where l is the cell size, te is the cell edge thickness, tf is the cell face thickness, (n) is the mean number of edges per face, and Zf is the face connectivity. 8 is typically ~0.5 for polyhedral cells and ~0.02 for spherical cells (58).
The anisotropy of extrudate properties has been investigated by local mechanical testing, in which a pin of 0.58-mm diameter was driven into cylindrical foams (21, 48). The force to successively break the foam walls was recorded, although conversion to strength units required assumptions to be made on the type of local deformation of the cell wall. At low densities, the surface of an extrudate was some 100 times stronger than the interior, although at higher densities similar values were recorded (Fig. 5). Not surprisingly, the surface layer showed only a slight dependence on density, although the interior strength increased strongly with density more closely in agreement with Ashby's closed-cell prediction. The principal contribution in the local test would be expected to be face bending, hence the higher power law, in agreement with prediction. The pin indentation test is also able to give one-dimensional structural information, since a characteristic force spectrum is obtained (Fig. 6). The separation of the force peaks has been compared with the distance between pore walls, derived from diameters drawn across scanning electron micrographs of cylindrical extru-date cross sections. This shows that the pin test provides some overestimation of the pore size because some spurious force events occurred, although this could be improved with signal filtering (48). Owusu-Ansah et al. (39) had earlier indicated extrudate porosity from the force-displacement signal of a modified War-ner-Bratzler test, albeit carried out on a bulk sample.
Experiments using a Charpy pendulum (Table 1) allowed calculation of the critical strain energy release rate Gc (32). Ashby (13) gives the value of the stress intensity factor, K1c, for tensile fracture of foams:
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