Research Papers

Effect of Substrate Compliance on Measuring Delamination Properties of Elastic Thin Foil

[+] Author and Article Information
C. Liu

Materials Science and Technology Division,
Los Alamos National Laboratory,
Los Alamos, NM 87545
e-mail: cliu@lanl.gov

Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received January 26, 2018; final manuscript received February 27, 2018; published online March 20, 2018. Editor: Yonggang Huang. The United States Government retains, and by accepting the article for publication, the publisher acknowledges that the United States Government retains, a nonexclusive, paid-up, irrevocable, worldwide license to publish or reproduce the published form of this work, or allow others to do so, for United States government purposes.

J. Appl. Mech 85(5), 051010 (Mar 20, 2018) (11 pages) Paper No: JAM-18-1055; doi: 10.1115/1.4039480 History: Received January 26, 2018; Revised February 27, 2018

Through the analysis of a model problem, a thin elastic plate bonded to an elastic foundation, we address several issues related to the miniature bulge test for measuring the energy-release rate associated with the interfacial fracture of a bimaterial system, where one of the constituents is a thin foil. These issues include the effect of the substrate compliance on the interpretation of the energy release rate, interfacial strength, and the identification of the boundary of the deforming bulge or the location of the interfacial crack front. The analysis also suggests a way for measuring the so-called foundation modulus, which characterizes the property of the substrate. An experimental example, a stainless steel thin foil bonded to an aluminum substrate through hot-isostatic-pressing (HIP), is used to illustrate and highlight some of the conclusions of the model analysis.

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Fig. 1

Model of a plate resting on an elastic foundation

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Fig. 2

Variation of the stiffness ratio of a plate resting on an elastic foundation to that of a rigidly clamped plate as function of the parameter β

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Fig. 3

(a) Distribution of surface mean curvature κmean for some selected values of parameter β and (b) location of the maximum mean curvature κmean (or the minimum mean strain ϵmean) as function of the parameter β

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Fig. 4

(a) Distribution of interface stress σn for some selected values of parameter β and (b) interfacial stress σn at the crack front r = R as a function of the parameter β

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Fig. 5

Variation of the two nondimensional functions, G(β) and Γ(β)

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Fig. 6

(a) Schematic of the bulge test specimen assembly, (b) image of cross section of the tested bulge specimen cut along the diameter of the disk, and (c) response of miniature bulge test of stainless steel thin foil bonded to aluminum substrate

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Fig. 7

Bulge profile w, mean strain ϵmean, and mean curvature κmean of test no. 1 at moment A indicated in Fig. 6(c)

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Fig. 8

Bulge boundary (dashed lines) determined by using local minima of mean strain εmean and local maxima of mean curvature κmean of test no. 1 at moment A indicated in Fig. 6(c)

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Fig. 9

The bulge profiles from test no. 1 at two different moments during deformation (δ/h=0.50 and δ/h=0.68) and the model fitting, which yields β=13.01. The profile of a plate bonded to a rigid substrate is also plotted for comparison.

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Fig. 10

Detailed motion over bulge surface from test no. 1 at moment of δ/h=0.68. While the out-of-plane (or “lift up”) motion w dominates the bulging process, the in-plane motion characterized by the radial displacement ur, can still be detected even for region r≥R. For r≥R, any nonzero difference between ur and −h(dw/dr)/2, which is due to the rotation of the plate's midplane from bending, would indicate shearing deformation through the thickness of the plate.




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