# Strength of Materials

When a solid is broken by a tensile force, surface area is produced. The minimum energy required to create the new surface is simply the result of the area and the surface energy.

Griffith equated twice the surface energy of the cross section to the strain energy needed to separate two adjacent layers of atoms.

The strain energy [eta] per unit volume of material is
[eta] = 1/2 [epsilon] [sigma]
where [eta] is the energy in joules per cubic meter, [epsilon] is the strain, and [sigma] is the stress in newtons per square meter. For a material that obeys Hooke's law
[eta] = [sigma]^2 / 2 [E]
where E is the Young's modulus. Tor two adjacent layers [x] meters apart
[eta] = [sigma]^2 [x] / 2 [E]
Equating the strain energy [eta] to twice the surface energy [gamma], gives
[sigma_max] = 2 ([gamma][E] / [x])^0.5
Where [sigma_max] represents the maximum stress that can be withstood without breaking assumping interatomic bonds obey Hooke's law up to failure. In reality interatomic force curve is roughly parabolic, so a better approximation to predict the theoretical strength of most solids is [sigma_max] = ([gamma][E] / [x])^0.5

 Material Surface Energy (J/m2) Young's Modulus (MN/m2) Theoretical tensile strength (MN/m2 x 104) Iron 2.0 210,000 4.6 Copper 1.65 120,000 3.1 Zinc 0.75 90,000 1.8 Aluminium 0.9 73,000 1.8 Tungsten 3.0 360,000 7.3 Diamond 5.4 1,200,000 1.8 Sodium chloride 0.115 43,000 0.62 Aluminium oxide 4.6 420,000 6.7 Ordinary glass 0.54 70,000 1.4