Elastic Analysis

Question 1

What is elastic Analysis?

Answer 1

• In the elastic analysis of metals it is assumed that elastic strain is a function of stress only.
• This is not strictly true since there is time dependence to the elasticity.
• In metals, the effect is very small and generally neglected, but in polymers the effect is much more significant.
• The general name for this time dependence is anelasticity.

Question 2

Anelasticity

Answer 2

• shows that if a strain e1 is applied to an anelastic material at time = t0 then the strain will slowly increase to e2, the completely relaxed strain, at time t=t1. The anelastic strain is e2 - e1.
• If the material’s now suddenly unloaded the strain decreases immediately by e1, followed by a slower decrease to zero strain known as the ELASTIC AFTEREFFECT.
• If the loading is applied so rapidly that there is no time for thermal equilibrium with the environment, i.e. constant entropy, adiabatic loading, there will be a temperature decrease.

Question 3

Compression

Answer 3

-this raises the temperature,and this effect is called the thermoelastic effect, though the temperature changes are very small.

Question 4

Isothermal Strain (E1)

Answer 4

If a specimen is stressed elastically at a slow rate then thermal equilibrium is maintained and an isothermal strain is produced.

Question 5

Adiabatic Strain (Ea)

Answer 5

If rapid, adiabatic, constant entropy loading occurs, there is no time for thermal equilibrium and a small temperature drop occurs with an adiabatic strain being produced.

Question 6

Mechanical Hysteresis Loop

Answer 6

If the specimen loses heat to the environment and cools and contracts along path DA, This results in a closed mechanical hysteresis loop. In practice if stressing is continuous, a more lenticular shaped loop is produced.

Question 7

Area of Hysteresis

Answer 7

• This is loop depends on the frequency of cycling. For very low frequency, isothermal cycling the area is low, and area is also low for very fast adiabatic cycling.
• At some intermediate frequency the area will be a maximum.

Question 8

Vibration Energy/Internal Friction

Answer 8

Vibration energy in crystalline solids may be dissipated by several mechanisms, other than the thermoelastic effect. These inlcude:

• Stress induced ordering of solute atoms.
• Grain boundary sliding
• Dislocation movements
• Bond rotation in polymers
• Moisture absorption in polymers.

Question 9

Forced Vibrations

Answer 9

• For Forced Vibrations, the specimen is driven at constant amplitude.
• For a fixed amount of energy per cycle, the maximum amplitude of vibration occurs at the resonance frequency. Internal friction studies are carried out at low stress and strain levels while energy dissipation at higher stress and strain levels is generally referred to as damping.

Question 10

Damping Capacity

Answer 10

This would help to reduce machinery noise, suppress vibrations and machinery, reduce the amplitude of resonant vibrations and reduce likelihood of fatigue.

• Cast Iron makes a better energy absorbing material than other alloys due to the inability of graphite flakes in the structure to transmit elastic waves.