Effect of pressure on pull-off of punch adhered to circular or 1-D rectangular plate
Introduction
Increasing or decreasing the strength of adhesion can be useful in a variety of applications, including robotic gripping and locomotion, pick-and-place operations, and transfer printing and assembly [1]. Changing applied pressure provides a means to modify adhesion strength. Attention here is focused on quasi-static pull-off of a rigid punch from a flexible plate. Similar analyses of the effect of pressure on pull-off have been presented for a long rectangular membrane [2] and a circular membrane [3].
Fig. 1(a) shows the cross section of the long rectangular plate, and Fig. 1(b) shows the cross section of the circular plate. The edges are clamped, and the pressure is positive in these schematics. First the punch is adhered to the flat plate, with no preload. Then pressure is applied and kept constant at a desired value. Next the punch is pulled upward until it separates (detaches) from the plate (i.e., pull-off occurs).
Both force control (in which the force F is increased monotonically) and displacement control (in which the punch deflection is increased monotonically) are analyzed. For the rectangular plate, often pull-off occurs when the contact length 2c reduces to zero (i.e., line contact), which has been called pinch-off [4], [5], [6], [7]. For the case of no pressure, similar problems have been investigated previously for a long rectangular plate [4], [6] and for a circular plate [8], [9], [10], [11], [12], [13], [14], [15].
Rectangular plates are analyzed in Section 2, followed by circular plates in Section 3. Concluding remarks are presented in Section 4.
Section snippets
Formulation
A thin, homogeneous, isotropic, linearly elastic, one-dimensional plate is considered, as shown in Fig. 1(a). It is initially horizontal (flat), and its edges are clamped (fixed). The plate has width 2, thickness h, modulus of elasticity E, Poisson’s ratio , and bending stiffness D /[12(1–)].
The plate is first subjected to uniform pressure p (positive if upward, negative if downward). Then a flat-ended, rigid, rectangular punch with width 2b is adhered to the top of the plate and
Formulation
A thin, homogeneous, isotropic, linearly elastic, clamped circular plate is considered, as shown in Fig. 1(b). It is initially horizontal (flat). Axisymmetric loading and deformation are analyzed.
The plate has radius a, modulus of elasticity E, Poisson’s ratio , and thickness h. It is first subjected to uniform pressure p. Then a flat-ended rigid cylindrical punch with radius b is adhered to the top of the plate and pulled upward with force F.
The contact region has radius c, which is initially
Concluding remarks
Two examples of quasi-static pull-off of a flat-ended, rigid punch from a linearly elastic, clamped plate have been considered. In Section 2, the punch and plate were long and rectangular, and a one-dimensional analysis was conducted. In Section 3, the cylindrical punch and plate were circular. A JKR-type theory of adhesion was adopted. Attention was focused on the effect of pressure (upward and downward) on the plate. The influence of the relative size of the punch was also investigated, as
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgments
The author is grateful to Michael Bartlett for introducing this topic to him, to David Dillard for helpful discussions, and to Benjamin Dymond for preparing the figures.
Funding
This paper did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors.
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Peel-off behavior of a double-plate adhesion system
2022, European Journal of Mechanics, A/SolidsCitation Excerpt :The predicted deformation has a good agreement with experimental results (Gong et al., 2017; Mastrangelo and Hsu, 1993). Since pressure applied on the slender structure might change the strength of adhesion, Plaut investigated the effect of pressure on peel-off behavior of different shapes of punch adhered to rectangular membrane (Plaut, 2021a), circular membrane (Plaut, 2021b), rectangular plate as well as circular plate (Plaut, 2021c). Yin et al. studied the peel-off behavior of a bilayer elastic film on a rigid substrate and established a peeling model to predict which interfacial debonding will occur first (Yin et al., 2022).