Materials

• Elastic properties of solid materials are studied under compression and tension forces.
• Density is the mass per unit volume.
• SI Units for density are kg/m3.
• In some texts, you will find some densities given in g/cm3.
• It is important that you use the SI units otherwise formulae will not work.
• 1 g/cm3 = 1000 kg/m3.
• Hooke’s Law states that if we load a spring, the extension or stretch is proportional to the force.
• The constant of proportionality is called the spring constant and is measured in newtons per metre (Nm-1).
• We can plot Hooke’s Law as a graph, where the gradient gives us the spring constant.
• If we apply a squashing force, the same principles apply.
• Stress and strain are important concepts in solid materials.
• If we stretch a wire, the amount it stretches by depends on its length, its diameter, and the material it’s made of.
• If we have two of the same material and length, the thicker wire will stretch less for a given load.
• Tensile stress is defined as the tension per unit area normal to that area.
• The term normal means at 90o to the area.
• Compression force per unit area, i.e., pressure, is also a term you may see in some text books.
• If we have a wire of the same material and the same diameter, the wire will stretch more for a given load if it is longer.
• Tensile strain is defined as the extension per unit length.
• Energy is the area under the force-extension graph.
• The energy is the area under the stress-strain curve.
• Stress-strain graphs are a development of force-extension graphs, taking into account the factors needed to ensure a fair test.
• A typical stress-strain graph looks like this: P is the limit of proportionality, where the linear relationship between stress and strain finishes; E is the elastic limit; Y is the yield point, where plastic deformation begins; UTS is the ultimate tensile stress, the maximum stress that is applied to a wire without its snapping; S is the point where the wire snaps.
• Stress-strain graphs can also show other properties such as brittleness, strength, and ductility.
• Curve A shows a brittle material, which is also strong because there is little strain for a high stress, and the fracture of a brittle material is sudden and catastrophic, with little or no plastic deformation.
• Brittle materials crack under tension and the stress increases around the cracks, with cracks propagating less under compression.
• Curve B is a strong material which is not ductile, steel wires stretch very little, and break suddenly, with a lot of elastic strain energy in a steel wire under tension and it will “whiplash” if it breaks.
• Curve C is a ductile material.
• Curve D is a plastic material, with a very large strain for a small stress, the material will not go back to its original length.
• The Young Modulus is defined as the ratio of the tensile stress and the tensile strain, Young modulus = tensile stress / tensile strain, with units in Pascals (Pa) or newtons per square metre (Nm-2).
• The Young Modulus describes pulling forces.
• The Young Modulus is the gradient of the stress-strain graph for the region that obeys Hooke’s Law, with the stress on the vertical axis when we would expect the stress to be on the horizontal axis.
• The area under the stress-strain graph is the strain energy per unit volume (joules per metre3).
• Strain energy per unit volume = 1/2 stress x strain.
• There are no units for strain; it’s just a number.
• Strain can sometimes be expressed as a percentage.
• When we stretch a wire, we have to do a job of work on the wire.
• If we release the wire, we can recover that energy, which is called the elastic strain energy.