Truncated Conical Indenter

The truncated conical intender is characterized by the radius of the blunt end , the inclination angle , the effective contact radius and the deformation depth (rigid body indentation). This solution is correct without restrictions only for rigid indenters (see [1]).

The contact radius can be deduced numerically using the relation that connects the geometrical parameters to each other:

(1)

such that the angle is introduced as:

(2)

Other parameters, such as load force , displacement and the stress profile are given by the following equations:

(3)

(4)

(5)

Definitions:

Poisson’s ratio of the substrate dimensionless,

Young’s modulus of elasticity of the substrate, [Pa],

Equivalent elastic constant , [Pa],

Normal load , [N]

References:

[1] Valentin L. Popov, Hanbook of Contact Mechnics, Exact Solutions of Axisymmetric Contact Problems, pg. 13, pg.29