Stresses in the helical spring wire:
From the free body diagram, we have found out the direction of the internal torsion T and internal shear force F at the section due to the external load F acting at the centre of the coil.
The cut sections of the spring, subjected to tensile and compressive loads respectively, are shown separately in the figure.
The broken arrows show the shear stresses arising due to the torsion T and solid arrows show the shear stresses due to the force F.
It is observed that for both tensile load as well as compressive load on the spring, maximum shear stress always occurs at the inner side of the spring. Hence, failure of the spring, in the form of crake, is always initiated from the inner radius of the spring.
The radius of the spring is given by D/2. Note that D is the mean diameter of the spring. The torque T acting on the spring is
If d is the diameter of the coil wire and polar moment of inertia,
The shear stress in the spring wire due to torsion is