Metals

Hell-Petch Equation:

Restricting or preventing dislocations from moving with the presence of grains can harden and strengthen a material. This equation shows how the yield strength of the material varies with the size of the grains within it.

Percent Cold Work:

Strain hardening (aka cold working) is when a material becomes stronger and harder as it is plastically deformed. This equation shows how much the material has been cold worked and therefore how much the yield and tensile strength have increased and ductility has decreased.

Chovrinovs rule:

Used to relate the solidification time in casting to the volume of the casting and surface area.

Equilibrium Concentration:

Mass Fraction of L or alpha Phase:

These equations are used to interpret binary phase diagrams at a specific temperature, as shown on the diagram.

Homogeneous Nucleation and growth equations:

• 1. A spontaneous phase transformation will occur when the Gibbs free energy has a -ve value. There are two contributors to this value, the volume free energy Gv (energy difference between solid and liquid phase) and the surface free energy.

  2. As the liquids, free energy increases atoms begin to cluster forming a solid particle. If the radius of this particle becomes greater then the critical radius (r*) growth continues but free energy decreases. If the radius is less then critical the cluster will redissolve into the liquid.

  3. Activation energy is the free energy required for the formation of a stable nucleus

  4. The volume of free energy is the free energy difference between the solid and liquid phases.

Avrami equation:

Shows how solids transform from one phase to another at a constant temperature.

Growth: (bottom equation)

Is the step other then nucleation in phase transformations. It begins after the critical radius has been reached and depends on the diffusion rate.