**2.1 Friction**

Friction arises from the interaction between moving solids in contact and hinders (sliding friction) or prevents (static friction) motion. The friction force is proportional to the normal load applied to the surface and the coefficient of friction. The coefficient of friction is determined, in part, by the bearing surface material. There are two coefficients of friction, static and dynamic. It requires a greater force to initiate sliding than to maintain it, so the latter is generally considered to be 70% of the former. The contact area also determines the frictional force. The true contact area for many bearing surfaces is far less than the apparent contact area, somewhere in the region of 1%.(Fig.1)

Fig. 1. Apparent (A) and Real (B) area of contact

This is due to the marked irregularity of the surfaces (asperities) at microscopic level. Only very small peaks from each surface contact each other.

The friction force is defined as the force acting tangentially to the interface resisting motion, when, under the action of an external force, one body moves or tends to move relative to another. The friction force F may be associated with sliding motion or with pure rolling motion of the bodies.

The coefficient of friction μ is a dimensionless number, defined as the ratio F/N between the friction force F and the normal force N acting to press the two bodies together. The kinetic coefficient of friction μk is the coefficient of friction under conditions of macroscopic relative motion between the two bodies, while the static coefficient of friction μs is the coefficient of friction corresponding to the maximum friction force that must be overcome to initiate macroscopic motion between the two bodies. F is approximately linearly proportional to N over quite large ranges of N. The equation

$$\mathbf{F} = \mathbf{\upmu} \mathbf{N} \tag{1}$$

is sometimes called "Amontons Law". The value of μ can be expected to depend significantly on the precise composition, topography and history of the surfaces in contact, the environment to which they are exposed, and the precise details of the loading conditions. Although tables of coefficients of friction have been published, they should not be regarded as anything more than general indications of relative values under the specific conditions of measurement. The coefficient of friction usually lies in the range from 0 to 1, although there is no fundamental reason why it need do so.

In order to initiate sliding, the bonds between the contact points need to be broken, thus explaining the higher force required to initiate movement with respect to maintaining it. The friction begins by cyclic elastic or plastic deformation of contact spots of the real contact area. Then it is transformed into elastic or plastic deformation energy within interlocking surface asperities and/or leads to crack initiation and propagation. This deformation may be responsible for the generation of particles. This (progressive) loss of particulate debris from the surface of a solid body due to mechanical action has been defined as wear. The adhesion of the surface atoms and molecules of body and counterbody contributes to friction. The probability of adhesion depends on mechanical properties and the tendency of atoms and molecules to react chemically. Both the deformation and adhesion contributions to friction can be distinctly lowered by means of surface modifications or coatings as well as by lubrication. At least 90% of the introduced energy is dissipated into heat, leading to an increase of the temperature within the contact zone. Depending on local normal forces and the relative velocity, the average as well as the flash temperatures may rise. Although the average temperature is primarily governed by the normal force, the flash temperature depends mostly on the relative velocity and lasts for only a few nanoseconds or milliseconds. The remaining 10% is dissipated by storing mechanical energy within lattice defects generated by cyclic elastic and plastic deformation, phase transformation or chemical reaction of body, counterbody, interfacial medium, and environment. Friction also results in the transfer of force from the articulating areas to the fixed interfaces.

### **2.2 Lubrication**

164 Recent Advances in Arthroplasty

carbon fiber–reinforced UHMWPE with a potentially improved wear resistance was clinically introduced. In the 1980s, a high-pressure recrystallized form of UHMWPE was clinically introduced for its improved creep resistance. In the late 1990s, many researchers confirmed that crosslinking of UHMWPE can substantially improve the wear performance of the polyethylene in hip joint simulators. Based on these in vitro analyses, a number of

According to the ASM International handbook, tribology is defined as the science and technology of interacting surfaces in relative motion and all practices related thereto. It includes the study of wear, friction, and lubrication. Total joint replacements have bearing surfaces that must transmit normal joint loads and motions. Low friction has been an important design objective for prosthetic joints for two reasons. First, if large shear forces due to friction are applied to the articulating surfaces, the risk of loosening may be increased. Second, the addition of frictional shear increases the stresses associated with surface damage due to contact, which can result in the release of wear debris to the

Friction arises from the interaction between moving solids in contact and hinders (sliding friction) or prevents (static friction) motion. The friction force is proportional to the normal load applied to the surface and the coefficient of friction. The coefficient of friction is determined, in part, by the bearing surface material. There are two coefficients of friction, static and dynamic. It requires a greater force to initiate sliding than to maintain it, so the latter is generally considered to be 70% of the former. The contact area also determines the frictional force. The true contact area for many bearing surfaces is far less than the apparent

This is due to the marked irregularity of the surfaces (asperities) at microscopic level. Only

The friction force is defined as the force acting tangentially to the interface resisting motion, when, under the action of an external force, one body moves or tends to move relative to another. The friction force F may be associated with sliding motion or with pure rolling

radiation cross-linked materials have been clinically introduced in the late 1990s.

**2. Tribology of articulating surfaces** 

**2.1 Friction** 

surrounding tissue that also increases the risk of loosening.

contact area, somewhere in the region of 1%.(Fig.1)

Fig. 1. Apparent (A) and Real (B) area of contact

motion of the bodies.

very small peaks from each surface contact each other.

Friction can be reduced by lubrication. The principal idea behind lubrication is to interpose a material between two contacting solids to minimize interaction between them. For example, wetting of the surfaces reduces adhesion. The extent of fluid film formation plays an important role in the wear process of artificial joints in vivo. The effectiveness of a lubricant film can be defined by the specific film thickness which is dependent on the viscosity of the lubricant, the relative velocity between body and counterbody, the pressure across the interface, and the roughness of the mating surfaces.

The Bearing Surfaces in Total Hip Arthroplasty – Options, Material Characteristics and Selection 167

fluid film and boundary lubrication. The coefficient of friction continues decreasing until full fluid film lubrication (FFL) is generated, where the articulating surfaces are separated by the lubricant. It is also called hydrodynamic lubrication and is divided into two groups depending on whether the two surfaces are conforming or not. Native joints are conforming (hydrodynamic lubrication) unlike artificial joints that deform elastically (elastohydrodynamic lubrication). Elastohydrodynamic (EHD) lubrication occurs when the pressure in the fluid film is sufficiently high to deform the asperities of the solid surfaces. Thus, even if the thickness of the fluid film is less than the heights of the asperities of body and counterbody, a total separation may be still achieved. Under realistic loads and in the presence of synovial fluid, metal-on-polyethylene hip joints articulate in the mixed film or boundary lubrication regime. Hard-on-hard bearings primarily work in the elastohydrodynamic and mixed film lubrication regime; however, with increasing femoral head size (>28 mm), a shift toward full fluid film (hydrodynamic)

Wear can be defined as damage to a solid surface, generally involving progressive loss of material, due to relative motion between that surface and a contacting substance or substances. Materials in contact are subjected to relative motion in many different applications. The creep and plastic deformation are not forms of wear per se because they do not produce wear debris but dimensional changes of the contacting surfaces. Also, corrosion is not directly related to wear because it can take place without any mechanical

It is important, especially when describing wear, to distinguish clearly between the nature of the relative motion responsible for the wear and the physical mechanisms by which the material is removed or displaced in wear. The wear mechanisms in bearing surfaces are as

The bonds that form between to surfaces need to be broken to allow movement. If the bonds are the weakest point then they will break. But sometimes one of the materials is weaker than the bonds so it breaks preferentially. Thus a layer of the weaker material lines the stronger material, changing the interface at which movement takes place. During mechanical action, these microjunctions are torn off, and fragments may become particles or be transferred from body to counterbody and vice versa, bringing about surface damage in the form of flakes and pitting. If the generated flakes and particles are bigger than the clearance of the bearing, they may act as abrasive particles or even block the joint.(Howcroft

When material is removed from a surface by hard asperities on the counterface or hard particles (third body) trapped between the two contact surfaces, abrasive wear

lubrication can be observed as well. (Smith 2001b; Dowson 2006)

**2.3 Wear and wear mechanisms** 

activation at all.(Buford 2004)

**2.3.1 Types of wear** 

**2.3.1.1 Adhesive wear** 

**2.3.1.2 Abrasive wear** 

occurs.(Howcroft 2008) (Fig.3)

follows:

2008)

Sommerfield number is the determiner of the thickness of the lubrication fluid and depends on a number of factors:


Sommerfield number ∝ Fluid viscosity x Sliding velocity/Applied pressure (2)

The higher the value, the thicker the lubrication film.(Howcroft 2008)

The wettability of the materials also plays a part. This is essentially describes how hydrophobic or hydrophilic they are. The ceramics are the most wettable of the currently used bearings.

The lambda ratio (λ) refers to the ratio of fluid-film thickness to the surfaces roughness. Lambda values greater than 3 imply that the fluid-film thickness is greater than the height of asperities on the articular surface and represent fluid-film lubrication. Lambda values between 1 and 3 represent mixed film lubrication, and values less than 1 represent boundary lubrication.

Lubrication between the bearing surfaces of hip implants and its effect on friction generated during articulation is commonly illustrated by a Stribeck diagram. (Fig.2)

Fig. 2. The Stribeck diagram of different bearing combination materials

The Stribeck curve is traditionally depicted in three phases. When the thickness of the fluid film is less than or equal to the average surface roughness of the articulating surfaces, boundary lubrication (BL) is achieved. In this phase, the asperities of the articulating surfaces are in contact at all times. It is not ideal and is more likely to occur in rough bearing surfaces, or as a result of third body formation or protein deposition. It is improved with better manufacture tolerances of the bearing surfaces. The longer implants remain in situ the more likely they are to develop this type of lubrication. As the thickness of the fluid film increases, the articulating surfaces become separated from each other. There is a transition stage called mixed lubrication (ML), where there is a combination of fluid film and boundary lubrication. The coefficient of friction continues decreasing until full fluid film lubrication (FFL) is generated, where the articulating surfaces are separated by the lubricant. It is also called hydrodynamic lubrication and is divided into two groups depending on whether the two surfaces are conforming or not. Native joints are conforming (hydrodynamic lubrication) unlike artificial joints that deform elastically (elastohydrodynamic lubrication). Elastohydrodynamic (EHD) lubrication occurs when the pressure in the fluid film is sufficiently high to deform the asperities of the solid surfaces. Thus, even if the thickness of the fluid film is less than the heights of the asperities of body and counterbody, a total separation may be still achieved. Under realistic loads and in the presence of synovial fluid, metal-on-polyethylene hip joints articulate in the mixed film or boundary lubrication regime. Hard-on-hard bearings primarily work in the elastohydrodynamic and mixed film lubrication regime; however, with increasing femoral head size (>28 mm), a shift toward full fluid film (hydrodynamic) lubrication can be observed as well. (Smith 2001b; Dowson 2006)
