Mechanism of Elastic Deformation
Elastic deformation
is reversible. Once the applied forces are removed, the object returns to its
original shape. Elastomers and shape memory metals
such as Nitinol exhibit
large elastic deformation ranges, as does rubber.
However elasticity is nonlinear in these materials. Normal metals, ceramics and
most crystals show linear elasticity and a smaller elastic range.
The
initial straight line (OP)of the
curve characterizes proportional relationship between the stress and the deformation (strain). The stress value
at the point P is called
the limit of proportionality:
σp= FP / S0
Where E is a constant, known as Young’s
Modulus or Modulus
of Elasticity.
The
value of Young’s Modulus is determined mainly by the nature of the material and
is nearly insensitive to the heat treatment and composition. Modulus
of elasticity determines stiffness - resistance of a body
to elastic deformation caused by an applied force.
The line OE in the
Stress-Strain curve indicates the range of elastic deformation – removal of the load at
any point of this part of the curve results in return of the specimen length to
its original value. The elastic behavior
is characterized by the elasticity limit (stress value at
the point E):
σel = FE / S0
For
the most materials the points P and E coincide and therefore σel=σp.
Mechanism of Plastic Deformation
Yield stress, Shear strength of
Perfect and Real Crystals
Critical
Resolved Shear Stress(CRSS).
Critical resolved shear stress is the component of shear stress, resolved in the direction of
slip in a grain. It is a constant for a given crystal. Since this is a threshold value,
it is called critical; and being a component of the applied stress, it is said
to be resolved.
Crystalline
materials tend to deform or fail by the relative motion of planes of atoms
under the action of stress. This motion is induced by the component of stresses
acting across the slip planes. The deformation process is a collective motion
of adjacent slip planes. But all the planes do not start deforming
simultaneously. The first slip in a single plane occurs when the shear stress
across the plane exceeds CRSS.
Temperature and crystal geometry influence the
minimum stress required to cause the shear.
A
pure crystalline solid, when pulled along different orientations, requires
different amounts of load in each instance for the very first slip to occur
though the stress required for the planes to slip remains same. This implies
that the Critical Resolved Shear Stress is greatly influenced by the
orientation of the slip plane with the tensile axis.
Schmid's Law states that the critically
resolved shear stress (τ) is equal to the force applied to the material (σ)
multiplied by the cosine of the angle with the glide plane (φ) and the cosine
of the angle with the glide direction (λ).
Resolved
shear stress is given by τ = σ cos Φ cos λ where σ is the magnitude of the
applied tensile stress, Φ is the angle between the normal of the slip plane and
the direction of the applied force and λ is the angle between the slip plane
direction and the direction of the applied force.
Hence
critical resolved shear stress is given by,
When sufficient load is applied to a
material, it will cause the material to change shape or deform. A temporary
shape change that is self-reversing after the force is removed, so that the
object returns to its original shape. The change in shape of a material at low
stress that is recoverable after the stress is removed is called elastic
deformation. Elastic deformation involves stretching of the bonds (but the
atoms do not slip past each other or twin which requires breaking of bonds).
As shown in the graph above, when
the stress is sufficient to permanently deform the metal, it is called plastic
deformation. Plastic deformation involves the breaking and remaking of atomic
bonds. Plastic deformation may take place by slip, twinning or a combination of
both methods.
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