mechanics of peeling for extensible elastic adhesive … · 2010-01-23 · in particular, the...

Proceedings of PACAM XI 11th Pan-American Congress of Applied Mechanics Copyright © 2009 by ABCM January 04-08, 2010, Foz do Iguaçu, PR, Brazil

MECHANICS OF PEELING FOR EXTENSIBLE ELASTIC ADHESIVE TAPES

Christopher Kovalchick, [email protected] Guruswami Ravichandran, [email protected] Graduate Aerospace Laboratories, California Institute of Technology Pasadena, CA 91125-5000 USA Alain Molinari, [email protected] Laboratoire de physique et mécanique des matériaux, Université de Metz Ile du Saulcy, 57045 Metz Cedex 1, France Abstract. The measurement of interface mechanical properties between an adhesive layer and a substrate is significant for optimization of a high-quality interface and is of significance to numerous applications including peeling and electronic packaging. A common method for measuring these properties is the peel test. Although analytical models exist for peeling of elastic tapes from smooth surfaces, there is a need for rigorous experiments in this area. Furthermore, several assumptions are made in the existing models regarding the mechanical and material properties of the tape and the testing conditions. These include inextensibility of the tape and negligible pre-strain prior to detachment. The assumptions require that the elastic energy term in the energy balance of the peel process be neglected. However, this term can become significant for elastomers at small peel angles, in which case the tape is considered to be an extensible linear elastic medium. The peel force at varying angles is determined for various commercial tapes. Tests are conducted using a newly-developed peel arrangement capable of peeel angles from 0 to 180 degrees. The peel zone and the tape are imaged in great detail using optical techniques. The influence of extensibility and pre-strain on adhesion is examined, and results are compared to a newly developed model of the peeling process accounting for these parameters. The dependency of adhesion energy on the peel angle is also investigated, and an attempt is made at modeling the peeling process as a mixed-mode fracture problem. Keywords: Peeling, Adhesion, Mixed-mode fracture

1. INTRODUCTION

The measurement of interface mechanical properties between an adhesive layer and a substrate is significant for optimization of a high-quality interface (Wei and Zhao, 2008). A common method for measuring these properties is the peel test, a technique first developed as a result of investigations on the surface energy that exists between two elastic solids in contact (Kendall et al. 1971). Recent work in peeling is of interest in a variety of scientific areas. There are several applications of peeling in the field of biomechanics, particularly in the area of gecko adhesion. A significant amount of work has been devoted to the multi-scale study of the gecko foot and the role adhesion plays in its functionality (Autumn et al. 2006; Pesika et al. 2006). In the microelectronics community, the focus of peeling has been on the delamination strength of thin films to silicon substrates (Leseman et al. 2007). Additionally, environmental conditions such as moisture and thermal gradients can degrade the strengths of devices due to strain mismatches between the film and the substrate. From an industrial standpoint, the peel test has been used primarily for comparative strength testing of materials for case-specific applications. These include quality control devices in which the ultimate peel strength of a material is a critical parameter.

Recently, the focus on the peel test has been to obtain a better understanding of the fundamental mechanics underlying the problem. The proposition of this test as one based upon first principles and fracture mechanics has generated a renewed interest in the subject, particularly in developing theoretical models of the process (Tsai and Kim, 1993; Kim and Aravas, 1988). Recent models are aimed at incorporating various parameters of the peeling process, such as the dissipation of plastic energy (Wei and Hutchinson, 1998), non-linear elastic effects (Williams and Kauzlarich, 2005), and the extensibility of the tape (Pesika et al. 2007). In particular, the process of peeling an adhesive film from a rigid substrate is analogous to a crack propagating in a medium. A significant amount of work has been dedicated to examining the mixed-mode fracture mechanics behavior and its effect on the peeling process (Thouless and Jensen, 1992; Hutchinson and Suo, 1992).

Although analytical models exist, there is a need for more rigorous experiments in these areas. Several assumptions are made in many of the models in the literature regarding the mechanical and material properties of the tape as well as the testing conditions. A common assumption is the inextensibility of the tape, which requires that the elastic energy term in the energy balance of the peel process be neglected (Kendall, 1975). However, this term can become significant for elastomers at small peel angles, in which case the tape should be considered as an extensible linear elastic medium.

The study here investigates the mechanics of peeling using a newly-developed peel apparatus. Experimental validation is achieved through a series of displacement-controlled tests in which the peel force is measured for a range


of peel angles. The steady-state peel force is measured at each angle and compared to the predicted value based upon the governing relations of Kendall and Rivlin. In order to develop a mixed-mode fracture mechanics model, the peel zone (referred to as the process zone) is treated as the cohesive zone in a fracture problem. The geometry of this process zone is quantified using an imaging technique in order to examine its behavior during the steady-state peeling process. 2. PHYSICAL BACKGROUND

Figure 1. Schematic of a peel test (Kendall, 1975)

Consider the peeling of an elastic thin film from a rigid substrate, shown in Fig. 1. Given parameters include the film thickness d, film width b, peel force F, the angle of peel between the film and the substrate θ, the extension, δ, of the peeled portion of tape c, and the length of the film to be peeled Δc. An energy balance of the process of peeling the film through the length Δc from point A to point B shows that the work done by the system is equal to the change of the stored internal energy of the system:

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WP =UE +US where W is the work due to peel, UE the elastic energy stored in the film due to extension of the peeled portion c, and US the surface energy due to the creation of new crack surfaces. Assuming a linearly elastic film with constant width and thickness, the extension of the tape in the peeled region is given by:

€

δ =FΔcEbd

where E is the elastic modulus of the film. The elastic energy term UE is:

€

UE =12Pδ =

F 2Δc2Ebd

The surface energy US is analogous to the fracture energy term in fracture mechanics, considering that the surface

energy here is due to the creation of new surfaces during the peeling process. It is equivalent to the amount of energy required to peel the film to a new location while at a constant peel angle:

€

US = −bGΔc where G is the adhesion energy, defined as the experimental energy required to fracture a unit area of interface. When the film is peeled from point A to point B, the point of application of the peel force F will fall a distance Δc+δ -Δc cosθ. Therefore, the work due to peel is given as:

€

WP = FΔc 1− cosθ +FEbd

Solving for G, the Kendall Equation is obtained:

€

G =F 2

2Eb2d+Fb1− cosθ( )


Note that this expression is quadratic in F/b, the energy release rate. If the film is assumed to be inextensible, the first term above (due to the elastic energy stored in the film) is neglected and the simplified expression, known as the Rivlin Equation, is:

€

Fb

=G

1− cosθ

The Kendall Equation includes the elastic energy of the tape, whereas the Rivlin Equation does not consider this

term. Experimentally, the assumption of inextensibility is valid for stiff materials with very large modulus. However, for soft materials such as tapes and other films with lower moduli, the extensibility of the tape may have a significant effect on the peel force, particularly at smaller peel angles. 3. EXPERIMENTAL RESULTS 3.1 Validation

Figure 2. Experimental peeling apparatus

The experimental setup above in Fig. 2 is designed to conduct a displacement-controlled peel test. The peel base can be adjusted in order to obtain the entire range of angles from 0°-180°. The peel force F is measured at the end of the extensible portion of the tape with a 500-gram ALD-MINI-UTC-M load cell (AL Design, Inc., Buffalo, NY, USA). An M-410.CG motorized translation stage (Physik Instrumente, Irvine, CA, USA) is used to apply a crosshead displacement u, which peels the tape at a constant rate from a glass substrate.

Peel tests are conducted for Scotch MagicTapeTM through a range of angles with the objective of determining the steady-state peel force F. Tests are conducted for angles of 30° to 120° at 10° increments. A crosshead displacement of u = 6 mm is imposed at a rate of 0.01 mm/s, and the peel force F is measured over a time period of t = 10 minutes. The results are plotted below in Fig. 3 and compared to the Kendall and Rivlin models. The elastic modulus for this material is E = 1.65 GPa, obtained independently with a uni-axial tensile test. The piece of tape used has width b = 3.175 mm and thickness d = 50 µm.


Figure 3. Peel force vs. angle, Scotch MagicTapeTM

At larger angles (e.g. 90°), the experimental results are in good agreement with both models. As the peel angle decreases, both the Kendall and Rivlin models overshoot the peel force (the Rivlin model to a greater degree). It should be noted that the adhesion energy G is selected as a fitting parameter when comparing the peel force and angle (G =100 N/m in Fig. 3). For a given steady-state peel force, it is clear from Fig. 4 below that the adhesion energy varies with peel angle. Furthermore, the adhesion energy G is not necessarily the same as the fracture energy when considering mixed-mode fracture. This will be investigated in detail in future studies.

Figure 4. Adhesion energy G vs. peel angle using the relationship for an extensible (Kendall) film 3.2 Process Zone Analysis

In order to investigate mixed-mode fracture behavior of the peeling process, the geometry of the process zone is measured by acquiring in situ images of the fibrils using a camera-lens combination, shown in Fig. 2. The process zone is defined as the region from the last detached fibril to the point where all fibrils are attached to the substrate. The length of the process zone is treated as the length of the crack, L, and the height of the process zone as the crack tip opening displacement, δ. The zone is imaged with a Uniq UP-2000CL B/W Digital CCD Camera (Uniqvision, Santa Clara, CA, USA) attached to an Infinity K2/S Long Distance Video Lens (Infinity, Boulder, CO, USA). Figure 5 below shows a single image of the process zone for a 90° peel test.


Figure 5. Peel zone for a 90° peel test, imaged laterally. The tape fibrils can be seen clearly, defining the process zone with crack-tip opening displacement δ and crack length L.

A sequence of images is acquired every 0.5 seconds for the duration of a peel test at a constant angle. Separate tests

are conducted for peel angles of 30°, 70° and 90°. The height and length of the zone are measured for each image using a simple MATLAB algorithm. Initial analysis is aimed at examining two phenomena: the steady-state behavior of the process zone geometry, and the dependency of the geometry on the peel angle. The shape of the process zone is compared at five (5) equal time increments throughout the steady-state for a given test. In all cases for all angles, the shape of the zone remains constant. A representative test is shown in Fig. 6, with a peel angle θ = 70°.

Figure 6. Process zone geometry, θ = 70°

Figure 7 displays the average height and length of the process zone for 30°, 70°, and 90° peel tests. From this graph, it is clear that as the peel angle θ decreases, the height δ decreases while the length L increases.

Figure 7. Peel zone length L and height δ as a function of peel angle


4. REFERENCES Autumn, K., Dittmore, A., Santos, D., Spenko, M., and Cutkosky, M., 2006. “Frictional Adhesion: A New Angle on

Gecko Attachment”, J. Experimental Biology, Vol. 209, pp. 3569-3579. Hutchinson, J.W., 1992. “Mixed-Mode Cracking in Layered Materials”, Advances in Applied Mechanics, Vol, 29, pp.

63-191. Johnson, K.L., Kendall, K. and Roberts, A.D., 1971. “Surface Energy and the Contact of Elastic Solids”, R. Soc. Lond.

A., Vol. 324: pp. 301-313. Kendall, K., 1975. “Thin-Film Peeling – The Elastic Term”, J. Phys. D: Appl. Phys., Vol. 8, pp. 1449-1452. Kim, K.S. and Aravas, N., 1988. “Elasto-Plastic Analysis of the Peel Test”, Int. J. Solids Structures, Vol. 24, No. 4, pp.

417-435. Kim, K.S. and Kim, J., 1988. “Elasto-Plastic Analysis of the Peel Test for Thin Film Adhesion”, Trans. ASME J. Eng.

Mater. Technol., Vol. 110, pp. 266-273. Leseman, Z.C., Carlson, S.P., and Mackin, T.J., 2007. “Experimental Measurements of the Strain Energy Release Rate

for Stiction-Failed Microcantilevers Using a Single-Cantilever Beam Peel Test”, J. MEMS, Vol. 16, No. 1, pp. 38-43.

Pesika, N.S., Tian, Y., Zhao, B., Rosenberg, K., Zeng, H., McGuiggan, P., Autumn, K., and Israelachvili, J.N., 2007.

“Peel-Zone Model of Tape Peeling Based on the Gecko Adhesive System”, J. Adhesion, Vol. 83, pp. 383-401. Thouless, M.D. and Jensen, H.M., 1992. “Elastic Fracture Mechanics of the Peel-Test Geometry”, J. Adhesion, Vol. 38,

pp. 185-197. Tian, Y., Pesika, N., Zeng, H., Rosenberg, K., Zhao, B., McGuiggan, P., Autumn, K., and Israelachvili, J., 2006.

“Adhesion and Friction in Gecko Toe Attachment and Detachment”, PNAS, Vol. 103, No. 51, pp. 19320-19325. Tsai, K.-H. and Kim, K.S., 1993. “Stick-Slip in the Thin Film Peel Test-I. The 90° Peel Test”, Int. J. Solids Structures,

Vol. 30, No. 13, pp. 1789-1806. Wei, Y. and Hutchinson, J.W., 1998. “Interface Strength, Work of Adhesion and Plasticity in the Peel Test”, Int. J.

Fracture, Vol. 93, pp. 315-333. Wei, Y. and Zhao, H., 2008. “Peeling Experiments of Ductile Thin Films along Ceramic Substrates – Critical

Assessment of Analytical Models”, Int. J. Solids Structures, Vol. 45, pp. 3779-3792. Williams, J.A. and Kauzlarich, J.J., 2005. “The Influence of Peel Angle on the Mechanics of Peeling Flexible

Adherends with Arbitrary Load-Extension Characteristics”, Tribology International, Vol. 38, pp. 951-958. 5. RESPONSIBILITY NOTICE

The authors are the only responsible for the printed material included in this paper.

mechanics of peeling for extensible elastic adhesive … · 2010-01-23 · in particular, the...

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