1. Introduction The cold deformation of materials results in energy being stored in them, which in turn increases their strength and reduces ductility. That is, metals and alloys get work hardened. When a cold deformed metal or alloy is annealed, its properties are restored due to “recovery” and “recrystallization”. On continued annealing, the grain size of the material may increase due to “grain growth”. The driving force for recrystallization is provided by the energy stored in the cold deformed material. The driving force for the grain growth is provided by the tendency of the material to decrease its energy by increasing the grain size and reducing the grain boundary surface area, thereby reducing the grain boundary energy of the system. The annealing process involves heating the material at a suitable temperature for a sufficient time to cause the rearrangement of atoms within the lattice. This process involves diffusion and is dependent upon the:
1. Amount of stored energy
2. Annealing temperature (the higher the temperature, the higher the atomic diffusion rate)
3. Annealing time (the longer the heating time, the greater the amount of atomic diffusion) Precipitate hardening is another method of increasing materials strength. Unlike cold working, proper precipitate hardening is achieved by alloying and heat treatment rather than physical deformation. The material requires a high solubility of one element, A, in a matrix, B with a solubility that decreases with a decrease in temperature in order for a particular alloy to be suitable for precipitate hardening. Once a material is deemed suitable, the application of two heat treatments is needed to cause precipitation of new particles. The first heat treatment is where the material is heated to high temperatures in order to create a solid solution of element A in B, followed by rapid quenching to keep the material in solid solution. The second heat treatment is performed at lower temperature to allow the diffusion of element A, which causes the formation of a new phase or particles called “precipitates” within the original B matrix. These new particles increase the strength of the material by hindering dislocation motion through the material. A 70% Cu – 30% Zn alloy, also known as Cartridge Brass has been selected for this laboratory. The commercial material was received from the supplier as a “cold-rolled” sheet. This material was annealed at 700°C, before further rolling, for two hours to eliminate any influence of the commercial deformation on the microstructure and mechanical properties of the material. This annealed brass was cold-rolled at the University of Manitoba to achieve 20%, 40% and 80% deformation defined as follows. The deformation of a sheet metal is expressed as “percentage deformation” given by

Each deformed strip was subsequently annealed at 400°C for different lengths of time. Some of the deformed and annealed strips, cut into small samples for hardness measurement, will be supplied during the laboratory session. Also the micrographs of the microstructure of all the samples will be provided. In addition, Aluminum that has undergone precipitate hardening heat treatments at 190℃ and 150℃ will also be supplied at different times of the precipitate hardening heat treatment for the purpose of hardness testing. Tensile strength and hardness of the material are both indicators of the metal's resistance to plastic deformation, and as such, they have a certain correlation. This correlation is most accurate for steels. The correlation is given between the tensile strength and Brinell hardness (HB). Since the hardness measured during the lab is in HRB units, it is necessary to first convert the measured hardness from HRB to HB using the following formula:

The relationship between the tensile strength (TS) and the Brinell hardness number (HB) is given by:

As in all measurements, there will be a scatter of data. Therefore, we have to