Research Papers

Examination of Prestressed Coating/Substrate Systems Using Spherical Indentation—Determination of Film Prestress, Film Modulus, and Substrate Modulus

[+] Author and Article Information
James A. Mills

Department of Civil Engineering and Engineering Mechanics,
Columbia University,
New York, NY 10027
e-mail: jam2001@columbia.edu

Hang Xiao

School of Chemical Engineering,
Northwest University,
Xi’an 710069, China;
Yonghong Zhang Family Center for Advanced Materials for Energy and Environment,
Department of Earth and Environmental Engineering,
Columbia University,
New York, NY 10027
e-mail: hx2152@columbia.edu

Xi Chen

School of Chemical Engineering,
Northwest University,
Xi’an 710069, China;
Yonghong Zhang Family Center for Advanced Materials for Energy and Environment,
Department of Earth and Environmental Engineering,
Columbia University,
New York, NY 10027
e-mail: xichen@columbia.edu

1Corresponding authors.

Contributed by the Materials Division of ASME for publication in the Journal of Engineering Materials and Technology. Manuscript received June 22, 2018; final manuscript received June 8, 2019; published online July 17, 2019. Assoc. Editor: Anastasia Muliana.

J. Eng. Mater. Technol 142(1), 011003 (Jul 17, 2019) (11 pages) Paper No: MATS-18-1190; doi: 10.1115/1.4043628 History: Received June 22, 2018; Accepted June 17, 2019

There have been many studies performed with respect to the indentation of thin films affixed to a corresponding substrate base. These studies have primarily focused on determining the mechanical properties of the film. It is the goal of this paper to further understand the role that the film plays and how a potential prestressing of this film has on both the film and substrate base. It is equally important to be able to understand the material properties of the substrate since during manufacturing or long-term use, the substrate properties may change. In this study, we establish through spherical indentation a framework to characterize the material properties of both the substrate and film as well as a method to determine the prestress of the film. It is proposed that through an initial forward analysis, a set of relationships are developed. A single spherical indentation test can then be performed, measuring the indentation force at two prescribed depths, and with the relationships developed from the forward analysis, the material properties of both the film and substrate can be determined. The problem is further enhanced by also developing the capability of determining any equibiaxial stress state that may exist in the film. A generalized error sensitivity analysis of this formulation is also performed systematically. This study will enhance the present knowledge of a typical prestressed film/substrate system as is commonly used in many of today’s engineering and technical applications.

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Fig. 1

Indenter/film/substrate model

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Fig. 2

Model of the spherical indentation on a prestressed elastic film/substrate system

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Fig. 3

Normalized load—penetration depth for different elastic modulus ratios, with R/h = 1.0, K = 0

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Fig. 4

Normalized P–δ data for various K values at EMR of (a) Ef/Es = 0.25 and (b) Ef/Es = 15.0

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Fig. 5

Data points from forward analysis overlaid with surface plots, f1 and f2, at (a) δx = h/2 and (b) δy = h/4

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Fig. 6

Reverse analysis error (a) with Es, as unknowns, (b) with Ef, σ as unknowns, and (c) with Ef, Es as unknowns

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Fig. 7

Normalized indentation load as a function of K = σps/Ef, at 0.5 ≤ R/h ≤ 10.0: (a) δx = h/2 and (b) δy = h/4

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Fig. 8

Error plot of reverse analysis, −0.10 ≤ K ≤ 0.10, 0.5 ≤ R/h ≤ 10.0

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Fig. 9

General algorithm of reverse analysis

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Fig. 10

Plots for dP (a) α1 + α3 and (b) α2 + α4 as each affects the potential error in (ps/Ef) over various Κ = σps/Ef, EMR = Ef/Es

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Fig. 11

Perturbation coefficient for indenter (a) force measurement and (b) displacement measurement



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