1. Stress

The term stress is used to express the loading in terms of force applied to a certain cross-sectional area of an object. From the perspective of loading, stress is the applied force or system of forces that tends to deform a body. From the perspective of what is happening within a material, stress is the internal distribution of forces within a body that balance and react to the loads applied to it. The stress distribution may or may not be uniform, depending on the nature of the loading condition. For example, a bar loaded in pure tension will essentially have a uniform tensile stress distribution. However, a bar loaded in bending will have a stress distribution that changes with distance perpendicular to the normal axis.

Simplifying assumptions are often used to represent stress as a vector quantity for many engineering calculations and for material property determination. The word "vector" typically refers to a quantity that has a "magnitude" and a "direction". For example, the stress in an axially loaded bar is simply equal to the applied force divided by the bar's cross-sectional area.

Some common measurements of stress are:
Psi = lbs/in² (pounds per square inch)
ksi or kpsi = kilopounds/in² (one thousand or 10³ pounds per square inch)
Pa = N/m 2 (Pascals or Newtons per square meter)
kPa = Kilopascals (one thousand or 10³ Newtons per square meter)
GPa = Gigapascals (one million or 10⁶ Newtons per square meter)

Types of Stress

Stresses occur in any material that is subject to a load or any applied force. There are many types of stresses, but they can all be generally classified in one of six categories: residual stresses, structural stresses, pressure stresses, flow stresses, thermal stresses, and fatigue stresses.

Residual stress

Manufacturing processes are the most common causes of residul stress. Virtually all manufacturing and fabricating processes such as casting, welding, machining, molding, heat treatment, plastic deformation during bending, rolling or forging introduce residual stresses into the manufactured object. Residual stress could be caused by localized yielding of the material, because of a sharp notch or from certain surface treatments like shot peening or surface hardening.

Structural stresses

Structural stresses are stresses produced in structural members because of the weights they support. The weight provide the loadings. These stresses are found in building foundations and frameworks, as well as in machinery parts.

Pressure stress

Pressure stresses are stresses induced in vessels containing pressurized materials. The loading is provided by the same force producing the pressure.

Flow stress 

Flow stress can be defined as the stress required to sustain plastic deformation at a particular strain. Flow stresses occur when a mass of flowing fluid induces a dynamic pressure on a conduit wall. The force of the fluid striking the wall acts as the load. This type of stress may be applied in an unsteady fashion when flow rates fluctuate. Water hammer is an example of a transient flow stress.

Thermal stresses

Temperature changes cause the body to expand or contract. If temperature deformation is permitted to occur freely, no load or stress will be induced in the structure. In some cases where temperature deformation is not permitted, an internal stress is created. The internal stress created is termed as thermal stress. Take note that as the temperature rises above the normal, the rod will be in compression, and if the temperature drops below the normal, the rod is in tension.

Fatigue stress

Fatigue stresses are due to cyclic application of a stress. The stresses could be due to vibration or thermal cycling.

In materials science, fatigue is the weakening of a material caused by repeatedly applied loads. It is the progressive and localized structural damage that occurs when a material is subjected to cyclic loading. The nominal maximum stress values that cause such damage may be much less than the strength of the material typically quoted as the ultimate tensile stress limit, or the yield stress limit.

Tensile stress is the stress state leading to expansion; that is, the length of a material tends to increase in the tensile direction. The volume of the material stays constant. When equal and opposite forces are applied on a body, then the stress due to this force is called tensile stress.

Compressive stress is the stress on materials that leads to a smaller volume. By compressive stress the material is under compression. Compressive stress leads to shortening.

Shear stress exist when two parts of a material tend to slide across each other in any typical plane of shear upon application of force parallel to that plane.

1. Strain 

Strain is the response of a system to an applied stress. When a material is loaded with a force, it produces a stress, which then causes a material to deform. Engineering strain is defined as the amount of deformation in the direction of the applied force divided by the initial length of the material. This results in a unitless number, although it is often left in the unsimplified form, such as inches per inch or meters per meter. For example, the strain in a bar that is being stretched in tension is the amount of elongation or change in length divided by its original length. As in the case of stress, the strain distribution may or may not be uniform in a complex structural element, depending on the nature of the loading condition.

If the stress is small, the material may only strain a small amount and the material will return to its original size after the stress is released. This is called elastic deformation, because like elastic it returns to its unstressed state. Elastic deformation only occurs in a material when stresses are lower than a critical stress called the yield strength. If a material is loaded beyond it elastic limit, the material will remain in a deformed condition after the load is removed. This is called plastic deformation.

1. Stress-Strain relation

During stress testing of a material sample, the stress–strain curve is a graphical representation of the relationship between stress, obtained from measuring the load applied on the sample, and strain, derived from measuring the deformation of the sample. The nature of the curve varies from material to material.

A typical stress-strain curve is shown in Figure 1. If we begin from the origin and follow the graph a number of points are indicated. 

Point A: At origin, there is no initial stress or strain in the test piece. Up to point A Hooke's Law is obeyed according to which stress is directly proportional to strain. That's why the point A is also known as proportional limit. This straight line region is known as elastic region and the material can regain its original shape after removal of load.

Point B: The portion of the curve between AB is not a straight line and strain increases faster than stress at all points on the curve beyond point A. Point B is the point after which any continuous stress results in permanent, or inelastic deformation. Thus, point B is known as the elastic limit or yield point.

Point C & D: Beyond the point B, the material goes to the plastic stage till the point C is reached. At this point the cross- sectional area of the material starts decreasing and the stress decreases to point D. At point D the workpiece changes its length with a little or without any increase in stress up to point E.

Point E: Point E indicates the location of the value of the ultimate stress. The portion DE is called the yielding of the material at constant stress. From point E onwards, the strength of the material increases and requires more stress for deformation, until point F is reached.

Point F: A material is considered to have completely failed once it reaches the ultimate stress. The point of fracture, or the actual tearing of the material, does not occur until point F. The point F is also called ultimate point or fracture point.

1. Hooke’s law.

Hooke's law - the law of mechanics determining the stress-strain relationship. It says that the deformation of the body under the influence of forces acting on them is proportional to this force. Ratio between the force and deflection is often called coefficient (module) elasticity.

This regularity, formulated by Robert Hooke (1635-1703) in the form ut Tensio sic vis (which stress the strength) remains true only for very large deformations, not exceeding called. border Hooke (also called proportional limit), and only for some materials. Hooke's law also assumes that the deformation of the body, in response to forces, followed immediately and completely disappear when the applied forces cease to operate. This simplification is only sufficient for bodies with negligible viscosity.

The simplest example of the application of Hooke's law is static stretching rod. Absolute extension of such rod is proportional to the force applied to the rod to its length and inversely proportional to the cross-sectional area of the rod. The constant of proportionality is the Young's modulus E

where:

F - tensile strength,

S - cross-sectional area,

Δl - the elongation of the rod,

l - length of initial.

Using the definitions of stress and strain can be said that the relative elongation is proportional to the stress, which can be written:

where:

- relative deformation,

- stress.