We analyze the deformation of the substrate matrix and the shear forces it is exposed to through the geometry of graphite flakes in the substrate from samples already subjected to breaking pressure applications up to 30 bar. Microscopic Images of the cross-section of the brake pad polished to a 0.1 μm scale were examined. Statistical analysis was conducted, state vectors and variance-co-variance matrix were defined, and considered every state as a distribution. Parameters for each “shear deformation stage” were estimated using Expectation-Maximization algorithm. Finally, a mixture model was identified for the distribution of graphite flakes across the rotor thickness.

The influence of localized corrosion on cementless titanium-alloy modular total hip arthroplasty was analyzed using numerical and stochastic modeling. Corrosion depth influences maximum stress significantly, thereby reducing the load carrying capacity. Numerical analysis revealed that the stress levels due to corrosion in the modular implants are influenced not only by the pit geometry, but also by the contact properties of the taper junctions. Subsequently, crevice corrosion was economically modeled with two parameters related to physical and chemical properties of the materials involved. The solution introduces a dimensionless number that determines whether anoxic conditions will be reached. The analysis confirms the powerlaw relationship for the exponent variation with the concentration gradient variation assumed by others. The results may be used in averting the progression to rapid corrosion growth through infusion of oxygen in the crevice at the appropriate time intervals. Stochastic modeling of crevice area and maximum depth shows a power-law increase in dispersion measures with exponent of 0.63--0.64 though the average increase follows a more modest exponent of 0.13– 0.15. A holistic approach, and continuous research towards the development of robust corrosion models is warranted so as to predict and enhance the design life of otherwise successful modular arthroplasties. A better understanding of the phenomenon may help alleviate early and catastrophic fractures.

Titanium alloy (Ti6Al4V (ASTM F-136)) is typically used for modular hip implant stems. This highly corrosion resistant alloy forms passive surface oxide films spontaneously. However, with modular designs, micro-motion may occur at the taper junctions during mechanical loading. Complex physical/chemical reactions take place which may result in pitting and crevice corrosion. Crevices between the taper junctions may allow the body fluids to enter and remain stagnant. These conditions make the modular tapers susceptible to fatigue and mechanically assisted crevice corrosion. When two or more surfaces are in close proximity, it leads to the creation of a locally blocked region in which enhanced dissolution may occur. The in vivo degradation of metal alloy implants compromises the structural integrity. Stochastic modeling of crevice corrosion is performed based on the mechanism behind the phenomenon. Sensitivity analysis is performed, and conclusions drawn.