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«UNIVERSITY OF CALIFORNIA Santa Barbara Design and Characterization of Fibrillar Adhesives A Dissertation submitted in partial satisfaction of the ...»

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Chapter 6 Fiber Articulation Chapters 3, 4, and 5 all used fiber geometry to enhance adhesive performance.

Chapter 6, instead, investigates the effect of testing procedure on adhesive performance. The fibers used were similar to the vertical semicircular fibers presented in Chapter 4, but they were slightly shorter and composed of PDMS using a different ratio curing agent to base elastomer. Testing procedures commonly use a vertical approach and retraction where the two surfaces are brought together perpendicular to their testing surfaces. This procedure has not been shown to be ideal for all gecko-inspired adhesives and was compared with non perpendicular approach and retractions. The testing procedures used different approach angles, shear lengths, and retraction angles to find the influence of movement, or articulation, on important adhesive properties of vertical semicircular fibers.

Chapter 6. Fiber Articulation

6.1 Introduction Tests on the gecko’s adhesive fibers have revealed the importance of articulation, how the structures are manipulated or moved during adhesive testing or placement, in achieving many of their desirable properties. It was discovered that setae that are first exposed to a compressive force and then pulled parallel to the surface have been shown to develop at least ten times the adhesion force after shearing, shear adhesion force, than those exposed to a compressive force without parallel movement, pure adhesion force [10]. Shear forces, like adhesion forces, also required a parallel movement in order to generate maximum shear values [10]. The shear and adhesion forces have been shown to behave differently in experiments where setal arrays are articulated along and against the direction of tilt [7, 120], with theoretical approaches offering further evidence of the importance of articulation [121, 111]. Single setae are able to adhere with a force of 20–40 µN using only a 2.5 µN preload, causing the ratio of adhesion force to preload force, µ′, to fall between 8–16 [12, 10].

A variety of different approaches have been undertaken in order to mimic the main functions of the adhesive found on the gecko [8]. The sizes of individual synthetic fibers can range from tens of nanometers to roughly a millimeter with a variety of processes being utilized. Attempted processes for creating smaller Chapter 6. Fiber Articulation structures have included etching of polymer materials [81], molding nanostructured templates [70], drawing of polymer fibers [49], electron beam lithography [30], and carbon nanotube growth [122]. Larger scale methods typically have used molding techniques to create vertical and angled fibers. The molds have been created in silicon using an angled etch for tilted structures [47], in silicon-on-insulator using the notching effect for mushroom-tipped structures [54], in PMGI using angled lithography for angled fibers [117], in SU-8 using dual angle lithography for wedge structures [83] and other more complicated fabrication approaches [78, 63].

Work aimed at creating adhesives, such as those above, has received the majority of the workload while the manner in which the adhesives are tested has received far less.

Both vertical and angled synthetic adhesives have been characterized using a vertical load-drag-pull test (vLDP) test (Section 3.2.3). For vertical [54, 37] or angled [77] fibers where contact is desired on the horizontal top face or there is no benefit to in-plane shearing, referred to here as top contact fibers, a vertical load-pull test achieves the desired contact. In-plane movement during testing is only implemented to find maximum shear forces that the adhesive can sustain since excessive in-plane movement has been shown to cause undesired side contact and lower the adhesion and shear force values [114, 53]. Low preload forces, and consequently high µ′ values, are typical of top contact structures since very little Chapter 6. Fiber Articulation force is needed to make sufficient contact across the top testing surface. For both vertical [109, 66, 88] and angled [98, 65, 19] fibers where contact is desired on the vertical or angled side or the adhesive benefits from in-plane shearing, referred to here as side contact fibers, the use of in-plane movement has allowed access to larger preferential areas of the fibers. Before shearing is possible, a preload force or distance must be applied. Since larger preloads are required to compress the side contact fibers a greater amount, the preloads for maximum contact areas can be significant and risk low µ′ values. The preload forces per fiber during vertical loading for angled side contact fibers should be lower than those needed for vertical side contact fibers due to the replacement of only compression with compression and bending of the fibers, but the forces on even angled side contact fibers are usually more than those needed for top contact fibers.

Angled approach and/or angled retraction tests, here referred to as angled load-drag-pull tests (aLDP) even though all testing stages may not be angled or in-plane shearing may not occur, targeting articulation have been performed.

Drag speeds over various shear lengths [35], patch areas [83], He++ ion irradiation doses [26], approach depths/preload forces [83, 98, 26] and retraction angles [83, 98, 26, 107, 55] have been systematically varied to characterize the adhesive, but no information regarding the performance of different approach angles was presented and the parameters used could be suboptimal. Tests using angled approach and/or Chapter 6. Fiber Articulation retractions have not been performed on top contact structures since the in-plane motion, as stated earlier, risks misorientation of the contact surface. Surprisingly, no characterization of vertical fiber adhesives using approach angle variation have been presented up to this point. Therefore, the result shown in this chapter are the first application of multiple angle testing to vertical structures as well as the first systematic variation of approach angle to be reported. A schematic of the testing procedure, with definitions for approach angle, θapp, approach depth, zapproach, and retraction angle, θret, shown in Figure 6.1.





Low preload forces during foot placement reduce the reaction forces from the substrate that a robot would have to counter, and therefore increase a robot’s stability. When adhesives are used with a climbing robot with g feet being placed at once during the fiber loading and f feet fully attached during the fiber loading, the minimum µ′ value of the adhesive to ensure that that the robot has the ability to remain adhered to the wall is given by Equation 6.1.

–  –  –

While a µ′min value for a four-legged robot could be as low as 0.33 with only one foot being placed at a time, the value for a robot mimicking the gecko’s foot placement pattern when climbing vertically would need to be at least 1 [9]. Many synthetic adhesives fall short of µ′ being greater than 1. To be able to achieve Chapter 6. Fiber Articulation Figure 6.

1: The angled load-drag-pull test used for the results presented here follows the described testing protocol shown. A load, generated using a perpendicular approach, first establishes contact between adhesive and glass puck testing surface. The adhesive is then articulated using different approach angles, shear lengths, and retraction angles. For the vertical load-drag-pull tests, the approach angle and retraction angle are both perpendicular (θapp = θret = 90◦ ). Positive directions, approach and retraction angles, and the zapproach depth are all defined in the manner indicated in the drawing. The glass puck is stationary and the adhesive is articulated during testing to match the way the adhesive would be engaged when integrated with a climbing robot.

Chapter 6. Fiber Articulation higher µ′ values when adhesion forces have reached their maximum value, the preload force must be lowered.

Angled side contact fibers should achieve higher µ′ values than similar vertical fibers during vertical testing because the increased compliance of the tilted fibers lowers the applied preload force for a given contact requirement. As an alternative to using tilted fibers, which can be more difficult to reliably fabricate, ABAQUS simulations on vertical fibers, similar to those fabricated and shown in Figure 6.2, were used to determine the reduction in preload forces when using different approach angles.

Using the modified Riks method solver in ABAQUS, the free tip of a single fiber, modeled as a two-dimensional wire with defined cross-sectional properties and Young’s modulus to match the fabricated fibers, was displaced at different angles to simulate fiber articulation during approach. Tensile forces could form as in the experiments, and the maximum vertical compressive force supported by the fiber during approach was multiplied by the number of fibers in the testing area to compare with the experimental results. For approach angles parallel to the fiber’s axis, a linear perturbation buckling simulation was performed to find the critical buckling load. The results, shown in Figure 6.3, show that approach angles can have a significant effect on the preload forces and the forces predicted by the simulation are in good agreement with the experimental results.

Chapter 6. Fiber Articulation Figure 6.

2: Scanning electron microscope (SEM) image of vertical half-cylinder PDMS micro-fibers of 15.0 µm height and 10.0 µm diameter which were used for the experimental results and as a model for the simulations. The cross-sectional shape is shown in white outline on the fiber below the X-, Y-, and Z-axes. The ±Xdirections are parallel to the straight long edge of the semicircular fibers; movement of the sample in the +Y-direction engages the flat face of the fibers; movement of the sample in the the −Y-direction engages the curved face of the fibers; +Z is the (vertical) loading direction, and −Z is the (vertical) unloading direction.

Articulation of the adhesive system to engage and release occurs in the Y-Z plane.

Chapter 6. Fiber Articulation For vertical fibers, a 90◦ approach resulted in the maximum reaction force across all approach angles, yet testing commonly uses this approach angle.

Approach angles less than 10◦ or greater than 170◦ resulted in the least amount of vertical compressive force during approach. The lower preload forces are a result of bending the fiber as opposed to the compression that occurs at or near perpendicular approaches. Differences between the experiments and simulations at angles close to 90◦ are likely from the inability to include a flat top surface on the top of the fiber in the simulations. The flat top surface would reduce the rotation of the top of the fiber and therefore increase the forces that the fiber could sustain before buckling. Differences between the simulations and experiments could also arise due to the glass puck (root mean square (RMS) roughness ≈ 70 nm), with peaks and valleys of roughness, that could unevenly load the fibers across the testing area.

Additional simulations were performed on 70◦ tilted fibers with the same geometry to distinguish any advantages of the tilt during loading. The cross-sectional properties and length remained the same, but the angle that the fibers made with respect to the +Z-axis was changed from 0 to 20◦. For approach angles between 0 and 180◦, the maximum and minimum vertical compressive forces for the 70◦ fibers, also shown in Figure 6.3, do not differ significantly from that of the vertical fibers. When approaching in the same direction as the angle of tilt, the Chapter 6. Fiber Articulation Figure 6.

3: The experimental and simulation values for the maximum vertical compressive reaction force supported during approach by the vertical and angled (20◦ from vertical) fibers using different approach angles. For vertical fibers, small (θapp ≤ 10◦ ) or large (θapp ≥ 170◦ ) approach angles significantly reduced the preload forces when compared to those using a vertical approach (θapp = 90◦ ). The experimental and simulation values are in good agreement across all approach angles for the vertical fibers. The range of force values for the angled and vertical fibers are similar, but for the angled fibers, a greater number of approach angles lead to low preload forces (0 ≤ θapp ≤ 30) and there is no longer symmetry about a vertical approach.

Chapter 6. Fiber Articulation vertical compressive reaction forces are less than the vertical fibers and the range of approach angles leading to small preload forces was wider.

However, when approaching against the angle of tilt, the reaction forces were higher for the tilted fibers. The simulations show that a vertical fiber can have preload forces that can be equal to those achieved using a tilted fiber during attachment provided that the correct approach angle is used.

It has been shown that an angled approach can greatly affect the preload forces during adhesive attachment. Side contact vertical fibers, which have been shown in the simulations to benefit from an angled approach, have yet to be characterized experimentally using an aLDP testing procedure. If adhesion and shear forces do not diminish with the new approach, the added benefits of articulation, including higher µ′ values for side contact fibers will be demonstrated. Unlike previous angled testing on fibers, the approach angle, shear length, and retraction angle, all of which describe the path taken during testing, have been systematically varied and the results, including the first reporting of the influence of approach angle, are presented in order to find an optimal articulation strategy.

Chapter 6. Fiber Articulation



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