Degree Granting Department
Autar Kaw, Ph.D.
Daniel Hess, Ph.D.
Craig Lusk, Ph.D.
functionally gradient materials, FEA, ANSYS, parabolic contact problem, Hertzian contact model
Thin films that are functionally gradient improve the mechanical properties
of film-substrate layered materials. Mechanical properties of such materials are
found by using indentation tests. In this study, finite element models are
developed to simulate the indentation test. The models are based on an
axisymmetric half space of a specimen subjected to spherical indentation. The
film layer through the thickness is modeled to have either homogeneous material
properties or nonhomogeneous material properties that vary linearly.
Maximum indenter displacement, and maximum normal and shear
stresses at the interface are compared between the homogeneous model and
the nonhomogeneous model for pragmatic contact length to film thickness ratios
of 0.2 to 0.4, and film to substrate moduli ratios of 1 to 200 to 1.
Additionally, a coefficient is derived from regression of the stress data
produced by these models and compared to that used to define the pressure field
in the axisymmetric Hertzian contact model. The results of this study suggest
that a displacement boundary condition to an indenter produces the same results
as a pressure distribution boundary condition.
The critical normal stresses that occur between modeling a film as a
nonhomogeneous and as a homogeneous material vary from 19% for a modulus
ratio of 2.5:1 to as high as 66% for a modulus ratio of 200:1 indicating that the
modeling techniques produced very different maximum normal stresses. The
difference in the maximum shear stress between the nonhomogeneous and the
homogeneous models varied from 19% for a 2.5:1 modulus ratio to 57% for the
200:1 modulus ratio but reached values as low as 6% for the 50:1 modulus ratio.
The maximum contact depth between the nonhomogeneous and the
homogeneous models varied from 14% for the 2.5:1 case to as much as 75% in
the 200:1 case.
The results from the reapplication of the pressure field derived from the
regression coefficients and the
R2 values from these regression models indicate
the correctness of the regression model used as well as its ability to replicate the
normal stresses in the contact area and maximum indenter displacements in a
FEA model for both the homogeneous and the nonhomogeneous models for
modulus ratios ranging from 2.5:1 to 200:1.
The agreement between the regression based coefficients and the force
based coefficients suggests the validity for the use of the theoretical
axisymmetric Hertzian contact model for defining the pressure field in the contact
area and displacements for both the homogeneous case and the
nonhomogeneous case for the considered film to substrate moduli ratios and
contact length to film thickness ratios.
Scholar Commons Citation
Daly, John Louis Jr., "On Comparison of Indentation Models" (2007). Graduate Theses and Dissertations.