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.
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Vandeperre, L.J., Wang, J. & Clegg, W.J. Maximum pore volume fraction and size for high fracture energy in porous bodies. MRS Online Proceedings Library 759, 23 (2002). https://doi.org/10.1557/PROC-759-MM2.3