Evaluation of energy dissipation involving adhesion hysteresis in spherical contact between a glass lens and a PDMS block
© The Author(s) 2017
Received: 12 October 2016
Accepted: 24 January 2017
Published: 3 February 2017
Adhesion hysteresis was investigated with the energy dissipation in the contact experiments between a spherical glass lens and a polydimethylsiloxane (PDMS) block. The experiments were conducted under step-by-step loading–unloading for the spontaneous energy dissipation. The force, contact radius, and displacement were measured simultaneously and the elasticity of the PDMS was confirmed. The work of adhesion was estimated in the loading process of the strain energy release rate. The total energy dissipation has been observed to be linearly proportional to the contact radius in the unloading process. The approximately constant gradient of the energy dissipation for each unloading process has been found. The result would provide how the dissipation is induced during the unloading as some interfacial phenomena. The fact has been discussed with some interfacial phenomena, e.g., the adsorbates on the surface, for the mechanism of adhesion hysteresis.
KeywordsAdhesion by physical adsorption Adhesion hysteresis Energy dissipation
Adhesion phenomena in contact problems using elastomers and soft materials play a significant role in design of devices, e.g., microfabricated adhesives [1–3] and wall-climbing robots [4, 5]. Theory of adhesive elastic contact [6–8] considering both of the elastic deformation and adhesion phenomenon in contact interface between elastic bodies is helpful for its applications. Since the adhesive elastic contact theory assumes the total energy equilibrium, contact process in the theory (i.e., consists of loading–unloading or advancing-receding contact) is reversible except for its mechanical hysteresis . However, it has been reported that adhesion hysteresis exists in some contact experiments [10–21]. This adhesion hysteresis shows a completely different force curve (force–displacement or force-contact area) between loading–unloading or advancing-receding in actual contact process. Adhesion hysteresis means that the actual contact process is not in equilibrium as assumed in the theory and also means that the total energy in the contact system is dissipated during the process. Therefore, investigating the energy dissipation is significant for understanding the mechanism and complementing the conventional theory.
The energy dissipation in the adhesive contact is mainly investigated and discussed using the strain energy release rate G (i.e., the energy required to separate unit contact area J/m2) [9–18]. Maugis and Barquins  first introduced a concept of linear elastic fracture mechanics into the Johnson–Kendall–Roberts (JKR) contact . They experimentally showed that G has a dependency on the crack speed , which is the so-called empirical relationship [11–14]. However, the relationship does not represent how the total energy dissipation changes during the contact process, and the mechanism of adhesion hysteresis is still on discussion assuming capillary condensation or adsorbed layer, etc. [17–19, 22–25]. In this paper, a polydimethylsiloxane (PDMS) block is used as the elastic materials, the contact processes between the PDMS and a glass lens have been investigated to evaluate the energy dissipation. Especially, the change in the energy dissipation during the processes is discussed using the elastic contact theory, assuming non-equilibrium.
Contact mechanics for evaluating energy dissipation
Although the adhesion hysteresis is observed in the measurements (F, Z, a), the measurements must satisfy Eq. (5) if a material behaves as an elastic material in the contact experiments. Therefore, Eq. (5) can be used to confirm the elasticity of the material when k, R are given and F, Z, a are measured in the experiments.
Spherical contact measurement system
The PDMS mixture for the PDMS block was made with a mixing ratio of 10:1 of the base polymer and curing agent for fully cross-linked rubber. The air bubbles in the mixture were removed through degassing in a desiccator under a vacuum of 2 kPa for 1 h. The degassed mixture was poured carefully into a mold (60 × 60 × 20 mm) that had a clean glass bottom for making the PDMS block surface smooth and flat. After the mold was filled with the mixture to about 10 mm high, the air bubbles were removed again for 10 min in the desiccator. The filled mold was cured in an oven at 60 °C for 12 h, and then the PDMS block was removed from the mold. The exposed side of the PDMS block in the heat curing was carefully glued to a glass slide (100 × 100 mm) with the same PDMS mixture. The sample was cured again in the oven at 60 °C for 12 h, and the PDMS block was permanently set on the glass slide. The glass lens and PDMS block were cleaned using an ultrasonic cleaner with ethanol and dried using a nitrogen spray gun. After 24 h from the setting of samples to the measurement system in a clean bench on a vibration isolation table, the experiment was conducted at the ambient conditions of 20 °C with 50% humidity.
The gross displacement Z was manipulated in step-by-step movements with a constant dwell time in every step for evaluating the spontaneous energy dissipation at a fixed Z. The amount of movement between steps was set at 1 μm (the speed of the motorized stage was set at 1 μm/s). The dwell time for every step was set at 15 s. The loading process was performed up to the maximum loading displacement (−Z max). After the loading process completed, the unloading process was performed until the lens detached. A dependence of the maximum loading displacement on the adhesion hysteresis has been reported [16, 20]. Hence, three different maximum loading displacement were chosen: −Z max = 10, 20, 30 μm, which is sufficiently smaller than the thickness of the PDMS block 10 mm.
Results and discussions
Experimental results and adhesion hysteresis
At each fixed Z (15 s dwell time) the changing of F and a is observed in Fig. 4, and the changing in entire process is fitted well with the calculated force F(Z, a) by Eq. (5) with the constant elastic modulus E *. This result suggests that the PDMS block behaves as an elastic material in the contact process. Also, adhesion hysteresis between the loading–unloading paths represents that the total energy is not in equilibrium state. Therefore, it can be considered that the energy dissipation is induced in the contact interface, not in the PDMS block, from a spontaneous process of the total energy toward an equilibrium at each fixed Z, i.e., the spontaneous energy dissipation.
Strain energy release rate and work of adhesion
Evaluation of energy dissipation
The energy dissipation is induced in the contact interface from a spontaneous process of the total energy toward an equilibrium at each fixed Z (15 s dwell time). And this relationship is also shown in Eq. (1) that ΔU total = − ΔU dissipation. Therefore, it can be considered that the total energy dissipation U dissipation calculated by Eq. (11) is a cumulative result of ΔU total at each fixed Z during 15 s in entire contact process.
The total energy dissipation and the gradient show that the contact process is not in equilibrium. Although the occurrence mechanism of the spontaneous energy dissipation is not clear, Fig. 5 shows that the total energy could not be fully stabilized state (G Z = Δγ) at a fixed Z within 15 s especially in the unloading, i.e., the amount of spontaneous energy dissipation ΔU dissipation at a fixed Z is limited within the dwell time. A not fully stabilized total energy affect a next step as a history by the step-by-step control of Z in every 15 s. In the larger maximum loading displacement −Z max, the more step is required to detach the lens from the PDMS, and it can be considered that the more history might be accumulated. Therefore, the larger value of gradient f is observed in the larger −Z max because of the accumulated history related to the amount of required step in the unloading process.
As expressed in Eq. (12), the gradient of total energy dissipation is calculated using G Z − Δγ (the dissipative term that the reversible term Δγ is excluded from the required energy to change unit contact area G Z ) and 2πa (the entire length of the crack tip). The dimension of the gradient f is J/m, and is also expressed as the dimension of the force N. In this paper, therefore, we define f as a dissipative force which is applied to 2πa during the receding contact. From this, it can be considered that the dissipative force would be induced by an unknown factor existed at the crack tip 2πa. An unknown factor might be an adsorbate on the surface gathered by −Z max, such as gases, liquids, uncross-linked PDMS fragments or etc. Although the mechanism is not clear, the approximately constant f and the dependency on −Z max observed in Fig. 7 suggests a hint how an unknown factor works at the crack tip 2πa.
The energy dissipation is evaluated in the contact process between the glass lens and the PDMS block. The experiments with the three maximum loading displacement −Z max were conducted. The results (Fig. 4) shows that the adhesion hysteresis would be occurred even using the elastic material (PDMS block). This suggests that the mechanism would be induced by some interfacial phenomena. Furthermore, it is found that the approximately constant gradient f (Fig. 7) of the total energy dissipation (Fig. 6) which has a dependency on −Z max. This fact would suggest that the dissipative force f (the gradient) is possibly induced by an unknown factor existed at the crack tip 2πa gathered by −Z max, e.g., an adsorbate on the material surface.
- G, G Z :
strain energy release rate
- Δγ :
work of adhesion
- U :
- F :
- δ :
- a :
- Z :
- R :
effective radius of curvature
- R 1, R 2 :
radius of curvature
- E :
- ν :
- E * :
- k :
- −Z max :
maximum loading displacement
- f :
gradient of total energy dissipation (or dissipative force)
DB and KT designed the research. DB performed the experiments and analysis. All authors contributed to the results and discussions. PH, SS and KT supported for DB to write the manuscript. All authors read and approved the final manuscript.
The authors declare that they have no competing interests.
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