Maximum pore volume fraction and size for high fracture energy in porous bodies
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Maximum pore volume fraction and size for high fracture energy in porous bodies Luc J. Vandeperre, Jiaping Wang and William J. Clegg Ceramics Laboratory, Dept. of Materials Science and Metallurgy, University of Cambridge Pembroke Street, Cambridge CB2 3QZ, U.K. ABSTRACT The fracture energy of a body containing pores might be expected to decrease linearly in proportion to the area fraction of material in the crack plane. However, there is experimental evidence that the fracture energy of porous materials only decreases when the pore volume fraction exceeds some critical value. To understand this, experiments have been conducted to directly observe the interaction between a growing crack with model distributions of pores. It is seen that cracks do not simply pass through the pores but spread around them causing the crack front to become curved and increase in length. For just two pores (or a line of pores) this is observed to continue until the crack has completely spread around the pores. It is observed that this increase in length increases the energy required for cracking, suggesting that the maximum fracture energy should rise with the volume fraction of pores. However, when this exceeds a certain value, the spreading crack front impinges on the pores ahead of the crack front before the maximum length of crack front due to bowing is reached. Beyond this critical volume of porosity, the resistance to fracture drops rapidly with porosity. Predictions of the relative fracture resistance of bodies containing spherical as well as cylindrical pores give good agreement with experimental observations, and are consistent with observations that the matrix fracture energy and pore size have little effect, provided the pores are much smaller than the sample. INTRODUCTION The effect of porosity on the fracture energy has been studied extensively in aluminium oxide, and the data [1-3] agree reasonably where the pore volume fraction is higher than ~ 0.2. At lower volume fractions of porosity, however, there is considerable scatter: the reported values are as low as 15 J m–2 and go up to 55 J m–2. As pointed out by Simpson [2], a difficulty in investigating the effect of porosity is that during densification other microstructural variables such as the grain size tend to change as well. The latter is most pronounced when the pore volume fraction is controlled by modifying the sintering conditions as in partial sintering. Indeed, a recent study on the effect of grain size and porosity on the fracture energy of partially sintered alumina has shown that for low volume fractions of porosity, it is the grain size and not the volume fraction of pores, which is the dominant factor in determining the fracture energy [4]. This is entirely consistent with the observation that when the sintering conditions are kept constant and the pores are introduced using fugitive particles, there is little change in fracture energy with porosity as long as the pore volume fraction is low [5]. Once the effect of the grain size is removed, the fra
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