The area under a force-extension (or compression) graph gives the work done. This is transferred to elastic potential energy within the material.
Elastic potential energy is given by:
Tensile stress is defined as the force applied per unit cross sectional area of the wire. The unit of stress is pascals.
Tensile strain is the fractional change in the original length of the wire. Strain is a ratio so has no units.
Within the limit of proportionality, stress is directly proportional to strain, The ratio of stress to strain for a particular material is constant and is known as the Young modulus, E.
The unit of Young modulus is the same as stress, Pa or Nm-2. It is equivalent to the gradient of the linear region of the stress-strain graph and a property of a material, not an object.
Stress-strain graph features:
- Limit of proportionality, P: the point up to which the material obeys Hooke’s Law (the graph is linear).
- Elastic limit, E: the point up to which the stress can be increased before the onset of permanent, plastic deformation,
- Yield points, Y1 and Y2: points where the material extends rapidly.
- Ultimate tensile strength, UTS: the maximum stress a material can withstand when being stretched before breaking. Beyond this point, the material may become longer and thinner at its weakest point (necking) before eventually snapping.
- Breaking point, B: the point at which the material snaps.
- Breaking strength: the stress vale at the point of fracture.
Characteristics of matter:
- Strong: a strong material that has a high UTS.
- Stiff: a material with a large Young’s modulus (and large force constant). Large gradient on stress-strain graph.
- Brittle: shows elastic behaviour up to its breaking point, without plastic deformation. Breaks when linear region ends.
Break due to spreading of cracks.
- Ductile: can be drawn into a wire, so shows plastic deformation. Linear region ends quickly.
- Polymeric: consists of long molecular chains. Behave differently depending on structure and temperature. Can stretch a great deal before breaking, but may show elastic or plastic behaviour.
- Tough: deforms plastically to reduce the spread of cracks. Requires a large amount of work (area under forceextension graph) to break.
- Hard: resistance to scratching and surface indentation.
Types of deformation:
- Elastic: returns to original length when force causing deformation is removed.
Plastic: permanent deformation/extension. Doesn’t return to original length when force is removed. Flow, slip or slide internally before breaking.