**2. The basic wear mechanisms emerging all types of materials**

Wear is described in the literature as the loss of material as a result of the change in the shape of friction surfaces. Many researchers have stated that there are 4 main wear

mechanisms causing the loss of material. These are adhesive wear, abrasive wear, and corrosive wear and wear resulting from surface fatigue (Archard, 1953; Moore, 1975; Suh and Saka, 1978; Williams, 1994; Summer, 1994). Similarly, many researchers have classified wear as heavy wear and light wear according to the wear magnitude.

A basic equation about wear is developed by Archard (1953). According to Archard (1953), wear on friction surfaces (w), is directly proportional to applied load (W) while inversely proportional to the strength of material (H).

$$\mathbf{W} = \mathbf{K} \times \frac{\mathbf{W}}{\mathbf{H}} \tag{1}$$

Theories on Rock Cutting, Grinding and Polishing Mechanisms 187

This ( *W Wi* ) means the total load applied by both surfaces.

**Figure 2.** Movement of a cone shaped abrasive on a soft surface (Williams, 1994)

W h x cot <sup>2</sup>

When depth of surface caused by the grain is given as material strength, load is defined as;

<sup>π</sup> <sup>2</sup> W x hcot x H

2tan W w x

If abrasive grain is prismatic instead of cone, wear becomes more complex. The structure of chip created as a result of wear is based on two angles to a great extends besides affecting forces. The first is contact angle which is the surface of abrasive grain on the side of moving angle in the direction of sliding. The second is the dihedral angle (2) which is the angle

Contact angle is very important for wear, because while abrasive grain cuts chips over

π H 

2

between the sides of pyramid in the direction of movement (Figure 3).

critical contact angles (c), it only breaks through or rubs in lower angles.

(3)

(4)

(5)

h, and cone angle is shown with .

Here normal load is given as;

As a result, wear is given as this equation;

If a solid material or a solid particle removes piece by scratching or rubbing, this is defined as abrasive wear. Abrasive wear comes through as long rents on surfaces in parallel with the friction direction. A simple model based on the assumption that there is not any change on grain, it only pass through soft material by rubbing it inside is presented in Figure 2. Here, normal load is shown with W, depth on the surface caused by abrasive grain is shown with

K which is non-dimensional in here is expressed as wear coefficient. This coefficient is changed into k=K/H including strength; this is the dimensional wear coefficient which is more widely accepted in engineering. This coefficient represents the volumetric wear (mm3) resulting from the shift in unit distance (m) under unit load (N).

When two materials are rubbed against each other, stresses on touch point can easily reach yield point. With the shearing effect of lateral force, material transfers from the surface of soft material to the surface of hard piece and sticks on. Wear developed this way is called adhesive wear. A simple demonstration of this is presented by Archard (1953) (Figure 1):

**Figure 1.** Material wear caused by the adhesion on friction surfaces (Archard, 1953)

Here, the diameter of contact point is shown as 2a, applied load is shown as W. It is thought that moving will be along the way shown as Path 2. For convenience, the part that will be abraded is assumed to be in the shape of a radius sphere and wear amount as a result of 2a amount of shifting. Wear per unit shifting distance is calculated as 1/3πa2, by dividing 2/3πa3 to 2a. As change in the shape is permanent, Wi load is presented as Wi = H a2 material strength and type. At the end, total wear is shown as;

$$\mathbf{w} = \frac{\pi}{3} \mathbf{x} \sum \mathbf{a}^2 = \frac{1}{3\pi} \mathbf{x} \sum \frac{\pi \mathbf{W} \mathbf{i}}{\mathbf{H}} = \frac{\mathbf{W}}{3\mathbf{H}} \tag{2}$$

This ( *W Wi* ) means the total load applied by both surfaces.

If a solid material or a solid particle removes piece by scratching or rubbing, this is defined as abrasive wear. Abrasive wear comes through as long rents on surfaces in parallel with the friction direction. A simple model based on the assumption that there is not any change on grain, it only pass through soft material by rubbing it inside is presented in Figure 2. Here, normal load is shown with W, depth on the surface caused by abrasive grain is shown with h, and cone angle is shown with .

**Figure 2.** Movement of a cone shaped abrasive on a soft surface (Williams, 1994)

Here normal load is given as;

186 Tribology in Engineering

mechanisms causing the loss of material. These are adhesive wear, abrasive wear, and corrosive wear and wear resulting from surface fatigue (Archard, 1953; Moore, 1975; Suh and Saka, 1978; Williams, 1994; Summer, 1994). Similarly, many researchers have classified

A basic equation about wear is developed by Archard (1953). According to Archard (1953), wear on friction surfaces (w), is directly proportional to applied load (W) while inversely

<sup>W</sup> w K x

K which is non-dimensional in here is expressed as wear coefficient. This coefficient is changed into k=K/H including strength; this is the dimensional wear coefficient which is more widely accepted in engineering. This coefficient represents the volumetric wear (mm3)

When two materials are rubbed against each other, stresses on touch point can easily reach yield point. With the shearing effect of lateral force, material transfers from the surface of soft material to the surface of hard piece and sticks on. Wear developed this way is called adhesive wear. A simple demonstration of this is presented by Archard (1953) (Figure 1):

<sup>H</sup> (1)

wear as heavy wear and light wear according to the wear magnitude.

resulting from the shift in unit distance (m) under unit load (N).

**Figure 1.** Material wear caused by the adhesion on friction surfaces (Archard, 1953)

material strength and type. At the end, total wear is shown as;

Here, the diameter of contact point is shown as 2a, applied load is shown as W. It is thought that moving will be along the way shown as Path 2. For convenience, the part that will be abraded is assumed to be in the shape of a radius sphere and wear amount as a result of 2a amount of shifting. Wear per unit shifting distance is calculated as 1/3πa2, by dividing 2/3πa3 to 2a. As change in the shape is permanent, Wi load is presented as Wi = H a2

π <sup>2</sup> 1 πWi W

3 3<sup>π</sup> H 3H (2)

w xa x

proportional to the strength of material (H).

$$\mathbf{W} = \mathbf{h}^2 \times \cot \mathcal{G} \tag{3}$$

When depth of surface caused by the grain is given as material strength, load is defined as;

$$\mathbf{W} = \frac{\pi}{2} \times \left(\text{hcot}\,\theta\right)^2 \times \mathbf{H} \tag{4}$$

As a result, wear is given as this equation;

$$\mathbf{w} = \frac{2\tan\theta}{\pi} \times \frac{\mathbf{W}}{\mathbf{H}} \tag{5}$$

If abrasive grain is prismatic instead of cone, wear becomes more complex. The structure of chip created as a result of wear is based on two angles to a great extends besides affecting forces. The first is contact angle which is the surface of abrasive grain on the side of moving angle in the direction of sliding. The second is the dihedral angle (2) which is the angle between the sides of pyramid in the direction of movement (Figure 3).

Contact angle is very important for wear, because while abrasive grain cuts chips over critical contact angles (c), it only breaks through or rubs in lower angles.

Theories on Rock Cutting, Grinding and Polishing Mechanisms 189

protector layer on these surfaces. If wear occurs because of mechanic factors and environment involves similar atmospheric conditions, this film layer will remove and a new layer will occur as a result of re-oxidation. Grains that are formed during removal of this layer can cause abrasive wear because of their solidity. Adhesive wear can also occur as a result of friction if a part of contacting surfaces is oxidized while another part is completely non-oxidized. As a result, if this corrosion layer is continuously removing because of wear, this will have a positive effect on wear process which is named corrosive wear (Summer, 1994). Wear as a result of surface fatigue occurs generally on metal materials rolling on one another similar to the bearings. Material in contact point tightens as a result of permanent change in the shape and material embrittlement occurs. This material cracks as a result of repetitive power; they spread on the surface in time and cause breakage of material in small

**Figure 5.** Beilby polishing mechanism developed by Bowden and Hughes (1937)

with various applications and in accordance with the purpose.

light smoothly and in a linear way (Coes, 1971; Samuels, 1971).

In the wear process resulting from surface fatigue, bigger grains remove from the surface when compared to adhesive or abrasive wear. Typical cavitations and scouring occur on

Abrading on the other hand, is the deliberate process of removing material from surfaces

Polishing is a process of abrading and it is defined as the process of removing unevenness and visible scratches by using abrasive material (Coes, 1971). So, polished surface reflects

Wear mechanisms that are stated until here explain unwanted material loss on surfaces.

pieces.

these types of surfaces.

**Figure 3.** Geometry of prismatic abrasive grain represented with two angle ((, 2) (Williams, 1994)

Dihedral angle also significantly affects the shape of chip. In very small 2 angles, abrasive grain breaks through the surface like a knife. When 2=180, it means there is a smooth surface vertical to the motion direction and this is a limiting value.

Relation between contact angle and dihedral angle developed by Kato et al. (1986) is given in Figure 4.

**Figure 4.** Relation between contact angle and dihedral angle with wear situations resulting from abrasive wear (Kato et al., 1986)

Corrosive wear occurs on surfaces that rubbed against each other with small vibrations and as a result of this, few ten micron grains are removed. Generally when irony surfaces are rubbed against one another, a reddish brown fragment is produced. This detritus is composed of solid iron oxide grains and behaves like polishing powder and make contacting surfaces smooth and shiny. This leads to the creation of a film in the shape of a protector layer on these surfaces. If wear occurs because of mechanic factors and environment involves similar atmospheric conditions, this film layer will remove and a new layer will occur as a result of re-oxidation. Grains that are formed during removal of this layer can cause abrasive wear because of their solidity. Adhesive wear can also occur as a result of friction if a part of contacting surfaces is oxidized while another part is completely non-oxidized. As a result, if this corrosion layer is continuously removing because of wear, this will have a positive effect on wear process which is named corrosive wear (Summer, 1994). Wear as a result of surface fatigue occurs generally on metal materials rolling on one another similar to the bearings. Material in contact point tightens as a result of permanent change in the shape and material embrittlement occurs. This material cracks as a result of repetitive power; they spread on the surface in time and cause breakage of material in small pieces.

188 Tribology in Engineering

in Figure 4.

abrasive wear (Kato et al., 1986)

**Figure 3.** Geometry of prismatic abrasive grain represented with two angle ((, 2) (Williams, 1994)

surface vertical to the motion direction and this is a limiting value.

Dihedral angle also significantly affects the shape of chip. In very small 2 angles, abrasive grain breaks through the surface like a knife. When 2=180, it means there is a smooth

Relation between contact angle and dihedral angle developed by Kato et al. (1986) is given

**Figure 4.** Relation between contact angle and dihedral angle with wear situations resulting from

Corrosive wear occurs on surfaces that rubbed against each other with small vibrations and as a result of this, few ten micron grains are removed. Generally when irony surfaces are rubbed against one another, a reddish brown fragment is produced. This detritus is composed of solid iron oxide grains and behaves like polishing powder and make contacting surfaces smooth and shiny. This leads to the creation of a film in the shape of a

**Figure 5.** Beilby polishing mechanism developed by Bowden and Hughes (1937)

In the wear process resulting from surface fatigue, bigger grains remove from the surface when compared to adhesive or abrasive wear. Typical cavitations and scouring occur on these types of surfaces.

Wear mechanisms that are stated until here explain unwanted material loss on surfaces.

Abrading on the other hand, is the deliberate process of removing material from surfaces with various applications and in accordance with the purpose.

Polishing is a process of abrading and it is defined as the process of removing unevenness and visible scratches by using abrasive material (Coes, 1971). So, polished surface reflects light smoothly and in a linear way (Coes, 1971; Samuels, 1971).

According to Beilby (1921), polishing results from a smearing a material on a surface which fills the gaps on surface. Beilby (1921) stated that this material has a structure that is completely similar to amorphous and it looses crystal structure. He didn't suggest a mechanism about smearing material on these surfaces. But later on, a mechanism was developed by Bowden and Hughes (1937). These researchers determined that very high temperatures were reached in the contact points of abrasive grains, as a result of rubbing solids against each other which caused them think that heat is significant in the process of polishing (Samuels, 1971).

Theories on Rock Cutting, Grinding and Polishing Mechanisms 191

sets. The second point is that material is removed from the surface during polishing process with a constant speed. Thirdly, a layer that has permanently deformed is created. This layer is highly similar to transformed layer that is created during abrading. When grinded and polished surfaces are examined, the significant similarity between them will be seen. Scale is the only difference. Most of the researches and studies on abrading and polishing process focus on metallic materials. Studies on brittle and fragile surfaces like rock surface are very

In this section, abrading and polishing processes that are based upon mechanic materials are taken into consideration. When abrading and polishing mechanisms are analyzed in these terms, it is seen that there is not a basic difference between them. By changing the abrasive material type and/or application style of gain size, abrading process can be transformed to

Explanation of abrading and polishing mechanism is possible only by revealing the type and aim of the applied process. So, mechanisms that occur at each application will be

Wear mechanism formed during the use of circular saw, grinding mills, and grinding

Abrading processes mentioned above have significant differences in terms of basic mechanism. This is why, each one of them will be analyzed and what kind of abrading

Circular saws is the cutting tool that is used the most in cutting and sizing of natural stones that are segments containing diamonds' welded around circular metal body. Grinding mills are used for process such as cutting, graving, shaping… etc. In the abrading operation mentioned until here, the process of wear results from simple geometrical situations with a linear movement between abrasive grain and material. When grinding mills are analyzed, if abrading operation occurs on the edge of grinding mill, the situation is simple. But if abrading is on the disc, the situation is complex. In the literature, abrading mechanism that occurs here is mentioned with the word grinding. The wear that occurs here is defined as a

Salmon (1992) tried to make a mathematical modeling for the abrading operation on the

**3. Wear mechanism that is formed during the use of circular saw,** 

 Wear mechanism during cutting process with diamond blade saws. Wear mechanism during cutting process with diamond bead system

Wear mechanism during surface polishing applications

and/or polishing mechanism develops will be put forward.

Wear mechanism during the use of sandpaper

**grinding mills, grinding stones**

limited.

polishing.

different from one another.

cutting stones.

micro-scaled grinding.

surface of grinding mill.

These applications can be lined as;

Unevenness on the original surface heat locally (until melting point) which is caused by friction transfers to the gaps (Figure 5). This material is transferred as a result of rapid cooling, it has an amorphous structure and constitutes Beilby layer.

On the other hand, Samuels (1971) didn't accept the existence of Beilby layer and tried to prove that Beilby layer doesn't occur with many proofs. According to Samuels (1971), there exists continuous material loss during polishing on surfaces that are physically polished. In addition, when polished surfaces are analyzed with microscope, scratches can be seen. This situation is completely opposite the existence of Beilby layer. Because Beilby stated that material fill the gaps during polishing. There shouldn't be a distinct material loss.

When physically polished surfaces are treated with acid, scratches on the surface appear. According to Samuels (1971), this situation can be explained with the deformed layer (as can be seen in Figure 6) rather than Beilby layer.

**Figure 6.** Comparison of Beilby and local deformation theory (Samuels, 1971)

According to Samuels (1971), one needs to explain three acceptations in order to explain physical polishing mechanism. The first is that, surfaces always have thin scratches or joint sets. The second point is that material is removed from the surface during polishing process with a constant speed. Thirdly, a layer that has permanently deformed is created. This layer is highly similar to transformed layer that is created during abrading. When grinded and polished surfaces are examined, the significant similarity between them will be seen. Scale is the only difference. Most of the researches and studies on abrading and polishing process focus on metallic materials. Studies on brittle and fragile surfaces like rock surface are very limited.

In this section, abrading and polishing processes that are based upon mechanic materials are taken into consideration. When abrading and polishing mechanisms are analyzed in these terms, it is seen that there is not a basic difference between them. By changing the abrasive material type and/or application style of gain size, abrading process can be transformed to polishing.

Explanation of abrading and polishing mechanism is possible only by revealing the type and aim of the applied process. So, mechanisms that occur at each application will be different from one another.

These applications can be lined as;

190 Tribology in Engineering

polishing (Samuels, 1971).

be seen in Figure 6) rather than Beilby layer.

According to Beilby (1921), polishing results from a smearing a material on a surface which fills the gaps on surface. Beilby (1921) stated that this material has a structure that is completely similar to amorphous and it looses crystal structure. He didn't suggest a mechanism about smearing material on these surfaces. But later on, a mechanism was developed by Bowden and Hughes (1937). These researchers determined that very high temperatures were reached in the contact points of abrasive grains, as a result of rubbing solids against each other which caused them think that heat is significant in the process of

Unevenness on the original surface heat locally (until melting point) which is caused by friction transfers to the gaps (Figure 5). This material is transferred as a result of rapid

On the other hand, Samuels (1971) didn't accept the existence of Beilby layer and tried to prove that Beilby layer doesn't occur with many proofs. According to Samuels (1971), there exists continuous material loss during polishing on surfaces that are physically polished. In addition, when polished surfaces are analyzed with microscope, scratches can be seen. This situation is completely opposite the existence of Beilby layer. Because Beilby stated that

When physically polished surfaces are treated with acid, scratches on the surface appear. According to Samuels (1971), this situation can be explained with the deformed layer (as can

material fill the gaps during polishing. There shouldn't be a distinct material loss.

cooling, it has an amorphous structure and constitutes Beilby layer.

**Figure 6.** Comparison of Beilby and local deformation theory (Samuels, 1971)

According to Samuels (1971), one needs to explain three acceptations in order to explain physical polishing mechanism. The first is that, surfaces always have thin scratches or joint


Abrading processes mentioned above have significant differences in terms of basic mechanism. This is why, each one of them will be analyzed and what kind of abrading and/or polishing mechanism develops will be put forward.
