Vadodara Institute Of Engineering

Name: Chaturvedi Anupam

Milan Patel

Topic : Elastic Materials

Teacher : Nirav Patel

Division : Mechanical 3

Sem : 3rd

Elastic Material

• Elasticity is the ability of a material to return to its original shape and size on the removal of external forces.

• Within certain load limits, mild steel, copper, polythene and rubber are examples of elastic materials; lead and plasticine are examples of plastic materials.

Homogeneous & Isotropic Material

• Isotropic means having the same properties in all directions.

• Homogeneous means having the same properties at all locations.

• For example a fine suspension of particles in a liquid can be isotropic but not homogeneous. An even-grained wood is (or at least could be) homogeneous but not isotropic.

Stress-Strain Relationship

• The relationship between the stress and strain that a particular material displays is known as that particular material's stress–strain curve. It is unique for each material and is found by recording the amount of deformation (strain) at distinct intervals of tensile or compressive loading (stress).

• We discuss about Stress-Strain Relationship for Ductile & Brittle Material.

• Ductile materials, which includes structural steel and many alloys of other metals, are characterized by their ability to yield at normal temperatures.

• Brittle materials, which includes cast iron, glass, and stone, are characterized by the fact that rupture occurs without any noticeable prior change in the rate of elongation.

Limits of Elasticity & Proportionality

• If a tensile force applied to a uniform bar of mild steel is gradually increased and the corresponding extension of the bar is measured, then provided the applied force is not too large. where extension is no longer proportional to the applied force is known as the limit of proportionality.

• Just beyond this point the material can behave in a non-linear elastic manner, until the elastic limit is reached. If the applied force is large, it is found that the material becomesplastic and no longer returns to its original length when the force is removed. The material is then said to have passed its elastic limit.

Yield Limit

• A yield strength or yield point of a material is defined in engineering and materials science as the stress at which a material begins to deform plastically. Prior to the yield point the material will deform elastically and will return to its original shape when the applied stress is removed. Once the yield point is passed, some fraction of the deformation will be permanent and non-reversible.

Ultimate Strength

• Ultimate strength, is the maximum stress that a material can withstand while being stretched or pulled before failing or breaking. Tensile strength is not the same as compressive strength and the values can be quite different.

• Two vises apply tension to a specimen by pulling at it, stretching the specimen until it fails. The maximum stress it withstands before failing is its ultimate strength.

Strain Hardening

• Strain hardening is generally defined as heating at a relatively low temperature after cold-working. During strain hardening the strength of the metal is increased and ductility decreased.

• To go a step further in explaining, if a low-carbon steel is cold-worked, or strained passed the yield point, then aged for several days at room temperature, it will have a higher yield stress after the aging. This happens because during the aging carbon or nitrogen atoms diffuse to dislocations, reanchoring them.

• Also, not everything can be strain aged, or recovered at low temperatures. The low carbon steel is just an example. Different materials will show different behaviours during recovery.

Proof Stress

• An approximation for the Yield point/Elastic limit for materials that don't have a definite one due to their structure.

• To find the approximation, a tangent is produced from the Proportional Limit. The points of intersection between the graph and the tangent defines the Proof Stress of the material.

• The line may be moved slightly to accommodate for certain materials.

• Examples are 0.1%/0.2% Proof Stress, where the tangent is produced from a point slightly (0.001) to the right of the Proportional Limit.

Factor of Safety

• Factor of safety (FoS), also known as (and used interchangeably with) safety factor (SF), is a term describing the structural capacity of a system beyond the expected loads or actual loads. Essentially, how much stronger the system is than it usually needs to be for an intended load. Safety factors are often calculated using detailed analysis because comprehensive testing is impractical on many projects, such as bridges and buildings, but the structure's ability to carry load must be determined to a reasonable accuracy.

• Factor of Safety = Material Strength/Design Load

Working Stress

the stress to which material may be safely subjected in the course of ordinary use.

Load Factor

the ratio of the average or actual amount of some quantity and the maximum possible or permissible.

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