Adhesion, cavitation, and fibrillation during the debonding process of pressure sensitive adhesives

We employ the finite-extensible Giesekus viscoelastic constitutive equation to model viscoelastic fluidlike adhesives and study theoretically their response during the debonding process from a rigid surface. We consider a cylindrical sample of soft pressure sensitive adhesive, confined between two solid disks, and assume that small cavities preexist at the adhesive-solid interface due to surface inhomogeneities. When the debonding process is initiated, and the upper disk starts to move, elongating the sample, the cavities expand laterally and weaken the sample. As the debonding process evolves, the cavities start to interact with each other and deform mainly in the direction of elongation; this leads to the formation of thin sheets of material that induce the fibrillation of the sample. At the late stages of the process, these fibrils become very thin, and adhesion is lost. To simulate this complex process that features multiple free surfaces and three-phase contact lines, we solve the full three-dimensional, transient momentum and mass conservation equations coupled with the constitutive equation that accounts for the non-Newtonian stress contribution. The governing equations are expressed in their Lagrangian form and solved with a Petrov-Galerkin stabilized, finite element formulation. The physical domain is discretized with an unstructured mesh that is adaptively reconstructed, allowing us to reach very high deformations of the initial sample. Our results are in qualitative agreement with experimental observations, both regarding the stress-strain curve and the shape of the cavities. Finally, by performing a parametric analysis, we investigate the role of the rheological and geometrical properties of the sample on the adhesion energy of the material.

Figure 1

Schematic of the flow geometry. Note that the origin of axes is placed at the center of the bottom plate, but is depicted outside the sample for clarity (the orientation remains the same).

Figure 2

(a) Storage $\left(G^{\prime }\right)$ and loss (G″) in small amplitude oscillatory shear (SAOS). (b) Startup uniaxial elongational viscosity (${\eta }_e^{+}$). (c),(d) Startup shear viscosity (${\eta }_s^{+}$) and startup first normal stress difference coefficient (${\mathrm{\Psi }}_1^{+}$), respectively. Symbols represent the experimental data by Padding et al. [29], while lines represent the predictions of the model for the same conditions.

Figure 3

(a) Minimum filament radius $R_{\min }$ vs time. Lines correspond to the predictions of the present work for three different spatial and temporal resolutions. Symbols correspond to the predictions by Bhat et al. [48]. The flow parameters are $\mathrm{Wi}=2$, $\beta =0.262$, $a=0.32$, $b=\infty$, and $A_R=1/3$. (b) Note that in this plot we have used the same sample to depict both the contours of a variable at the surface of the filament (bottom half), and the contours of another variable at the $yz$ plane (upper half). Upper half: contours of P,${\tau }_{yz}$, and ${\tau }_{yy}$ at $t=1.6$ using M3, at the cross-section plane ($x=0$). Lower half: contours of ${\tau }_{zz}$, ${\tau }_{xx}$, and ${\tau }_{xy}$ at $t=1.6$ using M3, at the free surface of the filament.

Figure 4

Reduced nominal stress ${\sigma }^{*}$ vs deformation $\lambda$. The insets depict the sample at a certain deformation along with contours of ${\tau }_{zz}$. The flow parameters are $\mathrm{Wi}=5$, $a=0.5$, $b=40$, $\beta =0$, $A_R=6$.

Figure 5

Cross section of the filament depicting (a) the mesh and (b) contours of ${\tau }_{zz}$ at the plane $x=0$ for $\lambda =4$. (c),(d) Same as (a) and (b) but for ${\tau }_{yy}$ at the plane $z=2$. The flow parameters are $\mathrm{Wi}=5$, $a=0.5$, $b=40$, $\beta =0$, $A_R=6$.

Figure 6

Reduced nominal stress ${\sigma }^{*}$ vs deformation $\lambda$ for various Wi. (b) Adhesion energy $W_{\mathrm{adh}}$ vs Weissenberg number. The rest of flow parameters are $a=0.5$, $b=40$, $\beta =0$, $A_R=6$.

Figure 7

PSA sample at various deformations and Wi, along with contours of ${\tau }_{zz}$. The rest of flow parameters are $a=0.5$, $b=40$, $\beta =0$, $A_R=6$.

Figure 8

Contours of the pressure field at the plane $z=3.8$ for $\lambda =4$ and different values of Wi. The rest of flow parameters are $a=0.5$, $b=40$, $\beta =0$, $A_R=6$.

Figure 9

Reduced nominal stress σ* vs deformation $\lambda$ for various values of $a$. (b) Adhesion energy $W_{\mathrm{adh}}$ vs mobility parameter. The rest of flow parameters are $\mathrm{Wi}=5$, $b=40$, $\beta =0$, $A_R=6$.

Figure 10

PSA sample for various values of the mobility parameter $a$ at $\lambda =4$, along with contours of ${\tau }_{zz}$. The rest of flow parameters are $\mathrm{Wi}=5$, $b=40$, $\beta =0$, $A_R=6$.

Figure 11

Reduced nominal stress σ* vs deformation $\lambda$ for various values of $b$. (b) Adhesion energy $W_{\mathrm{adh}}$ vs extensibility parameter. The rest of flow parameters are $\mathrm{Wi}=5$, $a=0.2$, $\beta =0$, $A_R=6$.

Figure 12

Startup first planar extensional viscosity vs time for various values of the extensibility parameter. The rest of the flow parameters are $\dot{\varepsilon }=10$, $a=0.2$, $\beta =0$.

Figure 13

Contours of ${\tau }_{zz}$ at the plane $x=0$ for $\lambda =6$ and various values of $b$. The rest of flow parameters are $\mathrm{Wi}=5$, $a=0.2$, $\beta =0$, $A_R=6$.

Figure 14

Reduced nominal stress σ* vs deformation $\lambda$ for various values of $A_R$. (b) Adhesion energy $W_{\mathrm{adh}}$ vs aspect ratio. The rest of flow parameters are $\mathrm{Wi}=5$, $b=40$, $\beta =0$, $A_R=6$.

Figure 15

PSA sample for various values of the aspect ratio $A_R$ at $\lambda =4$, along with contours of ${\tau }_{zz}$. The rest of flow parameters are $\mathrm{Wi}=5$, $b=40$, $\beta =0$, $A_R=6$.

Figure 16

Comparison of the predicted stress-strain curve vs various experimental data regarding acrylic polymers. The flow parameters of the simulation are $G={10}^5\mathrm{Pa}$, $\lambda ={10}^3\mathrm{s}$, $a=0.5$, $b=40$, ${\eta }_s=0\mathrm{Pa}\mathrm{s}$, $U=1\mu \mathrm{m}/\mathrm{s}$, and $A_R=8$.

Figure 17

Qualitative comparison of the experimental and theoretical trends. (a) Photo reprinted from Creton and Ciccoti [2]. (b) Photo reprinted from Lindner et al. [6]. (c),(d) Simulation results.

Figure 18

Qualitative comparison of the experimental and theoretical trends. (a) Photo reprinted from Yamaguchi et al. [8]. (b) Simulation results.

Figure 19

Predictions of the Rolie-Poly, MI, and Giesekus models for the reference PSA [29].

Figure 20

Reduced nominal stress σ* vs deformation $\lambda$ with different but uniform cavitation size. Our base case is also depicted for comparison purposes.