Profilometric Roughness and Contact Fatigue

Contact fatigue life prediction models have existed for half a century [1]. Recent refinements take into account the microstresses superimposed on the Hertz contact stress field as a result of roughness in the two contacting surfaces [2, 3, 4].These latter efforts are characterized by the use of some simple asperity geometry (rounded-top prisms in [2] and Greenwood-Williamson model using Hertzian second-order) asperity shapes in [4]), to calculate microstress fields under asperities. Given these stress fields, the models predict fatigue life (in cycles) by integration, over the stressed volume, of a relationship of the form: (1)$$ - \ell n(dS) = C{t^a}{z^b}{N^c}dV$$ where C is a constant, t a stress, z a linear dimension, dV a volume elements and dS a local survival probability, a, b and c are (positive or negative) numeric exponents.