
Mechanical
Properties
How
a material responds to a load is best expressed in terms of the size independent
quantities stress and strain. the diagram illustrates a cylindrical sample
of initial area A_{0} that is being loaded in tension by a force,
F. As a result of the application of this force the sample changes from
an initial unloaded length, L, to a final loaded length, L_{0}.
In terms of these quantities, the stress is given by: s
= F/A_{0},
and the associated strain by: e
= (L_{0}  L)/L_{0} = DL/L_{0}.
These quantities are known as the Engineering Stress and the Engineering
Strain.
In
the elastic response range for the material being tested stress and strain
are related through a material property known as an "Elastic Constant."
For the tensile situation illustrated the elastic constant is known as
Young's modulus and the elastic relationship is "Hooke's law." This is
written: s
= E e.
This linear relationship does not hold for all types of material. For example
a rubber remains elastic over a very large range of strains but the slope
of the stressstrain plot depends on the value of the strain. Materials
that behave in this way are nonlinear elastic materials and their elastic
modulus E* = (ds/de)
is strain dependent. The definition of E* used is for the "Tangent modulus"
for the nonlinear material.









