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Research Papers

Determination of Energy Release Rate Through Sequential Crack Extension

[+] Author and Article Information
Scott McCann

George W. Woodruff School of Mechanical
Engineering, Georgia Institute of Technology,
Atlanta, GA 30332
e-mail: mccann.scott.r@gmail.com

Gregory T. Ostrowicki

George W. Woodruff School of
Mechanical Engineering,
Georgia Institute of Technology,
Atlanta, GA 30332
e-mail: gtostrowicki@ti.com

Anh Tran

George W. Woodruff School of
Mechanical Engineering,
Georgia Institute of Technology,
Atlanta, GA 30332
e-mail: anh.vt2@gatech.edu

Timothy Huang

3D Packaging Research Center,
Georgia Institute of Technology,
Atlanta, GA 30332
e-mail: tim.huang@gatech.edu

Tobias Bernhard

Atotech Deutschland GmbH,
Berlin 10553, Germany
e-mail: tobias.bernhard@atotech.com

Rao R. Tummala

3D Packaging Research Center,
Georgia Institute of Technology,
Atlanta, GA 30332
e-mail: rtummala@ece.gatech.edu

Suresh K. Sitaraman

George W. Woodruff School of
Mechanical Engineering,
Georgia Institute of Technology,
Atlanta, GA 30332
e-mail: Suresh.sitaraman@me.gatech.edu

1Corresponding author.

Contributed by the Electronic and Photonic Packaging Division of ASME for publication in the JOURNAL OF ELECTRONIC PACKAGING. Manuscript received March 22, 2017; final manuscript received June 4, 2017; published online August 25, 2017. Assoc. Editor: Eric Wong.

J. Electron. Packag 139(4), 041003 (Aug 25, 2017) (9 pages) Paper No: EP-17-1033; doi: 10.1115/1.4037334 History: Received March 22, 2017; Revised June 04, 2017

A method to determine the critical energy release rate of a peel tested sample using an energy-based approach within a finite element framework is developed. The method uses a single finite element model, in which the external work, elastic strain energy, and inelastic strain energy are calculated as nodes along the crack interface are sequentially decoupled. The energy release rate is calculated from the conservation of energy. By using a direct, energy-based approach, the method can account for large plastic strains and unloading, both of which are common in peel tests. The energy rates are found to be mesh dependent; mesh and convergence strategies are developed to determine the critical energy release rate. An example of the model is given in which the critical energy release rate of a 10-μm thick electroplated copper thin film bonded to a borosilicate glass substrate which exhibited a 3.0 N/cm average peel force was determined to be 20.9 J/m2.

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Figures

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Fig. 1

Schematic for sequential crack extension (SCE). Nodes within a box are coupled.

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Fig. 2

Peel strength of 10 μm electroplated copper on borosilicate glass [41]

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Fig. 3

Domain for 2D plane strain analysis of 90 deg peel test under constant applied load

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Fig. 4

Stress–strain relationship for the copper thin film

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Fig. 5

Analysis domain and example finite element mesh regions

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Fig. 6

The summation of the incremental accumulated equivalent plastic strain from each individual load step during peeling in the copper thin film for P/b = 3.0 N/cm

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Fig. 7

The plastic strain in the copper thin film accumulated over one cycle showing where the plastic deformation occurs for P/b = 3.0 N/cm

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Fig. 8

External work, elastic strain, and plastic strain energy rates as the crack propagates from an initial crack length, anom = 100 μm, under a peel force of P/b = 3.0 N/cm for a 10 -μm thick film. Crack growth through regions A, B, C, and D corresponds to element size, δa, of 2, 1, 0.5, and 0.25 μm, respectively.

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Fig. 9

Steady-state energy release rate as a function of mesh density

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Fig. 10

(a) Tangential, (b) normal, and (c) shear stress fields near crack tip during steady-state peeling for P/b = 3.0 N/cm for a 10 μm film. Coordinates are in the global coordinate system. (a) σxx, (b) σyy, and (c) σxy.

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Fig. 11

Strain energy release rate calculated through SCE and VCCT as the crack propagates from an initial crack length, anom = 100 μm, under a peel force of P/b = 3.0 N/cm for a 10 -μm thick film. Crack growth through regions A, B, C, and D corresponds to element size, δa, of 2, 1, 0.5, and 0.25 μm, respectively.

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Fig. 12

External work, elastic strain, and plastic strain energy rates as the crack propagates and subsequently moving the peel force location beyond the initial crack length (region B2)

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Fig. 13

Relationship between critical energy release rate and peel force for a 10 μm electroplated copper film on a borosilicate glass substrate

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