Contact mechanics and measurement of surface energies

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CHAPTER 2 Experimental Study


In the attempt to develop a method that can be used to measure surface and interfacial energies of solids for a broader range of material types, the use of a flexible structure has been proposed. An elastica loop was chosen for use in this research. In the apparatus, the elastica loop is directly attached to the shaft of a stepper motor that is controlled by a computer. When the elastica loop is brought into contact with a flat substrate, the interfacial attractive force produces a measurable change in contact area. The contact pattern is observed in the monitor through a Nikon macro lens with a magnification factor of 50x, and the contact length is measured. At the same time, the force F between the loop and flat substrate is also measured using an analytical balance.
Distinct contact patterns of the elastica loop made of poly(dimethylsiloxane) [PDMS] in contact with a variety of substrates are observed, and the effect of anticlastic bending is eliminated in the center of the contact area due to the flattening of the loop. As compared to the classical JKR tests, the force applied is smaller, the contact length is larger, and the displacement of the loop applied is also larger. Large contact hysteresis with a tail due to interfacial interactions has also been observed in the tests.

Construction of elastica loop

To directly measure surface and interfacial energies of solids for a broader range of materials compared to the JKR technique, an elastica loop probe with characteristics of a compliant structure is prepared using the material of interest. To achieve the desired structural compliance, the elastica strip is prepared to be thin, uniform, smooth, and flexible in bending. During the test, the elastica loop is brought into contact with a rigid, flat surface made of, or coated with another material of interest, and the compliant structure permits measurable deformation due to small interfacial attractions. Through the analysis of the deformation, the interfacial energy between the two materials can be obtained. The analytical solution for an elastica in contact with a flat surface is given in Dalrymple’s thesis [46].
The dimensions of the elastica and the forces acting on the system are defined as follows. The total length of the elastica strip is 2L, the width of the strip is W, the thickness is t, the bending stiffness is EI, and the distance between the two ends of the strip is 2C. The ends of the elastica are first lifted, bent, and then clamped vertically at an equal height with a specified distance apart. When the bent elastica strip is brought into contact with a flat substrate, the contact length is a result of the applied load and the interfacial attractive force. The total the contact length is defined as 2B, and the resulting reaction force is indicated as F in Figure 2.1

Sample preparation and material property characterization

Sample preparation

In this study, the major material used for the elastica loop is SYLGARD 184 silicone elastomer (PDMS) provided by the Dow Corning Company because this material is very stable over a wide temperature range (-50°C to 200°C), and has a very low water absorption and very good radiation resistance. The choice of an elastomeric material for the elastica loop allows comparison of the results with findings obtained using the JKR method. This comparison is a necessary step to verify the methodology. The SYLGARD 184 silicone elastomer contains a silicone base and curing agents and is supplied in a two-part kit comprised of liquid components. The base and the curing agent were mixed in a ratio of 10 parts base to 1 part curing agent by weight with gentle stirring for about 10 minutes to minimize the amount of air introduced. The mixture then rested in air for 30 minutes to remove the air bubbles before use. The PDMS liquid mixture was then poured on a glass plate cleaned with acetone, and a doctor’s blade was used to spread the liquid and to control the thickness of the film to be 1.0 mm. SYLGARD 184 silicone elastomer offers a flexible cure temperature from 25°C to 150°C for various amounts of time, and requires no post-cure. In this study, after the PDMS liquid mixture was spread on the glass surface, the plate was then placed in a programmable oven. The curing process started from room temperature and the temperature was increased at a rate of 5°C/min until 100°C, where the temperature was maintained for 1 hour. Then the temperature was decreased to room temperature at a rate of 5°C/min. After curing, the film was peeled off from the glass plate. The product was a homogeneous, transparent, and flexible film with a final thickness about 0.2 mm, which varied slightly from batch to batch. Specimens were then cut from the film with appropriate dimensions for various mechanical tests.
Various substrates were selected to perform the measurement of surface energies. They were glass plates coated with PDMS, acetone-washed glass plates, polycarbonate [PC] plates, and a commercial cellulose acetate substrate (3M ScotchTM Transparent Tape 600). The preparation of the substrates was relatively straightforward and after preparation, all the substrates, as well as the elastomer films, were stored in a desiccator at room temperature with relative humidity controlled at 30%RH.

Tensile tests

The Young’s modulus of the elastica loop is directly related to the compliance of the loop and therefore is a very important factor in the analysis. The Young’s modulus of the elastomer was determined via tensile tests conducted as part of this study using an Instron 4505 universal testing frame. The tests were performed at room temperature under a constant crosshead rate of 5 mm/min using a pair of pneumatic grips to clamp the sample. Because the films are very thin (about 0.25 mm) and the modulus of the material is relatively low, attachment of an extensometer to the film would significantly affect the results of the measurement. To resolve this problem, the sample geometry was chosen to be a rectangular strip instead of the regular dog-bone shape, and the strain was calculated based on the ratio of the crosshead displacement to the sample’s original length between grips. To reduce end effects, the ratio of the length to the width of the samples was controlled to be greater than 10.
A typical stress-strain curve in the test from a particular batch of the PDMS material is shown in Figure 2.2. The Young’s modulus was obtained using a data fit algorithm of the linear portion of the curve. Figure 2.3, Figure 2.4, and Figure 2.5 show the modulus data for specimens from different batches. These figures indicate that the stress-strain curves are very repeatable within a given batch but differ slightly from one batch to another. Table 2.1 summarizes all the modulus data for all the different batches of the material tested. One possible reason for variations of the modulus among different batches is the lack of precise control of the ratio between the base material and the curing agent. As indicated by the data sheet provided by the Dow Corning Company, the content of the curing agent will have some effect on cure time and the physical properties of the final cured elastomer. Lowering the curing agent concentration will result in a softer and weaker elastomer; increasing the concentration of the curing agent too much will result in over-hardening of the cured elastomer and will tend to degrade the physical and thermal properties

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Orientation of the elastica loop

A narrow strip was first cut from the cured PDMS film prepared earlier. The ends of the strips were lifted, bent, and fixed vertically with a known separation distance. The specimen was then attached to a sample holder as shown in Figure 2.6. The angles of the PDMS strip at the fixed ends were 90°. The height of the loop, h, depended on the total length of the loop, 2L, and the distance between the clamped ends of the loop, 2C.


There are four major components in the experimental apparatus as indicated in Figure 2.7: 1) the displacement control device; 2) the force measurement device; 3) the optical system; and 4) the computer control and data acquisition system (not shown in the figure). The elastica loop is directly attached to the shaft of the stepper motor, which is a major part of the displacement device and is controlled by a computer. When the elastica loop is brought into contact with a flat substrate by the displacement device, the interfacial attractive force produces a measurable change in contact area. The contact zones are observed in the monitor through a Nikon macro lens using a magnification factor of 50x, and the contact length, 2B, can be measured directly from the monitor provided a careful calibration is performed before the test. At the same time, the contact force F between the loop and the flat substrate can be measured using an analytical balance mounted on the force measurement device. The whole contact sequence and data acquisition were controlled by the computer control and data acquisition system. In the following sections, detailed descriptions for each component of the apparatus are given.

Displacement control device

Based on the dimensions of the specimen and the deformation level of the loop induced by the interfacial interactions, a low speed, low vibration, and high-resolution displacement control system is required for the study. From a broad search of various positioning products, the IW-710 INCHWORM motor from Burleigh Instruments, Inc. was chosen as the major component for the high-resolution positioning system. This IW-710 INCHWORM motor uses compact piezoelectric ceramic actuators to achieve nanometer-scale positioning steps over several millimeters. This motor offers a range of motion for 6 mm and is featured with a mechanical resolution of approximately 4 nm over the entire range of motion with a maximum speed specified as 1.5 mm/sec. In addition, this motor has a very high lateral stability with a lateral shaft runout of ±0.2mm.
This instrument also provides a non-rotating shaft and forward and reverse limit switches, providing a convenient way to control the contact procedure. The motor can sustain a light load (less than 1000 grams), and consequently, the elastica loop was directly attached to the shaft in the tests. The position of the elastica loop is read through an integral encoder associated with the IW-710 motor. The resolution of the encoder is 0.5 mm with an accuracy up to ±1 mm. The motor and the encoder are controlled by the Burleigh 6200ULN closed-loop controller, which can be operated in either manual or computer control mode. In manual mode, the motor speed and the stop and start functions are all operated through the controller. In addition, the controller can actuate a moving procedure consisting of a series of predetermined increments with the size being as small as the resolution of the encoder. If the controller is operating under the computer control mode, the motor is controlled by the controller through the 671 interface with the computer in a bi-directional communication mode. The bi-directional interface has the following functions, which can be combined arbitrarily to perform a task: 1) load an absolute target displacement value; 2) load a step size; 3) set motor speed; 4) read current motor position; 5) read the current status of the motor and controller; 6) control position maintenance (On/Off); 7) perform motor stall test; 8) set zero reference and clear counter.
As the major component of the displacement device, the IW-710 motor is positioned in the apparatus as shown in Figure 2.8. The outer cylinder made of polycarbonate [PC] rests on the base of the analytical balance and is used to support the motor and reduce air circulation around the elastica loop. The inner PC cylinder has no connection with the motor and rests on the scale pan of the balance. The substrate is placed on the top of the inner cylinder with the surface of interest facing down. When the motor is controlled to move through the contact sequence, the elastica loop attached to the shaft is brought into contact with the substrate and then withdraws to separate the contact. The contact force is measured through the force measurement system, and simultaneously, the contact length is measured through the optical system.

Force measurement device

The attractive force between two solid bodies in this study is several milligrams, which requires a high-resolution force measurement device. To satisfy this requirement, an SA 210 analytical balance from Scientech, Inc. was chosen. This balance is equipped with a high standard of accuracy and has a resolution of 0.1 mg over the entire weight range of 210 grams. The balance is also equipped with a very reliable electronic filtering system, which helps to stabilize the weight reading when mechanical damping of the balance is insufficient. As a result, the display of the balance is prompt, clear, and reliable. In addition, the stability indicator in the balance will also show an “OK” sign when the reading is valid insuring reliable results. In the setup for this study, the analytical balance is placed on a vibration reduction table along with the optical system, and is connected to the computer through an RS-232 interface for the purpose of data acquisition

CHAPTER 1 Introduction 
1.1 Adhesion and role of the interface
1.2 Contact mechanics and measurement of surface energies
1.3 Outline of the study
CHAPTER 2 Experimental Study
2.1 Abstract
2.2 Construction of elastica loop
2.3 Sample preparation and material property characterization
2.4 Apparatus
2.5 Measurement using the JKR method
2.6 Measurement using elastica loop
CHAPTER 3 Numerical Analysis
3.1 Abstract.
3.2 Meshes and boundary conditions
3.3 Simulation of the loop formation
3.4 Contact simulation
CHAPTER 4 Comparison of Experimental, Numerical, and Analytical Results.
4.1 Analytical solution
4.2 Comparison of numerical and analytical results.
4.3 Comparison of experimental and analytical results
4.4 Sensitivity studies of errors
4.5 PDMS loop in contact with various substrates
CHAPTER 5 Conclusions and Recommendations for Future Work
5.1 Summary and conclusions
5.2 Limitations
5.3 Future work

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