Keywords

9.1 Introduction

Pressure-sensitive adhesives (PSAs) are used in a variety of applications where they can experience a range of strain rates from slow rates where they are expected to maintain a bond when subjected to a constant load to high strain rates common to the consumer electronic device, aerospace, and automotive industries where the PSA is required to withstand drop or impact events. Due to the viscoelastic mechanical behavior of PSAs, it is necessary to run tests at deformation rates which are relevant to the intended application. This often proves challenging for impact and drop-type loading as it is difficult to reach relevant strain rates using traditional load frames. Methods capable of measuring force and displacement during high-rate tensile and compression tests have been described previously [1,2,3]. These methods are often run using specialized instrumentation and can require relatively complicated data analysis.

In this work, test methods which isolate through-thickness tension and simple shear deformation and failure modes are presented. The tests methods are compatible with both instrumented drop towers for test speeds on the order of 1 m/s and standard screw-driven load frames for test speeds on the order of 10 mm/s or slower. In conjunction with rheological analysis, the time-temperature superposition principle is implemented to quantify failure properties of the adhesives at effective rates that could not be tested directly with either of the instruments described above. The viability of the time-temperature superposition method is investigated by comparing results from high-speed tests run on the drop tower and slow-speed tests run on the load frame shifted to effective rates based on the test temperature using the shift factors determined from the rheological analysis. The purpose of this work is to assess the viability of using time-temperature superposition to characterize PSA failure properties at rates that cannot be tested directly using standard test equipment by controlling the temperature at which the test is run.

9.2 Background

The viscoelastic mechanical properties of PSAs are well-known and commonly characterized using rheology techniques such as shear-mode dynamic mechanical analysis (DMA) master curves [4, 5] to quantify the rate dependency of these properties. The horizontal shift factors used to create the master curves can often be described by the Williams-Landel-Ferry (WLF) model [5] which has the following form:

$$ \log \left({a}_T\right)=\frac{-{C}_1\left(T-{T}_{\textrm{ref}}\right)}{C_2+\left(T-{T}_{\textrm{ref}}\right)} $$
(9.1)

where C 1 and C 2 are fitting constants, a T is the shift factor for temperature T, and T ref is the chosen reference temperature. This model assumes the material is linear viscoelastic and deformations are small.

Like the bulk mechanical properties, PSA failure is also a rate-dependent phenomenon [6]. Despite the PSA undergoing large deformations, Kaelble demonstrated that the WLF relationship from a shear rheology master curve could be used to create a master curve to describe the relationship between effective peel rate and steady-state peel force [7]. In addition, time-temperature superposition has been used several times to quantify rate-dependent failure properties of polymeric materials including PSAs and epoxies [6, 8,9,10,11,12].

For homogeneous, isotropic linear viscoelastic materials, energy dissipated during failure of a viscoelastic polymer is a combination of the surface energy required to create two new surfaces and the dissipation of elastic strain energy in the bulk due to viscoelasticity [13]. This concept is expressed using the functional form:

$$ W={W}_0\left(1+\varphi \left(v,T\right)\right) $$
(9.2)

where W is the total energy dissipated, W 0 is the critical energy required for the material to fail in the limiting case where the test speed is slow, and the test temperature is high, minimizing viscous effects. ϕ(v,T) is a dimensionless function of the testing rate and testing temperature representing viscous dissipation. For polymer systems that follow the time-temperature superposition principle, ϕ(v,T) = ϕ(a T*v), where aT is the shift factor used to scale the test rates run at a given temperature relative to effective test rates at the reference temperature T ref. A relationship between ϕ(a T*v) and loss tangent, also known as tan(δ), has been proposed previously based on strain energy release rate measurements using a probe tack test [14]. In addition, Xu and Dillard [15] described a relationship between tan(δ) and Mode I fracture toughness, indicating a correlation between energy dissipation due to bulk viscoelasticity and the apparent energy necessary to initiate fracture or failure in a viscoelastic polymer.

9.3 Experimental Setup

Experiments were completed for an acrylic foam tape with a nominal thickness of 1.1 mm. To complete this analysis, shear mode rheology, through-thickness tension, and double-overlap shear tests were completed. The experimental procedures for each of these tests are described below.

Shear Mode Rheology

A small strain shear-mode master curve was obtained as follows: an 8 mm diameter disk was punched from a 1.1 mm thick sheet of the adhesive. The liners were removed from the adhesive disk, and the disk was then loaded between 8 mm diameter parallel plates on an ARES-G2 strain-controlled rotational rheometer (TA Instruments, New Castle, DE, USA). Oscillatory shear frequency sweeps were conducted at temperatures from 150 °C to −80 °C in 5 °C increments. At each temperature step, the sample was subjected to oscillatory shear deformations with an initial strain amplitude of 5%, with frequencies ranging from 0.1 Hz to 50 Hz. Auto-strain was used to automatically adjust the strain amplitude downward to limit the torque on the rheometer to 20 g-cm. This ensured that the measurements were conducted in the linear viscoelastic range of the material, regardless of the current testing temperature. The resulting frequency sweeps were shifted onto a master curve using time-temperature superposition (TTS) with a reference temperature of 25 °C, optimizing for superposition of the shear storage modulus (G’). Prior to TTS, a baseline y-axis shift was applied to the dynamic modulus terms (shear storage modulus G’ and shear loss modulus G”), according to the following equation:

$$ {b}_T=\frac{T_{ref}}{T} $$
(9.3)

where b T is the vertical shift factor by which the dynamic moduli at temperature T (in Kelvin) were multiplied before shifting and T ref (in Kelvin) was the reference temperature of 298.15 K. This vertical shifting was performed to account for the entropic origin of polymer elasticity and hence improves the overall superposition of the dynamic moduli. Figure 9.1 shows the resulting master curves and the corresponding shift factors, a T. The WLF relationship (Eq. 9.1) was fit to the data where a T is the shift factor by which the frequencies (or rates) at temperature T are multiplied to create the master curve at the reference temperature, T ref, of 25 °C. The fit parameters were C 1 = 9.27 and C 2 = 170.2 K. As shown in Fig. 9.1b, the WLF relationship fits the data well for all temperatures tested.

Fig. 9.1
figure 1

(a) Storage modulus, G′; loss modulus, G″; and loss tangent, tan(δ); as a function of effective angular frequency and (b) associated shift factors as a function of relative temperature along with the fitted WLF model (solid line)

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Through-Thickness Tension

Tensile impact specimens were made by creating a construction of two stainless steel plates bonded with a layer of the acrylic foam tape. The test specimen geometry is shown in Fig. 9.2. Before applying the adhesive, the faces of the blocks were cleaned with isopropyl alcohol. After the alcohol evaporated, 3M Primer 94 (3M Company, St Paul, MN, USA) was applied. After the primer dried, the specimens were assembled. The assembled specimens were individually compressed for 30 s with a 4 kg weight. The specimens were then conditioned at 80 °C for 30 min. Following the heat treatment, the specimens were conditioned at 23 °C 50% RH for 48 h.

Fig. 9.2
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Geometry of the two substrate pieces used to make the through-thickness tension specimen. When assembled, the striker passes through the frame substrate and strikes the puck substrate. The bonded area is 225 mm2

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Drop Tower Test Method

Tensile impact tests were run using an Instron CEAST 3490 drop tower with crosshead 7510.021 and striker 7519.696 (Instron Corporation, Norwood, MA, USA). A 22 mm diameter, 5 mm thick striker tip was used. Specimens were constrained with a pneumatic clamp. Force and acceleration were measured with a +/− 22 kN piezoelectric load cell. The striker mass was 13 kg. Tests were run at temperatures between −30 °C and 100 °C. A drop height of 100 mm was used for all tests, corresponding to an impact velocity of approximately 1.4 m/s. Five replicates were run for each temperature and rate permutation.

Quasi-Static Test Method

Specimens for quasi-static tensile tests were made using the method described above. The fixture used to mount the specimens in the drop tower was adapted for an electromechanical load frame. Tests were completed on a Criterion Model 43 (MTS Corporation, Eden Prairie, MN, USA) with a +/− 10 kN load cell. A 19 mm diameter aluminum cylindrical flat punch served as the striker. Tests were run at rates between 0.1 mm/s and 8 mm/s and temperatures between −100 °C and 100 °C. Five replicates were run for each temperature and rate permutation.

Double-Overlap Shear

Shear impact specimens were made of three stainless steel blocks bonded with two pieces of the adhesive (Fig. 9.3). Similarly, quasi-static specimens were made by bonding two stainless steel posts with a single layer of adhesive. The 10 mm × 10 mm block faces were bonded with 10 mm × 10 mm of adhesive. Before applying the adhesive, the faces of the blocks were cleaned with methyl ethyl ketone and primed using 3M Primer 94. The assembled specimens were individually compressed for 30 s with a 4 kg weight. The specimens were then conditioned at 80 °C for 30 min. Following the heat treatment, the specimens were conditioned at 23 °C and 50% RH for 48 h.

Fig. 9.3
figure 3

Schematic of the double-overlap shear specimen used for the drop tower tests

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Drop Tower Test Method

Shear impact tests were run on using the setup and test parameters described above for through thickness tension with the exception that a 15 mm × 15 mm × 5 mm stainless steel striker tip was used.

Quasi-Static Test Method

Shear tests were run on a Criterion Model 43 universal test frame (MTS Corporation, Eden Prairie, MN, USA) using an MTS Acumen double-lap shear test fixture that was adapted for use in the Criterion load frame. Force was measured using a +/− 10 kN load cell. Tests were run at 1 mm/s, and test temperatures were between −80 °C and 100 °C. Five replicates were run for each temperature.

9.4 Results

Peak stress, peak energy density, total energy density, and critical strain were calculated for all tests. Peak stress is the maximum nominal stress. Critical strain is the engineering strain at which peak stress occurred. Peak energy density is the integral of force with respect to displacement normalized for adhesive volume from initial contact between the striker and specimen up to the displacement at which maximum force was achieved. Total energy density is the integral of force with respect to displacement normalized for adhesive volume from the point of initial contact until the end of the test. Following Kaelble’s approach [7], the strain rates at which the tests were run were shifted according to the WLF relationship for acrylic foam tape (Fig. 9.1b). Peak stress, peak energy density, total energy density, and critical strain were also corrected using the vertical shift factor (Eq. 9.3). The resulting master curves are shown for though-thickness tension and double-overlap shear in Figs. 9.4 and 9.5, respectively. For through-thickness tension, the master curves generated using the drop tower and quasi-static test method agree for the four metrics considered, indicating that time-temperature superposition is applicable. For double-overlap shear, peak stress and total energy density master curves agreed for the two approaches, but critical strain and peak energy density differed. The apparent shift between the drop tower and quasi-static data for critical strain may be due to differences in determining the initial contact for the drop tower and quasi-static test methods due to modifying the fixturing between the two instruments. The calculation for peak energy density is based on the critical strain value determined for each test. Therefore, discrepancies in critical strain between the two test methods are likely propagating through the analysis as discrepancies in peak energy density.

Fig. 9.4
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(a) Peak stress, (b) peak energy density, (c) total energy density, and (d) critical strain as a function of effective strain rate for through-thickness tension tests run on a drop tower and a load frame

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Fig. 9.5
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(a) Peak stress, (b) peak energy density, (c) total energy density, and (d) critical strain as a function of effective strain rate for overlap shear tests run on a drop tower and a load frame

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9.5 Discussion

Despite the tests described above being run at rates differing by approximately three orders of magnitude, the time-temperature superposition principle appears to be a valid tool for understanding the rate-dependent failure properties of the acrylic foam tape. While both instruments are capable of creating master curves, there are several aspects of the quasi-static test methods that are advantageous to the drop tower method. From a practical standpoint, load frames are more commonly available than drop towers, making the test method accessible without the need to purchase specialized high speed test equipment. In addition, master curves created using the quasi-static method covered a greater range of effective rates (Figs. 9.4 and 9.5). The drop tower tests were run from −30 °C to 100 °C due to the limits of the instrument’s environmental chamber. In contrast, the chamber used for the quasi-static tests can reach −115 °C. For the acrylic foam tape considered in this work, this is sufficiently cold to compensate for the slower test speeds, extending the range of the master curve beyond the limits of the drop tower method.

The quasi-static test method also offers the potential for improved force resolution. High-frequency oscillations were often observed in the measured force from the drop tower tests. An example of this behavior is shown in Fig. 9.6a for a test run at 1.4 m/s at a temperature of 60 °C. The force oscillations are believed to be related to the system dynamics of the instrument that are being excited at the point of impact and are forces that are not necessarily experienced by the adhesive. For comparison, the force response from a quasi-static test run at 1 mm/s and 0 °C is also shown in Fig. 9.6a. Using WLF shift factors to normalize time to T ref = 25 °C, these tests are expected to be similar, although not quite identical. The effective strain rate for the quasi-static tests was slightly faster than that of the drop tower tests, resulting in the test occurring over a shorter period as show in Fig. 9.6a. However, the shapes of the curves are roughly the same, and because the quasi-static test was run at a slow speed, the effects of system dynamics observed in the drop tower are not observed in the test data. This simplifies data post-processing and provides a clearer picture of the forces experienced by the adhesive.

Fig. 9.6
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(a) Comparison of drop tower and quasi-static tests run at an effective strain rate of approximately 20 1/s. (b) Comparison of quasi-static tests run at different temperatures showing the transition of the displacement at which peak force occurs

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The improved force measurements at this effective strain rate (~20 1/s) yield additional information that was not present in the drop tower data. In Fig. 9.4b, d, the quasi-static tests at this rate have a very large error bar for critical strain and peak energy density. When examining the force-time response in Fig. 9.6a, it appears that in this range of strain rates, there are two local maxima in the force response that are approximately equal in magnitude. The first is located at approximately 0.025 s, and the second is located at approximately 0.15 s. While peak force and total energy density are very similar for all replicates, the strain at peak force and the peak energy density have a large amount of scatter because the strain at peak force is switching between the two local maxima depending on which peak is greater in each test run. This behavior is not present at other rates because the second peak is dominant at lower effective strain rates, and the first peak is dominant at higher effective strain rates (Fig. 9.6b). This suggests a potential transition in failure mechanisms is occurring near an effective strain rate of 20 1/s, leading to the large scatter in the data. This material behavior was not evident in the drop tower data because the appearance of the local maxima was overwhelmed by high-frequency noise.

Peak energy density and total energy density master curves from the quasi-static through-thickness tension and double-overlap shear tests were compared to the tan(δ) master curve from the shear rheology experiment to investigate the correlation between failure energy and tan(δ) described in Eq. 9.2. For through-thickness tension tests (Fig. 9.7a), it was observed that the peak of the tan(δ) master curve occurred at an effective angular velocity that was similar to the effective strain rate at which maximum total energy density was reached. While both effective strain rate and effective angular velocity are plotted on the same axis, they are similar but not equivalent and are potentially the source of the horizontal offset observed between the energy master curves and tan(δ) master curve. The shapes of the two master curves are also similar suggesting that for this acrylic foam tape, small strain viscoelasticity is the primary mechanism for rate-dependent energy dissipation during failure. This was unexpected as the material underwent large strains prior to failure. The peak of the tan(δ) master curve also correlated with the local minimum observed in the peak energy density master curve around 100 1/s. This is in the same regime as the failure mechanism transition described earlier, suggesting that the change in failure mechanism may be related to the glass transition of the material.

Fig. 9.7
figure 7

Comparison of peak and total energy density master curves from the quasi-static test method and tan(δ) for (a) through-thickness tension and (b) double-overlap shear

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Double-overlap shear peak energy density and total energy density master curves are compared with the tan(δ) master curve in Fig. 9.7b. In this case, the maximum of the peak energy density master curve correlated with the tan(δ) master curve. However, unlike the through-thickness tension master curve, the total energy density master curve for double-overlap shear does not correlate with tan(δ). This is under further investigation and may indicate that unlike through-thickness tension, large strain effects are present, and small strain viscoelasticity is not the primary mechanism for rate-dependent energy dissipation.

9.6 Conclusion

Rate and temperature dependence of failure properties for an acrylic foam tape were investigated. Using shear rheology, through-thickness tension, and double-overlap shear tests, it was demonstrated that time-temperature superposition can be used to characterize failure properties of PSAs. This is advantageous because test temperature can be used to test at effective strain rates that the available test equipment is unable to reach. This avoids the need for specialized high-rate testing equipment. It was also demonstrated that by using slower speed tests along with lower temperatures, the force resolution could be improved over equivalent tests run approximately three orders of magnitude faster on a drop tower. A correlation between the energy density master curves and tan(δ) was also observed for through-thickness tension tests. The relationship between double-overlap shear energy density master curves and tan(δ) will be investigated further in the future.