⇒ As we mentioned in our notes on Hooke's Law, when two identical springs are joined in series, we saw that the spring extended twice as much as a single spring on its own
⇒ Similarly, if we join two spring in parallel, then the springs extend half as much as a single spring on its own
⇒ In each case, the property of the object depends on the dimensions of the object itself
⇒ If we want to compare materials fairly, rather than compare two different objects, then it is better to have a measurement that doesn't depend on the shape or size of the object
⇒ Tensile stress is a measurement of the force applied over the cross-sectional area of sample of material
⇒ Tensile strain is the ratio of the extension and original length of the sample
⇒ We can now use these quantities to calculate a measure of the stiffness of an elastic material that is independent of the shape of the sample of the material
⇒ This is called the Young Modulus, E, of the material
⇒ Young modulus is measured in Pa (or Nm-2)
⇒ This graph shows a stress-strain graph for copper
⇒ O-P on the graph represents the range of tensile stree for which the copper obeys Hooke's law
⇒ Point E on the graph represents the elastic limit
⇒ The yield point of the material is given by Y
⇒ The ultimate tensile stress (UTS) of copper is sometimes called the 'maximum strength' or 'strength of the wire'
⇒ Some materials will also show a phenomemon known as creep
⇒ A simple experimental set-up for copper can be used to measure its Young modulus
⇒ But, if you want to be accurate, you can use an experimental set-up like this:
⇒ Here, the left-hand wire is a reference wire that holds the main scale of the vernier calipers, usually calibrated in milimeters
⇒ The reference wire has a mass hung from it to keep it taut
⇒ The sample wire (made from the same material) is hung close to the reference wire and holds the smaller scale of the vernier calipers
⇒ As weights are added to the sample wire it extends, and the scale moves relative to the main scale - this allows the extension of the wire to be measured
⇒ Stress-strain graphs allow us to describe the properties of materials, and also to predict the stresses at which changes in these properties might occur
⇒ This graph compares the stress-strain graphs for four different materials: ceramic, steel, glass and copper
⇒ Steel is made by adding different elements to iron to form an alloy
⇒ The high-carbon steel shown in the graph is a strong but brittle material
⇒ Copper has a plastic region because it is a ductile material, and this makes it ideal for forming into wires for use in electrical circuits
⇒ The strain energy density is the strain energy per unit volume of a sample
⇒ From earlier we saw that: Strain energy = 1/2 F▵l
⇒ If l is the original length of the wire, and A is its cross section, then the volume of the wire is Al. Therefore:
⇒ Also see our notes on: