Fatigue and Stress Analyses of Rolling Contact
by
Y. Roger Jiang
Huseyin Sehitoglu
Department of Mechanical and Industrial Engineering
Abstract
Report 1 – Contact Fatigue Life Prediction Methods
Contact fatigue life estimates are reported using four different multiaxial fatigue criteria. The first class of models is characterized by second invariant of deviatoric stress amplitude or maximum shear stress amplitude modified by the hydrostatic stresses. The second class of models is based on the critical plane approach incorporating the shear stress range or shear strain range and the normal stresses and strains on the critical plane. The predicted lives are reported over several po/σ′y ratios in the range 1 to 3 (peak Hertzian pressure normalized by yield strength) and q/p (shear to normal traction) ratios in the range 0 to 0.4, Depending on the model the estimated fatigue lives varied with q/p ratio from 0 to 0.4, in the range 102 to 109 cycles. The limitations of these models in handling both the compressive normal stresses and the non-proportionality of normal and shear stress components are discussed. The distinction is made between cases where the shear stress direction is fixed in the critical plane and the situations when the shear stress vector may vary within the critical plane. The fundamental differences between subsurface versus surface crack initiation and the influence of plastic deformation on the results are discussed.
Report 2 – Cyclic Stresses for Contact with Different Tangential Load Distributions
This study determined the cyclic stresses under line contact for a Hertzian distributed normal force and three different kinds (Type I, II and III) of slip plus stick tangential force distributions. Under slip-stick conditions, the Dtmax location moved to contact surface when the Q/P (Total tangential force/Total normal force) ratio was as low as 0.1. The magnitude of maximum shear stress range, Dtmax, and the orientation of Dtmax plane was established. The variations of shear stress and normal stresses (t versus s) on the Dtmax planes changed with different tangential tractions. Slip plus stick conditions were identified for highest maximum shear stress range, Dtmax, and highest tensile normal stresses. When Q/P = 0.3, Dtmax reached as high as 0.85po, and the maximum tensile normal stress on the Dtmax plane was as high as 0.7po. The orientation of the planes of Dsmax and smax was also established. The Dsmax and smax were highest at the contact surface. The Dsmax was as high as 2.4po in the Type I, Q/P = 0.3 case. We made the important observation that the Dsmax and Dtmax planes became nearly coincident at increased Q/P levels. The results have direct implications in understanding failure locations, failure planes, fatigue parameters, and designing experiments to study the wheel shelling and spalling phenomena.
Report 3 – Multiaxial Fatigue of 1070 Steel under Proportional and Non-Proportional Loading
In view of the need to develop fatigue models for stress states encountered in contact loading situations, which were extensively documented in AAR Report #1 ’90, and AAR Report #2 ’91, proportional and non-proportional compression-shear loading experiments are conducted on 1070 Steel. The normal stress-strain behavior and shear stress-strain behavior are evaluated on the specimen coordinate planes and later resolved on material planes including the principal stress range planes and the planes of maximum shear strain range. Macroscopic crack growth directions coincided with the planes of maximum principal stress range for most cases. Several fatigue life prediction parameters are employed to correlate the experimental results, critical plane models which utilized the maximum shear strain, and principal stress amplitudes, and two bulk parameters which are the effective stress amplitude modified by the hydrostatic stress, and the plastic strain energy approach. Despite the occurrence of crack growth on maximum principal stress amplitude planes, the predictions based on shear strain range parameters exhibited better agreement with the experimental results compared to the principal stress amplitude. The predictions based on the effective stress amplitude underpredicted the fatigue damage particularly at long lives, while the predictions based on the plastic strain energy density parameter agreed well with the experiments. A new multiaxial fatigue parameter is forwarded which combines the shear and the principal stress-strain terms and whose maximum value, obtained by surveying all planes, dictates the multiaxial fatigue damage.
Report 4 – An Analytical Approach for Elastic-Plastic Stress Analysis of Rolling Contact
An analytical approach, based on a stress invariant assumption and a stress/strain relaxation procedure, is developed for determination of residual stresses and strains in rolling contact. For line contact problems, the proposed method provides residual stress results comparable to published results obtained using the finite element method. Upon comparison of residual stress results with Merwin-Johnson’s method. McDowell-Moyar’s method, the proposed approach provided closest agreement with the finite element method.
The proposed approach is applied to the calculation of contact stresses and displacements under normal and tangential tractions using 1070 wheel steel properties. The study shows that a driven wheel undergoes higher plastic shear strains, hence higher fatigue damage, compared to the driving wheel. Single surface, two-surface and multiple surface yield theories are employed, and the results (stresses, displacements) depended strongly on the details of the plasticity relations.
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