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Research Papers

A Stretch/Bend Method for In Situ Measurement of the Delamination Toughness of Coatings and Films Attached to Substrates

[+] Author and Article Information
M. Y. He, A. G. Evans

Department of Materials, University of California, Santa Barbara, Santa Barbara, CA 93106-5050

J. W. Hutchinson

School of Engineering and Applied Sciences, Harvard University, Cambridge, MA 02138

J. Appl. Mech 78(1), 011009 (Oct 13, 2010) (5 pages) doi:10.1115/1.4001938 History: Received February 22, 2010; Posted June 09, 2010; Revised June 25, 2010; Published October 13, 2010; Online October 13, 2010

A stretch/bend method for the in situ measurement of the delamination toughness of coatings attached to substrates is described. A beam theory analysis is presented that illustrates the main features of the test. The analysis is general and allows for the presence of residual stress. It reveals that the test produces stable extension of delaminations, rendering it suitable for multiple measurements in a single test. It also provides scaling relations and enables estimates of the loads needed to extend delaminations. Finite element calculations reveal that the beam theory solutions are accurate for slender beams, but overestimate the energy release rate for stubbier configurations and short delaminations. The substantial influence of residual stress on the energy release rate and phase angle is highly dependent on parameters such as the thickness and modulus ratio for the two layers. Its effect must be included to obtain viable measurements of toughness. In a companion paper, the method has been applied to a columnar thermal barrier coating deposited onto a Ni-based super-alloy.

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Figures

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Figure 1

A schematic of the notched four point bend test for determining delamination toughness, indicating the location of bonded stiffeners often need to assure delamination before substrate yielding

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Figure 2

(a) An optical image of the actual configuration used in the companion paper comprising a columnar thermal barrier coating deposited onto a Ni-based alloy; (b) a schematic of the specimen design and test procedure for the example of a coating on the periphery of a circular substrate. The precracking method is illustrated on the top right, and the subsequent two-point loading for ascertaining the delamination toughness is on the top left.

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Figure 3

Diagrams illustrating the mechanics methods used to obtain the energy release rate on a planar system with residual stress

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Figure 4

Beam theory predictions of the energy release rate as a function of delamination length for cases with zero residual stress. Also shown are selected finite element results for various levels of the relative span h/L. All of the results are for equi-thickness layers h2/h1=1 and for a loading span b/L=0.5 but differing modulus ratios, as indicated on the figures.

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Figure 5

Beam theory predictions of the energy release rate as a function of the level of residual stress in the coating for two different thickness ratios: (a) h1/h2=1, (b) h1/h2=3. All of the results are for E1/E2=4 and a loading span b/L=0.5.

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Figure 6

Beam theory predictions of the energy release rate as a function of the inverse residual compression in the coating for two different delamination lengths: (a) a/L=0.4 and (b) a/L=0.1. Also shown are selected finite element results for various levels of the relative span h/L. All of the results are for h1/h2=3, E1/E2=4, and for a loading span b/L=0.5.

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Figure 7

The mode mixity (phase angle) as a function of the residual stress. The results are for a/L=0.4, h1/h2=3, E1/E2=4, and for a loading span b/L=0.5.

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