Performance modelling in modern product development

Afera explored “performance modelling for adhesive tapes” in 3rd Session of TechSem 2021

Afera’s 29 April online Session, part of our 4-part 9th TechSem, was moderated by Afera Technical Committee Vice Chairman Ian Grace, who is also business development manager at Loparex B.V., and included 2 presentations followed by a Q&A section. During Afera’s 90-minute webinar, Tobias Waffenschmidt, senior engineer at 3M, discussed adhesives from experimental characterisation to computational modelling and simulation, and Matteo Ciccotti, professor of mechanics and physics of materials at ESPCI Paris PSL, linked peel, tack and shear in PSAs in a unified model for the audience. Below, each presenter has contributed an article and additional links to supporting information on his subject:

3M adhesive tapes: characterisation, modelling and simulation
by Dr. Tobias Waffenschmidt, senior engineer at 3M Deutschland

At 3M, we have noticed a trend towards virtual product design and optimisation and the demand from our customers for relevant modelling data. We therefore established a technology framework for material characterisation, modelling, finite element simulation, verification and validation. Depending on our customer’s needs, some things may be more relevant than others. Overall, we are aiming to bring all these different factors together to help our customers with their specific applications.

Sometimes customers come to us when they want to include one of our adhesive foam tapes into their finite element simulations. The questions are often very similar: Can you please provide us with Young’s modulus and Poisson’s ratio for your adhesive tape? The challenge here is that Young’s modulus and Poisson’s ratio, strictly speaking, do not exist uniquely. As can be seen from common stress-strain plots, the curves of 3M adhesive tapes are highly nonlinear, so a Young’s modulus cannot be defined uniquely. Furthermore, 3M adhesive tapes are highly viscoelastic. This means that it can make a huge difference whether you pull a tape slowly or rapidly. The higher the loading speed, the higher the stresses. The reverse effect can be observed when you pull a tape at higher temperatures: the higher the temperature, the lower the stress. The best way to model such behaviour is probably not by just using a linear-elastic material model based on Young’s modulus and Poisson’s ratio. Instead, you should consider using viscoelastic material models. With these kinds of material models, you can capture the nonlinearity and the rate-sensitivity pretty well. You can also request such models at our website here.

Of course, we regularly do characterisation tests for our adhesive tapes and create material models from these. But we also do advanced tests for validation. One particular validation test was a strip with a hole loaded under tension that we did together with a DIC system. The reason we chose this test is that it generates an inhomogeneous strain field, i.e. the strain is different over the surface of the sample. It basically contains contributions of all kinds of deformation states, like tension, shear, etc. As such, it is a good validation test to check whether the model can predict such a “deformation mix”. We simulated this example with a finite element model and got an almost perfect agreement between experiment and simulation.

3M adhesive tapes are also commonly used for vibration damping using the constrained layer damping technique. Assume that you have a metal panel which is vibrating somehow. Now, you want to reduce the vibration. One way to do this is to put a viscoelastic tape on top of the metal plate, and on top of the viscoelastic tape, you again add a stiff metal layer. If the metal plate periodically bends and vibrates, it causes shear deformation inside of the viscoelastic adhesive, because it is constrained by the aluminium layer at the top. This shear deformation now activates the dissipative mechanisms inside of the viscoelastic adhesive, and the structure is damped. We did a couple of tests on and simulations of an undamped plate and a damped plate. The agreement was very good in both cases. So, again, this gives us confidence in our material models and simulation approaches that we then can use for more advanced applications in this area.

About Dr. Waffenschmidt
Tobias Waffenschmidt is a CAE Specialist at 3M’s Corporate Research Laboratory in Neuss, Germany. His working areas at 3M cover the experimental characterisation, material modelling and numerical simulation of adhesive systems. This includes pressure-sensitive adhesives as well as structural adhesives. Having worked at 3M since 2015, Dr. Waffenschmidt holds a degree in mechanical engineering from the University of Siegen and a doctorate in computational mechanics from the Technical University of Dortmund.

Linking Peel, Tack and Shear in PSAs: towards a unified model in soft adhesives
by Prof. Matteo Ciccotti, professor of mechanics and physics of materials at ESPCI Paris PSL

The performances of pressure sensitive adhesives are generally evaluated using different loading geometries such as Tack, Peel and Shear Tests. It is difficult to link the behaviours of PSAs in these different geometries and to predict the result of one test from another, because the confinement of a soft and dissipative material prevents the use of standard fracture mechanics, which separates the interface debonding behaviour from the dissipation associated with the bulk deformation.

We presented here an original experimental investigation based on the modelling strategy proposed by Creton and Ciccotti. Using instrumented versions of both peel and tack measurements, we compared the adherence performances of a series of model PSAs based on styrene-isoprene block copolymers, while identifying the mesoscale mechanisms at play during debonding. This analysis method allows for modelling the contribution of the large strain rheology of the PSAs into the total work of debonding.

We clearly showed that both the adherence performances and local mechanisms can closely be related between peel and tack when considering both the similar confinement and similar strain rates of the fibrils that are spontaneously formed during debonding. We also presented recent developments of a new instrumented Shear Test, which is being used to complete the link between peel, tack and shear properties. This improvement in the understanding of the PSA performances opens the way to a sounder mechanical design of PSA-based joints. Read more in Prof. Ciccotti’s paper published by the Royal Society of Chemistry “Linking peel and tack performances of pressure sensitive adhesives” here.

About Prof. Ciccotti
Matteo Ciccotti has been a professor of mechanics and physics of materials at École Supérieure de Physique et Chimie Industrielles de la Ville de Paris (ESPCI Paristech, France) since 2010. He graduated in applied physics from the Università di Bologna (Italy) in 1996, where he also got his PhD in 2000 through studying the mechanics of rocks and their relation to earthquake dynamics. He then worked as a CNRS researcher at Université de Montpellier 2 (France) on the nanomechanics of slow crack propagation in oxide glasses. The present research projects at the Laboratory of Soft Matter Science and Engineering at ESPCI Paristech concern the space and time scales of the dissipation mechanisms in the fracture mechanics of polymers and composite materials. 3 main actual subjects are 1) the adherence energy of soft polymer adhesives; 2) the fracture energy of glassy polymers confined into fibre composites; and 3) the dissipation mechanisms during the impact failure of a laminated windshield. His achievements in the nanomechanics of slow crack propagation in oxide and polymer glasses earned him 2 international awards in 2016: the Darshana and Arun Varshneya Frontiers of Glass Science Award (The American Ceramic Society, USA) and the ECI Science Award (Engineering Conferences International, USA).

Q&A section

Adhesives: from experimental characterisation to computational modelling and simulation

Re: foam tapes, how do you simulate the effect of temperature? Dr. Waffenschmidt explained that if temperature is relevant for a particular application, which is not always the case, we usually make use of, for instance, the Williams–Landel–Ferry relationship, which performs well in a certain region, but sometimes not. You could perhaps use an Irenaeus relationship or a user-defined relationship, but usually they make use of the time-temperature superposition principle in the simulation model.

Re: the data for the simulated VHB, were the systems evaluated multi-layer or single-layer? It depends on the application. Most of their systems are multi-layer systems, but they mostly do not include the layered structure of the tapes explicitly in the model, because that is simply not efficient in terms of computational speed. Some of the tapes are layered, but they do not isolate the mechanical properties of the layer which may be different from each other. For shear and tension, for instance, I think that is a good approximation of what actually happens.

Is the equipment of your Tapered Double Cantilever Beam (TDCB) Tests readily available from machine builders? No, it is not – it is custom-built. For the TDCB Test, there are ISO and ASTM standards available, but Dr. Waffenschmidt is pretty sure that the major universal tensile testing machine suppliers do not supply such equipment, so they built it on their own.

You said that you can experimentally measure cohesive zone parameters for the 3 modes. How do you measure in mode 2, which represents sliding? You are right. There are some assumptions and approximations behind these. Mode 1 is certainly well-established and not that complicated. Mode 2 and especially mode 3 has some magic behind it. To simplify things a little bit, people usually assume that mode 2 is equivalent to mode 3, and they make that assumption as well. But then question is how you perform mode 2 measurements? For structural adhesive tapes, they make use of the Tapered End-Notched Flexure (TENF) Test. You can also perform this in a tapered version, but they cannot do that internally at 3M, because the samples get to be 80 centimetres long—so long that they do not fit into their testing machine. Because of this, they have restricted themselves to the shorter version of the TENF Test, which allows them to deduce GIIc in a sophisticated way. Here the agreement was good when they also compared it to numerical simulations. But of course friction plays a role, and to what extent friction perhaps superposes what you actually want to measure is a good question. Dr. Waffenschmidt said there is still plenty of work for them to do in this area. Dealing with these issues pragmatically, they first have to make use of what is established in the scientific literature.

If you do a Shear Test, if you wait for 3 days, then you have a 2-centimetre overlap which has slid, meaning that you have a typical strain of 1,000. Perhaps you have had some sliding, bad rupture of bonds or just rheology—it is difficult to tell. How do you get parameters out? The beauty of the PSAs and VHB tapes is that we discovered awhile ago that the results from the Shear Tests and the Butt Joint Tension Tests can be used directly to parameterise a cohesive zone model. So you do not even need fracture mechanical tests for the PSAs; you can make use directly of these “relatively simple” Shear Tests and Butt Tension Tests to parameterise your cohesive zone model. All this is highly rate-dependent, and that is where is starts getting complicated. To get the rate-, temperature- and thickness dependence into the cohesive zone model is what we are trying to achieve right now.

How would you model cyclic loading on structural adhesives? There is plenty of research currently being conducted in this area. Dr. Waffenschmidt said he would not utilise cohesive elements but model with continuum elements such as linear elastic and ideally acquire an S-N curve—a Bula curve for the adhesive—which is not that easy to do. And then compare the simulation results to the S-N curve to make sure you do not exceed the fatigue limit. He would stick to this “easy approach”.

What are the limitations of your modelling approach? What kind of hyperelastic-based model do you use? Adhesive thickness and temperature play a role in most models. We try to include the temperature- and strain-rate dependence in the models by making use of the WLF relationship. Re: hyperelastic potentials, that depends on the material: Sometimes a neo-Hookean or a Mooney-Rivlin is enough. Dr. Waffenschmidt tries to restrict themselves to the more simple potentials with fewer coefficients in order to avoid issues with convergence.

Is the modelling consistent between DMA data and finite strain data? Yes, Dr. Waffenschmidt tries to fit everything in simultaneously. For some tapes, they are able to fit the DMA data and the large-strain tensile butt tension and shear data into one single material model. This is not easy, but it is what they have done in the past.

How do you access high-strain rate or finite strain above 10%? We make use of drop-tower testing—drop towers that we have at our headquarters in St. Paul. Dr. Waffenschmidt’s colleagues there are able to perform high-strain rate tests at coupon level. It is not easy to calibrate material models to such “system-level” tests, but they have been successful in doing this in the past.

How accurate is your modelling approach for compressible foams re: transverse strain behaviour? If you really focus yourself on the compression behaviour and try to calibrate that accurately, the behaviour turns out to be fairly accurate.

In your opinion is the WLF shift factors approach sufficient to model thermal effects for finite strains? Probably not anymore, Dr. Waffenschmidt said. It has its limitations, and they make use of more sophisticated techniques at 3M for understanding thermal effects on large strains better. For Prof. Ciccotti, it was clear that it would not be sufficient, but in the 3 to 4 systems they tested recently, they could prove that the time-temperature shift factor which they use in linear rheology and which is easy to measure, they could also collapse most of our non-linear measurement. This was very surprising and interesting, but he does not know how this may be specific to the kinds of adhesives they use.

In your DIc example, defamation mainly influenced by compression behaviour, what about comparison of forces? For the strip with the hole, it was mainly tension-dominated. If the question is referring to compression of the rubber seal that Dr. Waffenschmidt showed in the introductory section, they also compared the forces to each other from simulation and tests (which he did not show in today’s presentation), but he feels they match each other pretty well, and the hysteresis was also covered. Those interested can contact Dr. Waffenschmidt for more information about this.

Can you explain in more detail why it is so difficult to model adhesive interfacial failure for adhesives with the Finite Element Methods? Dr. Waffenschmidt answered that the difficulty lies in the many various unknown factors which play a role in this, the surface energies or surface roughness of the substrates and things related to this that play a role at the interface. It is simply very difficult to generate representative material parameters and test data at the interface. The second, more practical reason why this is also not important from a practical point of view is that most of their customers are looking for cohesive failure, such as foam splits, because then they can be certain that everything went correctly in their application. If they have adhesive on both sides of the substrates, they are assured that with surface prep, everything was alright, and the weakest link in the bond is the adhesive. This is why, from a practical point of view, it does not really matter to Dr. Waffenschmidt as a simulation engineer who focuses on cohesive failure most of the time. In this case, he is prepared to answer most customer enquiries. Not all, but most of them.

In the recent presentation given by Steven Abbott, he discussed surface energy and how it is not directly related to adhesion; however, we treat many surfaces in order to improve adhesion, and we check the preparation levels by measuring surface energy – a sort of check to ensure that surface prep has been performed correctly. If not relying upon checking surface energy, what would you recommend in terms of surface preparation, because 3M supplies into automotive, involving adherence to metal? Sometimes you are adhering to plastics? Dr. Waffenschmidt emphasised that he is not an application engineer working directly with customers in these areas, but he has performed many tests in the lab. He has observed that sand- or grit-blasting or wiping with solvents such as MEK and n-heptane until no dirt comes off the surface anymore should already give you a nice, uniform surface which usually leads their tapes to fail and foams to split cohesively. This has worked for him in the lab, but he cannot guarantee that this will work for every real application case.

Linking peel, tack and shear in PSAs: towards a unified model in soft adhesives

If you were the owner of a small tape company and did not possess knowledge of the next level of testing—performance modelling—in-house, where would I go about obtaining this knowledge? Working with both formulators and users of adhesives and even holding instructional sessions, Prof. Ciccotti said that he aims at developing fundamental understanding and providing design concepts to anyone who would be interested. Anyone who is interested should contact him directly, as his team is very interested in learning from users of adhesives and tapes in developing their concepts.

Do you plan to co-operate with tensile machine manufacturers to incorporate models into their software to automatically compensate according to the model? Prof. Ciccotti has never thought about this, but if he knew there were such a need, that would be interesting.

You measured the static shear towards the end of the presentation. In the adhesive tape industry, static shear is quite a common tool. In the label industry, dynamic shear is used more often. Do you expect to focus more on dynamic shear in the future? Do you think it is a better tool than static shear? Dynamic shear is interesting. It is potentially very different, because when you go faster, you start having inertial problems or limitations in your backing, depending on the type of backing you use. You measure something different from just rheological effect. This is a very interesting topic, which is related to shock wave physics. Prof. Ciccotti plans to study this area further, but he wants to close off some more quasi-static rheological features first, completing the link between peel, tack and shear in a nice way, and then he will delve into inertial effect.

The peel force shown in many of the diagrams is along the plain of the substrate and the peel angle is considerably less than 90˚. Is there a reason for this other than showing the fibrils, because during the manual peeling and test method peeling, the angle is always 90˚, 180˚ or considerably sharper? Prof. Ciccotti said that, indeed, you could limit yourself to peeling at 90˚ for understanding the effect of rheology. But they wanted to study the effect of angles, because the angles progressively induce shear. If you move to a 0˚ angle, you move to a Shear Test completely. So if we want to model the transition from peel to shear, it would be interesting to move progressively from one to the other and find out how long the approaches converge and diverge.

Another interesting point is that in the original Kendall modelling around this topic, there was some interpretation about why the peeling force depends on the angle, a topic which is not unimportant, because if you use Kendall models, you will have an energy release rate. You are aware that force depends on the angle, but not necessarily the peeling energy. And if you want the peeling energy to change as observed, you either have to change the mode of the cohesive zones, or there can be a subtle question of changing the stress distribution along the peeling backing. That is what they wanted to see, if through their instrumental techniques, when they change the angle, how the shape of the cohesive zone changes and whether this change can lead us to understand why the fractured energy really depends on the angle. Prof. Ciccotti’s team studied this and published a paper about it in 2015.

At the bottom right-hand side of the 4th slide on the bottom, there is a graph of viscoelasticity (de Gennes, 1988) in which the rheological phase changes are labelled. They move from “soft solid” through to “liquid” through to “hard solid”. In most people’s minds, the rheological phase changes are from “liquid” to “soft solid” to “hard solid”. Why was the order different? Prof. Ciccotti expects that when a crack runs through, you have a sudden change of boundary condition which corresponds with starting loading—like if you relieve stress at this one point. The short time, which is high-frequency behaviour, will appear very close to the crack tip. Then when the crack progresses and more time has passed, you move progressively to longer time, which corresponds to lower frequency, so you go towards softer behaviour of your material. Note that the liquid moment takes place after the crack has gone through, a time of relaxation ago. After the time of relaxation, you start to creep. This gives a distance, if you multiply this by the velocity of propagation. For weakly crosslinked soft PSAs, when moving to even longer times (distances of peeling front), you recover a soft, relaxed elastic behaviour. On the other hand, for non-crosslinked PSAs, the long-term behaviour will be liquid-like, since creep is not limited by crosslinks. 

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