In this article, I shall define stress and strain and explain stress and strain curve. So let us start with our topic.
When an external force applied to a body changes the size or shape of the body then at each cross-section of the body an internal reactionary force is developed which tends to restore the body to its original state.
Define Stress and Strain
The internal restoring force acting per unit area of cross-section of the deformed body is called stress. Thus, if an external force ‘F’ is applied to the cross-sectional area ‘A’ of a body, then
Stress = F/A
and is expressed in newton/metre2 or Pascal.
The stress produced due to the force acting at perpendicular to the surface is called normal stress. It may be compressive or tensile.
A stress produced due to the force acting along the surface is called the tangential stress or shear stress.
When a part is loaded, and supports stress, it is deformed or strained from its original unstrained dimensions. The amount of strain in any direction depends upon the magnitude and duration of the stress, and upon the condition of the material.
Strain and unit strain are used synonymously to indicate the deformation per unit dimension. They are measured in a dimensionless unit such as cm per cm, or in percentage. The strain produced by uniaxial tension is known as elongation.
In case of perfectly elastic materials
- The strain always remains same for a given stress.
- The strain vanishes completely on removal of deforming force.
- Almost all elastic materials are abided by the Hook’s-law, according to which, up to elastic limits, the stress is proportional to strain.
Stress α Strain
or Stress/Strain = constant = E = modulus of elasticity
However, a very few engineering materials behave as perfectly elastic bodies because of structural imperfections and so, Hook’s law usually applies up to very small deformations.
For larger deformations, the linear relation between stress and strain no longer exists. Engineering materials like cast iron, non-ferrous metals and concrete show yield on the stress and strain curve from the very beginning. Soft vulcanized rubbers and materials of like character are distinguished by a large elastic strain.
Explain Stress and Strain Curve
In the static-load tests a gradually increased load is applied to the specimen, and the strain in the direction of loading is periodically measured until failure is approached.
The stress is calculated from the loads and the original dimensions of the specimen, and this stress is plotted graphically with respect to its corresponding strain. The resulting graph is called a stress and strain curve.
Stress and strain curves are a measure of the strength of a material the capacity of the material to support a load. The various strength properties taken from these curves are as follows.
Proportional Limit: As long as the stress and strain curve is straight from the zero point (origin), strain is proportional to stress and Hooke’s law of proportionality between strain and stress applies.
The value of stress at which the curve first bends to the right is termed the proportional limit. The proportional limit is high for steels and low for cast iron, copper, and aluminum.
Elastic Limit: The elastic limit is the maximum stress that can be applied to a metal without causing plastic deformation that will remain after the load is relaxed to zero.
The stress and strain curve does not show the elastic limit; it can only be found by successive loading and unloading of the test specimen. For ductile metals the elastic limit is normally just above the proportional limit but close enough that they are often considered as having the same value.
Cast iron, by contrast, has an elastic limit that is well above its low proportional limit and approaches the limit of its strength. For this reason, cast iron can be given little permanent set before rupture will occur.
Successively lower values of elastic limit have been determined for most metals as the sensitivity of strain-measuring devices has been improved. This may indicate that metals have no absolute elasticity during the first loading cycle. Or it may suggest that a minute amount of set remaining in the material is recovered only after a period longer than the testing time.
For practical purposes, however, the elastic limit based on observable permanent deformation in the customary testing procedure is a useful concept.
Permanent Set: When a metal remains deformed form its original dimensions after forces applied to it have been reduced to zero, it is said to have undergone plastic deformation, and the amount of deformation is called the permanent set.
Yield Point: At a certain stress, called the yield point, low-carbon and annealed medium-carbon steels begin to slip rapidly along atomic planes and a relatively large permanent set takes place with no increase (sometimes with a decrease) in load.
Ultimate Strength: The maximum stress that any metal will withstand before fracture is called its ultimate strength. The terms “tensile strength,” “compressive strength,” or “shear strength” are also used, depending on which type of stress is established. The ultimate is the highest stress which the stress-strain curve reaches.
Classification of Materials Based on Stress-Strain Curve
The nature of stress-strain curves for different materials varies with the elastic properties of the material. On this basis, materials may be classified into three elastic categories:
- Ductile Materials : These are the materials which have a large plastic region beyond the elastic limit i.e., the breaking point is far away from the elastic limit. Iron, copper silver, aluminum, etc. fall under the category of ductile materials. Rods of these materials can be drawn into wires.
- Brittle Materials: These materials have a very small plastic region so that their breaking point lie close to the elastic limit. Glass, dry clay balls, etc. fall under the category of brittle materials. These materials break into pieces on being beaten.
- Elastomers: These are the materials for which stress-strain graph is not a straight line even within the elastic limit, and the strain produced is in much larger proportion than the stress. Such materials have one plastic region, the breaking point lies just close to the elastic limit.
Rubber falls under the category of elastomers. It can be pulled to several times its length and still returns to its original length; and it just breaks when pulled beyond a certain limit. Thus, its elastic region is very large, but no plastic region.
Thanks for reading about “define stress and strain” and “explain stress and strain curve pdf”.
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