Within the limit of proportionality, the extension of a
material is proportional to the applied force
It follows, from Section 1.7, that:
Within the limit of proportionality of a material, the strain produced is directly proportional to the stress producing it
Young’s modulus of elasticity
Within the limit of proportionality, stress α strain, hence
stress = (a constant) × strain
This constant of proportionality is called Young’s modulus of elasticity and is given the symbol E. The value of E may be determined from the gradient of the straight line portion of the stress/strain graph. The dimensions of E are pascals (the same as for stress, since strain is dimension-less).
elasticity, E, include:
Aluminium alloy 70 GPa , brass 90 GPa, copper 96 GPa,titanium alloy 110 GPa, diamond 1200 GPa, mild steel 210 GPa, lead 18 GPa, tungsten 410 GPa, cast iron 110 GPa, zinc 85 GPa, glass fibre 72 GPa, carbon fibre 300 GPa.
Stiffness
A material having a large value of Young’s modulus is said to have a high value of material stiffness, where stiffness is defined as:
For example, mild steel is a much stiffer material than lead.
Since L and A for a particular specimen are constant, the greater Young’s modulus the greater the material stiffness.
Hooke’s law states that extension x is proportional to force F, provided that the limit of proportionality is not exceeded, i.e. x ∝ F or x = kF where k is a constant.
