Indenting a steel ball on the laminate surface looks similar to a standard hardness test like Brinell or Rockwell B. Since the glass spheres are varying in size, the hardness values (Depending on Parameters: Load on steel ball, diameter of steel ball and indentation diameter) would also vary. But normally, vickers hardness tests are used for composites (diamond indenter 1360 cone angle).

But since the glass balls are locked within the epoxy matrix, it becomes difficult to estimate the exact value of the contact stress, as the stress due to the load applied, gets distributed within the matrix and further onto the glass spheres. The stress transferred depends on the interfacial bonding between the epoxy and glass spheres.

However, once the indentations are made, the topographical study of the laminate surface at the indentation spots through SEM/ suitable microscopes would reveal the size of the glass spheres in the vicinity of the indentation.

The more the indentation diameter, lower would be the stress applied (due to the spread). Correlate this to the size of the glass spheres to make a conclusion. Have attached a paper on Brinell Hardness which you might find useful.

thank you, Anand.

For contact pressure calculations, you can refer to the textbook "Engineering Tribology" by Gwidon W. Stachowiak and Andrew W. Batchelor

http://www.sciencedirect.com/science/book/9780750678360

Best of luck

Hi Jintao,

It all depends on what you want. If you just want to model normal contact between two isotropic elastic spheres or between a sphere and a half-plane then the classical Hertzian formulae are appropriate. I've attached a link to a handy online calculator for these. If you need to include plasticity effects and/or the coupling between different constituents in your composite then perhaps approximate methods such as FEA are what you're after.

For Hertzian elastic contact between a pair of spheres, the maximum contact pressure is proportional to the effective radius to the power of -2/3. This means that (all other things being equal), the maximum contact pressure will be greater when you have a smaller glass sphere.

https://en.wikipedia.org/wiki/Contact_mechanics#Classical_solutions_for_non-adhesive_elastic_contact

http://www.amesweb.info/HertzianContact/HertzianContact.aspx