Wednesday, March 16, 2016

Mechanism of Elastic Deformation

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
This behavior conforms to the Hook’s Law .i,e, σ = E*δ
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 σelp.

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,
  
 max






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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