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Various formulae22, 23, 24 have been proposed to link the fracture toughness to the indenter type, crack geometry, load, and the properties of the materials under test. For indentation with a Berkovich tip, the mode I fracture toughness was obtained using Eq. (2), 24:
SEM micrographs showing radial cracks around the imprints of bulk specimens after sintering and indentation at different load (a) 1200C and 5 N, (b) 1100C and 500 mN, (c) 1000C and 2 N, and (d) 900C and 20 N. Note that the trenches in (c) were machined by FIB.
For a given load (500 mN), much longer cracks are found in a 1200C sintered film (b) with 15% porosity, compared to 1100C sintered bulk (a) with even much larger porosity (29%). Note that both images are at the same magnification and the indent sizes (triangles) are very close.
The results of this study raise two general issues regarding the application of indentation to measure the toughness of porous bulk materials and porous films on substrates. The first relates to the appropriateness of the analysis used for indentation of dense materials when applied to porous bulk materials. The present results show that the indentation toughness results are in good agreement with the SEVNB results for the porous bulk materials. This is at first unexpected because the permanent deformation mechanisms in dense and porous materials are different and some contribution from disruption of the particle networks and crushing densification might be expected under the indenter. Since this does not conserve volume, it would result in a smaller plastic zone for a given indenter depth and lower residual stresses on unloading. This would tend to lead to an overestimate of the toughness using Eq. (2) because a larger load would be required to give the same crack length. However, the FIB/SEM analysis under the indent shows no clear evidence of consolidation under the indenter. Furthermore, if anything the indentation toughness is consistently slightly smaller than the SEVNB toughness. Therefore, it is concluded that the permanent deformation in these porous materials does not involve significant consolidation and behaves macroscopically as if it were a dense effective material.
The second issue relates to the use of indentation to measure toughness for porous films on dense substrates. Despite the similar crack patterns exhibited in both LSCF bulk and films, it is worth noting that the toughness equation was originally developed for bulk materials and therefore its applicability for assessing film fracture toughness remains questionable25 even though it has been used to assess dense thin film fracture toughness by a number of researchers.15, 38 In the present work, we have found that indentation did not produce cracks in films sintered at 1100C and below. This cannot be attributed to a low toughness. Furthermore, much longer cracks in films sintered at 1200C compared with bulk specimen of similar porosity. It is therefore more likely that the standard analysis of the indentation method is not valid for these supported films. It might be expected that in general the toughness of a film on a substrate is inherently different from that of a bulk specimen of equal porosity. 2ff7e9595c
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