3.7.8Forces and Motion

Elastic and Plastic Deformation

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Lesson summary

3.7.8 Elastic and Plastic Deformation — OCR A Level Physics A notes: Distinguish elastic and plastic deformation, interpret loading and unloading graphs, and relate hysteresis to energy dissipation.A deformation is elastic if the material returns to its original shape and size wh…

permanent extension
elastic limit
Metal wire (ductile)
Rubber band
Brittle material
Worked example 1

Section 1 of 8Elastic deformation

A deformation is elastic if the material returns to its original shape and size when the deforming force is removed.

Elastic deformation

At atomic level, the atoms are displaced slightly from their equilibrium positions but their bonds are not broken and neighbours do not change place.

All the energy stored is recoverable as the object returns to its original dimensions (less any thermal losses).

The elastic region for many metals is a straight line on a force–extension graph,

but elastic does not always mean linear: a rubber band is elastic over a large range with a curved graph.

Section 2 of 8Plastic deformation

A deformation is plastic when the material does not return to its original size after the force is removed; it keeps a permanent extension (permanent set).

In metals plastic flow involves layers of atoms slipping over each other, helped by the movement of defects called dislocations,

so atoms settle in new neighbours.

Elastic limit

The graph reaches the elastic limit, the maximum force or stress for which the material remains elastic; in practice for many metals this is just beyond the limit of proportionality,

and beyond it the extension per unit force increases markedly.
- (the yield point for mild steel)

During plastic flow work is done which is transferred as thermal energy, so a bent paper clip warms.

Unloading from a point beyond the elastic limit, the graph follows a line roughly parallel to the original straight section, ending on the extension axis at the permanent extension.

Section 3 of 8Loading and unloading graphs

Metal wire (ductile). Loading: straight line to the elastic limit, then curves with large extension.

Loading and unloading graphs

Unloading from a point in the plastic region: a straight line parallel to the initial one, ending at a non-zero extension.

The area between the loading curve and the unloading line represents the energy dissipated (it becomes thermal energy in the wire),

while the area under the unloading line is the recoverable elastic energy.

Rubber band. The loading curve and unloading curve form a loop called hysteresis.

Loading and unloading graphs

The loading curve lies above the unloading curve,

so the area of the loop,
which is the energy per cycle, is dissipated as thermal energy inside the rubber.

Rubber returns to the original length when unloaded, so it is elastic despite the non-linear shape.

This property makes rubber useful for vibration damping, since vibration energy is converted to thermal energy.

Brittle material such as glass or ceramics: nearly linear to fracture, with very little plastic region.

Section 4 of 8Practical implications

Designers keep working stress below the elastic limit so structures do not sag permanently.

Metal-forming processes such as pressing car body panels deliberately cause plastic deformation.

Springs are made from material with a high elastic limit, such as spring steel.

Repeated loading and unloading beyond the elastic limit leads to fatigue failure, which is why a paper clip bent back and forth breaks.

A material that has been plastically stretched has a higher elastic limit afterward (work hardening).

Check your understanding by sketching each graph: the key identifiers are whether the unloading path returns to the origin, whether it is parallel to the loading line, and whether a loop exists.

Section 5 of 8Energy and applications

The energy ideas are unified by the force–extension graph: the total area under the loading curve is the work done on the sample; the area under the unloading curve is the energy given back.

Energy and applications

In a metal stretched beyond the elastic limit most of the work is dissipated as thermal energy.

Bungee cords and climbing ropes are designed to stay within their elastic range and to have a large energy capacity,

while crumple zones in cars use plastic deformation deliberately to absorb kinetic energy.

When describing a graph in an exam, state clearly the labelled regions: elastic, limit of proportionality, yield, plastic, and fracture.

Section 6 of 8Worked examples

A metal wire has a loading line of gradient 8.0 N mm⁻¹ up to its elastic limit. It is loaded to 30 N, giving extension 5.0 mm, and then unloaded along a line parallel to the original. Find the permanent extension, and the elastic energy released on unloading.
A rubber band is stretched and released and the force–extension loop has area equivalent to 0.40 J per cycle. What happens if it is cycled 50 times in 10 s and where does the energy go?

Section 7 of 8Key terms

Term	Meaning
Elastic deformation	Material returns to its original shape when the force is removed.
Plastic deformation	Permanent change of shape after the force is removed.
Elastic limit	Maximum stress beyond which permanent deformation occurs.
Yield point	Point where a ductile metal begins large plastic extension.
Hysteresis	Loading and unloading follow different paths, forming a loop.
Permanent set	Extension that remains after unloading.

Section 8 of 8Exam technique

Assuming elastic means obeying Hooke's law. A rubber band is elastic but non-linear.

Drawing the unloading line from the plastic region back to the origin; it should end at the permanent extension.

Saying that the area of the hysteresis loop is energy stored. It is energy dissipated.

Confusing the limit of proportionality with the elastic limit; they are close but not the same point.

Saying plastic deformation breaks all the bonds; atoms slip and form new bonds with neighbours.

Section 1 of 8Elastic deformation

Section 2 of 8Plastic deformation

Section 3 of 8Loading and unloading graphs

Section 4 of 8Practical implications

Section 5 of 8Energy and applications

Section 6 of 8Worked examples

A metal wire has a loading line of gradient 8.0 N mm−1 up to its elastic limit. It is loaded to 30 N, giving extension 5.0 mm, and then unloaded along a line parallel to the original. Find the permanent extension, and the elastic energy released on unloading.

A rubber band is stretched and released and the force–extension loop has area equivalent to 0.40 J per cycle. What happens if it is cycled 50 times in 10 s and where does the energy go?

Section 7 of 8Key terms

Section 8 of 8Exam technique

Marked practiceQuizzes for this lesson

A metal wire has a loading line of gradient 8.0 N mm⁻¹ up to its elastic limit. It is loaded to 30 N, giving extension 5.0 mm, and then unloaded along a line parallel to the original. Find the permanent extension, and the elastic energy released on unloading.