Spatial geometric effects on the friction coefficients of UHMWPe

Abstract

Multi-directional wear of ultra-high molecular weight polyethylene (UHMWPe) is of particular interest due to its wide-spread use as a bearing component polymer in orthopedic implants. To date, attempts to quantify wear mechanisms have depended greatly upon material orientation theories and average wear values over long periods in specific motions. This study introduces spatially resolved in situ friction coefficient measurements over relevant motion paths with a tribometer that provides uniform pressure and velocity under the pin. Normal and friction forces were measured simultaneously under dry and lubricated conditions during curvature-modulated paths. Spatially resolved friction coefficients increased with decreasing radius of curvature, which is consistent with the hypothesis that molecular chain alignment during unidirectional sliding is disrupted in multi-directional sliding.

Introduction

Orthopedic joint implants are increasingly used in younger and more active patients. Finite wear lives of these joints require multiple surgeries to carry these patients through long life. The state of the art bearing material, ultra-high molecular weight polyethylene (UHMWPe), has been the focus of significant efforts to improve wear performance in these implants. Creep, counterface roughness, third body wear and sensitivity of the material to multi-directional motion paths have all been cited as primary contributors to bearing failures in UHMWPe implants. This paper intends to address the friction trace of multi-directional motion paths and contextualize the results within current wear models.

Many authors have observed a directional dependence on wear rate of UHWMPe, which does not typically form transfer films in the presence of consistent lubrication. They have shown that wear rate, k (mm³/Nm), typically increases 10–1000 times with a deviation from linear pin-on-disk sliding. Laurent et al. [1] and Bragdon et al. [2] have shown that cumulative wear during walking gait cycles in the medial compartment of knee implants, where the directionality of sliding is greater, is over 100% higher than in the lateral compartment. This apparent multi-directional sensitivity emphasizes the need for extensive multi-directional testing of UHMWPe (Table 1). Turell et al. [3], [4] and Muratoglu et al. [5] have investigated wear of UHMWPe in a rectangular wear pattern to simulate total hip replacement (THR). They relate an aspect ratio of the pattern to the wear factor k and surmise that orientation or texturing of the UHMWPe in one direction will affect wear in multiple directions. Saikko et al. [6] determined that the wear factor k showed a strong power relationship with the aspect ratio, AR, of oval-shaped paths of the form $k\propto 1/\sqrt{\text{AR}}$. Gevaert et al. [7] performed multi-directional wear tests with a motion path composed of a five-pointed star with five crossing points. They conclude that there is a direct and quantitative relationship between the measurements of cross-shear angle and damage, and that the ratio of those measurements is indicative of a material's ability to resist wear in a cross-shearing configuration.

Hamilton et al. [8] proposed a geometrical/statistical parameter to describe wear damage to UHMWPe, assuming a probable orientation direction of the material and its subsequent changes in motion direction. This is compared to clinical tibial component wear in a total knee replacement (TKR) in which there is a multi-directional sliding motion path with a high aspect ratio. Wang [9] proposed a unified theory of wear for UHMWPe in multi-directional sliding using experiments with a rotating pin in unidirectional sliding. This theory considers two components of work dissipation: W_x is defined as the frictional work in the predominant direction of sliding. This component is assumed to contribute negligibly to wear; rather, it acts to orient and elongate fibrils that lead to low friction and wear. W_y is the component perpendicular to the predominant sliding direction. This component is hypothesized to dominate wear by rupturing crosslinks, and in general, preventing the formation of a stable sliding interface. W is the total work done. The work components are given in Eqs. (1), (2), (3), where they differ in their dependence on α, the cross shear angle (Fig. 1). It is defined for these equations as the angle between the velocity vector of a differential surface element and the predominant sliding direction. Other variables are as follows: μ is the friction coefficient from linear sliding with α = 0, P the contact pressure, $v$ the linear reciprocating velocity and ω is the angular velocity. Linear and angular velocities are decoupled because the tribometer used for that paper by Wang provides linear motion to the plate and angular velocity to the pin.

$$\Delta W_x=\frac{2\mu Pv}{\omega }\left(\alpha +\frac{\text{sin}(2\alpha )}{2}\right)$$

$$\Delta W_y=\frac{2\mu Pv}{\omega }\left(\alpha -\frac{\text{sin}(2\alpha )}{2}\right)$$

$$\Delta W=\Delta W_x+\Delta W_y$$

The governing parameter in this wear model is the cross shear angle. Changing friction coefficient was not addressed in this model, but based on the assumptions made for wear one would expect the friction coefficient to vary with varying motion paths.

To date, most models of the tribological behavior of UHMWPe have been based on gross empirical observations of wear as a function of shape parameters. Unfortunately, measurements of UHMWPe wear are inherently insensitive, generally requiring weeks to months of continuous sliding under relevant conditions to obtain a wear rate. These measurements represent average behavior over the entire motion path and do not probe the fundamental mechanisms specific to the tribological system. The primary aim of this study is to measure changes in friction coefficient of UHMWPe over a multi-directional motion using an apparatus designed to capture complicated friction traces. The secondary aim of this study is to identify trends in friction coefficient as a function of curvature intensity, as well as identify ramifications of these changes for specific current wear theories. It is hypothesized that friction coefficient is higher at location of more intense curvature or curvature changes due to the theories of surface orientation, which must inherently have a rate. Friction coefficient has not been widely studied or included in wear models or predictions because it is considered to be of secondary importance to wear in orthopedic bearing design. This study investigates these fundamental mechanisms in UHMWPe by synchronously measuring friction coefficient and position along relevant multi-directional motion paths. This type of in situ measurement may provide a basis for improved models and bearing designs.