Abstract
We modelled deep indentation in brittle materials via a tensorial approach in three dimensions. Experimentally, we performed deep indentation in base catalyzed aerogels. When deep indentation is performed in these materials, it appears a Hertzian cone crack for both experimental and numerical results. The cone angle (angle between the surface and the boundaries of the Hertzian cone) depends on the material in which indentation is performed. The Young moduli of the materials has no effect on these angles. The tendency is that materials with increasing Poisson ratios have a decreasing value of the Hertzian cone angle.
Highlights
Hertz (Hertz 1881) was the first to observe what is known as a Hertzian cone crack
We present Hertzian cone cracks for different aerogels in which we performed deep indentation
For a Poisson ratio of 0.25, we find a numerical cone angle of 36±3 which is close to the experimental values for Hertzian cone angle of 28−31o in Al2O3/SiC whisker composite (Zeng 1992a,Zeng 1992b), but larger than the value of the cone angle in soda lime glasses (Hertz 1881)
Summary
Hertz (Hertz 1881) was the first to observe what is known as a Hertzian cone crack. Mechanical characteristics of silica aerogels like their Young modulus, their Poisson ratio, their rupture threshold were already measured, there are few studies in which Hertzian cone angles were observed in these materials. We use here a numerical tensorial approach to model deep indentation in brittle materials. This method leads to a Hertzian cone crack numerically. We obtain Hertzian cone cracks with angles depending on the Poisson ratios of the modelled materials. The angles of the cone shaped cracks with respect to the surface of the material and obtained numerically depend on the Poisson ratios and correspond within the error margin to the experimental values of these angles
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