(55a) Structure Induced Breakage

The breakage kernel for a particular material generally depends on the type of material. Brittle materials tend to break in a particular mode while ductile materials behave differently and require much more shear to induce comminution. The resulting fragments will be different between the two types of breakage. If we limit the breakage models to simple homogenous particles, then overall porosity, binder strength, and elastic and plastic properties can be used to develop a breakage kernel. The orientation of particles or voids is not generally part of the kernel development because one cannot usually control the direction of force application in a general breakage event such as an impact with a wall or adjacent particle. Often the breakage mode depends on the total porosity of the particle and the mode of particle versus particle and particle versus wall interaction. This is true of systems where aggregates are bound together with some secondary material. In these systems, breakage occurs along random planes where shear and normal forces are greatest. There is no preferred orientation and the breakage rate and breakage selection function depend on the global structure defined by global variables such as porosity and size distribution of agglomerate. These global parameters determine how the random structure will break. For example, the ultimate yield stress depends on the porosity of the structure and size distribution of the aggregate. Porous concrete has a lower yield stress than more compact concrete. The rate of breakage of concrete then depends on this global porosity. In addition, in a system with homogenous particles, a glancing impact may induce fine particle attrition while a direct impact may result in fracture. Thus, breakage rate and breakage selection function depend on the number of glancing blows versus direct impacts in a particular piece of equipment or unit operation. So, breakage kernels can also incorporate the type of equipment by quantifying the ratio of impact types in that equipment and imposing that data on a homogenous material without a preferred breakage plane.

However, breakage also depends on the structure of the material. In some cases a uniform quasi-homogenous material may have a weak cleavage plane along a preferred crystal orientation. The orientation of these crystal planes in the particle can dictate the breakage pattern. In some cases the material comprising the particle is more or less homogenous, but the particle itself has a complex structure. Consider a potato chip with ridges, or a twisted pretzel, or a complex cereal particle designed with a pseudo-fibrous texture but made of homogenous dough and then baked. These particles are sensitive to breakage problems, but the mode of breakage is dictated by the structure of the particles. These structured particles are present in all industries. The ceramic scaffolding in catalytic converters is one example. The complex pressed or extruded ceramic shapes used as in electronic components are intricate shapes made of a very homogenous material. These intricate shapes are often prone to breakage. In cases where the structure of the particle determine the mode of breakage, a systematic look at stresses induced by random contacts of structured contacts can help determine the selection functions used in population balance models to describe breakage of these structured particles. We studied seven systems of structure particles. In each case the material making the structured particle was homogenous, but the particle was complex. We used a 3D CAD system to design particles with structures similar to the structure particles studied and then a FEM stress analysis to determine the critical stresses on the material when loaded with random contact points. The FEM analysis gave the pattern of stress distribution in the particle as well as the shape and size of the fragment that would form if the stress event was large enough to exceed the yield condition of the material. These fragments predicted from the FEM analysis were stored and used to determine the breakage selection function for the material. We also looked at the breakage sizes generated by a simple 3D truss model of the complex particles loaded with random contact loads. These are used to predict the selection function for the material and compared with breakage data from a tester that imposes simple stress-strain breakage on particles.