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Elasticity

Applied Science: BTEC Level 3 National Extended Diploma, topic 4.10.4

Elasticity

Elasticity is the tendency of materials to return to their original shape after the external forces (load) causing a deformation are removed.

Elasticity

Elasticity

  • An object is elastic when it comes back to its original size and shape when the load is no longer present.
Elastic limit

Elastic limit

  • The limit of proportionality is the largest stress value beyond which stress is no longer proportional to strain.
  • The object may still return back to its original size and shape when the load is removed.
  • The elastic limit is the point beyond which the object does not come back to its original size and shape when the load is removed.
Elastic strain energy

Elastic strain energy

  • When an elastic object is stretched, energy needs to be supplied to the object to stretch the object.
  • The supplied energy is the elastic strain energy.
  • The elastic strain energy can be determined from the area underneath a force-extension graph.
Elastic hysteresis

Elastic hysteresis

  • Elastic hysteresis is the difference in the elastic strain energy used to stretch an object and the strain energy as the load is removed.
  • This is the area between the loading and unloading curves on a force-extension graph.

Hooke's Law

Hooke's law is a proportional relationship between the force experienced and the extension observed. The relationship exists up to an elastic limit.

Hooke's law

Hooke's law

  • Hooke's law is the relationship that the force F experienced by an extensible object is proportional to its extension ΔL:
  • F α ΔL
  • The constant of proportionality is labelled k and is called the stiffness constant.
  • This gives the equation:
  • F = kΔL
  • The force acts to restore the object back to its original shape, so it acts in the opposite direction to that of the extension.
Limit of proportionality

Limit of proportionality

  • Hooke's law is a relationship between two quantities. But, this relationship does not always hold.
  • When a force-extension graph is linear, Hooke's law applies.
  • When a force-extension graph is non-linear, Hooke's law does NOT apply.
Elastic limit

Elastic limit

  • An object (e.g. a spring) is elastic if it returns back to zero extension when the load on it is removed.
  • The elastic limit is the maximum force the spring can sustain and then return to zero extension.
Gradient of force-extension graphs

Gradient of force-extension graphs

  • The gradient of a force-extension graph is the value of the constant of proportionality, k.
  • For springs, this is the familiar spring constant.

Test yourself on Elasticity

  • The elastic strain energy can be determined which property of a force-extension graph?

  • When will a spring obey Hooke's law?

  • Which of the statements about Hooke's law is true?

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