Modern State of Experimentation and Modeling in Contact Fatigue Phenomenon: Part II—Analysis of the Existing Statistical Mathematical Models of Bearing and Gear Fatigue Life. New Statistical Model of Contact Fatigue

Extension to finite life of a failure assessment diagram for contact fatigue loading

“…without the effect of inherent defects, while in the right part describe a linear relationship in the log-log scale. It is noteworthy that this linear trend is very close to that of experimental rolling contact fatigue tests results carried out on bearings [38,39], and also agree with the statistical model proposed by Kudish and Burris [40].…”

Investigation of rolling contact crack initiation in bainitic and pearlitic rail steels

“…The Tallian model utilizes orthogonal shear stress field that is strongly dependent on depth as in the LP approach and considers the Paris Law 14 . Despite its noteworthy advantages over Ioannides–SKF and LP models, Tallian model suffers from considerable shortfalls: negligence of crack initiation life, 14 incompatibility of crack propagation mechanism with the acquired experimental data, and a defect severity distribution that does not take into account the changes in crack size with ongoing deformation 15 . These issues were addressed by a statistical model proposed by Kudish and Burris, 15 which accounts for complete crack propagation up to failure by improving Tallian's model with additions to the Paris Law, such as the friction coefficient, residual stress distribution, fracture toughness, and initial crack size distribution and location 14,15 …”

“…14 Despite its noteworthy advantages over Ioannides-SKF and LP models, Tallian model suffers from considerable shortfalls: negligence of crack initiation life, 14 incompatibility of crack propagation mechanism with the acquired experimental data, and a defect severity distribution that does not take into account the changes in crack size with ongoing deformation. 15 These issues were addressed by a statistical model proposed by Kudish and Burris, 15 which accounts for complete crack propagation up to failure by improving Tallian's model with additions to the Paris Law, such as the friction coefficient, residual stress distribution, fracture toughness, and initial crack size distribution and location. 14,15 In contrast to engineering models, the mechanism-based counterparts rely on theoretical constants and incorporate all details, such as residual stresses and strain amplitudes 3,14 of the stress-strain state (under rolling contact), and thus, they can be used in combination with material failure models.…”

“…15 These issues were addressed by a statistical model proposed by Kudish and Burris, 15 which accounts for complete crack propagation up to failure by improving Tallian's model with additions to the Paris Law, such as the friction coefficient, residual stress distribution, fracture toughness, and initial crack size distribution and location. 14,15 In contrast to engineering models, the mechanism-based counterparts rely on theoretical constants and incorporate all details, such as residual stresses and strain amplitudes 3,14 of the stress-strain state (under rolling contact), and thus, they can be used in combination with material failure models. However, the difficulties associated with the modelling of RCF, such as high computational costs and loss of consistency in simulations when large con-tact loads are applied, 3 had initially limited the advance of mechanism-based modelling.…”

A Unified Approach to Contact and Structural Fatigue

“…The model is based on crack mechanics, kinetics of crack propagation, and statistical treatment of material defects. The foundation of the model follows from the analysis [1,2], a model of contact fatigue [3], and the asymptotic formulas for the stress intensity coefficients (see [4]) developed earlier. The model takes into account the local stress distribution, initial statistical distribution of defects versus their size, defect location and crack propagation directions related to the specific stress state of the material, material fatigue resistance parameters, etc.…”