Graduation Year


Document Type




Degree Granting Department

Mechanical Engineering

Major Professor

Autar Kaw, Ph.D.

Committee Member

Daniel Hess, Ph.D.

Committee Member

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.