Force-displacement curves

In this section we investigate the change in the shape of the force curves with varying material properties. A convenient representation are stress-strain curves, see figure 8.1. The stressσ always denotes here the nominal stressσ=F/A₀. The strain²is the displacementddivided by the initial film thicknessb. We study the stress-strain curves of a few selected materials that are representative for each type of behavior.

In the following, we describe the characteristics of the different stress-strain curves for the whole debonding process. Their different shape can be interpreted including the visual observation of the experiment. Observation in a top view gives more infor- mation about the evolution of the patterns, whereas the side view helps categorizing the mechanism of the final detachment. In general, we did not observe cavitation in the debonding of all our materials, except for rare cases of air trapped in pockets on the probe surface during the approach. Instead we invariably observed air fingers entering into the adhesive from the sides. Cavitation is controlled by the ratio of air pressure and elastic modulus. It is favored by high moduli, high adherence, and thin layers relative to the debonding speed [118]. As the materials investigated in this study were rather soft, the film thicknesses high, and the interaction between silicone and steel weak, cavitation was mostly suppressed.

Figure8.1(a)shows the typical stress-strain curve for a pure silicone oilr=0. As the forces were too weak for the experimental resolution with the Sylgard 184 oil, we performed tests with a higher viscosity PDMS oil (η= 100 Pa s) and different testing conditions (v= 8^µm/sandb₀= 50µm). The results stay qualitatively the same. The force first reached a peak value due to the stretching of the machine [43,40], then it decayed rapidly to forces below the experimental resolution. The oil-probe contact area formed a contracting circle that became smaller and smaller until only one thin fibril was left. This fibril was stretched in the tensile direction and became thinner until it finally broke up triggered by the Rayleigh–Plateau instability [90,95]. The force however was very early in the process so low that is was not possible to monitor the actual break-up. The maximum deformation was higher than 20.

Figure 8.1(b)displays the stress-strain curve for a material with r=0.10. This material is below the gel point. The peak shape resembles the case of the non- crosslinked oil. However, a very low force plateau is formed. The test was stopped before the actual break-up of the fibrils; the maximum strain value is expected to be very high (²_max>20).

Next we consider the material withr=0.11[figure8.1(c)]. G⁰andG⁰⁰are parallel over the whole range of frequencies, indicating that this material is close to its gel point. Such a material is typical of an under-crosslinked PSA , albeit with a much too low T_g to show high adhesion [130, 38]. Unlike before, the force did not decay continuously to zero, but a distinct force plateau was observed after a first strong decay. The plateau value was slightly increasing until it dropped slowly to very small values. The maximum deformation was very high (²_max>20). The experiment was stopped before the actual debonding was complete because the displacement of the probe was limited to d = 5 mm in our set-up. The plateau force in figure 8.1(c)

8.3. Force-displacement curves

0.04

0.03

0.02

0.01 0.00 F/A0 [MPa]

20 15 10 5 0

e

(a) Silicone oil, η = 100 Pa s, b = 50µm, v = 8^µm/s.

0.0030 0.0025 0.0020 0.0015 0.0010 0.0005 0.0000 F/A0 [MPa]

1.2 0.8

0.4 0.0

e

(b)r= 0.10,b= 230µm,v= 10^µm/s.

0.012 0.010 0.008 0.006 0.004 0.002 0.000 F/A0 [MPa]

25 20 15 10 5 0

e

(c)r= 0.11,b= 215µm,v= 10^µm/s.

0.03

0.02

0.01

0.00 F/A0 [MPa]

7 6 5 4 3 2 1 0

e

(d)r= 0.13,b= 215µm,v= 10^µm/s.

0.08 0.06 0.04 0.02 0.00 F/A0 [MPa]

1.2 0.8

0.4 0.0

e

(e)r= 0.16,b= 230µm,v= 10^µm/s.

0.06 0.05 0.04 0.03 0.02 0.01 0.00 -0.01 F/A0 [MPa]

0.6 0.4

0.2 0.0

e

(f) r= 0.3,b= 238µm,v= 10^µm/s. Figure 8.1.: Typical stress-strain curves of the different materials. Note the different scaling for each graph.

Chapter 8. The complete debonding process

0.06

0.04

0.02

0.00 F /A0 MPa]

4000 3000 2000 1000 0

d [µm]

3.0% adhesive 1.6% adhesive 1.3% adhesive 1.1% cohesive (no failure) 1.0% cohesive (no failure) 0.9% cohesive (no failure)

0.005 0.004 0.003 0.002 0.001 0.000 F /A0 MPa]

1200 800

400 0

d [µm]

Figure 8.2.: Comparison of the stress-displacement curves for different materials between 0.9% and 3.0% of curing agent. Right side: zoom.

corresponds to a very pronounced formation and stretching of fibrils, as observed visually. The fibrils were very likely to break up in the middle as the force was almost zero when we had to stop the test.

Increasing the crosslinker amount, herer=0.13, had an obvious influence on the stress-strain curve [figure 8.1(d)]. It still exhibited a strong force plateau, but the force dropped to zero at much smaller strains, and the debonding was complete at a smaller ²_max ≈ 6. The force plateau was again linked to the formation and stretching of fibrils. In contrast to r = 0.11, where the fibrils were breaking up in the middle, they eventually detached from the steel probe without leaving residues.

Such a cohesive to adhesive failure transition while forming fibrils is typical of lightly crosslinked networks and cannot occur for polymer melts since it requires strain hardening in the fibrils [66,50].

At r≈1.6 [figure8.1(e)], the stress-strain curves again changed their shape. We did not observe a plateau, but a continuous decrease in the force. The maximum deformation was smaller than 100%, indicating an interfacial process. Visual ob- servation showed that the material detached from the steel surface deforming the bulk only very weakly. The adhesion energy became very low. We did not observe any fibrils, the detachment was quite fast and without leaving traces on the probe.

The more curing agent was added, the smaller the maximum strain became. Fig- ure8.1(f) shows a typical curve forr=0.3. These last two stress-strain curves are typical of what has been observed for weakly adhering systems [69,58].

Figure8.2shows the stress-displacement curves and a zoom on the plateau region on one graph for all materials. The differences in in the force plateau and in the absolute values of maximum stress and maximum displacement are distinct.

Combining the shape of the stress-strain curves and visual observation of the debonding process, it was possible to discriminate three different types of debonding mechanisms. First, the debonding can becohesive, involving the formation of fibrils that eventually break up in the middle. In this situation, residues of the polymeric