Compressive strength

Compressive strength is widely used in testing the tensile strength because of the simplicity of the test. In the case of a sphere with diameter d, the compressive strength ac is related to the fracture force p by the equation:

The compressive strength of a sphere or a cylindrical sample loaded diametrically is greater than the corresponding tensile strength. In translating the compressive load into a tensile stress, the internal friction between moving particles must be overcome in addition to the tensile rupturing of the bonds in the fracture plane. Rumpf (1962) found that the ratio between tensile strength and compressive strength of moist limestone pellets took values between 0.5 and 0.8.

Figure 3 shows the compressive strength of cylindrical samples of commercial qualities of lactose and calcium hydrogen phosphate, both moistened with water. The particle size of the two powders is characterized by the geometric mean weight diameter, dgw, corresponding to the median of the particle weight distribution. Assuming a log-normal weight distribution, the geometric standard deviation sg expresses the ratio between diameters dM and dso corresponding to the 84% and 50% fraction of the weight distribution. The samples were prepared by very slow compaction in a tablet die of the moistened powders into cylinders of diameter 11.3 mm and length 4.6 mm. The investigated range of sample porosities is comparable with the intragranular porosities achieved by wet granulation of the powders. The strength of the compressed cylinders was measured by a diametrical compression test. Insofar as the samples were brittle, they fractured along the diameter parallel to the load. For lactose samples, the strength could not be measured at the higher liquid saturations because of a pronounced plastic deformation of the sample.

Figure 3 shows that the compressive strength of the moist samples is

LIQUID SATURATION (%) LIQUID SATURATION (%)

fig. 3 Compressive strength of moist samples of lactose (d^ = 56 jtm, sg = 1.8) and calcium hydrogen phosphate (dgw = 14 ¿tm, sg = 2.2). a: Lactose; porosity 43% (O), 37% (•) and 30% (V). b: Calcium hydrogen phosphate; porosity 50% (O), 37% (• ) and 30% (V). Reproduced with permission from Kristensen eta/. (1985a), Powder TechnoI. 44, 227-237. Elsevier Sequoia, NL.

LIQUID SATURATION (%) LIQUID SATURATION (%)

fig. 3 Compressive strength of moist samples of lactose (d^ = 56 jtm, sg = 1.8) and calcium hydrogen phosphate (dgw = 14 ¿tm, sg = 2.2). a: Lactose; porosity 43% (O), 37% (•) and 30% (V). b: Calcium hydrogen phosphate; porosity 50% (O), 37% (• ) and 30% (V). Reproduced with permission from Kristensen eta/. (1985a), Powder TechnoI. 44, 227-237. Elsevier Sequoia, NL.

dependent on porosity and liquid saturation. In the range of liquid saturations where the test samples are brittle, the compressive strength exceeds the tensile strength predicted by equation 5. Kristensen etal. (1985a) attributed this to effects of interparticle forces. The validity of the measurements was demonstrated by measuring the compressive strength of samples of moist glass spheres, which was found in reasonable agreement with equation 5. It appears, therefore, that the interparticle forces contributing to the strength of moist agglomerates, are significant in the case of powders with a wide size distribution; this is in agreement with the findings of Cheng (1968).

Experimental results on the tensile strength of moistened powders consisting of fine particles with a wide size distribution are presented by Eaves and Jones (1971,1972a,b). Using the traction table method, they found that the tensile strength of sodium chloride and potassium chloride samples increased significantly when a small amount of water was added. Further addition produced decreasing tensile strength values. With calcium phosphate samples, the tensile strength remained constant until the mass was saturated with water. Their results relate to samples with porosities above 60%. The compressive strength of moist samples of calcium carbonate with porosities below 50% was measured by Takenaka etal. (1981) using a diametral compression test. They found that the compressive strength has a maximum at liquid saturations of 20-30%. Beyond this range the strength was reduced as the liquid saturation increased, which is similar to the effect shown in Fig. 3.

The results shown in Fig. 3 were analysed according to a model for the tensile strength of single powders and binary mixtures presented by Chan etal. (1983). For a single powder, the model takes the form:

where A is a constant, a is a material characteristic expressing the intrinsic interaction between like particles in a pair, and t is the distance of separation between particles. It was found that the distance parameter t was constant at a particular porosity, independent of the moistening liquid, and that a was constant at a particular liquid saturation. The solid lines in Fig. 3 represent the compressive strength predicted by equation 7 using the estimated values of a and t. Figure 4 shows the estimates of a against liquid saturation in experiments where the samples were moistened with water or an aqueous solution of a copolymer of polyvinylpyrrolidone (PVP) and polyvinylacetate (PVA); a, which has the dimensions of work, diminishes as the liquid saturation increases. By extrapolation, it appears that for lactose the effect of particle interactions disappears at complete saturation,

Liquid saturation (%)

fig. 4 Intrinsic interaction parameter a for lactose (a) and calcium hydrogen phosphate (b). O, Samples wetted with water; •, samples wetted with a 10% m/m solution of Kollidon VA64 in water. Reproduced with permission from Kristensen eta/. (1985a), Powder Techno/. 44,

227-237. Elsevier Sequoia, NL.

Liquid saturation (%)

fig. 4 Intrinsic interaction parameter a for lactose (a) and calcium hydrogen phosphate (b). O, Samples wetted with water; •, samples wetted with a 10% m/m solution of Kollidon VA64 in water. Reproduced with permission from Kristensen eta/. (1985a), Powder Techno/. 44,

227-237. Elsevier Sequoia, NL.

while for calcium hydrogen phosphate some effect of the interparticle forces remains at complete saturation.

Figure 4 indicates that at medium liquid saturations, i.e. in the funicular liquid state, interparticle forces contribute significantly to the strength determined by compressive testing. As the liquid saturation is increased, the effects of the interparticle forces diminish so that the strength is expected to approach the strength resulting from mobile liquid bondings. It should be noted that the presence of a polymeric binder reduces the particle interactions.

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