What is depth sensing indentation and how is it different fr

What is depth sensing indentation and how is it different from conventional indentation hardness measurement? The maximum force at which the bond breaks was derived to be: Fmax=S_or_o/8. Where, So is the stiffness of the material and r_o is the equilibrium bond length. Assuming this, prove that the theoretical strength of a material: sigma max=E/8 (E=elastic modulus of a material)

Solution

In the DSI tests the applied load is registered as a function of indentation depth both during loading and unloading.
In this method the mean contact pressure at the maximum depth is used to characterize the plastic properties of materials. If, however, a considerable part of the deformation during the indentation is elastic, this pressure deviates significantly from the conventional hardness number which is determined by optical observation of the indentation trace. For example, in the limiting case of the ideally elastic material, the conventional hardness number tends to infinity while the mean contact pressure gives finite value since an elastic contact surface is developing between the indenter tip and the ideally elastic material.Depth sensing indentations are indentation experiments in which the load and the displacement of a hard indenter are measured continuously. The complete deformation history of the material indented is recorded as the load-displacement characteristics. The projected area of the indent is obtained from the depth of penetration, known as the geometry of the indenter. Thus hardness of the material is obtained without imaging the resulting impression. This makes the depth sensing indentation ideal for determining the property of small volumes of material, as in nano-indentation.

3. Given Fmax = S₀ R₀ /8

S₀ = Fmax / d where d= deformation in length (Formula)

This implies : (R₀ / 8 d) =1

d/ R₀   = 1/8

Now strength =( d / R₀ )E

= (1/8) E