Mechanics of material

Any material designing requires the stability of the material which is the basic requirement of any of designing. Before designing, material analysis is important. How material behaves even force is applied to it. What are types of stress, loading which are induced and affect the working? What are the capabilities (like hardness, stiffness, yield point saturation points, etc.) of material to endure the stress?

These all factors are covers in the mechanical engineering of mechanics of material. In mechanics of material, we discuss the behavior of a material under stress and strain, stress terms, stress-strain relations.

“Mechanics of material deals with the behavior of solid objects subject to stresses and strain. The mechanics of material is also called strength of the material.”

In the strength of the material, the properties of the material such as young’s modulus, ultimate tensile stress, yield point, Poisson’s ratio, and behavior of stresses and strains in structural members such as beams, columns and shafts are taken into account.

Before going deep into concepts of the behavior of a material under stress and strain conditions, we need to define some terms which may help out to better understanding the concepts.

Stress:

Stress is the measure of the internal forces that neighboring particles of a continuous material exert on each other.

It is equivalent to the pressure which is equal to the force acting per unit area.

∂ = F/A

The area can be the deformed area or undeformed depending upon the stress acting on the area and strength of a material.

It is a physical quantity and designated by sigma. The SI unit of stress is pascal which is equal to the km-1 s-2 and other units are psi, bar, etc.

Types of stress:

There are few types of stress which are

· Shear stress

· Normal stress

· Compressive stress

· Tensile stress

Shear stress:

When the two opposing forces acting parallel to each other then the stress produce is known as shear stress. It can be said that the sliding faces of material are parallel to each other during shear stress.

The stress which acts parallel to the surface of the material is called shear stress.

For example:

When we cut the piece of paper with scissors the stress acts along the parallel to the paper which is shear stress.

Normal stress:

When the deforming force is perpendicular to the cross-sectional area of the surface then the stress produce is called normal stress.

For example:

The volume of the body changes due to normal stress. Based on the dimension of force, the normal stress is further classified into

· Longitudinal stress

· Bulk stress or volumetric stress

Tensile stress:

The stress elongates the material along the axis of the applied load. In other words, the stress which is caused by pulling the material is called tensile stress.

For example:

The ductile material can exhibit the phenomenon of tensile stress.

Compressive stress:

The stress that acts to reduce the length of the material along the axis of the applied load is called compressive stress. In other words, the stress that causes the squeezing of the material.

For example:

The gas enclosed in the cylinder is compressed by compressed stress.

Stress or strength parameters:

The material strength is the capability of the material to endure stress or strain. There are some parameters used which are used to define the state of materials. These parameters help to determine the state and also to improve the capacity of the material. These parameters are

· Yield strength

· Tensile strength

· Compressive strength

· Fatigue strength

· Impact strength

· Charpy impact test

Yield strength:

The lowest stress which produces permanent deformation in the material is called yield strength.

Tensile strength:

The tensile strength of the material is the maximum amount of tensile which a material can endure before breaking. Tensile strength resists tension that is being pulled apart.

Compressive strength:

To compressive the material is to reduce the size of the material. The compressive strength is the capacity of a material or structure to withstand loads. The compressive strength resists being pushed together.

Fatigue strength:

The highest stress that a material can withstand for a given number of cycles without breaking is called fatigue strength.

The number of cycles that a material can endure before it breaks is heat treatment, impurities in the material, hardness of the material.

Impact strength

The capability of the material to withstand a suddenly applied load is called impact strength. It is expressed in terms of energy.

Strain:

The measure of deformation produces in the material due to stress or force applied is called strain. It is also known as the measure of change in dimensions of the material.

Strain parameter for resistance:

Few deformations parameters are produced in the material due to stress applied to the system. These parameters are

· Deformation

· Strain

· Deflection

Deformation:

The change in the geometry is created when forces or stress (such as gravitational fields, thermal expansion, accelerations, etc.) is applied to the system. It is expressed by the displacement field of the material.

Strain:

The deformation of material among the material field is called strain. It is a mathematical term that is equal to deformation per unit length. For example, in the case of uniaxial loading, the strain is equal to the quotient of the displacement and original length of the specimen.

Deflection:

The magnitude to which a structural element is displaced when the load is applied is called deflection.

The relation between stress and strain curve:

The relation between stress and strain is determined by the tensile or compressive test. In this test, the applied load is proportional to the deflection produced in a material. The values can be plotted as load-deflection curves. Load represents the stress which produces deflection which is called strain. The values of stress and strain obtained from the test can be drawn as the stress-strain curves.

There are important points on the curve which define the state of the system. These are

· Proportional limit

· Elastic limit

· Yield point

· Ultimate tensile stress

· Fracture point

Proportional limit:

The maximum stress which a material endure without losing the linearity of the stress-strain curve is called proportional limit. It is designed by p.

Elastic limit:

The maximum stress which a material can endure before set on the permeant deformation. When the stress is removed on this limit, the material can regain its original shape. The curve is not linear between the proportion limit and elastic limit.

Yield point:

The point on the stress-strain curve represents the value of stress above which strain will begin to increase rapidly. The point indicates the limit of elastic behavior and the beginning of plastic behavior. The point where the line intersects the stress-strain curve is known as the yield point.

Ultimate tensile strength:

The point that represents the maximum stress on the stress-strain curve is called ultimate strength. After reaching this point the ductile material will exhibit necking. The point is also known as tensile strength.

Fracture point:

The fracture point is the endpoint on the stress-strain curve where material fails and breaks into two pieces. This point is also known as the breaking point.

Mechanical properties of the material:

For the better functionality of machines or many other applications, it is important to note the mechanical properties of the material, which type of material is. These properties of the material are very common to observe the ability of material for various applications. These properties are

· Strength

· Hardness

· Toughness

· Hardness

· Brittleness

· Malleability

· Ductility

· Resilience

· Fatigue

· Creep and slip

Strength:

The ability of a material to oppose or resist the applied forces and deformation in the material is called the strength of the material. For smooth functioning of machines or applications of materials, it is necessary to have the strength of material to endure the applied forces or loads.

Hardness:

The ability of a material to resist the permanent change in shape due to external forces is called the hardness of the material. There are different types of hardness and have their different measure

· Scratch hardness

· Indentation hardness

· Rebound hardness

Scratch hardness:

The ability of a material to resist the outer scratches on the surface of the material which are due to applied forces or resistance is called scratch hardness.

Indentation hardness:

The ability of a material to oppose the dent which is due to punching of external hardness and sharp objects is called indentation hardness.

Rebound hardness:

The hardness which measures the height of the bounce of a diamond-tipped hammer dropped from a fixed height onto a material is called rebound hardness. It is also known as dynamic hardness.

Toughness:

The ability of a material to absorb the energy and get plastically deformed without fracture or brittle is called toughness. For the good toughness of the material, the material should have good strength and ductility. Toughness can be measure as the amount of energy per unit volume. Its unit is joule/m^3. It can also be determined by the stress-strain characteristics of a material.

Hardenability:

The ability of a material to attain hardness by heat treatment processing is called the hardenability of material. It can be determined by the depth up to which a material becomes hard. It is inversely related to the weldability of the material.

Brittleness:

The property of a material to get a fracture or break by applying force is called brittleness. Brittle objects cannot endure the energy forces or load and gets fracture without much strain. It is temperature-dependent. For example, some materials that are ductile at normal temperatures show brittle behavior at low temperatures.

Malleability:

The ability of a material to get deformed by compressive stress is called malleability. It is also known as the ability of a material to be formed in the form of a thin sheet by hammering or rolling. Malleability is also temperature-dependent. It increases with an increase in temperature.

Ductility:

The property of a material to get deformed by tensile stress is called ductility of the material. It is also known as the ability of a material to get stretched into a wire by drawing or pulling. It is also temperature-dependent. The ductility of material increases with an increase in temperature.

Resilience:

The ability of a material to absorb the energy when it deformed elastically by applying stress and release the energy when stress is removed is called resilience. The modulus of resilience is defined as the maximum energy that can be absorbed per unit volume without permanent deformation. It can be determined by integrating the stress-strain curve from zero to the elastic limit. Its unit is joule/m^3.

Fatigue:

The highest stress that a material can withstand for a given a number of cycles without breaking is called fatigue.

The number of cycles that a material can endure before it breaks is heat treatment, impurities in the material, hardness of the material.

Creep and slip:

The property of a material that indicates the tendency of a material to move slowly and deform permanently under the influence of external mechanical stress is called creep and slip. Creep is more severe in materials that are subjected to heat for a long time. A slip in the material is a plane with a high density of the material. This is due to long-time exposure to large external mechanical stress within the limit of yielding.

Types of loading:

There are three types of loadings these are

· Transverse loading

· Axial loading

· Torsional loading

Transverse loading:

When the load is applied or forces act perpendicular to the longitudinal axis of the member, this type of loading is called transverse loading. This loading causes the members to bend and deflect from their original position, while inner tensile and compressive straining are associated with a change in curvature of the material. Transverse loading also induces shear forces that cause shear deformation of the material and increase the transverse deflection of the member.

Axial loading:

The loading which acts along the line of the axis of the object is called axial loading. If the axial load passes through the neutral axis, then it is called concentric loading. If the force is not acting through the neutral axis, then it is called eccentric loading.

This loading is collinear with the longitudinal axis of the member. These forces cause the member to shorten or stretch. Axial loading can be calculated by using

∂ = F/A

∂ = is the normal stress

F = is the axial force

A = cross-sectional area of surface

Torsional loading:

The load which imparts the turning effect is called torsional loading. Two equal and opposite external applied forces acting on parallel planes cause twisting action.

Designing factors:

Machines parts fail when they are subjected to a non-steady and continuously varying load below the yield point. This is due to fatigue failure. Machine designing requires the stability of a material. Stability of material means how much load material can endure without fracture or brittle. For the better designing of machine parts, some factors are required which may help out for the stability of the material. These factors are

· Factor of safety

· Margin of safety

The factor of safety:

The factor of safety includes the actual load-bearing capacity of a structure or component. It is the designing criteria that must achieve. The factor of safety can be expressed as

FS = UTS/R

Where,

FS = the factor of safety

R = The applied stress

UTS = ultimate stress

The margin of safety:

When the material or parts of a machine are designed according to code law and design requirement this is called the margin of safety of the material.

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World of Mechanical Engineering