**1. Introduction**

Modular junctions are commonly used in orthopaedics, such as the head-neck taper junction in total hip replacement, to allow flexibility at the time of surgery. The aim is to generate a rigid connection between the modular components. However, fretting wear occurs due to the small-amplitude relative motions that occur at the interface under physiological loads in the body. In addition, fretting wear can remove the passive oxide layer of the metal alloy, and, with the presence of the body fluid, re-passivation occurs within the small crevice at the junction, which causes fretting corrosion [1,2]. These phenomena produce particulate debris and metal ions, which, in turn, can cause adverse local tissue reactions and, ultimately, clinical failure [3–5].

The mechanical behavior of the taper connection is dependent on a number of parameters. The material combination used at the taper [6] and the taper mismatch angle [6–9] can be controlled by the design and the manufacturing process. The type of the mechanical load as a result of daily activities can also influence the mechanical behavior of the taper junction [10,11]. Since the components are assembled intraoperatively, the assembly force is important not only to avoid loosening and dissociation after implantation [12,13] but also to establish a favorable mechanical environment to

minimize fretting. There is variation between the manufacturers' recommendations on how to impact the femoral head [14], from a single light tap to several sharp hammer blows. The impaction forces generated by surgeons can vary significantly from approximately 300 N to an excess of 7500 N [15]. To date, the majority of studies [12,16–18] investigating the influence of the assembly force have focused on the dissociation force as the metric to assess the performance of the taper. Assembly forces from 2 kN to 15 kN have been investigated and a linear relationship with the dissociation force has been reported [12,16]. The dissociation force is always lower and varies between 42% [17] and 91% [18] of the assembly force. Rehmer et al. [12] reported a similar linear relationship between the assembly force and the twist off torque. Increasing the impaction force has also been shown to increase the contact area [6,19] and reduce the micro-motion [18,20] between the head and the trunnion. These studies generally sugges<sup>t</sup> that a high assembly force can achieve a high degree of initial stability and fixation in the head-neck junction to more reliably withstand mechanical loads of daily activities without disconnection.

However, very few studies have attempted to address the important question of whether the assembly force has an influence on the material removal by fretting wear over an extended period. Bitter et al. [18] developed a combined experimental and finite element (FE) study to analyze the influence of assembly force (2, 4, and 15 kN) on the fretting wear of a Ti-6Al-4V femoral stem in contact with a Ti-6Al-4V taper adaptor. Their experimental results showed large standard deviations in terms of volumetric wear and no significant difference was found between the three tested assembly forces. However, it was reported that, when increasing the assembly force, the fretting wear reduces at the taper interface. They also used a simplified FE modelling approach simulating accelerated fretting (did not incorporate geometry updates to account for material loss). Employing a simplified version of the Archard equation, they defined a total wear score for the interface using the contact pressure and relative micro-motion for each contact node. As a major simplification, their model was not able to track the fretting wear process over several cycles of sliding. No correlation was found between the predicted wear scores (from the FE analysis) and the experimental volumetric wear [18]. In another FE analysis, English et al. [21] modelled a CoCr head and a titanium neck with a zero angular mismatch to estimate the material loss and contact pressure at the junction subjected to two million cycles of walking gait loading. This work was extended to explore the influence of assembly force, and they reported that higher assembly forces resulted in lower fretting wear [22]. However, they still used the critical simplification of zero angular mismatch for the junction in the dry condition. The materials modelled in the previous studies did not include the common combination of CoCr head and CoCr neck. Furthermore, the existing taper angle mismatch between the head and neck components has been ignored in the previous fretting wear studies while the angular mismatch has been found to significantly influence the mechanics of the junction [6,23]. Therefore, it could have a significant effect on fretting wear as a mechanically driven process. More importantly, the previous FE simulations have often assumed a dry condition for the contacting materials of the junction. However, the existence of body fluid at the interface of the junction may control the frictional characteristics and wear characteristics, which may influence the fretting wear behavior.

This work aims to simulate the fretting wear process and predict the material removal in a CoCr/CoCr head-neck junction through an adaptive finite element modelling approach. To achieve more realistic outcomes, the taper junction was modelled to have a distal contact with a real angular mismatch between the head and neck with the presence of simulated physiological body fluid. The main research objective was to evaluate the effect of assembly force on the material loss and fretting wear process in this type of taper junction.
