Strain Energy During Mechanical Milling: Part I. Mathematical Modeling

In this study, we formulate a mathematical model that can be implemented to calculate the amount of strain energy both introduced to (U _i) and stored in (U _s) metal powders during mechanical milling. The theoretical analysis presented in this study proposes that the strain energy is primarily induced by normal and shear strains, and moreover, that the contributions from torsion can be neglected. This theoretical framework was implemented to evaluate the influence of various mechanical milling processing parameters on U _i and U _s. The calculated results show that the magnitude of U _i increases with increases in the following processing parameters: attritor diameter, impeller’s rotational frequency, and ball-to-powder mass ratio, and the magnitude of U _i increases with a decrease in diameter of the milling media. The percentage of the shear strains’ contribution to the total U _i is insensitive to the mechanical milling processing parameters, varying within the range of 35 pct to 42 pct. The calculated magnitude of U _s ranges from a few to a few tens of joules per gram, which is three to four orders of magnitude lower than that of the calculated U _i. Although with respect to the mechanical milling processing parameters, the calculated U _s has trends similar to those for U _i, the changing rates of U _s are much lower than those for U _i.