Subcritical Failure of Soft Acrylic Adhesives under Tensile Stress

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Subcritical Failure of Soft Acrylic Adhesives under Tensile Stress A. Lindner,†,‡ T. Maevis,§ R. Brummer,| B. Lu¨hmann,§ and C. Creton*,† Laboratoire de Physico-Chimie Structurale et Macromole´ culaire, E.S.P.C.I., 10, Rue Vauquelin, 75231 Paris Cedex 05, France, tesa AG, R&D Raw MaterialssPolymer Physics, Quickbornstrasse 24, D-20253 Hamburg, Germany, and Beiersdorf AG, Analytics Department, Unnastrasse 48, D-20245 Hamburg, Germany Received March 9, 2004. In Final Form: June 22, 2004 The mechanisms of failure over time of a series of model acrylic pressure-sensitive adhesives under a moderate level of stress has been investigated with a probe method. Two competing mechanisms of failure have been observed: a progressive nucleation of cavities under stress and the propagation of existing cavities at the interface between the probe and the adhesive layer. Homogeneous creep of the adhesive was never observed as the only failure mechanism. In situations where the resistance to crack propagation was good relative to the resistance to cavitation, extensive nucleation of cavities was observed until a material-dependent and stable value of stress was achieved. On the other hand in situations were the resistance to crack propagation was weak, propagation led invariably to a complete failure of the adhesive bond. In addition to the stress relaxation, the energy dissipation was studied allowing to distinguish the different adhesives even further. This allowed determination of the optimal amount of a comonomer (acrylic acid) that had to be added to improve the long-term resistance of the adhesives under study. Further more we investigate the compliance of the confined adhesive layers and compare the obtained results to predictions from theoretical models.

1. Introduction While failure and fracture mechanisms of brittle polymers have been studied extensively and are now rather well understood, the fracture properties of soft polymers or polymer-based materials have been the focus of much less attention. This class of materials can be loosely defined as being solid (which cannot flow) with elastic moduli below 1 MPa. To obtain such a low modulus while retaining a solid character, all these materials are based on a polymeric network of cross-link points (chemical or physical) keeping together a highly mobile matrix (well above its glass transition temperature Tg) which in itself has all the characteristics of a liquid. Since these soft materials are not able to flow, very large deformations will lead to failure by fracture or cavitation. One classical application where soft polymers are used is the self-adhesive label or tape which is based on a layer of pressure-sensitive adhesive (PSA). However, from a more general point of view, PSAs represent a larger class of deformable and viscoelastic materials, which are also found in food science, biological structures, and cosmetics. Their interactions with interfaces remain largely unexplored territory, and by studying the failure mechanisms of soft materials, we contribute to the understanding of the adhesive properties of such materials as well. PSAs are generally not used in applications where a high mechanical strength is required, but on the contrary many of them are expected to sustain a moderate level of stress over a long time. The maximum level of stress which occurs in service conditions can be as much as 10 times * To whom correspondence should be addressed. E-mail: [email protected]. † Laboratoire de Physico-Chimie Structurale et Macromole ´ culaire, E.S.P.C.I. ‡ Current address: Laboratoire des Milieux De ´ sordonne´s et He´te´roge`nes, PMMH, E.S.P.C.I., 10, Rue Vauquelin, 75231 Paris Cedex 05, France. § tesa AG, R&D Raw MaterialssPolymer Physics. | Beiersdorf AG, Analytics Department.

lower than the stress necessary to make the layer fail rapidly. However current studies of adhesive failure focus mainly on the rapid failure of the adhesive bonds.1-5 Therefore little is known about the mechanisms by which PSA detach from a surface after a certain time making it very hard to predict the time to failure from the knowledge of the rheological properties of the adhesive and of the chemical nature of the adherent surface.6 Nevertheless, over the years the PSA industry has devised several empirical strategies to improve the longterm resistance of PSA under a steady stress. A crucial parameter seems to be the balance between “adhesion” and “cohesion”, words which are written on purpose between quotes since they need to be defined within this context. Cohesion generally means here the ability to sustain stress in a tensile experiment, while adhesion means the interfacial interactions between polymer and substrate. A more scientific way to assess the adhesive and cohesive properties of a PSA may be the parameters Gc (critical energy release rate) and E (Young’s modulus), which have been used respectively to characterize the resistance to crack propagation7,8 and to the growth of macroscopic cavities within the adhesive layer.7,9 Two molecular variables which can be adjusted to vary these properties are the degree of cross-linking and the concentration of a specific component which has an affinity for the surface. Discussions in the literature remain (1) Lakrout, H.; Sergot, P.; Creton, C. J. Adhes. 1999, 69, 307-359. (2) Brown, K.; Hooker, J. C.; Creton, C. Macromol. Mater. Eng. 2002, 287, 163-179. (3) Crosby, A. J.; Shull, K. R. J. Polym. Sci., Part B: Polym. Phys. 1999, 37, 3455-3472. (4) Zosel, A. Int. J. Adhes. Adhes. 1998, 18, 265-271. (5) Zosel, A. J. Adhes. Sci. Technol. 1997, 11, 1447-1457. (6) Zosel, A. J. Adhes. 1994, 44, 1-16. (7) Crosby, A. J.; Shull, K. R.; Lakrout, H.; Creton, C. J. Appl. Phys. 2000, 88, 2956-2966. (8) Maugis, D.; Barquins, M. J. Phys. D: Appl. Phys. 1978, 11, 19892023. (9) Gent, A. N.; Lindley, P. B. Proc. R. Soc. London, Ser. A 1958, 249A, 195-205.

10.1021/la049388s CCC: $27.50 © 2004 American Chemical Society Published on Web 09/08/2004

Failure of Soft Acrylic Adhesives

however very empirical10 or rely on experiments where the two variables cannot be readily separated.11 In this article we investigate how a series of model adhesives (representing a common family of PSA) fails over time under a moderate applied tensile stress. Our polymers are statistical copolymers in which we have varied the mole fraction of a polar comonomer with a special affinity to the surface. We have chosen acrylic copolymers because they can be prepared with PSA properties without adding low molecular weight resins.12 From the point of view of varying material properties, we have incorporated various amounts of acrylic acid as a comonomer to impart some polarity. This comonomer is classically added in commercial PSAs, and its effects on the adhesive and cohesive properties of acrylic polymers during rapid bond failure have been investigated.1,13-16 Key results are a strong increase in the adhesive interactions but also a significant increase of the longest relaxation time of the polymer and a moderate increase of the glass transition temperature. The increase in cohesive properties has been attributed to the existence of hydrogen bonds forming nonpermanent physical crosslinks between acid groups. Part of the reason of the lack of scientific understanding of what controls long-term strength is that the most standard methods used to assess the resistance to a shear stress are very simplistic, i.e., a weight applying a constant shear stress over a standard surface of adhesive bond with a simple measure of the time to failure.17 Some more sophisticated techniques involve the measurement of the displacement as a function of time under a constant stress.6,18 However, none of these methods focuses on the detailed mechanisms by which failure occurs. This aspect may be particularly important since, for lightly crosslinked polymers typical of PSA applications, failure occurs very rapidly and catastrophically at a time which cannot be simply predicted from rheological data.6 On the other hand extensive progress has been made recently in the understanding of the short-term adhesive properties (the so-called tackiness) of PSA1,2,15,19 and of simple and complex fluids20-23 by the use of a tensile method fitted with a video camera. This relatively simple test geometry consists of a flat cylindrical probe removed from a thin film. Because the diameter of the probe is typically much larger than the thickness of the adhesive film, this test is equivalent to a tensile test between two parallel plates. (10) Tse, M. F. J. Adhes. 1995, 48, 149-167. (11) Aubrey, D. W.; Ginosatis, S. J. Adhes. 1981, 12, 189-198. (12) Everaerts, A. I.; Clemens, L. M. In Adhesion Science and Engineering, Vol. 2 Surfaces, Chemistry and Applications, 1st ed.; Chaudhury, M., Pocius, A. V., Eds.; Elsevier: Amsterdam, 2002; pp 465-534. (13) Falsafi, A.; Tirrell, M.; Pocius, A. V. Langmuir 2000, 16, 18161824. (14) Ahn, D.; Shull, K. R. Langmuir 1998, 14, 3637-3645. (15) Lakrout, H.; Creton, C.; Ahn, D.; Shull, K. R. Macromolecules 2001, 34, 7448-7458. (16) Lindner, A.; Lestriez, B.; Lu¨hmann, B.; Brummer, R.; Maevis, T.; Creton, C. To be published (17) PSTC. Test methods for pressure sensitive adhesive tapes, 13th ed.; Pressure Sensitive Tape Council, 2000. (18) JIS Z 0237 Testing method of pressure-sensitive adhesive tapes and sheets, In Japanese Industrial Standards; Japanese Standards Association, 2002. (19) Creton, C.; Hooker, J. C.; Shull, K. R. Langmuir 2001, 17, 49484954. (20) Derks, D.; Lindner, A.; Creton, C.; Bonn, D. J. Appl. Phys. 2002, 93, 1557-1566. (21) Francis, B. A.; Horn, R. G. J. Appl. Phys. 2001, 89, 4167-4174. (22) Poivet, S.; Nallet, F.; Gay, C.; Fabre, P. Europhys. Lett. 2003, 62, 244-250. (23) Tirumkudulu, M.; Russell, W. B.; Huang, T. J. Phys. Fluids 2003, 15, 1588-1605.

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These studies showed that the first stage of failure of a PSA layer in tension is the formation of cavities at the interface between the probe and the adhesive film.1 However these cavities do not necessarily lead to rapid detachment of the PSA and can be quite stable.2 We explore here how modifications of the chemical structure of the PSA can affect its resistance to catastrophic failure and in particular to the formation and interfacial growth of multiple cavities when applying a moderate tensile stress over a long time. While it is clear that applying a tensile stress is not equivalent to applying a shear stress, in many practical applications the applied stress may be a combination of tensile and shear so that our experiments will give us interesting insights into the possible mechanisms of failure of the adhesive bond over time. 2. Materials and Methods 2.1. Materials. The model adhesives used in this study consist of a series of acrylic copolymers based on 2-ethylhexyl acrylate (2-EHA) as base monomer. They contain as comonomer increasing amounts (2 wt %, 4 wt %, and 8 wt %) of acrylic acid (AA). Adhesives will be referred to as 2AA, 4AA, and 8AA, respectively. The advantage of using polyacrylates is that the pure polymers exhibit PSA properties without any need of additional formulation ingredients such as tackifying resins etc. All copolymers were synthesized via free radical polymerization in solution. 2AA, 4AA, and 8AA exhibit an average molecular weight of Mw ∼ 1200-1500 kg/mole and a polydispersity index PD ) Mw/Mn ∼ 7-9 (polystyrene standards used for calibration). Special emphasis was given toward the formation of as little variation as possible for the molar weight and molar weight distribution of the three polymers. Cross-linking was performed by use of 0.4% of Ti-chelate ((Ti(IV) bis(acetylacetonato))-diisopropylate), which was added to the organic solution just prior to the coating step. Films of the dried, cross-linked polymer were obtained by coating the concentrated adhesive solutions onto a 36 µm thick siliconized release film (siliconized PETP) using a semiautomatic lab coater equipped with a standard comma blade. Solvent evaporation was done by storing the freshly coated release film for 60 min at room temperature (23 ( 2 °C, 50 ( 10% relative humidity) and subsequently for 60 min at +120 °C to allow the crosslinking. Finally the open side of the adhesive was covered with a second release film. Samples were stored at least 1 week at room temperature prior to performing mechanical and adhesive testing. Cross-linked adhesives after 1 week of storage showed gel contents of ∼60% as measured by extraction. Prior to testing, one of the release films was peeled off and the adhesive was manually pressed against a 1 mm thick precleaned standard microscope glass slide. The second release film was then peeled off. Both surfaces of the film have therefore been in contact with a siliconized release film. Previous experience with various similar adhesives indicated that silicone transfer to the adhesives surface takes place but does only slightly influence adhesive properties (less than 10% loss in peel after 48 h of contact with release liner at +40 °C and 0.02 MPa contact pressure, and less than 5% Si in adhesive surface using ESCA). 2.2. Methods. The mechanics of the probe test have been extensively studied,24-26 and here we will only (24) Creton, C.; Lakrout, H. J. Polym. Sci., Part B: Polym. Phys. 2000, 38, 965-979. (25) Lin, Y. Y.; Hui, C. Y.; Conway, H. D. J. Polym. Sci., Part B: Polym. Phys. 2000, 38, 2769-2784.

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Figure 1. (a) Schematic view of the experimental setup for a standard probe test. A cylindrical probe is brought into contact with the adhesive layer from below and is then subsequently removed from the latter. During this debonding process one measures the force F and the displacement h as a function of time. (b) Typical stress-strain curve for the debonding of the adhesive during a classical probe test obtained from the measurements of the force F and the displacement h.

summarize the main features and the main experimental parameters which can be obtained from the method. A schematic view of such a probe test can be seen in Figure 1a. A cylindrical probe is brought into contact with a thin film of adhesive at a given velocity Vapp. The probe is maintained in contact with the film at a given pressure Pc (the displacement of the probe is actually kept constant while the force relaxes slightly) for a given contact time tc and is then subsequently removed from the adhesive at a constant debonding speed Vdeb. During the debonding process, the force F and the displacement h are measured as a function of time. We define h as being the timedependent thickness of the adhesive layer and h0 as the initial layer thickness. The measurements allow a stress σ versus strain curve to be deduced (Figure 1b), where σ is the nominal stress σ ) F/A, with A the area of contact between the probe and the adhesive during the compressive stage, and ) (h - h0)/h0. The shape of the stressstrain curve obtained during such a fast detachment of the probe from the film can be used to characterize the adhesive performance of the material tested and depends on the rheological properties of the adhesive layer and on the interfacial interactions between the adhesive and substrate. Typical characteristic values that are extracted from such a curve are the maximum tensile stress σmax, the stress at the plateau σplateau, the maximum nominal strain to failure max, and the adhesion energy Wadh (the integral under the curve) as shown in Figure 1b. In this paper however we report new experiments with the same geometry and experimental device. The standard procedure has been modified in such a way that the displacement of the motors driving the probe is stopped at a given moment during the initial stages of the debonding process.27,30 The system, under tensile stress, (26) Cheng, L.; Xia, X.; Yu, W.; Scriven, L. E.; Gerberich, W. W. J. Polym. Sci., Part B: Polym. Phys. 2000, 38, 10-12. (27) Josse, G.; Sergot, P.; Dorget, M.; Creton, C. J. Adhes. 2004, 80, 87-118.

Figure 2. (a) Force and displacement of the motors for a relaxation test as a function of time. The motors are stopped at a given moment, and the adhesive is allowed to relax for a given time tstop. (b) Displacement of the motors and deformation of the glass slide, the adhesive layer, and the setup during the relaxation tests.

is then left to relax for a given time tstop. At the end of the stop the displacement of the probe is resumed until complete debonding of the adhesive occurs. This is depicted in Figure 2a, showing the displacement of the motors and a typical force curve as a function of time. We use a custom-made apparatus27 computer controlled with LabView software. The detailed setup is the following (see Figure 3): an adhesive layer is deposited on a glass slide which is then fixed on a sample holder in the apparatus. The probe is brought into contact with the adhesive layer from below. The debonding process is visualized through the glass slide from above with a microscope coupled to a CCD camera. The force is measured during the debonding process using a 50 N load cell (manufactured by Entran, with an accuracy of 0.1 N), and an optical sensor (Philtec D63 LPT with a resolution of 0.2 µm) is used to measure the displacement between the probe and the sample holder. Since the setup is not completely rigid, but on the contrary has a relatively high compliance, not only the adhesive but also the apparatus is stretched during debonding. The total system can be divided into three components all undergoing deformations during the test (Figure 2b): the glass slide, the adhesive layer, and the rest of the setup. The actual displacement of the motors driving the test is the sum of these three displacements

∆motor ) ∆slide + ∆hadh + ∆setup

(1)

Note that we define all differential displacements ∆ to be zero when the force is zero. At this moment the thickness of the adhesive layer equals h0 and thus ∆hadh corresponds


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Figure 3. Experimental setup for the relaxation tests. The probe is brought into contact with the adhesive layer from below. The debonding process is visualized through the glass slide from above with a microscope coupled to a CCD camera. The force is measured during the debonding process using a load cell and an optical sensor is used to measure the displacement between the probe and the support of the glass slide. The control of the motors via a LabView program allows stopping the displacement of the latter during the debonding process. Sketch courtesy of A. Chiche.30

to h(t)-h0 (see Figure 1a). The strain is thus defined as

) ∆hadh/h0

(2)

In particular, due to the compliance of the apparatus, stopping the motors does not mean that the strain of the adhesive remains constant. On the contrary, when the motors are stopped during the test, the glass slide is in general already bent and the setup is stretched, storing in this way elastic energy that can be released during the relaxation process. We will consider the glass slide and the setup as linear springs characterized by their compliance Cslide and Csetup. These compliances have been measured experimentally and one finds Cslide ) 0.3 µm‚N-1 for the glass slide of 2 mm thickness and Csetup ) 2 µm‚N-1. The force applied to the three components is identical and equals

F(t) ) ∆slide(t)/Cslide ) ∆hadh(t)/Cadh(t) ) ∆setup(t)/Csetup (3) Cslide and Csetup being constant a decrease of the force decreases the displacement of the setup as well as the displacement of the glass slide. For a constant displacement of the motors, this leads to an increase of the displacement of the adhesive during the relaxation process. Using the displacement measured by the optical sensor ∆sensor ) ∆slide + ∆hadh, it is possible to obtain the exact displacement of the adhesive layer as a function of time

∆hadh(t) ) ∆sensor(t) - Cslide F(t)

(4)

From these results we can also extract the instantaneous value of the compliance of the adhesive layer defined as

Cadh(t) ) ∆hadh(t)/F(t)

(5)

which is of course not constant as a function of time. In summary, since in our case the apparatus and slide are, at least at the beginning of the experiments, more compliant than the layer, our “relaxation” test is performed neither at fixed displacement (as would a real relaxation test) nor at fixed force but is more representative of a situation where a moderate force applied to an adhesive

Figure 4. Stress σ as a function of time t for 2AA on steel. A test without stop and three tests with stops at different initial values of σ0: stop 1, σ0 ) 0.08 MPa; stop 2, σ0 ) 0.16 MPa; stop 3, σ0 ) 0.25 MPa. For all stops tstop is 180 s.

layer is allowed to relax, while at the same time deforming the adhesive. In this way some of the elastic energy stored in the setup is released during the stop and the apparatus performs external work on the adhesive. Further more the adhesive itself relaxes and releases also elastic energy. Note that even if the tests we perform show both, relaxation of the force and displacement of the adhesive layer, we will for simplicity reasons in the following often use the term relaxation only. The experiments we report are performed using the following experimental conditions: We use an adhesive layer of 100 µm deposited on a glass slide of 1 mm thickness. The probe is approaching the sample at Vapp ) 20 µm/s, it is then maintained in contact with the sample at the contact pressure Pc ) 0.7 MPa for tc ) 1 s. The debonding speed is fixed at Vdeb ) 10 µm/s, and the stops last for tstop ) 180 s. The experiments are performed at room temperature (25 °C). We use a probe having a diameter of 6 mm, which is made of steel with an average quadratic roughness Ra of 14 nm. Some tests have also been performed on a low adhesion surface, namely, a very thin layer of ethylene-propylene (EP) copolymer coated on the steel probe. The coatings were made by spin coating solutions of 1 wt % EP in xylene on stainless steel probes. The resulting layer had a thickness of approximately 60 nm. Only a limited number of tests (about five) could be performed without damaging the thin EP film, and thus the probe had to be changed regularly. 2.3. Relaxation Test: Example. In the following, typical observations made during such a relaxation test will be described. As an example we chose the results obtained for the 2AA adhesive on the steel surface. Figure 4 shows the nominal stress as a function of time for a nonstop test and for three relaxation tests on steel. The relaxation tests were, for both EP and steel, always performed during the increase of the force in the beginning of the debonding process before catastrophic failure is observed. The beginning and the end, after 180 s (3 min), of the relaxation process can be clearly distinguished for the three different stops in the force-time curves. Note that the stops going from stop1 to stop3 are performed at increasing values of the stress at the beginning of the relaxation. The level of tensile stress at which the test is stopped and the adhesive allowed to relax will be referred to as σ0 in the following. Since this early loading stage is essentially elastic at those deformation rates, increasing initial values of σ0 correspond also to an increase in the amount of elastic energy stored in the adhesive layer at the beginning of the stop. It is quite clear from Figure 4 that significant relaxation of the stress is taking place during the stop.

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Figure 6. Displacement of the adhesive ∆hadh during the stops for 2AA on steel. Same stops as Figure 4. Note that the adhesive is already stretched and ∆hadh is thus not zero at the beginning of the stop.

Figure 5. (a) Detail of the relaxation of the stress during the stops for 2AA on steel, same stops as Figure 4. (b) Relaxation of the stress for 2AA on EP for three stops at different initial values of σ0: stop 1, σ0 ) 0.13 MPa; stop 2, σ0 ) 0.15 MPa; stop 3, σ0 ) 0.22 MPa. For all stops tstop is 180 s.

We will now look at the relaxation step in more detail. Figure 5a shows the stress relaxation of the 2AA on steel for the three different stops. In all cases, there is a significant decrease in the tensile stress applied to the adhesive during the stop. Figure 5b shows the same relaxation process for 2AA however on the EP surface. Here we will not discuss the results in detail, but one can already note that the relaxation of the tensile force when the adhesive is adhered on EP is significantly different compared to the observations made on steel, implying therefore that σ(t) not only is a material property but depends also on adhesive properties. As we discussed earlier, the relaxation of the adhesive is not taking place in fixed grip conditions but the adhesive layer undergoes both a decrease in tensile stress and an increase in tensile deformation. Figure 6 represents ∆hadh, the increase in thickness of the adhesive layer, as a function of time. Note that the displacement is not zero at the beginning of the stop as the adhesive is already stretched when the test is stopped. The initial displacement is obviously larger for larger σ0. The strongest increase of the displacement during the stop is taking place for stop3, but also in this case it only reaches values of about 10 µm, corresponding to an additional deformation of the adhesive layer of about ) 0.1 during the stop. Also for the 4AA, the maximal deformation observed during the stop is of the order of ) 0.1, while for the 8AA, a displacement as high as 20 µm, corresponding to a deformation of 0.2, is observed for the stop at the highest σ 0. Note that for all adhesives, several experimental runs, using different samples, were performed. It turns out that due to the sensitivity of the experiments some scatter in the absolute values is observed between runs. The comparison of the different runs shows, however, that the

basic features are reproduced from one test to another. For the following analysis we chose rather to use one representative example per adhesive instead of working with average values. 2.4. Rheological Characterization and Standard Adhesive Performance. For our model acrylic adhesives standard probe tests as well as a complete rheological characterization have been performed and are reported elsewhere.16 In the following section we will only give a brief summary of the results already obtained. For all adhesives the debonding process can be broken into different stages that are respectively cavitation, growth of cavities, fibrillation, and final debonding.1,28 Cavitation takes place at the beginning of the debonding process, while the stress increases (for a typical stressstrain curve see Figure 1b). Growth of the cavities leads to a decrease of the nominal stress until the fibrillation stage is reached, leading to a plateau value of the stress. Finally, detachment of the fibrils occurs and complete debonding of the adhesive layer takes place. An increase in AA content in the acrylic adhesive has two main effects: it modifies the bulk rheological properties of the adhesive, increasing its shear modulus G′ and its dissipative character tan δ, and it also increases its adhesive interactions with the surface. On the steel surface this leads (for not too high debonding speeds) to an increase of the maximal stress σmax, the stress at the plateau σplateau, and the maximal strain max with increasing AA content, and thus to an increase of the adhesive performance as shown in Figure 7 where the typical stress-strain curves obtained for a standard probe test are shown for the three different adhesives. Note that the probe tests shown here have all been performed using the same experimental conditions as for the relaxation tests. In particular, the debonding speed is 10 µm/s. Since the initial thickness of the layer h0 is of 100 µm, the complete duration of a standard test at Vdeb ) 10 µm/s is of the order of 1 min. The results obtained for a standard test on EP are also shown in Figure 7. One can conclude that σmax as well as max are dramatically reduced on EP compared to steel. The effect is even more pronounced on max due to the fact that the fibrillation stage is completely suppressed. Furthermore it is interesting to note that the differences between the adhesive properties of the different acrylic copolymers nearly disappear on EP whereas they are clearly visible on steel. The results for σmax, σplateau, and max are summarized in Table 1. (28) Creton, C.; Fabre, P. The Mechanics of Adhesion. In Adhesion Science and Engineering; Elsevier: Amsterdam, 2002; Vol. 1, pp 535576.


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Figure 7. Standard tack test: stress as a function of strain for 2AA, 4AA, and 8AA on steel and EP. Table 1. Maximal Stress and Strain for the Different Acrylic Adhesives on Steel and EP σmax (MPa)

max

2AA 4AA 8AA

Results Obtained on Steel 0.29 4.5 0.40 5.1 0.56 6.3

2AA 4AA 8AA

Results Obtained on EP 0.25 0.46 0.34 0.43 0.28 0.41

σplateau (MPa) 0.13 0.15 0.19

3. Observation of Failure Mechanisms and Relaxation Behavior under Low Stresses To interpret correctly the stress-strain curves which are measured during the tests, it is essential to identify the mechanisms of failure which are responsible for the decrease in stress over time. In the following, we give a qualitative description of what is observed during the stops starting with the experiments on steel. We chose to describe as an example 2AA and 8AA in detail. This is illustrated on the video captures shown in Figure 8, which are always taken at the beginning and at the end of the relaxation stage for the different stops. For each adhesive, a stop at low initial stress (1a and 2a) and a stop at high initial stress (1b and 2b) are shown. To describe precisely the deformation mechanisms, we need here to define the terms “cavitation” and “propagation”. As described extensively in earlier publications,1,2,29 PSA under a tensile stress develop cavities. These cavities appear where surface defects were initially present,30 and we can optically detect them when their size becomes of the order of a few micrometers. The cavities grow then rapidly to a size of the order of the thickness of the film. At that stage, two different mechanisms can be observed: either the cavity stops growing and new cavities progressively nucleate, eventually filling the space previously occupied by the adhesive film, or the cavity continues growing laterally in a disklike shape until it comes in contact with an adjacent disklike cavity.19 The process of nucleation of new cavities under constant stress will be called “cavitation”, while the growth of the existing cavities in the plane perpendicular to the tensile direction is referred to as “propagation”. In our relaxation tests, a tensile stress is applied to the adhesive layer with a spring (the apparatus) and the system is left to minimize its stored elastic energy by increasing its compliance over time. This increase in compliance can occur through three main dissipative (29) Chiche, A.; Pareige, P.; Creton, C. C. R. Acad. Sci. Paris, IV 2000, 1, 1197-1204. (30) Chiche, A. Ph.D. Thesis, Universite´ Paris VII, Paris, 2003.

mechanisms: bulk relaxation of the viscoelastic adhesive, fracture by the formation of cavities, and growth of preexisting cavities. Video captures taken during the force relaxation process can reveal whether cavitation or propagation takes place. These observations will allow determination of whether the cavities will eventually coalesce or whether individual cavities persist and allow thus to form a foamlike structure when the adhesive layer is stretched further. This last question is of particular importance to the long-term stability of the adhesive bond, since a coalescence of individual cavities would rapidly lead to the complete detachment of the adhesive.19 For the 2AA adhesive, during the stop at low initial stress (1a) not much is visible during the 3 min stop: only little cavitation and little propagation is taking place. For the stop at higher initial stress (1b) there is still only little evidence of appearance of new cavities, but the cavities that were formed before the stop grow in size, i.e., some propagation takes place. However the propagation is not strong enough to lead to coalescence of individual cavities. As can be seen on the snapshots on the right side of Figure 8, 8AA shows a quite different behavior. Already for the stop at low initial stress quite a high number of new cavities appear during the relaxation step. For the stop at high initial stress this number increases even more. The preexisting cavities however grow only slightly. We now turn to the case where the same adhesives are detached from a probe coated with a film of ethylenepropylene, representative of a low adhesion surface. Figure 9 shows the debonding process for 2AA on EP. In this case no cavitation at all is observed during the relaxation of the tensile stress: the cavities that were formed before the stop grow however substantially and some fingering instabilities growing from the edges of the probe are also observed. The qualitative observations from Figure 8 and Figure 9 are quantitatively translated into Figure 10 and Figure 11 that show the debonded area and the number of cavities as a function of time for the experiments shown on the snapshots. Note that in all cases the data shown on the graphs correspond to the experiment performed at the highest initial value of stress σ0. Figure 10 and Figure 11 show that the cavitation and propagation behaviors of the two different adhesives 2AA and 8AA on steel are significantly different. While the total debonded area is about the same for both adhesives, for 2AA there is little new cavitation and the existing cavities grow. For 8AA on the contrary, most of the new debonded area is accounted for by the nucleation of new cavities. This difference in behavior between the two adhesives leads to cavities with very different sizes at the end of the stop. For 2AA the average projected cavity radius is around 200 µm, while it is only of 90 µm for 8AA. Note that the qualitative observations made for 4AA (not shown here) reveal that the debonding mechanism of 2AA and 4AA is very similar. In the case of the 2AA adhesive, Figures 10 and 11 also show the substantial growth taking place on the EP surface leading to a high percentage of debonded area at the end of the stop for the same number of separate cavities nucleated before the stop. Although the observation of the debonding patterns provides invaluable qualitative information on the details of the mechanism, the force and displacement data collected during the relaxation step can be quantitatively analyzed and compared to material properties. When looking at the relaxation behavior of 2AA on steel as shown in Figure 5a, one can note that the decrease in stress slows down toward the end of the stop and finally

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Figure 8. Snapshots taken during the relaxation process for 2AA (left) and 8AA (right) on steel. The picture on top is always taken at the beginning of the stop (t ) 0) and the picture on the bottom at the end of the stop (t ) 180 s). 1a represents a stop at a low initial stress level (σ0 ) 0.08 MPa, σ0/σmax ) 28%) whereas 1b represents a stop at higher initial stress (σ0 ) 0.25 MPa, σ0/σmax ) 85%) for 2AA. One observes little cavitation, but some growth of the existing cavities. 2a represents a stop at low initial stress (σ0 ) 0.14 MPa, σ0/σmax ) 25%) and 2b at higher initial stress for 8AA (σ0 ) 0.45 MPa, σ0/σmax ) 81%). In this case one observes the nucleation of new cavities.

Figure 9. Snapshots taken during the relaxation process for 2AA on EP. The picture at the bottom at the end of the stop (t ) 180 s for a and b, t ) 15 s for c): (a) stop at a low initial stress level (σ0 ) 0.13 MPa, σ0/σmax ) 51%); (b) stop at intermediate initial stress (σ0 ) 0.15 MPa, σ0/σmax ) 59%); (c) stop at high initial stress level (σ0 ) 0.22 MPa, σ0/σmax ) 86%). The picture on top is always taken at the beginning of the stop. On the low adhesion surface, no cavitation but substantial growth is observed.

reaches a nearly constant value σF. While we cannot exclude the possibility of a further relaxation for longer stops, we believe however that this additional relaxation can be considered as a small correction to our results.

Another observation supports this hypothesis. When visualizing the debonding process, one observes that most of the growth and cavitation takes place during the first 60 s. When comparing a snapshot taken at t ) 60 s and


Figure 10. Debonded area/total area in % as a function of time for selected experiments on steel and EP. The represented experiments were always chosen at the highest σ0 available: 2AA on steel (σ0 ) 0.25 MPa, σ0/σmax ) 85%), 8AA on steel (σ0 ) 0.45 MPa, σ0/σmax ) 81%), and 2AA on EP (σ0 ) 0.22 MPa, σ0/σmax ) 86%). Note that snapshots corresponding to these experiments can be seen in Figure 8 and Figure 9.

Figure 11. Number of cavities as a function of time. Same experiments as for Figure 10.

Figure 12. Final stress σf as a function of initial stress σ0 for the different adhesives on steel. The solid line represents the case of no relaxation, σf equal to σ0. The dotted lines represent the threshold value for σf.

at t ) 180 s, one can hardly see any difference. This holds for all experiments performed on steel. It is interesting to represent all experiments on a master curve where σF is plotted as a function of the initial stress σ030 (Figure 12). While, even for the stops at low σ0, some relaxation takes place, when σ0 is increased toward σmax, the relaxed stress σF tends toward a plateau value independent of σ0 for the different adhesives. Admittedly this value is not clearly defined for the 2AA, but for the 4AA and 8AA adhesives the stops at high σ0 all clearly relax toward the same final value σF* which seems thus

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Figure 13. Same representation as Figure 12, but the initial and final stresses are normalized by σmax.

to be a material property of the adhesive independent of the value of σ0. As shown in Figure 7, the peak stress σmax observed during a nonstop test is very different for all three adhesives. When the stresses are scaled with this peak stress σmax (obtained in a standard probe test at Vdeb ) 10 µm/s), it becomes apparent that the data measured for the three different adhesives can be plotted in a master curve (Figure 13). This is a potentially useful result implying that the threshold stress can be reasonably well predicted once σmax is known. It should be pointed out however that the peak stress is dependent not only on the properties of the adhesive but also on the population of defects initially present at the probe/film interface or in the bulk of the adhesive.29,30 Other features of the probe tack curve, less sensitive to the roughness of the adherent, such as the plateau stress σplateau (Table 1) lead to a slightly better scaling of the stresses, and in this case the threshold value tends toward σF* ∼ 0.8σplateau. This observation leads us to suggest that the threshold value observed might be determined by the material properties only. This is in agreement with observations made by Chiche30 and Roos40 and holds as long as the debonding mechanism is not substantially changed by the change of the roughness of the probe. Note, that due to the little differences between σmax and σplateau in our case, we will in the following always use σmax to scale the stresses observed. We will now discuss the results obtained on the low adhesion surface EP. The relaxation behavior as can be seen for the example for 2AA (Figure 5b) is very different from the one observed on steel. In general, the relaxation of the force is much faster in the case of EP. Furthermore one observes that the magnitude of the force relaxation increases with increasing σ0 so that σF decreases with σ0 until complete debonding (σF ) 0) is observed at the highest σ0 (Figure 14). In summary, on the high adhesion surface, the final stress σF at the end of the relaxation tends toward a constant value implying that the adhesive has the potential to remain bonded for a long time. For all adhesives tested, this value corresponds to approximately 0.8σplateau measured at Vdeb ) 10 µm/s and thus at an initial strain rate of 0.1 s-1. On the low adhesion surface EP the behavior is significantly different: σF tends toward zero when σ0 is increased and one observes complete debonding of the adhesive during the relaxation process, implying that it would be very difficult to obtain a long-term bond of this adhesive on such a low adhesion surface and no value of σF* can be identified. This qualitative difference is

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Figure 14. Final stress σf as a function of initial stress σ0 for the different adhesives on EP. The solid line represents the case of no relaxation, σf equal to σ0.

Figure 16. Dissipated energy for 2AA, 4AA, and 8AA on steel as a function of σ0.

The setup also releases elastic energy during the stop, and as the displacement of the adhesive is not zero during the stop, the setup performs external work on the adhesive. This work can be calculated in a straightforward way using the stress-displacement curve (see Figure 15) and then corresponds to the area under the curve

Wext ) {1/2(σ0 + σf)}(∆hf - ∆h0)

(7)

approximating the area by a square and a triangle. One can thus obtain the total dissipated energy as

δW ) ∆Eel + Wext

(8)

which simplifies to Figure 15. Sketch of a force displacement curve during the stop showing the external work and the elastic energy stored in the system.

essential since many of the PSA applications sustain a very modest stress but are not expected to spontaneously detach over time. 4. Energy Dissipation during the Relaxation Behavior In the previous section we discussed the relaxation process by analyzing the final values of σ at the end of the stops. In this chapter we will extend the discussion further and analyze quantitatively the energy dissipated during the relaxation process for the different adhesives. In this way we not only consider the relaxation of the stress but also take the deformation of the adhesive into account. As the adhesive layer relaxes, elastic energy stored in the adhesive layer and in the apparatus is released and instantly dissipated. To calculate the elastic energy which is dissipated during the relaxation, we perform an approximate energy balance assuming a purely elastic behavior of the adhesive layer (Figure 15) at the beginning and at the end of the stop. It has been shown for nonstop tests16,27 that the slope of the stress-displacement curves observed at the beginning of the debonding is independent of the debonding speed for the adhesives we use here. This justifies the assumption of a purely elastic behavior at the beginning of the stop. During the relaxation process, the adhesives behave obviously not purely elastically. However as discussed in section 3, the relaxation of the stress slows down toward the end of the stop and the stress reaches a nearly constant value as a function of time again. So at the end of the stop a purely elastic behavior can be assumed again and one obtains

∆Eel ) E0 - Ef ) 1/2(σ0*∆h0 - σf*∆hf)

(6)

δW ) 1/2(σ0*∆hf - ∆h0*σf)

(9)

Note that for the moment we do not distinguish where the energy is dissipated but look only at the total energy dissipation. It is however clear that there are at least two main components that contribute to the energy dissipation: viscous dissipation in the bulk and dissipation due to formation of a new surface area, either by crack propagation at the interface or by formation of new cavities. Strictly speaking creation of new surface area is always accompanied by viscous dissipation so that bulk and interface cannot be easily separated. Figure 16 shows the energy dissipated during the stops for 2AA, 4AA, and 8AA. First of all, it is interesting to point out that in all cases the energy dissipated during the relaxation process is significantly larger than the elastic energy stored in the adhesive layer at the beginning of the stop (E0 ∼ 0.7 J/m2) implying that the external work performed by the setup is not negligible and that we may be testing more adhesive creep than adhesive relaxation. We choose here to represent the dissipated energy as a function of the initial stress level σ0 which corresponds for example to the requirement of the same practical application. When comparing 2AA and 4AA, one observes distinctly less dissipation for 4AA in agreement with the lower stress relaxation observed for this adhesive (Figure 12). This is further more accentuated by a smaller deformation of this adhesive under stress compared to 2AA. The 8AA has however a surprising behavior: based on its bulk rheological properties and in agreement with the lower stress relaxation observed (Figure 12), one would expect to see even less dissipation for 8AA than for 4AA. However due to the larger deformation of this adhesive under stress, a significantly higher dissipation is observed. One is tempted to correlate this to the strong cavitation taking place for this adhesive during the stop.


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The compliance of the adhesive layer is defined as

Cadh(t) ) ∆hadh(t)/F(t)

(10)

First of all, it is useful to discuss the purely geometric effect on the compliance. If a probe is removed from an infinite elastic layer of Young’s modulus E, the compliance of the layer is given by31

C0 ) 3/(8Ea)

Figure 17. Dissipated energy for 2AA, 4AA, and 8AA on steel as a function of σ0/σmax.

(11)

where a is the diameter of the probe. When the thickness of the layer is no longer infinite, the compliance decreases and this problem has been addressed for elastic layers by analytical approximations and numerical simulations.32-34 Shull et al. give a semiempirical correction for the compliance of a thin elastic layer as a function of the confinement a/h0 of the adhesive assuming infinitesimal strains and full friction between the probe and the adhesive layer

C0/C ) f(a/h0) ) 1 + {0.75/((a/h0) + (a/h0)3) + 2.8(1 - 2ν)/(a/h0)}-1 (12)

Figure 18. Comparison dissipated energy on steel and on EP as a function of σ0 for 2AA and 4AA.

This peculiar behavior of the 8AA is even more apparent if we represent the dissipated energy as a function of σ0/ σmax (Figure 17). With this normalization, the 2AA and 4AA adhesives behave identically while the 8AA dissipates much more energy. Finally, what is the situation on the low adhesion EP surfaces? Figure 18 compares the dissipated energy on steel and on EP for 2AA and 4AA. One observes, as expected, that the energy dissipation for both adhesives is higher on EP than on steel. Note that it is also faster, reaching for example for 2AA and for the stop at highest initial stress a final value for the dissipated energy after about 15 s. At this point complete debonding has occurred, and thus no further dissipation takes place. This result reflects clearly the poor stability of the adhesive bond on such a low energy surface. Furthermore the differences between the two adhesives are less pronounced on EP, as was also observed for the nonstop tests. From the point of view of material properties, it is however interesting to note that, on EP, 4AA dissipates more energy than 2AA, in contrast to what was observed on steel. 5. Comparison with Rheological Properties In the previous section we compared the level of dissipated energy for the different materials and different values of σ0. In all cases this energy is dissipated through a decrease in stress and an increase in deformation. On combination of both effects in one variable, the dependence of the instantaneous compliance of the layer with time can be modeled simply with a combination of a geometric model designed for elastic layers and a creep compliance function of the material determined with rheological measurements. The discrepancies between model and experience can then be interpreted in terms of failure mechanisms.

The adhesives we use here are nearly incompressible, but as the compliance of the elastic layer depends strongly on the Poisson’s ratio ν, we will here estimate the deviations from ν ) 0.5 for our materials. To do so we use a typical value for the bulk modulus K ) 109 Pa 35,36 and the shear modulus G ) 105 Pa. E can be approximated as E ) 3G, and using ν ) 0.5(1 - E/3K) then leads to ν ) 0.49995. Admittedly eq 12 is very sensitive to the precise value of ν, but the error on ν is rather small. If we assume that the bulk modulus K can vary between 0.5 and 2 GPa and the shear modulus G between 0.01 and 0.1 MPa, one finds ν ) 0.49995 ( 0.00005. This leads to an error on the absolute value of C0/C of about 30%. For an adhesive with G ) 0.1 MPa, eq 12 predicts C0 ) 420 µm/N for a ) 3 mm, while the predicted compliance of a 100 µm thick layer is only C ) 0.015 ( 0.005 µm/N. Experimentally the compliance of the layer that we measure at the beginning of the relaxation for the different stops is found to be for 2AA typically about C ) 0.8 µm/N and C ) 0.2 µm/N for 8AA. The lower compliance of 8AA is explained by the higher modulus of the latter. One can however note that the experimental values are more than 1 order of magnitude higher than the value predicted by eq 12. This discrepancy cannot be explained by the error on ν. Good agreement between eq 12 and experimental results has been shown for not too confined geometries;37 however the very confined layers we use here might be outside of the range of validity of eq 12. This might be due to the breakdown of some of the assumptions made in the calculation of the compliance such as perfect bonding at the probe surface or infinitesimal strains at the edge of the contact. In the very confined geometries we use, a small increase in the thickness of the adhesive layer leads to a strong shear deformation at the edges (a value of (31) Johnson, K. L. Contact mechanics, 1st ed.; Cambridge University Press: Cambridge, 1985. (32) Ganghoffer, J. F.; Gent, A. N. J. Adhes. 1995, 48, 75-84. (33) Gent, A. N. Rubber Chem. Technol. 1994, 67, 549-558. (34) Shull, K. R.; Ahn, D.; Chen, W. L.; Mowery, C. L.; Crosby, A. J. Macromol. Chem. Phys. 1998, 199, 489-511. (35) Ougizawa, T.; Dee, G. T.; Walsh, D. J. Polymer 1989, 30, 16751679. (36) Dee, G. T.; Ougizawa, T.; Walsh, D. J. Polymer 1992, 33, 34623469. (37) Webber, R. E.; Shull, K. R.; Roos, A.; Creton, C. Phys. Rev. E 2003, 68, 021805.

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Figure 19. J(t) as a function of t for 2AA, 4AA, and 8AA (symbols) and power law fit (represented by the lines) for creep tests at fixed load τ ) 1000 Pa.

∆hadh of 1 µm leads already to a deformation of 30% at the edge of the contact). A further extension of the analysis of Shull et al. has been performed by Lin et al.25 considering also the frictionless case. In the case of a nearly incompressible material (as is the case for the acrylic adhesives), their predictions for the compliance are however for both cases in excellent agreement with the results of Shull et al.34 For the following analysis we will thus concentrate on the time dependence of the compliance, regardless of its absolute value. This will allow us to obtain information about the relaxation process taking place during the stop. In general the increase in compliance over time can be due to the following: relaxation in the bulk (decrease in the elastic modulus), reduction of the area effectively bonded with the probe, or finally a decrease in the degree of confinement caused by the formation of cavities or by cavity (or finger) growth during the stop.37 If we compare directly the time dependence C(t)/C(t)1s) of the compliance of the layer with the compliance function of the adhesive J(t), we will be able to approximately extract the contribution of bulk relaxation to the increase in the compliance with time. The creep compliance of the adhesive is obtained as follows: creep tests performed at different loads (τ ) 100, 500, and 1000 Pa) are used to obtain J(t). For each of these experiments the load τ is fixed and the deformation of the adhesive γ(t) is recorded. These results allow thus to calculate J(t) ) γ(t)/τ which is represented by the symbols in Figure 19 as a function of t for the different adhesives. Note that the results shown are those obtained for τ ) 1000 Pa. The experimental results can be well described by a power law of the form J(t) ) k1*tn (represented by the lines). The values of the fitting parameters k1 and n are given in Table 2. When the fits are performed, results obtained for different loads (not shown here) lead to slightly different absolute values of J(t) (and thus slightly different k1) but show always the same exponent n. As we will mainly be interested in the time dependence of the relaxation in the following, we choose to use always the results obtained for τ ) 1000 Pa. Further more the fluctuations of k1 for different loads are small compared to the differences between the different adhesives. Given that proviso, the absolute value of J(t) decreases from 2AA to 4AA and finally to 8AA while its time dependence is slightly stronger for 8AA, which is more dissipative. Before using J(t) from the creep tests to predict the time dependence of the compliance of the layer, we should

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Figure 20. Relaxation of the normalized compliance C as a function of time during the stop for 2AA on steel. The solid line represents the prediction from the rheology, whereas the dotted lines are the results obtained from the tack tests. Stop 1 and stop 3 are chosen in an exemplary way to represent one stop at low stress (σ0 ) 0.08 MPa) and one at high initial stress (σ0 ) 0.25 MPa). Table 2. Fit Parameters for the Relaxation of G(t) ) k1tn 2AA 4AA 8AA LOW

n

k1 (kPa)

-0.17 -0.18 -0.20 -0.26

16 23 47 13

recall here that for our relaxation tests we observe a combination of stress relaxation and creep of the adhesive. Our tests are thus identical to neither the creep test described above, where the load is constant, nor a pure relaxation test used in rheology where one fixes the displacement and monitors the stress relaxation. However the typical power-law functions of J(t) which are measured for PSA render legitimate the use of J(t) instead of a more complicated function of the relaxation and creep functions. Since we have seen that the absolute value of the compliance cannot easily be predicted, we will concentrate on its time dependence. To do so, we normalize the results from the probe tests as well as those obtained from the rheological measurements to the value at t ) 1 s. If we assume further more that ν is not time dependent and use a constant value for the confinement a/h0, we can now compare the measured time dependence of the compliance of the layer with the measured creep compliance of the adhesive. The results obtained in this way show for 2AA (Figure 20) that the compliance measured directly from the probe tests increases slightly faster than that predicted by the rheological measurements. In the case of 2AA the debonding of the interface during the relaxation is very small and can thus be neglected. The stronger relaxation might thus be attributed to cavitation taking place during the stop. One expects the appearance of cavities during the stop to decrease the confinement of the layer which would then lead to an increase in the compliance.37 However the observed effect on the compliance is surprisingly small. Naively one could expect a stronger influence as even a small number of cavities decreases the area of connected surface (see snapshots in Figure 8) and thus the confinement significantly. The small influence of the appearance of new cavities might be due to the fact that for our experiments the boundary conditions are intermediate between the frictionless case and the perfect bonding case. Therefore, the parabolic pressure profile observed for perfect bonding may already be altered in the very


Figure 21. Relaxation of the normalized compliance C as a function of time during the stop for 8AA on steel. The solid line represents the prediction from the rheology, whereas the dotted lines are the results obtained from the tack tests. Stop 1 and stop 4 represent one stop at low initial stress (σ0 ) 0.13 MPa) and one at high initial stress (σ0 ) 0.22 MPa).

Figure 22. Relaxation of the normalized compliance C as a function of time during the stop for 2AA on EP. The solid line represents the prediction from the rheology, the dashed line represents the prediction from the rheology corrected by the debonded area, and the dotted lines are the results obtained from the tack tests. Stop 1 and stop 3 represent one stop at low initial stress (σ0 ) 0.13 MPa) and one at high initial stress (σ0 ) 0.22 MPa).

beginning of the test by the boundary conditions. In this case the appearance of a not too high number of new cavities changes the compliance only slightly. The increase of the compliance for the layer of 8AA is compared to the predictions from rheology in Figure 21. For this adhesive, the increase in compliance is always significantly more pronounced than the creep of the adhesive would predict. Since the video captures show that, even for the highest value of σ0, the decrease in loadbearing area due to the appearance of cavities is at the most 20%, this cannot explain an increase in compliance of a decade. In this case a large number of new cavities appear during the stop, and the sharp increase in compliance might thus be due to a decrease in the effective degree of confinement of the layer, i.e., the relevant a in the a/h0 expression of eq 12 is no longer given by the radius of the probe but by the distance between neighboring cavities. When the adhesive is debonded from a low adhesion surface, the situation is in many respects clearer. On Figure 22, the compliance of the adhesive layer is compared to the prediction from rheology. One can immediately conclude that in this case the relaxation of the adhesive

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is much faster than that predicted from the rheological measurements alone. This is in agreement with the fact that strong propagation of cavities is observed at the interface during the stops and that the contact area is thus decreasing strongly (see Figure 9). We can try, in this case, to account for the debonded area and correct the prediction from rheological measurements by using the real contact area. To do so the debonded area has been measured from the snapshots as a function of time as can be seen in Figure 10. We then assume that the real contact area is circular and calculate the radius a as a function of time. We then use eq 12 and replace a/h0 by a(t)/h0. When the predictions are corrected from eq 12 in this way, they are in reasonable agreement with the experimental results from the probe test. This suggests that the fact that the contact area is obviously not circular, as can be seen on the snapshots (Figure 9), does not affect the compliance in a significant way. This result is rather surprising, and in contradiction with the result obtained for the 8AA on steel. 6. Discussion The main results of our investigations can be divided into three categories which will be now separately discussed. First of all we have obtained some results which should be generally valid for soft adhesive materials, in particular we have identified failure mechanisms and modes which are active when the material is kept under moderate levels of tensile stress. Then we have obtained some results which are more specific to the acrylate model system which we have used and in particular on the effect of the presence of acrylic acid in the polymer on its adhesive properties. Finally we have developed some new analysis and experimental methods potentially useful to assess and compare the long-term strength of these adhesives. We identified two important failure mechanisms that occur when a soft adhesive is kept under a tensile load: the nucleation of new cavities and the growth of these cavities as cracks at the interface between the adhesive and the adherent. When the adhesives were bonded to a steel surface, both mechanisms were observed, while on EP surfaces only crack propagation was observed under our experimental conditions. We never observed homogeneous creep of the adhesive as the only failure mechanism regardless of the loading conditions and surface and chemical composition of the adhesive. This is an important result since it clearly shows that unless the sensitivity of these specific mechanisms to the molecular structure of the adhesive is understood, there will be no hope to predict the lifetime of the bond. Since cavitation and crack growth are processes that entail locally large strains of the adhesive, it is highly unlikely that linear viscoelastic properties alone will be able to predict the nucleation or growth of these cavities. When the adhesives were adhered on steel surfaces, the system comprised of the adhesive layer and the apparatus (in series) appeared to evolve toward an equilibrium position (within the time frame of our experiment). This equilibrium position could be characterized by two parameters: the equilibrium stress σF and the energy dissipated during the partial failure process. The existence of this nonzero equilibrium value suggests that for that particular adhesive/surface combination the bond could last a very long time without catastrophic failure. On the contrary when the adhesives are adhered on EP surfaces, the behavior is significantly different. Cavities that were formed in the initial loading stage always propagated as interface cracks over time, leading

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either to a spontaneous failure of the adhesive bond or to a very significant decrease in stress. No new cavity was observed during the stop of the motors, and no equilibrium value σF was recorded. This very different behavior may indicate the existence of two different types of substrates: those where cavity growth can be stabilized or nearly stopped, implying the existence of a threshold adhesion energy G0 (at vanishing crack velocities) much larger than the thermodynamic work of adhesion, and those where the adhesion energy is simply a function of crack speed with a limiting value G0 of the order of thermodynamic values. The second type of substrate could not really sustain stress over a long time. This existence of two categories of substrates is an important point of further investigation which would need further data on a wider range of systems. Finally we have precisely measured the compliance of very confined adhesive layers and compared these results with current models.25,34 In all cases the experimentally observed compliance of the layer is significantly higher than what is predicted by the theoretical models. This is in contradiction with previously published results on less confined layers, where the models based on linear elasticity of incompressible layers fared much better.37 Interestingly the century old Stefan equation38 predicts very well the force displacement curve of a Newtonian fluid layer under traction20,22 with similar degrees of confinement as our solid layers. At this stage one can only speculate that the large strain deformation at the edge of the contact 40 and maybe the boundary condition at the film/probe interface invalidate the model for large degrees of confinement of the layer but further work to elucidate this point is clearly needed. Furthermore, in most cases, the time dependence of the compliance during the relaxation process could be well predicted by a simple model which did not take into account properly the effect of a change in confinement due to the appearance of new cavities but simply considered a change in load-bearing area with time. The second type of result which should be discussed is the effect of acrylic acid on the failure mechanisms. We specifically synthesized model acrylic systems with identical molecular weight distribution and identical crosslinking conditions, to avoid any coupling effects due to a change of both comonomer and molecular weight. Furthermore we chose molecular compositions and architectures (in terms of gel fraction) which are extremely close to the composition of real adhesives. Therefore our study is the first that really can claim to investigate the effect of acrylic acid on the adhesive properties of PSA. Several key results merit further discussion. While the existence of an equilibrium value of stress was found for all three adhesives on steel, the equilibrium position σF increased with the amount of acrylic acid. This value of σF could be predicted by the results obtained for σmax from a standard probe test: σF is approximately given by σF ) 0.3σmax for all three adhesives. When considering now the dissipated energy on steel, one observes for identical σ0 less dissipation for 4AA than for 2AA in agreement with the lower stress relaxation observed for this adhesive. Surprisingly, for the 8AA a higher dissipation was found, which is in disagreement with the further increase of the elastic modulus G′ observed (38) Stefan, J. K. Akad. Wiss. Math. natur. Wien 1874, 69, 713-735. (39) Josse, G. Ph.D. thesis, Universite´ Paris VI, Paris, 2001. (40) Roos, A. Ph.D. thesis, Universite´ Paris VI, Paris, 2004.

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for this adhesive. This finding is accentuated when considering the dissipated energy as a function of σ0/σmax. In this case a master curve is observed for 2AA and 4AA; the 8AA however dissipated significantly more. This peculiar behavior is due to strong cavitation observed for this adhesive, but the underlying reasons behind this poor resistance to cavitation relative to the elastic modulus remains unknown. It is of course tempting to interpret these results in terms of the rheological and adhesive properties of the three adhesives. Concerning σF, the respective values obtained for the three different AA contents correlate well qualitatively with the increase in elastic modulus G′ observed with increasing AA content. However the question of defining a characteristic frequency precludes a detailed comparison. The prediction of the amount of dissipated energy during the relaxation is even more complex since it is sensitive to their resistance both to cavity nucleation and to cavity growth. What can be said however, by analyzing both the images and the amount of dissipated energy, is that the 8AA adhesive seems to have a different balance in properties than the two others, with a very high resistance to interfacial cavity growth, but a much lower relative resistance to cavity nucleation. An attempt to quantify these two types of resistance for elastic systems by the parameters Gc and E has been recently made for elastic systems,7 but an extension to highly viscoelastic systems remains difficult. When considering the dissipated energy on EP, it is the softer 2AA that dissipates less energy under low stress. On the other hand the standard probe test does not discriminate between the three different adhesives on this surface which are equally weak. This interesting result shows the difficulty of a direct comparison between rheological properties and adhesive performance. The sharp difference in behavior between the two substrates highlights the importance of adhesive interactions. On steel, resistance to crack propagation is high, so that the most important property the adhesive must have is a good resistance to the formation of cavities. On the contrary on EP surfaces, resistance to cavitation is not very important because failure occurs by crack propagation. It is the balance between these two properties that has to be optimized. Clearly these two properties are not sensitive to the same mechanical properties of the adhesive. The cavitation mechanism is mainly controlled by the elasticity of the adhesive, given by G′,1,9 while the resistance to crack propagation is mainly controlled by the interfacial interactions and by the dissipative properties of the adhesive G′′ or tan δ.8,39 Our results show that on steel the best adhesives are the more elastic 8AA and 4AA, while on EP it is the softer 2AA adhesive which is the most resistant to crack propagation. From the point of view of the methodology, we have identified two parameters to characterize the behavior of our adhesives under a tensile stress: namely, the equilibrium stress σF and the dissipated energy during the relaxation Ediss. We have also studied the evolution of the compliance of the layer under stress. The two parameters do no reveal the same effects: while σF is well correlated with the peak stress in a standard probe test, the level of dissipated energy has shown a distinctly different behavior of the 8AA adhesive. For practical purposes, it is not yet clear which parameter is the most significant at this stage and further work is needed to understand the relevance of what we have found, but it is likely that depending on the detailed load situation, one property or the other will be most relevant.


The comparison between the time dependence compliance of the layer and the creep compliance function (or the relaxation function) of the adhesive can be a useful tool in the case where no visualization of the debonding mechanism is available. In all cases where extensive debonding by cavitation or crack propagation was observed, the compliance of the layer increased faster than that predicted by the material function. Conclusion The stated goal of this study was to investigate a new method to assess the long-term resistance of a pressuresensitive adhesive under a moderate level of stress. Because the typical tests used in industry for this property are long and costly, it is highly desirable to develop a reliable short-term test which could predict the lifetime of a particular adhesive bond. We developed a specific test where the adhesive was kept under tensile load by a spring with a known stiffness while the deformation and average stress over time were monitored in conjunction with a video observation of the fracture mechanisms. This test was then applied to a series of model acrylic copolymers representative of commercial acrylic PSA. We have shown that confined layers of PSA under a moderate level of stress fail over time by two distinct mechanisms which compete with each other to relax the stress and involve the deformation of the adhesive layer: the nucleation of cavities in the bulk of the layer, which relax the hydrostatic pressure component, and the propagation of interfacial cracks. Depending on the nature of

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the surface and on the adhesive, the balance between these two mechanisms can be shifted toward one or the other mechanism. We never observed homogeneous creep of the adhesive as the only failure mechanism regardless of the loading conditions and surface and chemical composition of the adhesive. As a result the lifetime of such an adhesive bond cannot be simply predicted by a rheological function such as the relaxation modulus or the creep compliance. An important question raised in the Introduction is that of the relevance of a relatively quick test such as the probe test of adhesion on long-term resistance to failure. On the basis of our results, the value of σmax on steel is a good predictor of the long-term resistance to failure for the acrylic adhesives on steel. However in some cases as on the low adhesion surface EP, or when strong cavitation is observed, the relaxation tests add essential information that cannot be obtained from the standard probe test only. Although we remain with some unanswered questions, we believe that a methodology combining careful mechanical measurements with in situ observations of the failure modes is essential to understand which material and surface parameter control the long-term shear resistance of a PSA. Acknowledgment. We thank Alexandra Roos and Arnaud Chiche for useful discussions and invaluable help with the experiments. We gratefully acknowledge the financial support of the European Commission under the GROWTH program of the 5th framework program. Project No. G5RD-CT2000-00202 DEFSAM. LA049388S

Subcritical Failure of Soft Acrylic Adhesives under Tensile Stress

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