Manufacturing and Mechanical Properties of Engineering Materials | Manufacturing Science

In this article we will discuss about the manufacturing and mechanical properties of engineering materials. Learn about:- 1. Structure of Matter 2. Metals and Alloys 3. Deformation and Mechanical Properties.

Manufacturing and Mechanical Properties of Engineering Materials

Structure of Matter:

The properties of a material are intimately connected to its basic molecular structure. Some knowledge of this structure is therefore essential for under­standing the various macroscopic properties exhibited by the material. A general characteristic of all solids is their capability to retain definite shapes, and so we start from the mechanics of bonding between the molecules forming a solid.

Bonding of Solids:

When two atoms are sufficiently close to each other, the outer electrons are shared by both the nuclei. This results in an attractive force between the two atoms. This force increases with the decrease in distance between the two atoms, as shown in Fig. 1.1. However, the two atoms do not collapse as a repulsive force is generated when the two nuclei come very close.

This repulsive force increases rapidly with decreasing interatomic distance. The equilibrium interatomic distance d_e is that distance when the attractive and the repulsive forces are equal in magnitude (Fig. 1.1). The slope of the repulsive force curve is always more than that of the attractive force curve at the point of intersection A of the curves. Therefore, the equilibrium is of stable nature.

The mechanism is one of the various possible interactions resulting in bonding between atoms, and is known as covalent bonding. In a given solid, one or more bonding mechanisms can be simultaneously operative.

The nature of a bonding mechanism depends on the electronic structure of the atoms involved. The bonding mechanisms predominant in solids include metallic bonding (in metals) and the van der Waals bonding (in molecular crystals). In a metal, a large number of free electrons are present, resulting in the formation of a common electron cloud, the rest of the system consists of positively charged ions which are held together by the cloud (Fig. 1.2a).

The mecha­nism of bonding in alloys is similar. Since the inert atoms do not possess free electrons, the metallic bonding mechanism cannot be operative. In such instances, however, a very weak short range attraction is generated due to the van der Waals force. The origin of this force is attributed to a rapidly-fluctuating dipole moment.

Figure 1.2b shows two molecules at a distance d, each of which has a symmetric charge distribution. All the three different overall configurations of the charge distributions, shown in the figure, lead to the development of an attractive force though individually the molecules are neutral. This of bonding is very weak and is active in weak and low melting point materials such as paraffin and plastics. It is obvious that the strength of the bond controls the properties, e.g. melting point, of a material.

Crystal Structure:

The properties of a material depend not only on the bond strength but also on the arrangement of the atoms. In all metals and in many nonmetallic solids, the atoms are arranged in a well-ordered pattern. Such solids are commonly called crystalline solids. Of course, in a large number of situations, the whole solid is seldom composed of one single crystal. Instead, a very large number of small, randomly-oriented crystalline grains form the whole solid. Such materials are termed poly crystalline. Figures 1.3a and 1.3b show a single crystal and a polycrystalline solid, respectively.

In a crystal, we can identify the unit cell the repetition of which forms the whole crystal. The structure of a crystal is identified and described by this unit cell. The three commonly-observed crystal structures in metals are shown in Fig. 1.4.

Of these three basic structures, the fcc and the cph crystals have the most dense packing. The interatomic distance in such crystals is of the order of 10^-7 mm. The crystal structures of some common metals are given in Table 1.1.

When a liquid metal solidifies by cooling, the atoms arrange themselves in regular space lattices, forming a crystal. The crystallization starts simultaneously at various places within the liquid mass. Figure 1.5 shows the growth of the crystal grains and the ultimate formation of the polycrystalline metal.

Most metals have only one crystal structure. A few metals, however, can have more than one type of crystal structure. Such metals are called allotropic. Table 1.1 indicates that iron is an allotropic metal.

A number of material properties, in general, can be associated with the type of crystal structure. For example- the bcc structures are usually harder, whereas the fee structures are more ductile. In cph structures, the ductility is low.

Crystal Imperfections:

Some properties of a crystalline solid depend on the basic crystal structure of the solid. However, in almost all instances, the crystals are not perfect, i.e., the lattices are not without imperfections. These imperfections govern most of the mechanical properties of crystalline solids (see Table 1.2).

The study of the crystal imperfections and their effects on the properties of a material is a subject by itself. In our discussion therefore, we shall give only those concepts that will be required for an understanding of the vari­ous phenomena associated with different processes, e.g., plastic deformation and heat treatment.

The imperfections in a crystal lattice structure can be classified as follows:

(i) If an imperfection is restricted to the neighbourhood of a lattice point, the imperfection is referred to as a point defect. This type of imperfection can be due to various reasons. Figure 1.6 illustrates the three different types of point defects.

In Fig. 1.6a, one lattice atom is missing, creating a vacancy. Since an atom vibrates about its lattice position, the tendency of the atom to jump out of its regular position creating a vacancy increases rapidly with its energy, i.e., the temperature. For example- the usual order of vacancy at 500°C is one in 10¹⁰ which increases to one in 300 at 2000°C. It is possible to increase the vacancy density at a given temperature by rapid cooling or extensive plastic deformation.

In Fig. 1.6b, an atom is occupying an abnormal position. Such an atom is called an interstitial impurity atom. An interstitial impurity can be caused when an atom possesses large enough thermal energy or when its energy is increased by nuclear bombardment. In Fig. 1.6c, a regular lattice position is occupied by an atom of a different material.

(ii) If an imperfection extending along a line has a length much larger than the lattice spacing, the imperfection is called a line defect or, commonly, a dislocation. Two common, simple types of dislocations are illustrated in Fig. 1.7.

When an extra half-plane of atoms is accommodated by distorting the regular lattice arrangement (as done with the XX’ half-plane in Fig. 1.7a), the resulting defect is termed as edge dislocation. Another type of distortion, resulting from a movement of the lattice atoms from their regular ideal positions, is shown in Fig. 1.7b.

Such a defect is called a screw dislocation. The line separating the deformed and the undeformed regions is normally called the dislocation line. In Figs. 1.7a and 1.7b, the dislocation lines are XY. The dislocation density is defined as the total length of all the dislocation lines per unit volume.

In a single crystal, the minimum attainable dislocation density is of the order of 100-1000 per cm², whereas the density in a normal polycrystalline solid is as high as 10⁷—10⁸ per cm².

(iii) When an imperfection extends over a surface, the imperfection is known as surface defect. Figure 1.8 shows a common type of surface defect known as twins. Twins are normally produced when a metal is stressed at a low temperature. The grain boundaries in a polycrystalline solid can also be considered as surface defects.

There are other types of crystal imperfections and the real situation, in general, is quite complex.

Metals and Alloys:

The various types of materials used in engineering practice include, among others, metals, alloys, ceramics, and polymers. Of these, metals and alloys are commonly used. Metals are rarely used in pure form, and the desired properties are normally obtained by suitably alloying different metals.

Alloys, unlike most pure metals, do not have a fixed melting point. Also, certain conditions have to be satisfied to make an alloy of two or more materials.

Solid Solutions:

An alloy can be defined as a mixture of two or more materials, of which at least one must be a metal. The material having the largest percentage composition in the mixture is called the solvent and the remaining are called the solutes. Such a mixture is called a solid solution.

In the solid state, the solute atoms can be present in the solvent in two different ways. When the size of the solute atoms is small enough so that they can occupy the interstitial spaces of the solvent matrix (Fig. 1.9a), the solid solution is of the interstitial type. For normal metals, the only useful material which can be accommodated in the interstitial spaces is carbon.

The other type of solid solution is formed when the solute atoms occupy the regular matrix position by replacing some solvent atoms (see Fig. 1.9b). Such a solution is normally termed as a substitutional solid solution. In some solid solutions with two components, there is no restriction on the percentage composition.

Equilibrium Phase Diagrams:

The important metallurgical changes that take place when a mixture of different metals and/or materials is gradually cooled from a liquid state are best described with the help of an equilibrium phase diagram. Phases are characterized by the boundaries across which discontinuities exist in the physical properties.

Even a pure material can be in different phases, namely, solid, liquid, or vapour. More­over, even within the solid state, there can be different phases, each characterized by a different crystal structure. When cooling is sufficiently slow, we can assume that all the phases involved in the transformation process at a given temperature are in equilibrium with one another.

Though, in general, the transformation of phases is governed by temperature composition and pressure, the latter plays an insignificant role in the processes that we shall consider.

A convenient way of describing the phase transformations is a diagram where the phases at different combinations of temperatures and compositions are indicated. Such a diagram is called an equilibrium phase diagram. For example- let us take the simple case of the Cu-Ni alloy which forms a solid solution without any restriction on the percentage composition.

The equilibrium phase diagram for this alloy is shown in Fig. 1.10a. It has been obtained by considering the cooling curves for various compositions of the alloy.

Figure 1.10b shows three typical cooling curves; here, the start and the end of the solidification process are indicated by S and E. Figure 1.11 shows the physical state of the mixture. It is evident that there are three distinct regions in this
phase diagram. In the region at the top, the entire material is in the liquid state, whereas in the bottom region, the entire material is in the solid state. Further, in the intermediate region, the material is in the form of a mixture of solid and liquid.

The boundary APB (Fig. 1.10a) is called the liquidus and indicates the temperature beyond which the composition will be entirely in the liquid state. Similarly, the boundary AQB, indicating the temperature below which the composition will be totally solid, is called the solidus.

Using Fig. 1.10a, we can determine the relative proportion of liquid and solid. The ratio of solid and liquid for a composition C at a temperature θ is XZ/ZY. Moreover, the composition of the solid portion at the temperature θ is given by the abscissa of the point Y. Similarly, the composition of the liquid portion at this temperature is given by the abscissa of the point X. It may be noted from Fig. 1.11 that when there is no restriction on solid solubility, the solid state of an alloy looks like a pure metal. Such an alloy is called a single-phase alloy where nothing but the grain boundaries are distinguishable.

The example we have considered is quite simple as there is no restriction on solid solubility. However, the situation becomes complex when two metals, having no restriction on solubility in the liquid state, are only partially soluble in the solid state. Complete insolubility in the solid state is another extreme case.

Let us consider the equilibrium phase diagram of this extreme situation. A solution of NaCl and H₂O can be taken up as an example in this category. Figure 1.12 shows the corresponding equilibrium phase diagram. From the nature of this diagram, it is obvious that at a particular composition (i.e., 23.5% NaCl), the mixture, like a pure material, has a specific freezing point (i.e., -22°C).

This signifies simultaneous solidification of both NaCl and H₂O. Such a mechanical mixture of two solids is referred to as the eutectic. This eutectic composition is seen to have the minimum melting (freezing) temperature, and hence the name eutectic (which, in Greek, means easy melting). As before, let us consider a mixture of composition C at a temperature θ. The solid portion (Fig. 1.12) is seen to be pure ice (H₂O), whereas the liquid has a composition given by the point X. On further cooling, the point JF shifts towards the eutectic point E.

At -22°C (normally called the eutectic temperature), the entire solid is ice and the liquid mixture has the eutectic composition. As no mixture can remain in the liquid state below this temperature, with further cooling the entire liquid mixture solidifies simultaneously. Thus, the solidus becomes a horizontal line through the eutectic point E below which the whole mixture is in the solid state.

As is evident from Fig. 1.13, due to simultaneous solidification of both the components, it is difficult to distinguish the different phases in an eutectic composition. Below the eutectic composition, the solid mixture consists of the eutectic mixture and solid H₂O. This mixture is called hypoeutectic.

Beyond the eutectic composition, the solid mixture has the eutectic mixture and solid NaCl; this region is normally referred to as hypereutectic.

The situation is slightly more complicated when the materials are partially soluble in the solid state. Partial solubility means that one component can form a solid solution with the other only up to a maximum concentration. This is normally the case with metallic alloys. A typical equilibrium phase diagram is shown in Fig. 1.14. First of all, let us assume that the maximum solid solubility of A in B is independent of temperature and is given by the percentage composition X_A.

The single-phase solid solution having the composition of A from 0 to X_A is called the α-phase (say). Similarly, the solid solution of B in A having the composition of B from 0 to Y_B is called the β phase.

The actual maximum solid solubilities vary with temperature, as indicated by the dashed lines. Below the eutectic temperature θ_e, the entire material is a mixture of two solid solutions, namely, α and β. However, at the eutectic composition, it is difficult to distinguish between the α-and β-phase and this composition is therefore represented as αβ instead of α + β. Figure 1.15 shows the nature of the alloy at various states.

There are other types of phase transformations similar to the eutectic trans­formation. During an eutectic transformation, a single-phase liquid changes to a two-phase solid. A similar transformation from a single-phase solid is called an eutectoid transformation.

Another transformation, also taking place at a constant temperature, is known as peritectic. In this case, however, above the peritectic temperature, the sys­tem exists in the form of a two-phase liquid-solid mixture. When the system is cooled to the peritectic temperature, all the liquid solidifies and the atoms diffuse into the already existing solid, forming a single-phase solid. When such a transformation starts from a two-phase solid-solid mixture, the transformation is called a pertectoid. (We shall see some of these transformations in Fig. 1.17.)

The manufacturing properties of an alloy depend on the properties, distribu­tion, size, and shape of the various phases present, and on the nature of phase interfaces. The most commonly used alloy in engineering is that of iron and carbon, popularly known as steel. So, a somewhat detailed discussion on iron- carbon diagram (equilibrium phase diagram of Fe and Fe₃C) will be useful. The carbon present in steel is in the form of Fe₃C (called cementite) containing 6.67% of C.

Pure iron has two different allotropic forms. Figure 1.16 shows the cooling curve of pure iron. Between 1537°C and 1400°C, the solid iron exists in the form of bee crystals and is commonly known as δ-iron. From 1400°C to 910°C, the crystal structure is fee, the corresponding name being γ-iron. Below 910°C, the structure again changes back to bcc, and this phase is referred to as α-iron (however, there is no basic structural difference between the α- and the δ- phase). Figure 1.17 shows the iron-carbon equilibrium diagram.

In this figure, the portion involving the δ-phase is not of much interest so far as the normal manufacturing processes are concerned because the temperature is very high. For casting processes, the liquid-solid transformation at 1125°C is significant, whereas for heat treatment of steels, the transformations around 723°C play an important role.

At 1125°C, the solubility of cementite in iron is limited to 2% as indicated by the point A in Fig. 1.17. This solid solution of γ-iron and Fe₃C is commonly termed as austenite. In the bcc phases (i.e., α- and δ-phase) of iron, the solubility of Fe₃C is much smaller (around 0.33% in the a-phase and 0.1% in the 5-phase, as indicated by the points C and B in Fig. 1.17).

The solid solution of Fe₃C in α -iron is called ferrite. The eutectoid (E’) composition of ferrite and cementite is referred to as pearlite which consists of alternate thin laminates of cementite and ferrite. The different structures for the various phases of steel are indicated in Fig. 1.18. As can be noticed, the structure of ferrite is thick and rounded, whereas that of cementite tends to be thin and needle-like. Ferrite is soft and cementite is very hard.

The transformation of austenite into ferrite and cementite is achieved only when the cooling is slow. A rapid cooling rate transforms austenite into a metastable phase, known as martensite. Depending on the composition and temperature drop, there exists a minimum cooling rate for such a transformation. Martensite is brittle and this property limits its applicability.

Theoretical temperatures across which a change of phase occurs can be found out from Fig. 1.18. For a composition C₁, the lower and the upper critical temperatures are  θ^lc₁ and θ^uc₁ . Similarly, for a composition C₂, the critical temperatures are θ^lc₂ and θ^uc₂.

Deformation and Mechanical Properties of Materials:

Most conventional manufacturing processes involve deformation of the work material. Such a deformation caused by the work load is dependent on the mechanical properties of the material. Moreover, the choice of manufacturing processes, tools, dies is also guided by such properties.

Elastic and Plastic Deformation:

In the absence of any external force, the distance between a pair of atoms is d_e. The net interatomic force varies with the atomic spacing in a manner shown in Fig. 1.19. Under the application of an external tensile force, the interatomic distance increases beyond d_e to maintain the equilibrium. If the external tensile force is of magnitude P, then the interatomic distance should be d_A so that the net interatomic force is an attractive force of the same magnitude.

If d_A is not very much different (of the order of 5%) from d_e, then, upon removal of the external force, the atoms attain their original positions. A similar behaviour is also observed with an external compressive force (when d_A < d_e). This behaviour is called the elastic behaviour and the associated deformation is termed as elastic deformation.

The phenomenon we have described for a pair of atoms is true also for normal solids even on a macroscopic scale. It may be noted from Fig. 1.19 that the tangent to the curve at the point d_e coincides with the curve over a small range on either side of the point d_e. Thus, the external force is proportional to the change in the interatomic distance. Hence, within the elastic behaviour, most solids follow a linear force deformation rule, and are therefore called linear elastic solids.

Now, let us consider a crystal lattice with regularly spaced atoms, as shown in Fig. 1.20a. Under the externally applied shear force (indicated in this figure), the upper layers of atoms move to the right and the lower layers move to the left. When the applied force reaches a sufficiently high value, the crystal lattice looks as in Fig. 1.20b. Here, all the atoms are again in equilibrium and will remain thus if the external force is removed. Thus, a permanent deformation is produced in the crystal lattice.

This permanent set is termed as plastic deformation and cannot be recovered upon withdrawal of the external load.

Next, let us find the amount of shear stress necessary to effect the slip between two layers of atoms in the perfect lattice we have described. Referring to Fig. 1.21a, we assume, as a first approximation, that the shear stress τ and the amount of movement of the layer, x, are related as-

 

Surprisingly, the experimentally-observed value of the shear stress necessary to produce a slip is found to be much less (of the order of 100 times) than the value we have calculated. This discrepancy can be explained only by bringing in the concept of imperfections which are always present in an actual lattice structure.

Figure 1.22 explains how the movement of an edge dislocation, rather than the bodily movement of a whole plane of atoms, can cause a slip. This necessitates a much smaller value of the shear stress as can be appreciated from the following analogy.

Let us consider a thick, heavy carpet, lying on a floor, which has to be moved through a distance δ (Fig. 1.23). We can immediately visualize that a very large force will be needed if the whole carpet has to be bodily moved over the distance δ. The same effect, however, can be realized very easily if first a fold is made at one end of the carpet to move that end by the distance δ and then this fold is moved across the entire carpet length.

As dislocations help in a slip, the shear stress necessary to cause the slip will increase if the crystal tested is too small and has very few imperfections. Thus, the strength of a crystal depends on its size. This decrease in the strength of a crystal with the increase in its size is called the size effect.

Further, with increasing deformation, more and more dislocations move and start interacting with one another. These interactions impede the mobility of various dislocations and, as a result, the strength of the material increases. This increase in the strength due to the immobility of dislocations is known as strain hardening; it implies an increase in the strength of a material due to its deformation.

In a polycrystalline solid, the grain size also affects the strength of the solid. As the grain boundaries impede the dislocation movement, a small grain size having a large boundary area to volume ratio results in a high strength of the material. Similarly, a large grain size providing a small boundary area results in a low strength.

Tensile Testing:

Quite a few useful mechanical properties of a material can be obtained by sub­jecting the material to the tensile test. This test, being very simple to conduct, is most common. In this test, a standard specimen is elongated at a slow, con­stant rate (most often by hydraulic means) and the corresponding force at every instant is recorded.

The force deformation relation is often expressed in terms of an engineering stress-strain curve. The engineering stress (σ) is defined as the applied load (P) divided by the original cross-sectional area (A₀) of the speci­men. The engineering strain (e) is defined as the ratio of the increment in length (Δl) over the original length (l₀).

l₀ is sometimes called the gauge length and Δl represents the change in this length when the applied load is P. The stress-strain description renders the load deformation relation independent of the specimen geometry and can be taken as the description of the material properties.

Figure 1.24 shows typical stress-strain curves of some engineering materials. In Fig. 1.24a, we note that, initially, the stress-strain relationship is linear up to the point A. This point is known as the proportionality limit. The point B, just above the point A, is called the elastic limit.

Elastic limit is defined as the greatest stress up to which a material deforms elastically without any permanent set. Beyond e_B, the stress value drops suddenly and the material is said to yield. This point (Y), just after B, is called the upper yield point. The stress value is seen to rise again with strain from the point C. This point is called the lower yield point. The material is observed to be strain hardened beyond C.

The stress value reaches a maximum at the point D, and the corresponding stress is known as the ultimate tensile strength. At this point, the cross-sectional area of the specimen starts reducing drastically with high localized deformation, and this phenomenon is termed as necking. If the elongation is continued further, the specimen ultimately ruptures at the point E, and the corresponding stress is called the breaking (fracture) strength of the material.

The strength of a material in the elastic and the plastic regions is represented by the yield stress (σ_y) and the ultimate stress (σ_u), respectively. The capability of withstanding plastic deformation is another important mechanical property of an engineering material. This, in fact, reflects the ability of the material to distribute the localized stresses, thus lowering the tendency of crack formation.

This property is commonly referred to as the ductility of the material. Ductility is expressed by the percentage elongation, i.e., the percentage strain at the frac­ture point. Thus, larger percentage elongation means higher ductility. Moreover, the strain (see Fig. 1.24a) at the point D (where necking starts) represents the amount of plastic strain a material can withstand without localized deformation.

This is used as an index of the formability of the material and is useful in some sheet metal forming operations. In the linear elastic behaviour, the constant of proportionality between the engineering stress and the engineering strain is known as Young’s modulus or the modulus of elasticity.

It should be noted at this stage that most of the materials, unlike mild steel, do not show any precise proportional limit, elastic limit, or yield point (Fig. 1.24b). In such instances, the yield stress is defined as follows. A line parallel to the tan­gent of the stress-strain curve at the origin is drawn from the point representing 0.2% strain. This line intersects the stress-strain curve at the point Y. The stress level at this point Y is then taken as the yield stress. In fact, the strain at the yield point for mild steel is 0.2%, and the yield stress just defined is sometimes called 0.2% yield stress.

The typical stress-strain curve for a brittle (non-ductile) material is shown in Fig. 1.24c. As can be seen, the material fractures with very little or no plastic strain. (If the percentage elongation is less than 5%, the material is considered to be brittle.)

Yet another important mechanical property is the ability of a material to absorb energy in the plastic range. This is given the name toughness. It is difficult to define toughness and the index commonly used to describe it is the total area under the stress-strain curve up to the fracture point. It represents the work done on a material per unit volume.

Figure 1.25 compares the toughness of two different materials, of which one is stronger and the other more ductile. It is obvious that toughness reflects the combined effect of strength and ductility.

Referring back to the stress-strain curve, we may point out that when the deformation of a specimen is no longer negligible (say, when necking begins), the actual stress should be defined as the ratio of the load (P) and the instantaneous area (A_i) rather than the original area. This ratio P/A_i is called the true stress. Similarly, the true strain should also be defined on the basis of the instantaneous deformation. True strain (ԑ), when the length is l_i, is defined as –

where e is the engineering strain = (l_i – l₀)l_0. It is obvious that, for e ≪ 1, ԑ ≈ e. The true stress versus true strain curve is indicated by the dashed line in Fig. 1.24b. This curve shows a continuous strain hardening of the material up to the fracture point, a phenomenon not revealed by a stress-strain curve.

The stress-strain curve of a material is too complicated to be represented by a simple mathematical relationship amenable to analysis. As such, for purposes of analysis, the curve is idealized in various ways, keeping only those basic features that are important for a given problem. Figure 1.26 shows some idealized curves.

Let us now see what happens if a material, loaded beyond the yield point, is unloaded completely and reloaded. If the material is unloaded from the point B (see Fig. 1.26c), the unloading curve BC is then parallel to the initial elastic curve given by the line OA. The permanent strain is given by OC, whereas the amount of strain recovered is given by CB^’. Thus, the total strain at B is thought of as consisting of two parts, namely, the elastic part CB’ and the plastic part OC. The reloading curve follows the lines CB and BD.

Another important mechanical property, which is not obtained from tensile testing but is relevant in the context of manufacturing processes, is hardness. Hardness is a very ill-defined term and is normally used to indicate the resistance of a material to plastic deformation.

However, the nature of plastic deformation needs to be specified, and hardness refers to the plastic deformation caused by indentation. There are various standard tests which designate the hardness of different materials by using numbers on prescribed scales. The most commonly used numbers are Vickers, Brinell, and Rockwell. These empirical numbers are calculated on the basis of indentation tests with a known applied load and the area or depth of the resulting impression.

Friction and Wear:

It is well-known that whenever a solid surface slides over another, a resist­ing force, commonly referred to as the friction force, and develops. The friction phenomenon was first scientifically studied by Amonton and Coulomb. Since this phenomenon is extremely complicated, we shall restrict our discussion on it to a very elementary level.

Then, with the help of such an oversimplified and elementary model, certain important and fundamental aspects of friction can be easily understood.

Let us consider two solid surfaces in contact, as in Fig. 1.27. Though a surface may appear smooth and plain, in reality no solid surface is perfectly smooth. Asperities are always present in a solid surface, and when two bodies are brought in contact, the real contact takes place only at certain high points.

At the beginning of the contact, the real contact area is zero and very large localized stresses develop, causing plastic deformation of the contact regions. Thus, the area of real contact continues to increase till it is large enough so that the corresponding stresses do not cause any further plastic deformation.

If we assume a rigid plastic model of the materials and if σ is the yield stress in compression (of the weaker material), then the real area of contact all over the mating surfaces can be expressed as A_real ≈ N/σ, where N represents the applied load. Large stresses and plastic deformations cause the upper contamination layers, which are always present, to tear off and the real materials come in contact.

This results in a welding of the asperity junctions, and the sliding of one body above the other will be possible only after these welded asperity junctions are sheared. If τ is the yield shear stress of the weaker material, then the force required to shear off a junction with a total area of A_real is F≈A_real τ. This shearing force is the friction force. The ratio of the friction force and the normal force is found out as

It is obvious from this equation that the ratio fi, normally termed as the coefficient of friction, depends only on the materials in contact. For better results, τ and σ, should be taken for the alloy formed (at the junctions) due to heavy cold work and welding.

The foregoing model, yielding μ = τ/σ, is valid only when the real area of contact is much smaller than the apparent area of contact. If the normal load N is gradually increased, A_real increases and approaches the apparent area of con­tact A. Once A_real reaches a value equal to A, the shear force F (i.e., the friction force) will not increase even if N is increased.

This is illustrated in Fig. 1.28. Under such a situation, mechanisms other than the welding of asperity junctions become active, making the friction phenomenon quite complex. One such im­portant mechanism is the locking of asperities. The coefficient of friction then varies and tends to increase with increasing load.

When a solid surface slides over another, both the surfaces are subjected to a gradual loss of material.

A fraction of the material lost from one surface may be transferred to the other body, whereas the rest gets removed in the form of small (wear) particles. This process of gradual loss or transfer of material from a body (in contact with another) is known as wear. The three major mechanisms of wear, relevant to the manufacturing processes, are abrasion, adhesion, and diffusion.

If one of the surfaces contains very hard particles, then these, during the process of sliding, may dislodge material from the other surface by the ploughing action. This mechanism is called abrasion.

When the bodies in contact are of a similar nature, the asperities on the contacting surfaces tend to get welded. Sliding causes fracture of these welded junctions and material is lost from both the surfaces. The wear due to this mechanism is referred to as the adhesion wear.

Atoms in a metallic crystal lattice always move from a region of high concentration to that of low concentration. This process is known as diffu­sion. The rate of diffusion depends on the concentration gradient and the existing temperature.

Since the rate increases exponentially with temperature, the diffusion mechanism plays a predominant part at high temperatures. When two dissimilar bodies slide over each other, the atoms of various constituent elements diffuse across the junction, leading to wear on both the bodies; this process is known as diffusion wear.