“small” scars with a width of approximately 40 μm. The mean depth of the scars, for all scar sizes, was  kept constant at approximately 2 μm. Representative images of the “large” scar and the “small” scar are  shown in Figure 4.  Two defects were induced on each Si 3N4ball in a set of bearings. The scars on each ball were placed  approximately 45 degrees apart and oriented roughly 45 degrees relative to each other. The number of  balls in each bearing with scars varied depending on the purpose of the test. If the test was conducted to  study the influence of scar size on bearing fatigue life, then all the balls in the bearings contained scars for a total of 64 scars (4 bearings per test, 8 balls per bearing, and 2 scars per ball). Statistical analysis showed that 2 scars on each 7/16-inch-diameter ball ensured (with 99.9% probability) that at least one of  the 64 scars would be run over during the test, assuming that the balls maintained orientation through the entire duration of the test. On the other hand, if a test was conducted to study the influence of scar frequency on bearing fatigue life, then only two balls (ball 1 and ball 5) in each bearing contained scars for a total of 16 scars. It was also necessary to track the balls inside each bearing in order to properly document the progression  of the scars after testing. A small slit was gently scribed onto the phenolic cage (ball retainer) using a razor blade prior to inserting the balls. The slit provides a reference to identify the location of the first ball, e.g., ball 1 is the first ball to the right of the slit. Figure 4. Examples of artificially-generated scar s: “large” scar (left) and “small” scar (right). Finite-Element Modeling Development of Finite-Element Models for Parametric Studies Three-dimensional finite-element models (FEMs) of Si 3N4balls contacting steel raceways were  developed and compared against the analytical Hertzian contact stress solution. The FEM results for the elliptical contact patch size and parabolic contact stress distribution on the surface of the ball within the contact zone matched the Hertzian solution. Similar partial validations were completed for ball bearings contacting a flat surface. In addition, a subroutine was written to simulate the normal and traction loadsgenerated from a ball bearing contacting either a curved or flat surface. This subroutine allowed the non-linear contact conditions present in the original FEMs to be replaced, significantly reducing the solve time for the models. These prior FEMs were leveraged and improved upon in preparation for the numerical FEM validation (Figure 5).  The high fidelity models included elements in the grain-size level (microns). These models were  enhanced to provide more flexibility for future parametric studies. The FEMs were split into regions of varying mesh density based on the required stress resolution. Therefore, a large portion of the quarter  symmetry model was changed to quadratic tetrahedral elements that could rapidly reduce in size in the  contact region. Constraint equations were developed using the “tie” command in ABAQUS to enforce surface to surface continuity and facilitate coarse-to-fine mesh transitions. This strategy allowed for  multiple model variations with different element sizes in the contact region, as shown in Figure 6. 132