1884 Journal of the American Ceramic Society-Fair et al. Vol. 88. No. 7 stress within the layers, edge cracks are observed for layer thick nesses greater than a critical value given by Ic 0.342 where Ge is the critical energy release rate, E is the elastic mod- ulus of the layer, and or is the residual compressive stress in the In the current studies of the polyhedra architectures, it was shown that tensile stresses exist throughout the compressive lay- ers The magnitude of these tensile stresses is much smaller than those that exist at and near the surface; they are smaller than the tensile stresses within the polyhedra. These tensile stresses also act in a direction perpendicular to the interface between the compressive regions separating the polyhedra. The current stud ies also show that only triaxial compressive stresses exist in the oe2 100um Z5A42 un separating region where three polyhedra are adjacent to on another(these would be known as three-grain junctions in a Fig. 6. SEM micrographs at various magnifications showing a non- polycrystalline material). It is interesting to speculate that these (-60 um)55 vol% mullite/45 vol% alumina layers posite with thick bonded region on the fracture surface of a com impressive regions might block the extension of cracks within the layers separating the polyhedra in the same manner as the compressive regions might block the extension of cracks that extend within the polyhedra. Unfortunately, the effect of the The fracture surfaces are labeled M (for mullite)in the compressive stresses at the junctions on stopping cracks could ons where no Si signal was ol not be studied in the current work because edge cracks (or ten- are labeled A (for alumina) and indicate that the crack sile stresses at the center of compressive regions) would cause gated through the alumina core. Si is detected on nearly all pol failure, as observed. Such a study would first require coating the hedral facets, indicating that failure was probably caused external surface with a compressive layer the linking of edge cracks on the tensile surface of the specime that then propagated down through the compressive layers aid- In the current studies, edge cracking was observed for com- posites containing laye ith the largest compressive stress (55 ed by the residual tensile stress in the layers vol% mullite). Although the magnitudes of the tensile stresses deep within the layer are expected to be much smaller than those on the surface, they will aid in extending the edge crack. Thus, VI Discussion the edge cracks observed in the polyhedra composites would be (1) Tensile Stresses in Compressive Layers expected to extend deeper relative to the laminar composite stresses exist at and near the surface of the compressive layers (2) Flaws Controlling Strength due to the lack of constraint of differential strain near the sur The strength of the bodies fabricated with either coated or un- face. The tensile stresses are very large and act in a direction coated spheres, compressed into polyhedra, was controlled by that is perpendicular to the interface between the two different flaws pre-existing between the polyhedra, namely, either void layers At the surface, they are approximately equal in absolute located where the polyhedra did not join together during defor- magnitude to the biaxial compressive stresses deep within the mation, or from edge cracks on the surface. The lower strength compressive layer and disappear at a distance from the interface f the monolith fabricated with uncoated spheres relative to the that is approximately equal to the thickness of the compressive slip-cast monolith was caused by the large voids at the intersec- layer. These large tensile stresses can cause small cracks to ex- tion of polyhedra that did not completely deform. These voids tend along the center line of the compressive layer to a depth were the major flaw population for all materials that did not that is approximately equal to the thickness of the compressive exhibit edge cracking. Similar flaws are well known for consol- layer. It has been shown that the extension of surface cracks dated, spray-dried powders. Although the deformation of single along the centerline of the compressive layer, know as edge pheres was studied as a function of several variables that in- racks, depends on both the magnitude of the tensile stress and cluded soaking periods in different aqueous solutions used to the thickness of the compressive layer. For a given residual formulate the slurries that were used to make the spheres, evidence suggested that the spheres should have fully deformed under the applied pressure. Snyder and Lange have shown that Tensie suface such voids are a result of trapped air during consolidation. Further experiments are needed to address this problem. For the composites, either edge cracks or the residual tensile stresses at the surface of the compressive layers were one prin- 300m cipal cause for the lower strength of the composites relative to the monoliths. as discussed above. large residual tensile stresses exist on the surface of the compressive layer, and smaller resid ual tensile stresses exist within nearly the entire compressive layer. When combined with the applied tensile stress, the resid ual tensile stress on the surface can cause catastrophic crack ex tension,even if the edge crack does not pre-exist prior to the graphs of mating fracture surfaces of compo plication of the external stress Within the different composite architectures studied here, the ith results of EDX analysis: M, mullite: A, alumina. strength decreased and the topographical features that identify acture surface just beneath the tensile surface is pre- the polyhedra on the fracture surface increase(see Fig 4)wit te, suggestive of a link-up of edge cracks as the failure Increasing layer thickness and mullite content. Increasing the mullite content will increase the biaxial compressive stressThe fracture surfaces are labeled M (for mullite) in the regions where Si was detected; regions where no Si signal was obtained are labeled A (for alumina) and indicate that the crack propa￾gated through the alumina core. Si is detected on nearly all pol￾yhedral facets, indicating that failure was probably caused by the linking of edge cracks on the tensile surface of the specimen that then propagated down through the compressive layers aid￾ed by the residual tensile stress in the layers. VI. Discussion (1) Tensile Stresses in Compressive Layers Previous studies for laminar composites have shown that tensile stresses exist at and near the surface of the compressive layers due to the lack of constraint of differential strain near the sur￾face.1 The tensile stresses are very large and act in a direction that is perpendicular to the interface between the two different layers. At the surface, they are approximately equal in absolute magnitude to the biaxial compressive stresses deep within the compressive layer and disappear at a distance from the interface that is approximately equal to the thickness of the compressive layer. These large tensile stresses can cause small cracks to ex￾tend along the center line of the compressive layer to a depth that is approximately equal to the thickness of the compressive layer. It has been shown that the extension of surface cracks along the centerline of the compressive layer, know as edge cracks, depends on both the magnitude of the tensile stress and the thickness of the compressive layer.1 For a given residual stress within the layers, edge cracks are observed for layer thick￾nesses greater than a critical value given by tc ¼ GcE 0:34s2 r (13) where Gc is the critical energy release rate, E is the elastic mod￾ulus of the layer, and sr is the residual compressive stress in the layer.1 In the current studies of the polyhedra architectures, it was shown that tensile stresses exist throughout the compressive lay￾ers. The magnitude of these tensile stresses is much smaller than those that exist at and near the surface; they are smaller than the tensile stresses within the polyhedra. These tensile stresses also act in a direction perpendicular to the interface between the compressive regions separating the polyhedra. The current stud￾ies also show that only triaxial compressive stresses exist in the separating region where three polyhedra are adjacent to one another (these would be known as three-grain junctions in a polycrystalline material). It is interesting to speculate that these compressive regions might block the extension of cracks within the layers separating the polyhedra in the same manner as the compressive regions might block the extension of cracks that extend within the polyhedra. Unfortunately, the effect of the compressive stresses at the junctions on stopping cracks could not be studied in the current work because edge cracks (or ten￾sile stresses at the center of compressive regions) would cause failure, as observed. Such a study would first require coating the external surface with a compressive layer. In the current studies, edge cracking was observed for com￾posites containing layers with the largest compressive stress (55 vol% mullite). Although the magnitudes of the tensile stresses deep within the layer are expected to be much smaller than those on the surface, they will aid in extending the edge crack. Thus, the edge cracks observed in the polyhedra composites would be expected to extend deeper relative to the laminar composite. (2) Flaws Controlling Strength The strength of the bodies fabricated with either coated or un￾coated spheres, compressed into polyhedra, was controlled by flaws pre-existing between the polyhedra, namely, either voids located where the polyhedra did not join together during defor￾mation, or from edge cracks on the surface. The lower strength of the monolith fabricated with uncoated spheres relative to the slip-cast monolith was caused by the large voids at the intersec￾tion of polyhedra that did not completely deform. These voids were the major flaw population for all materials that did not exhibit edge cracking. Similar flaws are well known for consol￾idated, spray-dried powders. Although the deformation of single spheres was studied as a function of several variables that in￾cluded soaking periods in different aqueous solutions used to formulate the slurries that were used to make the spheres, all evidence suggested that the spheres should have fully deformed under the applied pressure. Snyder and Lange have shown that such voids are a result of trapped air during consolidation.11 Further experiments are needed to address this problem. For the composites, either edge cracks or the residual tensile stresses at the surface of the compressive layers were one prin￾cipal cause for the lower strength of the composites relative to the monoliths. As discussed above, large residual tensile stresses exist on the surface of the compressive layer, and smaller resid￾ual tensile stresses exist within nearly the entire compressive layer. When combined with the applied tensile stress, the resid￾ual tensile stress on the surface can cause catastrophic crack ex￾tension, even if the edge crack does not pre-exist prior to the application of the external stress. Within the different composite architectures studied here, the strength decreased and the topographical features that identify the polyhedra on the fracture surface increase (see Fig. 4) with increasing layer thickness and mullite content. Increasing the mullite content will increase the biaxial compressive stress Fig. 6. SEM micrographs at various magnifications showing a non￾bonded region on the fracture surface of a composite with thick (B60 mm) 55 vol% mullite/45 vol% alumina layers. Fig. 7. SEM micrographs of mating fracture surfaces of composite with thick (B60 mm) 55 vol% mullite/45 vol% alumina layers. Fracture sur￾faces are marked with results of EDX analysis: M, mullite; A, alumina. Note that the fracture surface just beneath the tensile surface is pre￾dominantly mullite, suggestive of a link-up of edge cracks as the failure mechanism. 1884 Journal of the American Ceramic Society—Fair et al. Vol. 88, No. 7