Stress—Strain Behavior

Elastic deformation. When the stress is removed, the material returns to the dimension it had before the load was applied. Valid for small strains (except the case of rubbers).

Deformation is reversible, non permanent

Plastic deformation. When the stress is removed, the material does not return to its previous dimension but there is a permanent, irreversible deformation.

In tensile tests, if the deformation is elastic, the stress-strain relationship is called Hooke's law:

s = E e

That is, E is the slope of the stress-strain curve. E is Young's modulus or modulus of elasticity. In some cases, the relationship is not linear so that E can be defined alternatively as the local slope:

E = ds/de

Shear stresses produce strains according to:

t = G g

where G is the shear modulus.

Elastic moduli measure the stiffness of the material. They are related to the second derivative of the interatomic potential, or the first derivative of the force vs. internuclear distance. By examining these curves we can tell which material has a higher modulus. Due to thermal vibrations the elastic modulus decreases with temperature. E is large for ceramics (stronger ionic bond) and small for polymers (weak covalent bond). Since the interatomic distances depend on direction in the crystal, E depends on direction (i.e., it is anisotropic) for single crystals. For randomly oriented policrystals, E is isotropic.

4. Anelasticity

Here the behavior is elastic but not the stress-strain curve is not immediately reversible. It takes a while for the strain to return to zero. The effect is normally small for metals but can be significant for polymers.

5. Elastic Properties of Materials

Materials subject to tension shrink laterally. Those subject to compression, bulge. The ratio of lateral and axial strains is called the Poisson's ratio n.

n = e_lateral/e_axial

The elastic modulus, shear modulus and Poisson's ratio are related by E = 2G(1+n)

Date: 2015-01-02; view: 885