On the peeling of elastic tapes from viscoelastic substrates: Designing materials for ultratough peeling

https://doi.org/10.1016/j.triboint.2019.106060Get rights and content

Highlights

  • The viscoelastic damping of the substrate material in the peeling process of elastic thin tapes is theoretically investigated.

  • The number of relaxation times of the substrate can signicantly modify the peeling mechanism.

  • Our investigation may help in the design process of viscoelastic materials.

  • A preliminary comparison between our theoretical predictions and experimental data of the literature shows the accuracy of the proposed model.

Abstract

The present paper deals with the peeling of an elastic thin tape from a viscoelastic substrate. A previous investigation of the authors has disclosed several physical aspects of such phenomenon by focusing the attention on an ideal viscoelastic substrate with one-single relaxation time. However, for real viscoelastic solids, the spectrum of relaxation times may cover more than 10 decades. For this reason, it is of interest investigating the influence of the number of relaxation times on the peeling mechanism. More specifically, it is possible to enlarge the frequency range where the material shows significant damping and energy dissipation by increasing such number. This may help in properly designing viscoelastic materials with ultra-tough adhesion properties. As a practical example, a widespread viscoelastic material is considered, the PMMA (polymethyl methacrylate), which presents high damping at low-frequencies, thus making tough the peeling behavior at small velocities.

Introduction

In the last few years, the scientific community has devoted increasing attention to the study of adhesion between surfaces. Nature provides the most inspiring examples and great amount of biological species, such as many insects, spiders and lizards, which are able to adhere and quickly detach from several surfaces. This is why researchers, in the last decades, have tried to mimic such marvellous capacities, at first by deeply investigating the properties of the contacting surfaces. It was found that the mushroom-shaped pillars [1] exhibit very high adhesive performance, and several studies [[2], [3], [4]] have disclosed that the origin of such behavior lays in the shape of the terminal plate. Moreover, in some insects [5,6], the architecture of the pads enhances adhesion, therefore microwalls covered by a thin film have been proposed in some studies [7,8]. Attachment/detachment mechanisms of gecko spatula have been deeply investigated, through several peeling models [[9], [10], [11], [12], [13], [14], [15], [16]], as well as many experimental and theoretical studies have been carried out, aimed at calculating the peeling force required to detach thin films from rigid or compliant substrates [[17], [18], [19], [20], [21], [22], [23]]. This problem is crucial in many practical applications, such as in the adhesion of medical bands on human skin, which is a very compliant viscoelastic material [[24], [25], [26], [27], [28], [29], [30]]. In this context, the adherence of this kind of adhesives in contact with viscoelastic substrates has been extensively studied in the last years [[31], [32], [33], [34], [35], [36],52].

It is important to observe that the peeling phenomenon and more complex fracture problems are strictly related each other. Moreover, in a viscoelastic material the energy dissipation in the bulk makes the energy release rate G not easily to be defined and the work of adhesion w does not completely describe the crack growth process [37,38], since the entire process is related to different viscoelastic properties of the polymer [[39], [40], [41], [42], [43]].

In a so compelling research context, the authors in Ref. [44] proposed a new approach to investigate the interface crack propagation. In this paper, the theoretical study is extended to real-like viscoelastic substrates, by considering an increasing number of relaxation times in the Prony series, to correctly describe the response of the material. Moreover, the case of the peeling of an elastic tape from a PMMA (polymethyl methacrylate) substrate, whose viscoelastic response is characterized by 11 relaxation times (Ref. [45]), is presented.

Section snippets

Peeling of an elastic thin tape from a viscoelastic substrate with more than one relaxation time

Here, we briefly recall the methodology developed in Ref. [44], at which the reader can refer for more details, by investigating the case of a viscoelastic substrate with a spectrum of relaxation times covering numerous decades. To this end, consider an elastic tape of width b and thickness d adhering on a viscoelastic substrate (Fig. 1) and peeled off by a constant vertical force P. The thickness d represents the only length of scale of the problem, therefore, we expect that interfacial

Results

In order to evaluate the influence of the spectrum of relaxation times characterizing the elastic modulus of the viscoelastic substrate, we first compare three ideal materials with 1, 3 and 5 relaxation times. For the first material we assume τ=2103[sec] and E0=105 [Pa]. For the other two materials with three and five relaxation times, we take τi=τ10k[sec], with i={1,2,3} and k={1,0,1}, and i={1,2,3,4,5} and k={2,1,0,1,2}, respectively. The real and imaginary parts of the viscoelastic

Conclusions

In this paper, we have investigated the effect of the viscoelastic damping in the substrate material on the peeling of elastic thin tapes. Specifically, by properly increasing the number of relaxation times in the viscoelastic modulus, it is possible to enlarge the frequency range in which material damping and energy dissipation occur. This condition gets adhesion ultratough, in the sense that stable peeling occurs at arbitrarily high loads. As a result, the detachment velocity of the tape can

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.

Acknowledgement

L.A. and G.C. acknowledge support from the Italian Ministry of Education, University and Research (MIUR) under the program Department of Excellence" Legge 232/2016 (Grant No. CUP - D94I18000260001).

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      Citation Excerpt :

      A rigorous limit of the dimensionless detaching speed V′=Vτ/d≈0.59, where V, τ and d are the actual interfacial detaching speed, the viscoelastic relaxation time of substrate material and the thickness of elastic strip respectively, for the steady-state peeling on a strong viscoelastic substrate was always found for various peeling angles [21]. Introducing multiple viscoelastic relaxation times of the substrate material was found to enable the material to show significant damping and energy dissipation in a wider frequency range [18]. But the influence of multiple relaxation times, as well as the saturated/initial modulus ratio representing the degree of the viscoelasticity, on the stable and controllable speed range, were not examined.

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