**3. Results**

#### *3.1. Contact Pressure and Contact Length*

As shown in Figure 4, when increasing the assembly force from 2000 N to 5000 N, the contact pressure increased in magnitude over the length of the neck, and the contacting region between the head and neck (contact length) also increased toward the proximal side of the neck. This confirms that a higher assembly force can further push the neck into the head, which induces greater normal contact forces. Thereby, larger contact pressures and more engagemen<sup>t</sup> between the head and neck surfaces (longer contact). As more loading cycles were applied (increase in the number of cycles), the peak contact pressure decreased in magnitude. The maximum magnitude of contact pressure for cases with assembly forces of 2000 N, 3000 N, 4000 N, and 5000 N decreased from 206, 257, 265, and 337 MPa at 25,000 cycles to 169, 243, 258, and 294 MPa at 1,025,000 cycles, respectively, in the super-lateral sector of the neck. These graphs can also help investigate the contact length between the head and neck. Non-zero contact stresses at any region of the surface indicate that there is contact between the head and neck in that region. After 25,000 cycles, the percentage of the neck, which is in contact with the head for cases with assembly forces of 2000 N, 3000 N, 4000 N, and 5000 N, were 48%, 64%, 75%, and 79%, respectively. These total contact lengths remained nearly constant after 1,000,000 cycles of fretting wear.

**Figure 4.** Variation of normal contact stress over the neck length in both super-lateral and infero-medial sectors under different assembly forces and after 25,000 and 1,025,000 loading cycles.

## *3.2. Micro-Motions*

For all the assembly forces, the micro-motion at the contacting interface tends to increase from the proximal side to the distal side (Figure 5) and the magnitude of the micro-motion reduces when increasing the assembly force. The junction assembled with 2000 N had the largest micro-motions compared to the other cases with a range of 0.41 to 0.51 μm. There appears to be minimal changes in the micro-motion after 1,000,000 load cycles (Figure 5).

**Figure 5.** Relative micro-motion at the contacting interface over the neck length (super-lateral sector) for different assembly forces after 25,000 and 1,025,000 cycles.

#### *3.3. Material Loss*

Material removal over the neck length was calculated as the total area under the curve of wear depth versus the neck length in both the super-lateral and infero-medial sectors. This represents the lost area from the original edges (super-lateral and infero-medial sectors) of the 2D model. It can be seen in Figure 6a that the trend of the lost area over the number of loading cycles is linear for all of the assembly forces studied. The values of area loss for di fferent assembly forces and at di fferent cycles were almost equal in both the head and neck. Therefore, this figure only presents the area losses of the neck. Increasing the assembly force results in an increase in the lost area at the taper junction. For instance, when the assembly force was increased from 2000 N to 5000 N, the area loss increased from 5.28 × 10−<sup>3</sup> mm<sup>2</sup> to 16.3 × 10−<sup>3</sup> mm<sup>2</sup> in the neck after 1,025,000 cycles.

Figure 6b shows the e ffect of assembly force on the rate and location of the fretting wear damage in the form of wear depth (after 25,000 and 1,025,000 number of cycles) in the neck. It is noted that very similar depth of wear results were found in the head at the same number of cycles. These graphs can help compare the wear depth at di fferent assembly forces, and locate the wear damage at the interface. It can be seen that the wear depths in the assembly force of 5000 N (with a maximum 0.779 μm) was significantly higher than that of the assembly force of 2000 N (with a maximum 0.413 μm).

**Figure 6.** (**a**) Lost area versus number of cycles for different assembly forces and (**b**) depth of wear over the neck length after 1,025,000 cycles.

## **4. Discussion**

In this work, the fretting wear mechanism and material loss were investigated in a CoCr/CoCr head-neck junction with a real angular mismatch in a PBS solution and under normal walking gait loading. The junction was assembled with various forces ranging from 2 kN to 5 kN to represent low-to-high impaction forces applied by surgeons in practice. The area loss from the edges of the most critical plane of the junction (as an indicator of material loss in the junction) showed a linearly increasing pattern over the fretting wear cycles. This could help estimate the degree of material loss after several million cycles of fretting wear.

The results of this work revealed that contact pressure, contact length, and relative micro-motion at the interface of the junction are the key parameters that can influence the material loss caused by fretting wear. Figure 5 showed that, when increasing the assembly force, relative micro-motion between the head and neck components reduces considerably, which o ffers more stability to the junction. According to the Archard equation, wear is proportional to both the contact pressure and relative micro-motion (amplitude of sliding). Even though the relative micro-motions decrease in the firmly assembled junctions, the significant increase in the contact pressure (induced over greater contact regions) leads to a net increase in fretting wear and, consequently, material removal. The results showed that a higher assembly force can induce a longer contact at the interface. This can extend the surface on which fretting wear is to occur and can, therefore, increase the extent of material removal. As shown in Figure 6a (for the studied taper design and material combination), increasing the assembly force results in more material loss. This is in contrast with the English's results [22] where higher assembly forces were reported to reduce fretting wear. On the other hand, Bitter's experimental results [18] showed no rational relation between the assembly force and the volumetric wear. The wear volume reduced when increasing the assembly force from 2 kN to 4 kN, and then slightly increased when increasing the assembly force from 4 kN to 15 kN. They found large standard deviations in their wear volume results (no significant di fference between the three tested assembly forces). Bitter's FE simulations were too simplified and did not incorporate geometry updates to account for material loss due to the process of fretting wear. One immediate di fference between the two previously mentioned studies and the present work is the material combination. In this study, the material combination is CoCr/CoCr, while they used CoCr/Ti and Ti/Ti combinations. Material properties, particularly the modulus of elasticity, can influence the behavior of the contact, especially the relative micro-motion. The angular mismatch within the junction is the major di fference between the present work and their studies. The authors have previously shown that the existence of angular mismatch has a significant e ffect on the contact length, contact pressure, relative micro-motion, and, accordingly, the wear damage [23]. In English's model, zero mismatch was assumed between the head and neck taper angles. Therefore, the contact length would always be constant (due to having no angular mismatch).Furthermore, increasing the assembly force reduces the relative micro-motion at the head-neck interface, which, in turn, reduces the amount of material loss. However, in this work, the contact between the head and neck is not perfect. Therefore, increasing the assembly force increases the contact length in the head-neck junction, which results in increasing the material loss. Bitter's et al. [18] did not mention if there was an actual angular mismatch in their head-neck samples. Therefore, valid statements cannot be made to directly compare and discuss their results with those of this study in terms of the mismatch angle's influence.

Assembly force, as an intraoperative surgical parameter, can play an important role in the fretting wear damage to the head and neck components. This study was developed for a particular design including a CoCr/CoCr material combination with a distal angular mismatch of 0.01◦. This, together with the contradicting results reported previously [18,23], may sugges<sup>t</sup> that further research is required to investigate the influence of the assembly force on the fretting wear behavior, considering various angular mismatches as well as di fferent material combinations and loading profiles of other daily activities before making a certain suggestion to clinicians in terms of a recommended force for assembling head-neck taper junctions. Moreover, fretting corrosion in the head-neck taper junction is a

combination of mechanical fretting wear and electro-chemical corrosion processes. The scope of this study was to investigate the influence of assembly force (as a mechanical parameter) on the material loss at the head-neck junction of hip implants. Hence, the model was developed to simulate only the mechanical fretting wear process in the junction. However, corrosion can play an important role in the behavior of the contact and, thus, the amount of material loss. The authors of this study have developed a new adaptive finite element model to simulate fretting corrosion at metallic interfaces [30]. This model has been successfully used to simulate fretting corrosion for only a simple geometry. Further research is required to use this new and complex model to simulate fretting wear corrosion in head-neck taper junctions.
