Machine Design
According to Rankine's theory, the failure occurs at a point in a member

When the maximum principal strain in a biaxial stress system reaches the strain at the elastic limit as determined from a simple tension test
When the strain energy per unit volume in a biaxial stress system reaches the strain energy at the elastic limit per unit volume as determined from a simple tension test
When the maximum principal stress in a biaxial stress system reaches the elastic limit of the material in a simple tension test
When the maximum shear stress in a biaxial stress system reaches the shear stress at elastic limit in a simple tension test

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Machine Design
The elasticity is the property of a material which enables it to

Retain deformation produced under load permanently
Resists fracture due to high impact loads
Draw into wires by the application of a tensile force
Regains its original shape after deformation when the external forces are removed

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