Tactile Probe Indentation Mechanics and Creep Compliance in Elastomers
Automated tactile probe indentation extracts true elastomer creep compliance only when test routines correct for finite ramp rates and substrate stiffening.
Sneddon Solution
Meaning
Generalised relationships for axisymmetric indenters define the relationship between penetration depth and contact area for various probe shapes. The sneddon solution provides the analytical framework for calculating the displacement of an elastic half space under a rigid punch of any smooth profile. This framework provides the basis for almost all modern nanoindentation software.
The model assumes small strains and ceases to apply when the indentation depth causes large scale plastic upheaval at the surface.
Integral Transform
Hankel transforms convert the partial differential equations of elasticity into algebraic forms that are easier to solve. The resulting expressions relate the load directly to the square of the penetration depth for a conical tip. This mathematical elegance allows for real time data processing during a measurement run.
Geometry Function
Coefficients in the equation change depending on whether the tip is a sphere, a cone or a flat cylinder. A cone produces a linear relationship between the stiffness and the depth while a sphere follows a non linear path. Accurate identification of the tip geometry is the primary readiness question for any hardness audit.
Elastic Recovery
Unloading data follows the same analytical form as the loading phase in a purely elastic material.