Strain behaviour

Plastic deformation during collision between two agglomerates dissipates the kinetic energy of the system and thus improves the probability for a successful coalescence. Kapur (1978) claimed that an agglomerate with a small fracture strain is more prone to breakage than one with a large fracture strain, even when the tensile strength is the same in both cases. The stress-strain relationship is, therefore, one of the principal factors governing agglomerate growth by coalescence.

2 40

2 40

Fig. 5 Stress-strain relationship with cyclic loading and unloading for a moist sample of calcium hydrogen phosphate with porosity 45% and liquid saturation 57%. Reproduced with permission from Kristensen etal. (1985a), Powder Techno!. 44, 227-237. Elsevier Sequoia, NL.

Fig. 5 Stress-strain relationship with cyclic loading and unloading for a moist sample of calcium hydrogen phosphate with porosity 45% and liquid saturation 57%. Reproduced with permission from Kristensen etal. (1985a), Powder Techno!. 44, 227-237. Elsevier Sequoia, NL.

Figure 5 shows the stress-strain relationship with cyclic loading and unloading for a cylindrical calcium hydrogen phosphate sample moistened with water and submitted to uniaxial stress. Although the sample behaved in a brittle way when exposed to the compressive stress, it is apparent that the strain is far from that of an ideal elastic-brittle body. The strain at stresses well below the fracture stress is partially plastic. Schubert (1975) has shown a similar strain behaviour in moist limestone samples exposed to tensile stresses.

Figure 6 shows the normalized strain of cylindrical samples of lactose and calcium hydrogen phosphate submitted to a uniaxial compressive test by applying a load to the end of the cylinder. The physical characteristics of the two powders were the same as those described in Fig. 3, but the moistening liquid used for the results presented in Fig. 6 was an aqueous PVP-PVA copolymer solution. The dotted lines in the two graphs indicate the condition when the sample becomes strained as a perfect plastic body, i.e. the strain is maintained at a constant stress. For lactose, the normalized strain increases with the liquid saturation, and perfect plastic strain is seen at saturations well below 100%, while for calcium hydrogen phosphate saturations close to 100% are required to achieve plasticity.

Figure 6 demonstrates that the moist samples change from being brittle into a state characterized by plastic deformation when the liquid saturation is increased to a certain range which depends on the packing density of the solid particles. Figure 7 compares the liquid saturations which produce

fig. 6 Normalized strain AUL of cylindrical samples of length L at maximum compressive stress, a: Lactose samples wetted with a 10% Kollidon VA64 solution in water, porosity 43% (O), 37% (•) and 30% (V). b: Calcium hydrogen phosphate samples wetted with the same solution, porosity 50% (O), 43% (•) and 37% (V). Reproduced with permission from Holm ei a/. (1985b), Powder Technol. 43, 225-233. Elsevier Sequoia, NL.

LIMITING LIQUID SATURATION (%)

fig. 7 Comparison of the liquid saturation required to achieve plastic deformation of moist samples and the limiting liquid saturations at which the compressive strength becomes controlled by mobile liquid bondings. Lactose; ■, calcium hydrogen phosphate.

plastic deformation (c.f. Fig. 6) with the liquid saturations at which the tensile strength caused by mobile liquid bondings (equation 5) equals the compressive strength shown in Fig. 3. Figure 7 demonstrates that the change from brittleness into plasticity occurs when the strength of the agglomerates becomes controlled entirely by mobile liquid bondings, i.e. when the inter-particle forces become insignificant because of the 'lubricating' effect of the liquid.

The differences between the strength and strain behaviour of lactose and calcium hydrogen phosphate can partly be attributed to differences in the cohesional strength of the two systems, which in turn is dependent on the inherent physical character of the solid and, particularly, to the different particle size distributions. In general, the finer the particles, the greater become the tensile and compressive strengths. The liquid requirements to achieve plastic strain are supposed to be influenced by the size dispersion of the particles and their shape. However, according to experiences with melt granulation of lactose, the aqueous solubility of lactose may also influence the liquid requirements to achieve plasticity (see section on process and product variables).

Was this article helpful?

0 0

Post a comment