Modeling and verification of ultra-high molecular weight polyethylene wear in multi-directional sliding

Abstract In a separate paper in this volume, the authors have discovered that the total wear of ultra-high molecular weight (UHMWPE) polyethylene moving along a circular path is directly proportional to the number of motion cycles and independent of the sliding distance per cycle. This is in conflict with common tribological principles particularly the Archard Equation that states that wear is proportional to load and sliding distance. The authors have also discovered that when the wear rate is defined as the volume loss per unit sliding distance (mm 3 /mm) rather than volume loss per cycle (mm 3 /cycle) it is directly proportional to the curvature ( k ) or the inverse of the sliding circle radius ( 1 / r ). Curvature is the mathematical equivalence to “cross-shear”. The present study attempts to quantify the effects of the “cross-shear” motion, sliding distance, load and contact area on the wear of UHMWPE both theoretically and experimentally. The theoretical approach starts with a single postulate that wear is proportional to the frictional work input multiplied by a “cross-shear” factor—sliding path curvature. For an UHMWPE with a nominal contact area A moving along a circular path l ( l= 2 πr , r is the radius or 1 / r is the curvature) under a normal load W , the volumetric wear rate per cycle of motion (Δ V / N ) is then deduced, which follows a simple equation: Δ V / N = KW 2/3 A 1/3 or Δ V = KW 2/3 A 1/3 N . A comprehensive set of experiments were carried out on a hip joint simulator with UHMWPE having different nominal contact areas ( A ) and under different peak loads ( W ). The relationship between wear rate and contact area and load was verified with near-perfect accuracy.