0/k=7, the plastic strains increase progressively with each pass of contact cycles and result in plastic ratchetting. The normal residual stresses, however, quickly reach a steady state after few contact cycles.

Effect of Non-Steady State Loading on Rolling-Sliding Contact Stress

2010 ◽  
Vol 97-101 ◽  
pp. 1207-1211
Author(s):  
Jun Guo ◽  
Xue Song Jin ◽  
Ze Feng Wen ◽  
Qi Yue Liu
Keyword(s):  
Steady State ◽  
Residual Stresses ◽  
Tangential Force ◽  
Rolling Contact ◽  
Sliding Contact ◽  
Cyclic Plasticity ◽  
Wave Crest ◽  
Elastic Plastic ◽  
Steady State Rolling ◽  
Residual Strains

The stresses, strains, and deformations produced by repeated, two-dimensional non-steady state rolling-sliding contact were analyzed using an elastic-plastic finite element model. An advanced cyclic plasticity model was used. The non-steady state rolling contact was restricted to a harmonic variation of the normal Herztian contact pressure. Repeated rolling and sliding were simulated by multiple translations of a set of varying normal and tangential surface tractions across an elastic-plastic semi-infinite half space. The non-steady state loading considered results in a wavy contact surface profile. The surface displacements and wave depth of the wavy deformation increase with increasing rolling passes, but the increases in wave depth per rolling pass (ratchetting rate) decay. The residual stresses and strains near the wave trough of the residual wavy deformation are higher than those near the wave crest. The results are in agreement with the experimental observations. The tangential force has a greater influence on the residual strains than on the residual stresses.

Observation of Fatigue Fracture on PEEK Shaft against Alumina Bearing’s Ball under One-Point Rolling Contact

2016 ◽  
Vol 878 ◽  
pp. 137-141 ◽  
Author(s):  
Hitonobu Koike ◽  
Genya Yamaguchi ◽  
Koshiro Mizobe ◽  
Yuji Kashima ◽  
Katsuyuki Kida
Keyword(s):  
Fatigue Fracture ◽  
Rolling Contact Fatigue ◽  
Rolling Direction ◽  
Contact Fatigue ◽  
Rolling Contact ◽  
Hertzian Contact ◽  
Subsurface Crack ◽  
Mechanical Elements ◽  
The One ◽  
Alumina Ball

Tribological fatigue failure of the machined PEEK shaft was investigated through the one-point type rolling contact fatigue test between a PEEK shaft and an alumina ball, in order to explore fatigue fracture mechanism of frictional parts working at high frequency in various mechanical elements. Due to Hertzian contact of cyclic compressive stress, the subsurface crack occurred within approximately 300 μm depth from thesurface and propagated along the rolling direction. After that, the subsurface crack propagation direction changed toward the surface. The flaking occurred on the raceway of the PEEK shaft when the subsurface crack reached to the PEEK shaft surface.

An Extension of CEB Elastic-Plastic Contact Model

2007 ◽  
Author(s):  
A. Sepehri ◽  
K. Farhang
Keyword(s):  
Contact Force ◽  
Tangential Force ◽  
Three Dimensional ◽  
Tangential Direction ◽  
Asperity Contact ◽  
Force Component ◽  
Normal Contact ◽  
Elastic Plastic ◽  
Force Components ◽  
Plastic Parts

Three dimensional elastic-plastic contact of two nominally flat rough surfaces is by developing the equations governing the shoulder-shoulder contact of asperities based on the Chang, Etsion and Bogy (CEB) model of contact in which volume conservation is assumed in the plastic flow regime. Shoulder-shoulder asperity contact yields a slanted contact force consisting of both tangential (parallel to mean plane) and normal components. Each force component comprises elastic and elastic-plastic parts. Statistical summation of normal force components leads to the derivation of the normal contact force for the elastic-plastic contact akin to the CEB model. Half-plane tangential force due to elastic-plastic contact is derived through the statistical summation of tangential force component along an arbitrary tangential direction.

Stress Analysis of SS316L Tube Die Expansion for High Pressure Gas Coolers

2020 ◽  
Author(s):  
Zijian Zhao ◽  
Abdel-Hakim Bouzid
Keyword(s):  
Residual Stress ◽  
High Pressure ◽  
Plastic Material ◽  
Research Work ◽  
Material Behavior ◽  
Isotropic Hardening ◽  
Plastic Behavior ◽  
Expansion Process ◽  
Elastic Plastic ◽  
Stress States

Abstract SS316L finned tubes are becoming very popular in high-pressure gas exchangers and particularly in CO2 cooler applications. Due to the high-pressure requirement during operation, these tubes require an accurate residual stress evaluation during the expansion process. Indeed, die expansion of SS tubes creates not only high stresses when combined with operation stresses but also micro-cracks during expansion when the expansion process is not very well controlled. This research work aims at studying the elastic-plastic behavior and estimating the residual stress states by modeling the die expansion process. The stresses and deformations of the joint are analyzed numerically using the finite element method. The expansion and contraction process is modeled considering elastic-plastic material behavior for different die sizes. The maximum longitudinal, tangential and contact stresses are evaluated to verify the critical stress state of the joint during the expansion process. The importance of the material behavior in evaluating the residual stresses using kinematic and isotropic hardening is addressed.

Elasto-Plastic Contact Stress Analysis of Hardened Elements under Repeated Contact Loading

2019 ◽  
Vol 823 ◽  
pp. 91-96
Author(s):  
Chang Hung Kuo
Keyword(s):  
Plastic Deformation ◽  
Stress Analysis ◽  
Contact Stress ◽  
Surface Hardness ◽  
Hardened Layer ◽  
Rolling Contact ◽  
Plastic Behavior ◽  
Contact Loading ◽  
Cyclic Plastic ◽  
Elastic Plastic

An elastic-plastic contact stress analysis is presented to study cyclic plastic deformation of surface hardened rolling elements under repeated contacts. The rolling contact is simulated by a Hertz contact loading moving across an elastic-plastic half-space. An exponential model with hardness varying with depth is employed for the surface hardened components, and the Chaboche nonlinear hardening rule is used to model cyclic plastic behavior of contact elements. Numerical results show that the hardened layer can effectively reduce the plastic deformation near contact surface. The contact elements with sufficient surface hardness may reach elastic shakedown state under repeatedly rolling contact. As the hardened layer reaches a certain depth, e.g. two times of half contact length, however, the effects of case depth on plastic strain and residual stress become negligible after hundred contact cycles.

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