If a brittle material is locally compressed (statically, or dynamically) a ring crack starts at the surface. Due to the stress distribution in the bulk of the material, the ring crack growth at an angle (say 65°) from the axi-symmetry line.
The attached photo shows a perfect cone generated by impact of a steel sphere (at 150 m/s) on a flat SiC tile that was adhered to an aluminum alloy block.
What controls the cone-crack angle? Material properties or the stress distribution or both, and how?
Dear Erik
Please describe the problem more. What shows the picture? is it a crack?
Dear Erik, is the cone in the picture represent the fragment separated from the SiC tile after impact loaing? If so, the configuration really corresponds to internal stress distribution. The material properties weakly influence on cone-crack angle. Particularly, because stress distribution depends on friction coefficient in contact of indenter (in your case this is steel ball) with target (SiC tile). For the thorough analysis of this interesting topic see, please, famous book "Contact Mechanics" of K.L. Jonson (1985, 1987). Best regards, Serge
The picture shows a cone that was created due to the cone-crack phenomena that occurs by steel sphere impact on a SiC tile (from top-to-down). The flat tile was glued to an Aluminum backing block. After the impact the tile has been removed, but the cone remained at the surface of the Al-block. Hence the SiC tile now has a conical crater of the same shape as the cone.
Apart from this straight cone, we also have cones that show a transition (widening) in angle about half-way the tile thickness.
Question that I have is what determines the cone angle(s)?
I think the both of material property and stress wave influence the cone crack phenomena. Below link may be helpful:
http://docs.lib.purdue.edu/dissertations/AAI1510251/
The formation of Hertzian cone observed during indentation of brittle materials due to the difference in ultimate strength strength of brittle materials under tension and compression. This is described in detail in the paper: Batanova O.A., Matvienko Yu.G. Regularities of crack initiation under the edge chipping and indentation of brittle materials // Physical Mesomechanics – 2015. – V. 18. – No. 2.- P. 22-36 (in Russian).
Spacibo Yury,
Do you have an article in English as well?
R ni garasho govarit par Ruskii....
What controls the cone-crack angle?
A general way to solve this type of problem is to construct a crack model, calculate the crack extension force G (per unit length of the crack front), look for crack configuration that maximizes G. This configuration would give the cone-crack angle. We can expect the cone-angle to depend on the stress distribution inside the material and on Poisson's ratio. It may be easier to start with a two-dimensional crack system corresponding to the impact of a long cylinder on a flat SiC tile. I see no difficulty with formulae in this last particular problem. I have used this methodology in a recent work entitled " A theory of the fracture of rectangular bars bent by terminal transverse load and couple", see our contributions in ResearchGate.
For the perfect cone obtained by the impact of a sphere on a flat surface, the crack dislocations have a circular shape; the problem is more complicated but the methodology remains unchanged.
Dear Erik
I now have a solution to the problem mentioned above (rectilinear contact pressure of a cylinder on a flat boundary). Do you observe that the shear modulus plays no role in the observed cone crack angle (quasistatic failure)? It appears to me that only Poisson's ratio plays a role.
Thanks in anticipation for your answer
Patrick
The condition providing the cone crack angle is given in our study by the relation dG / dthetha = 0, where G is the crack extension force per unit edge length of the crack and thetha is the cone crack angle. This condition only depends on Poisson's ratio.
Please see our contribution in Research Gate : "Fracture Mechanics in a three-dimensional elastic half space under the rectilinear contact pressure of a cylinder ".
I am very interested in this subject beginning with your Q&A question
Sincerely
Patrick A.
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