Breakage elastic-plastic

In addition to particle size reduction, roller compaction and tableting are other downstream processes that will likely to be impacted by the mechanical properties of the milled extrudate. In the case of tableting, the extrudate may be subjected to localized high stresses which can induce particle breakage, elastic deformation, and/or plastic flow that affect compactability and tablet hardness. 

It is important to differentiate between brittie and plastic deformations within materials. With brittie materials, the behavior is predominantiy elastic until the yield point is reached, at which breakage occurs. When fracture occurs as a result of a time-dependent strain, the material behaves in an inelastic manner. Most materials tend to be inelastic. Figure 1 shows a typical stress—strain diagram. The section A—B is the elastic region where the material obeys Hooke s law, and the slope of the line is Young s modulus. C is the yield point, where plastic deformation begins. The difference in strain between the yield point C and the ultimate yield point D gives a measure of the brittieness of the material, ie, the less difference in strain, the more brittie the material. 

During compaction, primary particles are packed, re-arranged and can undergo deformation and possibly breakage. These events can occur sequentially or in parallel. The mechanical strength of a tablet may strongly depend on the mechanical properties of the primary particles and the particle-particle interactions within it. It is essential that the particles deform plastically or rupture since the stored elastic strains can weaken the tablet on release (Roberts and Rowe, 1987). 

The mechanism of densification of particulate solids (Fig. 6.6) includes, as a first step, a forced rearrangement of particles requiring little pressure followed by a steep pressure rise causing brittle particles to break and malleable ones to deform plastically. During the entire process, porosity decreases so that fluids which originally occupied the pore space of the bulk feed must be able to escape and the initial elastic deformation must have sufficient time to either cause breakage or convert into plastic deformation (see also Section 8.1). These requirements limit the speed of densification and, therefore, the production capacity. 

A quantitative explanation of the effect requires an advance in fracture mechanics. Griffiths theory explains fracture in a perfectly elastic material as dependent on crack depth. This has been extended to cover the situation where there is a small zone of plastic deformation ahead of the crack. The problem is more difficult when the pla.stic deformation is large compared to the crack size, and, as far as I know, there has been no treatment of the situation when plastic deformation covers the whole thickness of the specimen over an appreciable length. Any analysis would also require an understanding of the transition in material from crystalline yielding to looking and chain breakage and the form of the local stress-strain curve beyond that which is measured. 

Material yield point modulus of elasticity E (kN mm elastic stiffness (F=Fp) (kNmm ) plastic stiffness kpi (s = 0.98sb)(N mm ) breakage point ... 

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