《Energetic Materials》chapter 2.pdf

27 2 Size Reduction U. Teipel, I. Mikonsaari 2.1 Fundamentals of Size Reduction Size reduction efficiency is largely a function of the material properties of the solid material in question. In order to split particles into ever smaller units, linear fractures that spread through the solid must develop. To create such fractures, loads must be applied to the outer surface of the particles, either from a grinding tool or from neighboring particles. These loads cause deformation that creates a stress field within the particles. Defects in the particles, such as imperfections in the particle lattice structure, promote the formation of fractures [2.1]. 2.1.1 Material and Crack Behavior The material behavior of solids can be described as linearly elastic, plastic or viscoelastic (see Chapter 12). For a linearly elastic material, stress is proportional to the applied deformation. The proportionality factor is a characteristic material property, which is a constant value called the elastic modulus, denoted E: σ = E ⋅ ε (2.1) where s is the tensile stress and e the extensional deformation. When a load is imposed, materials with a large elastic modulus deform very little before fracture onsets. Such materials are classified as ‘brittle.’ For materials with a small elastic modulus, even small stresses result in large deformations; such materials are termed ‘rubber-elastic.’ This behavior can be described as shown in Fig. 2.1. Here, the area under the curves is proportional to the energy input (per unit volume) required for the size reduction process. One sees that this total energy required is much less for brittle materials (a) than for elastics (b), even though the so-called fracture stress, sB, is con