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:

σ = E ε

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 = dσ/dε}

Shear stresses produce strains according to:

_{τ = G γ}

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. inter nuclear 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.

Yield criteria and macroscopic aspects of plastic deformation

Gross plastic deformation of a polycrystalline specimen corresponds to the comparable distortion of  the  individual grains  by  means of slip.  During deformation, mechanical integrity  and coherency are maintained along the grain boundaries; that is, the grain boundaries is constrained, to some degree, in the shape it may assume by its neighboring grains. Before deformation the grains are equiaxed, or have approximately the same dimension in all directions. For this particular deformation, the grains become elongated along the directions. For this particular deformation, the grains become elongated along the direction in which the specimen was extended.