Breakage Theory Essay

According to Schönert (1996), breakage occurs in a bed of particles when contact force act on the particle. This contact force generates pressure and shear on the surrounding particles or walls causing inelastic deformation and finally breakage.
It can be suggested from literature survey that breakage mechanisms reported by various authors were based on various factors involved during the breakage process. Some of these factors include; the number of particles, arrangement or confinement of particles, particle history (presence of crack), particle shape and nature of applied force such as the working surface. Adequate understanding of these factors, material properties and interaction have been used as a basis for the approach for modelling

However, the ones that have been widely studied and reported to significantly show accurate results are briefly highlighted. These are: linear spring dashpot model, non-linear (Hertz-Mindlin) spring dashpot model and elastic perfectly plastic contact model (Mishra, 2003a).
According Mishra (2003a), the linear spring dashpot model assumes a constant stiffness and the interactions between particles are elastic. The contact force at each incremental time ∆t in the normal direction is given by equation 2.4:
"F" _"nor" ("t+∆t" )"= " "F" _"nor" "(t) - " "v" _"nor" "k" _"nor" "∆t + " "D" _"nor" "v" _"nor" 2.4
Where: Fnor (t+∆t) = the normal component of the force at an increased ∆t Fnor (t) = Normal component of the force at the previous ∆t vnor = Normal component of the relative velocity knor = Normal stiffness Dnor = Normal component of the damping coefficient
The Hertz-Mindlin contact model differs from the linear-spring dashpot model by varying the normal stiffness (knor) with the level of overlapping of the contacting particles. The force-displacement of the model in relation the applied pressure is given by Equation 2.5. Equation 2.6 gives the force-displacement relationship when the elastic properties of the particles are