Stress, strain & the Young modulus
Posted in Physics, MaterialsStress
Stress is a measurment of strength, it is how much pressure a material can withstand without undergoing physical change. There are a number of different types of stress.
Tensile strength/fracture stress
Tensile strength or fracture stress is the amount of stress a material can be put under before it fractures.
Yeild stress and yeild stength
Yeild stress or yeild strength is the amount of stress a material can take before it deforms permanently.
Caclulating stress
Stress is the pressure a material is under, that is the force per area. Stress is given the symbol sigma.
Where F is the force in Newtons and A is the cross sectional area in metres.
Strain
Strain is a measurement of how much a material has stretched. Stress causes strain on a material. Strain is a ratio between the original length of the material and the amount it has extended by, therefore:
Young's modulus
Young's modulus is a measurement of stiffness. It describes how much a material will stretch (strain) when put under a given stress. The calculation of the Young's modulus of a sample of material is therefore:
Stress-strain graphs
You need to be able to use and recognise the parts of a graph of stress plotted against strain:
The first thing to know is that the area under the curve represents the toughness of the material - how much it resists stress.
Between the origin and point A the material is said to be elastic - the ratio between stress and strain is constant, obeying Hooke's law. In this region the material will return to it's original size.
Hooke's law
Hooke's law relates the force, F, acting upon a material and it's extension, x, using the equation:
Where k is some constant.
Point A on the graph shows the elastic limit of the material, beyond this point the material will not obey Hooke's law and won't return to it's original shape when the stress is removed.
The plastic region refers to the curve between points A and B. Here the rate of the extension increasing is going up. At point B the material undergoes 'necking' - the cross sectional area of the material decreases.
Point C is the fracture point, where the material splits into two.