|
When
a material experiences an applied uniaxial tensile stress,
s, it displays a strain
response, e.
In the initial stage of strain, the response is linear in the stress and
may be described by Hooke's law: s
= E e.
E is an elastic constant, Young's modulus. A material exhibiting this behavior
over the complete range of elastic deformation is known as a linear elastic
material. Some materials have a non-linear relationship between stress
and strain, a behavior exhibited by materials such as a rubber. These are
nonlinear elastic materials for which the slope of the stress-strain curve,
(ds/de)e,
is the strain dependent elastic modulus, the Tangent modulus.
Elastic
deformation continues until the yield stress of the material if it is ductile,
after which the material plastically deforms. A brittle material fractures
before any plastic deformation occurs and its complete deformation range
is elastic.
For
an applied shear stress, t,
the shear strain, g,
is given by: t
= G g,
where G is the shear modulus. If the material is subject to a hydrostatic
pressure, p, the volume strain, (dV/V), is given by: p
= K (dV/V), where K is the bulk modulus.
In the elastic deformation range, another elastic constant, Poisson's ratio,
describes the ratio of lateral to longitudinal strain for a material in
uniaxial tension and is given by: n
= - (ex
/ ez),
where the z axis is the tensile axis.
|
|
