Hooke's law is valid for only small deformation. Hooke's principle defines that the extension produced in the wire is directly proportional to the load applied within elastic limit. i.e. within extension, elastic limits ∝ load applied.
Later on it was achieved that this principle is applicable to all types of deformation such as compression, bending, twisting etc and thus a modified form of Hooke's law was given as stated below.
"Within elastic limit, the stress developed is directly proportional to the strain produced in a body"
i.e. stress ∝ strain or, stress = E * strain
where E is a constant and is known as the modulus of elasticity of the material.
Stress Strain Relationship For A Wire
The relationship between stress and strain in a wire is illustrated by the graph shown in the adjoining graph. The areas are referred to as given:
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OA = Elastic region, Hooke's law is valid.
AB = Elastic region, Hooke's law is not true
A = proportional limit
B = Elastic limit(strain £1 %) or yield point
BD = Plastic deformation
OE = Permanent set
CD = Plastic flow
D = Fracture point (Corresponding stress is called breaking stress/ tensile strength)
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Elastomers: The substances which can be stretched to large values of strain are called elastomers. e.g. elastic tissue of aorta, the largest artery carrying blood from the heart.
TENSILE STRENGTH OR ULTIMATE STRENGTH : The stress at which the specimen breaks or reptures ultimately is called ultimate strength.
MODULUS OF ELASTICITY: According to Hooke's law, within elastic limit, stress ∝ strain
or stress = E * strain or E = a constant,
Where E is known as coefficient of elasticity or modulus of elasticity of a body which depends upon the nature of material of the body and the manner in which the body is deformed. Thus, particles of elasticity or coefficient of elasticity of a body is defined as the ratio of the stress to the corresponding strain given, within the elastic limit.
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