Richard G. Rateick

A Statistical Damage Mechanics Model for Subsurface Initiated Spalling in Rolling Contacts

Fatigue lives of rolling element bearings exhibit a wide scatter due to the statistical nature of the rolling contact fatigue failure process. Empirical life models that account for this dispersion do not provide insights into the physical mechanisms that lead to this scatter. One of the primary reasons for dispersion in lives is the stochastic nature of the bearing material. Here, a damage mechanics based fatigue model is introduced in conjunction with the idea of discrete material representation that takes the effect of material microstructure explicitly into account. Two sources of material randomness are considered: (1) the topological randomness due to geometric variability in the material micro-structure and (2) the material property randomness due to nonuniform distribution of properties throughout the material. The effect of these variations on the subsurface stress fields in rolling element line contacts is studied. The damage model, which incorporates cyclic damage accumulation and progressive degradation of material properties with rolling contact cycling, is used to study the mechanisms of subsurface initiated spalling in bearing contacts. Crack initiation as well as propagation stages are modeled using damaged material zones in a unified framework. The spalling phenomenon is found to occur through microcrack initiation below the surface where multiple microcracks coalesce and subsequent cracks propagate to the surface. The computed crack trajectories and spall profiles are found to be consistent with experimental observations. The microcrack initiation phase is found to be only a small fraction of the total spalling life and the scatter in total life is primarily governed by the scatter in the propagation phase of the cracks through the microstructure. Spalling lives are found to follow a three-parameter Weibull distribution more closely compared to the conventionally used two-parameter Weibull distribution. The Weibull slopes obtained are within experimentally observed values for bearing steels. Spalling lives are found to follow an inverse power law relationship with respect to the contact pressure with a stress-life exponent of 9.35.

A Numerical Model for Life Scatter in Rolling Element Bearings

Fatigue lives of rolling element bearings exhibit a wide scatter due to the statistical nature of the mechanisms responsible for the bearing failure process. Life models that account for this dispersion are empirical in nature and do not provide insights into the physical mechanisms that lead to this scatter. One of the primary reasons for dispersion in lives is the inhomogeneous nature of the bearing material. Here, a new approach based on a discrete material representation is presented that simulates this inherent material randomness. In this investigation, two levels of randomness are considered: (1) the topological randomness due to geometric variability in the material microstructure and (2) the material property randomness due to nonuniform distribution of properties throughout the material. The effect of these variations on the subsurface stress field in Hertzian line contacts is studied. Fatigue life is formulated as a function of a critical stress quantity and its corresponding depth, following a similar approach to the Lundberg-Palmgren theory. However, instead of explicitly assuming a Weibull distribution of fatigue lives, the life distribution is obtained as an outcome of numerical simulations. A new critical stress quantity is introduced that considers shear stress acting along internal material planes of weakness. It is found that there is a scatter in the magnitude as well as depth of occurrence of this critical stress quantity, which leads to a scatter in computed fatigue lives. Further the range of depths within which the critical stress quantity occurs is found to be consistent with experimental observations of fatigue cracks. The life distributions obtained from the numerical simulations are found to follow a two-parameter Weibull distribution closely. The L 10 life and the Weibull slope decrease when a nonuniform distribution of elastic modulus is assumed throughout the material. The introduction of internal flaws in the material significantly reduces the L 10 life and the Weibull slope. However, it is found that the Weibull slope reaches a limiting value beyond a certain concentration of flaws. This limiting value is close to that predicted by the Lundberg-Palmgren theory. Weibull slopes obtained through the numerical simulations ranee from 1.29 to 3.36 and are within experimentally observed values for bearing steels.

Impedance Characterization of Anodic Barrier Al Oxide Film Beneath Porous Oxide Layer

Electrochemical impedance spectroscopy (EIS) is a common technique used in the assessment of the thickness of anodic oxide films formed on Al and its alloys. However, it is shown here that the resistance (R) values obtained from EIS data are highly dependent on the solution in which the measurements are made, while the capacitance (C) values are independent of the solution conditions and are therefore a much more reliable means of determining oxide film thickness and other properties. We also show that the experimental EIS data for unsealed porous anodic oxides formed on top of a barrier Al oxide film in acidic solutions exhibit only a single time constant, with very little influence seen from the overlying porous oxide layer on the apparent R and C values. The reason for this is demonstrated by utilizing the Laplace equation to calculate the electric field induced in the oxide, which confirms that the EIS response of these films can generally be assumed to reflect the properties and coverage of the underlying barrier oxide film.

Evaluation of Stresses Around Inclusions in Hertzian Contacts Using the Discrete Element Method

Inclusions are the primary sites for subsurface fatigue crack initiation in bearing contacts. To understand the mechanisms of subsurface crack nucleation under contact loading, a detailed description of the stress field around these inclusions is necessary. This paper presents a new approach to computing stresses in an inhomogeneous medium where inclusions are treated as inhomogeneities in a homogeneous material matrix. The approach is based on the Discrete Element (DE) Method in which the material continuum is replaced by a set of rigid discrete interacting elements. The elements are connected to each other along their sides through springs and dampers to form the macro-continuum and undergo relative displacements in accordance with Newtons laws of motion under the action of external loading. The spring properties are derived in terms of the overall elastic properties of the continuum. The relative motion between elements gives rise to contact forces due to stretching or compression of the inter-element springs. These forces are evaluated at each time-step and the corresponding equations of motion are solved for each element. Stresses are calculated from the inter-element joint forces. A Hertzian line contact case, with and without the presence of subsurface inclusions, is analyzed using the DE model. The DE model was used to determine stresses for an inclusion-free medium that compares well with that obtained from the continuum elasticity models. Parametric studies are then carried out to investigate the effects of size, location, orientation, and elastic properties of inclusions on the subsurface stress field. Both inclusions that are stiffer and/or softer than the base material are seen to give rise to stress concentrations. For inclusions that are stiffer than the base material (semi-infinite domain), the stress concentration effect increases with their elastic modulus. The stress concentration effect of a softer inclusion is higher than that of a stiffer inclusion. Inclusions that are oriented perpendicular to the surface give rise to much higher von Mises stresses than the ones that are oriented parallel to the surface. There is little change in the maximum von Mises stress for inclusions that are located deep within the surface.