Radial edge cracked tablets

All the techniques for the determination of the critical stress intensity factor so far described involve the preparation of compressed rectangular beams or plates that require special punches and dies and in some cases high tonnage presses. The ideal specimen shape for pharmaceutical materials is the right-angled cylinder or a flat-faced tablet. Such a shape has recently been

fig. 17 Geometries for (a) edge opening and (b) diametral compression method for measuring critical stress intensity factors for radially edge cracked tablets. F, applied load; d, tablet diameter;

c, crack length.

fig. 17 Geometries for (a) edge opening and (b) diametral compression method for measuring critical stress intensity factors for radially edge cracked tablets. F, applied load; d, tablet diameter;

c, crack length.

investigated by Kendall and Gregory (1987) who reported three methods of determining the critical stress intensity factor of precracked specimens, i.e. (a) edge opening (Fig. 17a), (b) diametral compression (Fig. 17b) and (c) pin loading. They concluded that while the first of these was the best test, all had advantages over other test procedures because of their exact theory, simple sample preparation, ease of precracking, straight-forward loading and low propagation forces. The first two methods have recently been evaluated on tablets of microcrystalline cellulose (Avicel PHI01) by Roberts and Rowe (1989).

Both the tests involve the introduction of a precrack into the edge of the disc. In edge opening the critical stress intensity factor is given by (Kendall and Gregory, 1987):

c

-1/2

Id

where F is the peak load for cracking, as in Fig. 17a, while for diametral compression the critical stress intensity factor is given by (Kendall and Gregory, 1987):

1.586

where F is the compressive force for cracking (Fig. 17b). In both cases c is the crack length, t is the tablet thickness and d is the tablet diameter.

When testing microcrystalline cellulose (Avicel PH101) Roberts and Rowe (1989) first prepared tablets of varying porosity using 15 mm flat-faced punches on an instrumented tablet press. After precracking using a scalpel blade (Plate 7) the cracked tablets were stressed using either edge opening, in which tablets were gripped using the air jaws of a tensometer and pulled apart (Plate 8), or diametrally compressed with the crack vertical between the plattens of a tensometer. During extensive testing it was concluded that, of the two techniques, edge opening was the preferred option as it gave the most stable crack propagation and the effects of crack length were minimal. However, the diametral compression test was found to have the same value provided crack lengths were limited to between c/d values of 0.34-0.6.

Extrapolation of the measured values of critical stress intensity factors of specimens over the porosity range 7-37% using linear, exponential (equation 40) and a two-term polynomial (equation 39) gave values as shown in Table 12. In all cases values obtained from diametral compression were higher than those from edge opening. However, all values are significantly higher than those determined from measurements on beams and plates.

The reasons for this variation in the results from these different test procedures have been discussed by York etal. (1990) specifically for microcrystalline cellulose. The problem lies in the difficulties in the introduction of a two-dimensional sharp crack into a specimen and accurate measurement of its length and velocity on the application of load. Ideally, KIC should be independent of crack length and for those materials which exhibit a flat crack growth resistance curve all methods of measurement should produce equivalent data for KlCo. However, many materials, especially ceramics (Munz, 1983) have been shown to exhibit rising crack resistance curves and hence the method of crack induction and notch geometry become critical. These measurements on specimens with sawn or

Table 12 Critical stress intensity factors of microcrystalline cellulose using radial edge cracked tablets (Roberts and Rowe, 1989)

Method

Equation

Kico (MPam1/2)

Edge opening

Linear

1.91

Diametral compression

Linear

2.11

Edge opening

Exponential

2.24

Diametral compression

Exponential

2.98

Edge opening

Polynomial

2.31

Diametral compression

Polynomial

2.35

machined notch will always produce lower values of k,c than those where the crack is introduced by a controlled flaw. This is the case for the doubletorsion method and radially edge cracked tablet as in these methods the total amount of crack extension at maximum load is always higher. This is direct evidence that microcrystalline cellulose has a rising crack growth resistance curve (Roberts and Rowe, 1989) and that this is the reason for the variation.

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