When a spring is extended a distance Dy,
with a force fy, the
spring constant k is defined as....
k = fy/Dy
For a steel spring the value of k is the same for all
extensions.
Note: the spring constant k is a property of
the spring, not a property of the steel the spring is made from.
Young's modulus is defined in the same way as the spring constant,
but modified so that the modulus is a property of the material,
not the specific sample.