On the wall slip phenomenon of elastomers in oscillatory shear measurements using parallel-plate rotational rheometry: I. Detecting wall slip

Accepted Manuscript On the wall slip phenomenon of elastomers in oscillatory shear measurements using parallel-plate rotational rheometry: I. Detecting wall slip Bastian L. Walter, Jean-Paul Pelteret, Joachim Kaschta, Dirk W. Schubert, Paul Steinmann PII:

S0142-9418(17)30249-0

DOI:

10.1016/j.polymertesting.2017.05.035

Reference:

POTE 5041

To appear in:

Polymer Testing

Received Date: 1 March 2017 Revised Date:

19 May 2017

Accepted Date: 24 May 2017

Please cite this article as: B.L. Walter, J.-P. Pelteret, J. Kaschta, D.W. Schubert, P. Steinmann, On the wall slip phenomenon of elastomers in oscillatory shear measurements using parallel-plate rotational rheometry: I. Detecting wall slip, Polymer Testing (2017), doi: 10.1016/j.polymertesting.2017.05.035. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

ACCEPTED MANUSCRIPT

On the wall slip phenomenon of elastomers in oscillatory shear measurements using parallel-plate rotational rheometry: I. Detecting wall slip Bastian L. Waltera,∗, Jean-Paul Peltereta , Joachim Kaschtab , Dirk W. Schubertb , Paul Steinmanna a Chair

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of Applied Mechanics, Friedrich-Alexander-University Erlangen-Nuremberg, Egerlandstraße 5, 91058 Erlangen, Germany b Institute of Polymer Materials, Friedrich-Alexander-University Erlangen-Nuremberg, Martensstraße 7, 91058 Erlangen, Germany

Abstract

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A systematic study is presented in order to reveal the occurrence of wall slip of pre-prepared elastomeric samples characterized with the use of rotational rheometry. To exclude effects that could be attributed to additional functional fillers, both an unfilled (primarily used) and lightly silica reinforced (complementary system) silicone rubber are evaluated. Cylindrical samples are prepared by casting using a standardized methodology and examined by means of a stress-controlled parallel-plate rotational rheometer. As a control test, samples are also cured within the rheometer (in situ), thereby fixing them to the measuring plates and firmly establishing their response in “no-slip” conditions. The experiments suggest that wall slip, postulated to be caused by an adhesive failure at the sample-plate interface, may occur if the deformation is sufficiently large and no cohesive failure is present. It is detected by an increase in the loss modulus that is related to the adhesive failure associated with local dynamic friction, resulting in increased dissipated energy. Direct (via raw waveform data and normalized Lissajous figures) and indirect (via fast-Fourier-transformation) analysis of the overall system response for a single steady state deformation cycle provided further insights into the mechanism of wall slip.

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Keywords: wall slip, adhesive failure, measuring artifact, large amplitude oscillatory shear, silicone rubber, parallel-plate rotational rheometry

1. Introduction

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For many years elastomeric materials have been character- 24 ized with respect to their dynamic mechanical behavior using 25 well-established experimental methodologies and equipment. 26 This includes, for instance, double lab simple shear experi- 27 ments using a servo-hydraulic actuator [1], a dynamic mechan- 28 ical analyzer in tension mode [2], rotational rheometry (ARES 29 rheometer) in torsion-rectangular mode [3], a Rubber Process 30 Analyzer [4], and parallel-plate rotational rheometry using ex 31 situ pre-prepared cylindrical samples bonded to the measuring 32 plates by an adhesion primer [5]. All these techniques ensure a 33 perfect force transfer onto the sample during the experiment up 34 to a certain deformation amplitude. 35 Recently there has been increased interest in the study of 36 field-responsive materials, such as magnetorheological elas- 37 tomers (see, for example, [6]). For this purpose, experiments 38 have been preferentially conducted using rotational rheome- 39 try, the only commercial apparatus currently available with a 40 magneto-coupled device. More specifically, a parallel-plate 41 configuration in conjunction with ex situ pre-prepared cylindri- 42 cal samples is typically used. Following an extended literature 43

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∗ Corresponding

Author Email address: [email protected] (Bastian L. Walter) URL: http://www.ltm.uni-erlangen.de (Paul Steinmann)

Preprint submitted to Polymer Testing

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survey on experiments generally conducted with pre-prepared elastomeric samples using rotational rheometry (see, for example, [7]), it was noted that there is a lack of information regarding techniques or sample treatments used to ensure that the specimen is firmly bonded to the measuring plates. Furthermore, a large number of researchers appear to convert the procedures developed to characterize viscoelastic fluids in order to study their solid counterparts. The viscoelastic nonlinearities typically observed by this methodology in conjunction with the use of pre-prepared specimens are often interpreted as material nonlinearities or, in the case of composites, nonlinearities related to micro-structural changes. However, there remains the question as to the effectiveness of the force transfer over the entire applied shear strain amplitude during these experiments. To put this into context, experiments of this nature are typical in the characterization of magnetorheological elastomers (see, for example, [8–12]) and other field-responsive rubber-like polymeric materials. Further difficulties may then arise due to the modified field-generative experimental configurations, as often visibility of the sample is impaired by the specialized apparatus design. The integrity of the sample-apparatus bond can therefore not be verified for the entire duration of the experiment. However, the loss of perfect adhesion, and consequently force transfer onto the elastomeric specimen, results in a relative displacement (non-constant velocity) at the sample-plate interface. The presence of this exMay 25, 2017

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2. Experimental setting

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2.1. Materials and sample preparation To separate effects that are related to the wall slip phenomena from those caused by any particles present in the elastomer, an unfilled room-temperature-curing 2-component silicone rubber (RTV-2) is primarily used in this investigation. Consequently, confounding phenomena (for example, the Payne effect) that could be attributed to functional reinforcing fillers typically present in commercial silicone rubbers (such as fumed silica) are excluded. In addition a commercially available, lightly fumed silica reinforced (approximately 2 vol.-%) liquid silicone rubber (LSR) is also used to qualitatively verify some experimental results. Both are polydimethylsiloxanes (PDMS) crosslinked by a platinum catalyzed addition reaction. The raw materials, namely vinyl-terminated PDMS with a cross-linker and vinyl-terminated PDMS with a platinum catalyst, are mixed in the ratio of 2:1 (RTV-2) and 1:1 (LSR). They are weighed with a precise scale (XA503S, Mettler-Toledo) and are homogenized using a SpeedmixerTM (DAC 150 SP, Hauschild) mixing at 2000 min−1 for 3 min at room conditions (25 ◦C). The 20 ml mixtures (always from the same batch) are subsequently degassed using a desiccator equipped with a vacuum pump. Rectangular 1 mm thick sheets are prepared by casting (using a custom made two part mold), during which the material is cured at 25 ◦C (RTV-2) or 120 ◦C (LSR) for at least 16 h in an oven (VT 6060 M, Thermo Scientific). Lastly, cylindrical samples (also referred to as “specimens”) of 20 mm are punched out of the sheet. The variation in the thickness of the samples is ±5 %. This method of sample preparation is referred to as the “standard” protocol or procedure. As a control test, samples are cured within the rheometer (in situ) and are, therefore, expected to be firmly bonded to the plates2 . Hereafter this experimental approach is referred to as the “control” protocol. Due to the low viscosity of the uncured mixtures a gap of 0.5 mm (as opposed to 1 mm for the ex situ pre-prepared samples) is used. The preparation conditions, including mixing and curing, are identical to the standard protocol. Therefore the materials, as measured by the cross-link density, are identical when compared to their respective counterparts. Measures taken to prevent possible sources of systematic error are listed and discussed in the supplementary information.

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rheometer. However, we limit the current discussion to the detection of slip by the analysis of experiments conducted with two methods of sample preparation (in situ and ex situ specimen curing, resulting in different specimen-plate bonding properties), two rotor surface topologies (smooth and serrated) and several methods of interpreting the data as measured from the rheometer software.1

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perimental artifact, known as wall slip (for a discussion on this105 issue with respect to fluids see [13] and the recent review by106 Hatzikiriakos [14]), potentially leads to a systematic error of107 the obtained experimental data and consequently its misinter-108 pretation. 109 From the authors’ point of view, the interpretation and pro-110 posed conclusions of experimental data conducted using this111 technique are, therefore, often questionable. This also includes (coupled) constitutive models derived from the ambigu-112 ous experimental observations. Overall, there appears to be a scarcity of critical discussion on the reliability of experiments113 performed at large shear strains using a parallel-plate configu-114 ration, in particular with reference to the inhomogeneous shear115 stress and strain distribution along the sample radius. 116 Wall slip is a recognized phenomenon that has been thor-117 oughly investigated in systems comprising polymer solutions,118 emulsions, particle suspensions (see [13, 15–17] and references119 therein), colloidal gels [18] and polymer melts (see [19, 20] and120 references therein). It leads to a systematic underestimation of121 rheological quantities such as the viscosity and the presence of122 an apparent yield point. Typically, the absence of wall slip is123 shown in parallel-plate rheometry either by the independence124 of the results from the gap size (see [21] and references therein)125 or by tailoring the physical (roughness) or chemical (surface en-126 ergy) measuring plate surface properties to promote maximum127 adhesion and thus force transfer onto the sample. The use of128 sand blasted, cleated or serrated rotor surfaces is assumed to129 prevent its occurrence, or delay it to larger shear deformations130 [15, 18, 22]. The cleated geometry introduced by Nickerson131 and Kornfield [22] can be used to eliminate wall slip in a va-132 riety of materials including fluids, suspensions and soft tissues133 that are prone to slip. 134 Regardless, the physical mechanism leading to wall slip, its135 detection and possible correction in systems such as suspen-136 sions, colloidal gels or polymer melts differs from that one ex-137 pects in soft solid bulk materials. In suspensions and colloidal138 gels it is generally believed that wall slip is related to the pres-139 ence of a thin layer of fluid adjacent to the test sample [15, 18].140 Polymer melts can possess two different slip mechanisms,141 namely weak slip (flow-induced chain detachment/desorption)142 which is only observed in linear polymer melts and strong slip143 (chain disentanglement) [20]. In the present work it is postu-144 lated that in viscoelastic solid materials slip might be caused by145 an adhesive failure (either global or local) at the sample-plate146 interface. 147 Although it is an accepted phenomenon, the literature on the148 topic of wall slip with respect to elastomeric materials is sparse;149 the authors are not aware of any publications devoted to this150 topic. In summary, to the best of the authors’ knowledge, it151 has not yet been firmly established whether slip mechanisms152 are precluded from experiments conducted with parallel-plate rotational rheometers and elastomers when using ex situ preprepared samples (with no adhesive treatment) in conjunction with specialized rotor geometries. In this work, a comprehensive and systematic study is presented in order to reveal possible wall slip when dealing with viscoelastic solids in conjunction with a parallel-plate rotational

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1 Although the development of a “slip model” to correct erroneous data (e.g. taking the coefficient of friction [23, 24] into account) would be of public interest (e.g. as done in [25, 26] for linear polymer melts) this would go very much beyond the scope of this work. 2 After the experiments, it was found that these specimens remained firmly bonded to the plates and it was necessary to immerse the parallel-plate set up in toluene in order to separate the sample from the plates.

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Figure 1: Serrated rotor and sketch of its surface profile. This design of rotor is primarily used to characterize magneto-rheological materials. Visible at the outer rim is a guard ring, present in both rotor types, that prevents the flow of magneto-rheological fluids around the rotor rim [27].

2.2. Oscillatory rheology

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2.3. Fast-Fourier-transform (FFT) rheology Fast-Fourier-transform rheology has been established as a powerful tool in the investigation and quantification of nonlinear viscoelasticity in oscillatory shear experiments (see [29] and references therein). In particular, it has been utilized to detect differences between materials that exhibit similar nonlinear viscoelastic behaviors (see [30, 31] and references therein). Concerning large amplitude oscillatory shear (LAOS), a comprehensive review on the subject is given in [31]. As an alternative to FFT rheology, Lissajous figures (as presented in [32, 33] and references therein) can also be used to analyze and quantify the nonlinear viscoelastic behavior. At large excitation amplitudes the material response is no longer sinusoidal. The viscoelastic behavior becomes significantly nonlinear and higher harmonic contributions become more pronounced. The storage modulus G0 (ω, γ0 ) and loss modulus G00 (ω, γ0 ) become, in addition to frequency ω, dependent on the applied strain amplitude γ0 5 . Under steady state conditions, the nonlinearity of the shear stress can be represented as a Fourier series of odd harmonics6 [37, 38]

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Oscillatory shear measurements are performed in a stress-186 controlled rotational rheometer (MCR 502, Anton Paar)3 equipped with a Peltier temperature control system set at 25 ◦C.187 A titanium parallel-plate configuration (20 mm), with the op-188 tion of two rotor types, is employed and the direct strain os-189 cillation (DSO) mode of the rheometer is utilized4 . The sta-190 tionary base plate (stator) and one of the rotors (PP20/MRD/Ti)191 have a smooth surface, whereas only that of the second rotor192 (PP20/MRD/Ti/P2) is serrated. Geometrical aspects of the ser-193 rated rotor, which has a pitted size of 0.5 mm, are shown in194 fig. 1. 195 In order to detect possible wall slip of elastomeric samples,196 both the ex situ pre-prepared standard and the in situ cured con-197 trol specimen are characterized by oscillatory strain sweep ex-198 periments in the strain range of 10−5 to 4 at 25 ◦C and constant angular frequency ω of 10 rad s−1 . Before each measurement a static normal force FN = 10 N is applied for 120 s to precondition the system, and is kept constant for the duration of each experiment. This results in a partial penetration of the serrated rotor surface (tips) into the sample’s upper surface. From the sample thickness and measured gap size the penetration was approximated to be 0.15 mm for RTV-2 and 0.18 mm for LSR. Table 1 summarizes the conditions used in each experimental protocol. Steady state waveform data with 512 sampling points per cycle are recorded and post-processed (using RheoCompassTM v1.13). From this, the evolution of the shear stress amplitude σ0 , storage modulus G0 and loss modulus G00 (more specifically, their 1 st harmonic) are obtained as a function of γ0 , the maximum applied shear strain amplitude at the sample’s outer

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rim. In the later text, the presented results are always the arithmetic average of values determined for at least three individual samples.

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3 To facilitate the conduction of experiments on magnetic field-responsive materials (to be studied at a later stage), the apparatus is also equipped with a magneto-rheological device (MRD 170/1T, Anton Paar) that obscures the view199 of the sample during the experiment. 200 4 The Modular Compact Rheometer MCR 502 provides two different oscillation modes to perform strain-controlled oscillatory measurements, namely the traditional strain oscillation and the DSO modes. In the traditional mode a stress sine wave is applied and the stress amplitude is iteratively adjusted until the desired strain amplitude is reached. In contrast, in DSO mode real-time position control of the strain sine wave is performed. For further information regarding the DSO mode the authors refer to [28].

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σ (t, ω, γ0 ) =

∞ X   σ0,n (ω, γ0 ) sin (nωt + δn (ω, γ0 )) , (1) n=1,odd

where the parameters σ0,n (ω, γ0 ) and δn (ω, γ0 ) are, respectively, the stress amplitude coefficient and the phase shift of the nth harmonic. To facilitate the quantification of the higher harmonic contributions, the normalized stress intensity of the n-th harmonic is commonly defined as σ0,n , (2) In/1 = σ0,1 where σ0,1 is the fundamental wave (1 st harmonic) of the stress response. 5 The rheometer software filters out the higher harmonic contributions and therefore solely provides the moduli for the agitation frequency [27]. 6 It should be noted that even harmonics may also need to be considered, as they have been detected during experiments [19, 34] and computational studies [35, 36] of wall slip.

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Protocol Standard Control

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3. Results and discussion

The outline of this section is as follows: In section 3.1 experimental results, as measured and computed by the rheometer software, are shown to demonstrate nonlinear viscoelastic behavior as observed in ex situ pre-prepared cylindrical samples, thereby providing a “macroscopic-view” of the overall system behavior. Comparison is then made between these cases and those using in situ cured samples, highlighting differences in the observed results. In section 3.2 a deeper evaluation of these results is conducted by investigating the recorded steady state waveform data. Lastly in section 3.3 a FFT analysis is performed to quantify the degree of nonlinearity of the strain and stress waveforms as detected by both protocols. Any inhomogeneities associated with the use of a parallel-plate config-255 uration in large amplitude oscillatory shear measurements are256 neglected. The LAOS experiments are not performed to ana-257 lyze true rheological material nonlinearities, but rather solely to258 demonstrate relative differences resulting from the use of both259 260 protocols that are related to the wall slip phenomena. 3.1. Evolution of dynamic shear stress, loss and storage moduli

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Before any comparative studies can be performed, it is first264 necessary to establish the reproducibility of the standard testing265 approach. The experiments were conducted using the serrated266 rotor (smooth stator) which, in combination with an applied ax-267 ial preload, is supposed to prevent slip between the sample and268 measuring plate. 269 Figure 2 shows the storage and loss modulus obtained by270 means of identical oscillatory strain sweep experiments for four271 pre-prepared standard samples (RTV-2) produced from a sin-272 gle batch. It is observed that the experimental reproducibility273 is very high, even at very large shear strains (γ0 ≈ 1). Both274 G0 and G00 possess a pronounced linear viscoelastic regime,275 in which the shear stress amplitude σ0 is directly proportional276 4

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It is crucial to note that the overall physical interpretation de-247 to the applied strain amplitude γ0 . Typical of the viscoelasscribed above is valid for the entire strain regime only when248 tic solid-like behavior expected for cross-linked rubber is that using cone-plate rotational rheometry. Utilization of a parallel-249 G0  G00 within the linear viscoelastic regime. However, at plate configuration at large shear strains results in an inhomo-250 γ0 ≈ 0.025 strain softening occurs. At this point the storage geneous strain distribution along the sample radius. Therefore,251 modulus starts to decrease whereas the loss modulus increases all results that are to be presented in the following sections are,252 and passes through a local maximum. Furthermore, it is obwhenever exceeding the linear viscoelastic regime, only qual-253 served that a cross-over in G0 and G00 is present and located itatively representative in the sense that we may demonstrate254 very close to this maximum. relative differences in the outcome of experiments conducted using both protocols. That is to say that these rheological quan10 10 sample 1 sample 3 tities might differ from those expected to be measured with a sample 2 sample 4 10 cone-plate configuration and therefore do not necessarily reflect the true rheological behavior of the tested material.

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Figure 2: Reproducibility of the oscillatory strain sweep experiments using the standard protocol (as detailed in table 1) on the RTV-2 material performed using a serrated rotor (smooth stator). The slight data scatter visible in G00 at low strains is due to resolution issues pertaining to the rheometer.

The measured nonlinear viscoelastic response, in particular the evolution of the storage and loss moduli (cross-over excluded), is comparable to the evolution of G0 and G00 typically obtained for particle reinforced rubbers (refer to [5, 39] and references therein). A strong comparison can be made between these observations and the experimental results of Clément et al. [5], who also used a parallel-plate configuration. However, there are no additional functional particles present in the RTV2 silicone rubber and, therefore, such an increase in G00 and the presence of a maximum is not expected [40]. The same holds for the cross-over, which would imply that for oscillatory shear strains γ0 > 0.2 the response is more viscoelastic fluidlike than solid-like since G00 > G0 . Therefore, the questionable experimental results detected by the standard procedure needs to be compared with the in situ cured control protocol to verify whether this nonlinear viscoelastic behavior is realistic or a measuring artifact related to the experimental method. A comparison of the RTV-2 as characterized by the standard and control protocol is made in fig. 3(a). The measurements using the control protocol are also highly reproducible, however they yield higher values of the measured moduli within the linear viscoelastic regime and a completely different strain

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dependency. Within experimental uncertainty the control spec-313 imen, which is firmly bonded to the plates thereby eliminating314 any slip effects, exhibits a nearly linear viscoelastic behavior315 over the entire range of the applied strain amplitude. 316 Through the evaluation of a second, complementary material317 using both experimental configurations, influences of the elas-318 tomer on the deviation in the observed response can be estab-319 lished. Figure 3(b) shows a set of data comparable to fig. 3(a)320 but for the lightly silica reinforced LSR material. Similar trends321 are demonstrated for both silicone rubbers, thereby providing322 qualitative verification that the overall system response is in-323 dependent of the tested elastomer. The experimental results324 achieved by the standard protocol using the serrated rotor con-325 figuration (smooth stator) are again lower than those of the con-326 trol sample. Overall, the evolution of σ0 , G0 and G00 are qualita-327 tively similar to those presented for RTV-2 (standard protocol)328 but offset to larger excitation amplitudes. For the standard pro-329 tocol it was additionally observed that the recorded value for330 σ0 tends towards a plateau value at high shear strains. With re-331 spect to the control protocol strain softening is observed for the332 333 in situ cured LSR samples above γ0 = 0.1. 334 It is concluded that the phenomena described above for the 335 standard protocol, neglecting effects related to the inhomoge336 neous stress-strain distribution along the sample radius, is a 337 consequence of wall slip. We consider wall slip to be caused 338 by an adhesive failure at the interface between the specimen 339 and the measuring plate. This is achieved once the critical 340 stress required to overcome the static friction is attained. As 341 the control sample is firmly bonded to the plates (which, as342 suming no delamination, results in perfect adhesion and force transfer throughout the entire duration of the experiment), it is deduced that the marked difference in the results between the two experimental protocols must be due to the presence of wall slip in the standard procedure. This primarily leads to the strain softening and the associated significant decrease in the storage modulus for the standard protocol.

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Figure 3: Comparison of the oscillatory strain sweep experiments for both materials using the standard protocol (serrated rotor, smooth stator) to the control protocol (smooth rotor and stator). With the control protocol the maximum torque limit of the rheometer (230 mN m) was reached at γ0 = 0.5 for RTV-2 and γ0 ≈ 1.5 for LSR.

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The evolution of G00 can be explained as follows: Slip is initiated at the point of highest stress on the sample-plate interface which, due to the parallel-plate geometry, is nominally at the sample’s outer rim. Due to the strain gradient along the plate radius, even if inhomogeneous in its nature, the local shear stress, and therefore the area of local slip, is dependent on the applied strain amplitude and increases with an increase in γ0 . It is assumed that, associated with the adhesive failure (and in conjunction with the oscillatory shear stress) is a stick-slip behavior wherein the material locally displaces to release (stored) energy and becomes re-attached to the plate once a stress below the critical value is attained. This recurring phenomenon generates dynamic friction and results in a dissipation of energy, which can be observed as an increase in the loss modulus. However, the cause of the local maximum in G00 remains unclear. We hypothesize that it might be related to the coefficient of friction and its velocity dependence (for example, see [23, 24]), but further experiments must be conducted to establish the reason for its presence. The moduli within the linear viscoelastic regime measured using the standard protocol are lower than those obtained with the control procedure. This discrepancy is related to geometrical aspects (namely the serration) and the gap setting7 . The tips only partly penetrate the specimen upon application of a static normal load (see section 2.2). Therefore, the true gap (as measured by the sample thickness) is larger than the value used by the rheometer software to perform the experiment and the applied deflection at a certain computed shear strain is smaller than expected. Consequently, the values of the shear deformation and the moduli (G0 , G00 ) are systematically underestimated. 7 The “zero-gap” condition is calibrated by applying a static normal force of 1 N between the base plate and rotor. With the serrated rotor, at this condition there remains an additional volume between the base of the serrations and the base plate. This volume is partially filled by the elastomer as a result of the static preload. It contributes to the measured response but is not accounted for, nor corrected, by the rheometer software.

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Figure 4: Photograph of transparent LSR sample upper surface, overlaid on a textured surface, after testing up to γ0 = 1 and γ0 = 4 with the standard protocol (serrated rotor, smooth stator).

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the shear stress, loss and storage moduli, as well as the evolution of wall slip. The results of this study and a discussion of the findings are shown in the supplementary information. Focusing on the evolution of the dynamic shear stress and moduli, it can be stated that wall slip leads to a significant strain softening together with an increase in G00 due to imperfect force transfer associated with dissipative processes, namely friction. The onset of slip can be detected by a significant increase of the loss modulus leading to a maximum in G00 and cross-over in G0 and G00 . For different low-damping materials, the critical strain at which slip commences is influenced by its modulus. A lower shear modulus leads to lower stresses at the sampleplate interface for a fixed strain amplitude, and ,therefore, a higher strain at which slip starts to occur. However, attention has to be given to highly filled reinforced rubbers, where this phenomenon might overlap with a real nonlinear material response related to the reinforcing filler (e.g. fumed silica or carbon black), known as the “Payne” or “Fletcher-Gent” effect. Lastly, it is important to reinforce a point mentioned in section 1 that, when characterizing field-responsive materials, it is not possible to attain visual access to the sample during the experiment. Consequently, any slip and buckling effects as seen in the complementary experiments cannot be visualized and confirmed using specialized field-responsive configurations. In summary, in unfilled elastomeric systems a pronounced increase in G00 is a clear indicator of the onset of slip. From fig. 3 it would appear that slip is initiated in the standard protocol with the serrated rotor at approximately γ0 = 0.01 for RTV-2 and γ0 = 0.1 for LSR. As wall slip in the standard protocol utilizing the serrated plate is very well defined (slip only at the serrated rotor surface) and highly reproducible, all experiments presented in the following sections are performed by means of the serrated rotor only. However, it should be noted that for the purpose of performing small amplitude oscillatory shear (SAOS) experiments, the smooth measuring plate (as discussed in the supplementary information) is preferred as results derived from this configuration are consistent with the in situ cured control results. Its use removes the systematic error associated with the zero-gap setting, and therefore provides the correct values of the storage and loss modulus at low strains. Regardless of the absence or presence of wall slip it should

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In addition to this, the penetrating rotor tips induce a locally384 non-uniform stress distribution, thereby further affecting the ex-385 perimental outcome. 386 As a further confirmation of the presence of slip, a wear pat-387 tern present on the sample’s upper surface caused by the rotor388 tips is detected after the experiment. Shown in fig. 4 are post-389 experiment samples comprising LSR. They were made to un-390 dergo very large strains and a pronounced pattern was produced391 on their upper surface. Further analysis of these surfaces con-392 ducted using a laser scanner are shown in the supplementary393 information. From these analyses it has been confirmed that394 visible in the photographs is the evolution of grooves in the sur-395 face made by the rotor tips during the process of slip. It should396 be noted that there exists an inner region where no abrasion has397 occurred due to the stress being lower than that necessary to398 initiate slip. No wear pattern was visible on the back side of the399 400 sample which was in contact with the smooth base plate. Consequently, it is proposed that wall slip is present in the401 standard protocol at the serrated rotor surface only. This propo-402 sition has been visually verified in complementary experiments403 using a high-speed camera in conjunction with an alternative404 apparatus. Since it is not possible to attain visual access to405 the sample when using the current experimental configuration406 (see footnote 3), a second stress-controlled rotational rheome-407 ter (DHR-3, TA Instruments) equipped with an ETC dispos-408 able plate configuration (TA Instruments) has been used for this409 purpose. Oscillatory strain sweep experiments were repeated410 using similar experimental conditions to those used in the pri-411 mary analysis. A custom made (alumina) serrated rotor set-up412 was manufactured according to geometrical aspects of the ser-413 rated rotor (PP20/MRD/Ti/P2) used in the primary investiga-414 tion. Shown in fig. 5 are two frames captured from the high-415 speed camera which clearly illustrate the relative motion of the416 serrated rotor to the sample at high strains, and lack thereof at417 low strains. Whereas the sample remained firmly bonded to the418 smooth base plate (within visual experimental uncertainties), a419 significant relative displacement between the sample and the420 serrated rotor surface was observed at large shear strains, lead-421 ing to the previously described the visible wear pattern. 422 Further studies were conducted using a smooth rotor to de-423 termine the influence of the rotor geometry on the evolution of424

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again be reinforced that data, as measured by the parallel-plate456 configuration, are not suitable for the determination of true rhe-457 458 ological nonlinear viscoelastic material quantities. 459

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3.2. Waveform data 460 Wall slip significantly affects the shape of the recorded stress461 waveform, in particular it leads to an asymmetric or even462 chaotic non-sinusoidal stress response [18, 19, 25, 34, 35, 41].463 However, yielding affects the stress waveform in a similar man-464 ner [41, 42] and, therefore, either phenomenon might easily be misinterpreted as the other. Slip can be excluded as a confounding factor only by performing experiments with at least two different gap heights at a fixed frequency and strain amplitude. Yielding is verified if the waveforms, as determined by both experiments, are identical8 , otherwise the detection of slip is confirmed (see [41] and references therein). The recorded data underlying the results in fig. 2 are further analyzed to investigate how slip affects the steady state (equilibrium) strain and stress waveforms measured during the experiments. Figure 6 shows a representative example of steady state waveform data for the strain γ (t) and corresponding shear stress σ (ω, t) as obtained for four individual samples (same batch) with the standard protocol (serrated rotor, smooth stator) and strain amplitude γ0 = 1. From the shear stress waveform, it can be seen that a combination of viscoelastic behavior and slip leads to a significant asymmetric, non-sinusoidal response with a pronounced phase shift. It is also observed that the applied strain waveform deviates from a perfect sine curve (discussed further in section 3.3),465 likely affecting the corresponding shear stress and viscoelastic466 moduli. Regardless of the presence of numerous inhomoge-467 neous nonlinearities (e.g. plate serrations; large deformations468

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when using parallel-plates), the overall reproducibility of the data is very high. To reinforce the deficiencies in this experimental procedure, we highlight once more that the use of a parallel-plate configuration results in an inhomogeneous stress-strain distribution along the sample radius. Therefore, when performing measurements in the nonlinear viscoelastic regime the recorded strain and stress waveforms, and corresponding rheological quantities, are not truly representative of material’s rheology.

469

8 As

470

the custom made two part casting mold produces only a 1 mm thick specimen, this criteria concerning the gap separation and the representative471 sample thickness cannot be evaluated in this study. 472

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Figure 5: Photographs of oscillatory strain experiments conducted using a secondary apparatus that allowed visual access to the tested sample; also see supplementary MP4 files. Collinear representative points on the stator, rotor and sample were marked before the sample was preloaded or deformed. The relative displacement between the serrated rotor and sample is clearly shown in fig. 5(b).

4

= 1.0, T= 25°C = 10 rad/s, F

N

= 10 N

RTV-2

-2x10

*

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t

Figure 6: Reproducibility of the waveform data at γ0 = 1 obtained for four individual RTV-2 samples using the standard protocol with a serrated rotor (smooth stator) at ω = 10 rad s−1 and FN = 10 N.

To firmly establish that these loss mechanisms are indeed related to wall slip, the overall system response measured at the onset of increase in the loss modulus, its peak values, and beyond its maxima for the two materials investigated is presented in fig. 7. Therein the evolution of slip as detected by the change in normalized stress response σ (ω, t) /σ0 is illustrated for an increasing excitation amplitude with comparison to the in situ cured control response. The large difference between the data

ACCEPTED MANUSCRIPT RTV-2 control protocol

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(a) Onset of wall slip for RTV-2 (γ0 = 0.01) and LSR (γ0 = 0.1) 1.0

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(b) At the local maximum in G00 for RTV-2 (γ0 = 0.15) and LSR (γ0 = 1)

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(c) Beyond the local maximum in G00 for RTV-2 (γ0 = 0.5) and LSR (γ0 = 3.3)

Figure 7: Comparison of the normalized stress waveform (left) and Lissajous figure (right) obtained for two materials using the standard (serrated rotor, smooth stator) and control protocol at ω = 10 rad s−1 and FN = 10 N. Note that the depicted data points represent a portion of the 512 sampling points taken per period. For (c), there is no data from the control protocol for LSR as the torque limit of the rheometer is exceeded.

473 474 475 476 477 478 479 480 481 482

attained for the non-slip (control) versus the slip (standard) con-483 figuration is evident in this figure. Up to the onset of slip (de-484 tectable as an increase of G00 in fig. 2, visually approximated to485 be at γ0 = 0.01) the normalized stress response is sinusoidal,486 which is expected within the linear viscoelastic regime. The normalized Lissajous figure is ellipsoidal and the dissipated en-487 ergy, given by the area within the curve, is very small. With in-488 creasing strain amplitude, the effect of the wall slip phenomena489 becomes evident as the normalized stress response proceeds to490 be progressively less sinusoidal and the apparent phase shift (a491 492

8

combination of viscoelasticity and slip) increases. Associated with this is an increase in energy dissipation primarily due to an increase in the area of local dynamic friction present at the sample-(serrated) rotor interface. As the shear strains at which slip is initiated is different for both materials, data corresponding to specific characteristic points related to the evolution of G00 are shown in fig. 7. We define these characteristic points through γ0max which is the strain at the maximum in G00 as measured using the standard protocol. Furthermore, as the magnitude in applied strain and

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stress response is different for each material in each configu-529 3.3. Fast-Fourier-transformation of the waveform data ration at these distinct points, all data have been normalized. FFT transformation of the waveform data is used to quantify The results clearly show that the normalized response is inde-530 531 the nonlinearities obtained in the stress response (as shown in pendent of the investigated material as a quantitatively similar 532 fig. 7). As it is important, it must be indicated once more that behavior is detected at the evaluated points. Before the onset of 533 this method has not been applied to analyze nonlinear material slip, the highly elastic (viscoelastic) response of both materials 534 effects, but rather solely to detect relative differences in both is captured in both the standard and control configurations. At 00 max 535 protocols related to slip and to detect the onset and the developthe maximum in G (γ0 /γ0 = 1), there is a marked deviation 536 ment of the wall slip phenomena. between the control and standard protocols, the latter of which The FFT transformation is of particular interest since the dedemonstrates a very dissipative nature. This deviation is even537 more pronounced beyond this point (γ0 /γ0max = 3.3), with the538 velopment of even harmonics [19, 34, 35] is considered as an 9 normalized stress waveform showing increased asymmetry and539 indicator of wall slip . Such components of the waveform have 540 in the past been generated and quantified for fluid systems by a greater phase shift. 541 means of FFT rheology [31, 36]. Therefore it is expected that It has been established that there is a link between the evolu-542 a relationship between the higher harmonics and, if present, the tion of G00 and the normalized stress-strain response in rubber-543 onset of wall slip can be inferred. like, viscoelastic materials with low damping properties. From544 Both the pre-prepared standard (serrated rotor configuration) these results it is hypothesized that the evolution of slip is gov-545 and in situ cured control specimens have been analyzed with reerned by, amongst others factors, the friction coefficient at the546 spect to the normalized stress intensity of the 2nd harmonic conslip surface (dependent on the applied normal force and veloc-547 tribution (I ), the result of which is shown and compared with 2/1 ity [23, 24]) and the viscoelastic properties of the elastomer. 548 the normalized stress intensity of the 3rd harmonic contribution To quantify the apparent degree of nonlinearity present due549 I3/1 in fig. 9. Beyond the range of experimental uncertainties, to wall slip, the difference in the phase shift between the control550 no even harmonic is present, neither in the standard protocol and standard protocols are evaluated. The relationship between551 possessing pronounced slip nor in the control protocol. With a rd the applied strain and phase shift directly resulting from slip552 focus on the point at which the 3 harmonic becomes prevalent, ∆slip = |δslip − δno slip | for the two materials is illustrated in fig. 8.553 it can be stated that wall slip is clearly associated with an inAs had been previously observed, it is apparent that the sample554 crease in this odd higher harmonic in conjunction with the used composition affects the threshold strain (and therefore stress)555 equipment. To qualify this, we note that this harmonic is hardly required to initiate slip. At strains less than γ0 ≈ 0.01 for RTV-556 detectable in the control specimen at γ0 = 0.5 (the torque max2 and γ0 ≈ 0.1 for LSR the overall system response is identical557 imum of the rheometer for this material and these experimental for both protocols, clearly indicating that there is no slip present558 conditions). The above result remains aligned with those obin the system. Note that although this is a direct measurement559 tained by the analysis of the steady state waveform data and of the slip effect (and removes the influences of material non-560 Lissajous figures presented in section 3.2. Figure 10 illustrates the evolution of the odd stress intensities linearities), the values predicted here are comparable to those561 initially suggested through the increase in G00 from fig. 3 (re-562 I3/1 , I5/1 and I7/1 with strain as obtained for both materials meafer to section 3.1). Above these strains slip is registered by the563 sured using the serrated rotor (smooth stator). Within the LVE 564 regime up to the onset of slip no odd higher harmonic contriburheometer as an increase in the phase shift (∆slip ). 565 tions are found (within the bounds of measuring uncertainties). 566 The deviation in the recorded intensity at low shear strains, ob567 servable up to γ0 = 10−4 , can be attributed to resolution issues 1.2 568 of the rheometer related to torque or angular deflection. It is 1.0 569 noted that the normalized stress intensity I3/1 starts to increase 0.8 570 at a strain amplitude slightly greater than that at which the loss 571 modulus is found to change, previously concluded as that strain 0.6 572 associated with the onset of wall slip. The point of increase in 0.4 573 I5/1 , approximately γ0 ≈ 0.15 for RTV-2 and γ0 ≈ 1 for LSR, is 574 close to the maximum in G00 , as can be seen in fig. 2. For RTV0.2 575 2, above γ0 = 0.3 the normalized stress intensity I7/1 also starts 0.0 576 to increase slightly, indicating the presence of further nonlin577 earities in the system. This was not observed in the response -0.2 10 10 10 10 10 10 578 for LSR within the applied strain amplitude. slip

494

|

493

= 10 rad/s, F

N

-5

-4

-3

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-2

= 10 N, T = 25°C -1

0

(-)

Figure 8: Phase shift ∆slip = |δslip − δno slip | associated with slip for both materials using the standard (serrated rotor, smooth stator) and control protocols at ω = 10 rad s−1 and FN = 10 N.

9 The

origin of even harmonics remains ambiguous and a point of contentious discussion within the literature (see, for example, the paragraph on even harmonics in [31]). The existence or lack of even harmonics is not necessarily an indicator of the presence or absence of wall slip (see, for example, [43]).

9

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Figure 9: Comparison of the normalized stress intensities of the 2nd (left) and 3rd (right) harmonic contribution obtained by oscillatory strain sweep experiments (RTV-2; standard protocol) performed by means of a serrated rotor (smooth stator) with the RTV-2 control protocol at ω = 10 rad s−1 and FN = 10 N.

0.10

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As previously mentioned, it appears that at high shear defor-602 mations the applied oscillatory strain (depicted in fig. 6) also603 deviates from a perfect sine in the standard protocol, and there-604 fore might compound the shift in the stress response away from605 sinusoidal. For this reason the strain waveform is also char-606 acterized with respect to higher harmonic contributions using607 FFT. From this it is possible to assess the degree of deviation608 from the ideal applied sinusoidal strain. The result of this anal-609 ysis is also shown in fig. 10 for both elastomers under investi-610 gation. As was anticipated from the visual inspection the ex-611 citation is ideally applied in the “non-slip regime” and appears612 less sinusoidal, possessing odd higher harmonics at and beyond613 the onset of slip. As opposed to I7/1 , which appears to be of614 similar magnitude for both stress and strain, the evolution of615 I3/1 and I5/1 differs for these quantities. More specifically, it is noted that the normalized stress intensities are greater than the normalized strain intensities after a certain excitation am-616 plitude. From this it can be concluded that the non-sinusoidal stress response, and therefore the apparent nonlinear viscoelas-617 tic behavior, is due to a combination of wall slip and issues618 related to strain control. The latter is likely directly linked to619 the use of a stress-controlled rheometer in conjunction with the620 DSO mode. In this particular case the real-time strain position621

AC C

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Figure 10: Normalized stress and strain intensities of the 3rd , 5th and 7th odd harmonic contribution obtained by oscillatory strain sweep experiments performed using the standard protocol and a serrated rotor (smooth stator) at ω = 10 rad s−1 and FN = 10 N.

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control is disturbed by wall slip. Nevertheless, using a strain-controlled rotational rheometer (for which such control issues are not expected) results in a similar trend in the evolution of σ0 , G0 and G00 as shown in fig. 3(a). This was observed using an ARES rheometer (Rheometric Scientific) equipped with a similar parallel-plate configuration (alumina, custom made serrated plate according to (PP20/MRD/Ti/P2)). The oscillatory strain sweep experiments were performed on pre-prepared RTV-2 specimens using identical experimental conditions (preload, angular frequency and temperature). However, for technical reasons it was not possible to extract the waveform data and, therefore, a discussion with respect to section 3.2 and section 3.3 is not possible to verify the observations presented therein. 4. Conclusions The occurrence of wall slip in elastomeric materials when characterized by means of parallel-plate rotational rheometry is investigated by performing oscillatory strain sweep experiments using pre-prepared specimens (common practice) and in situ cured control samples (revised procedure). Both experimental configurations produce highly reproducible data. In the

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The authors’ would like to reinforce that using a parallelplate configuration in conjunction with large shear strains results in an inhomogeneous stress-strain distribution along the sample radius. Therefore, all experimental data recorded within the nonlinear viscoelastic regime are not suitable for the determination of true rheological material quantities. An important conclusion of the investigation is that data in the literature may be misleading insofar as nonlinear effects measured in elastomeric materials by oscillatory parallel-plate rotational rheometry using ex situ pre-prepared samples, specifically without any techniques or sample treatment to ensure perfect force transfer onto the specimen, may not be related to material properties (for example, viscoelasticity or microstructural changes) but rather due to wall slip. Any deviations from the thoroughly tested experimental protocols established in the prior literature for elastomers should therefore be carefully considered and re-evaluated where appropriate. A noteworthy case for which this finding is of particular importance is that of the characterization of magnetorheological elastomers by means of the magneto-rheological device (Anton Paar) or magneto-rheological accessory (TA Instruments). For both of these sets of apparatus, a visual observation of the sample during the experiment is not possible due to the presence of the magneto-rheological testing equipment. Further work is being conducted to study the influence of experimental conditions and material properties on the onset and development of the wall slip phenomena.

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standard procedure using a serrated rotor configuration (smooth680 base plate) a pronounced nonlinear viscoelastic behavior is ob-681 served in two materials, both being silicone rubbers (one lightly682 silica reinforced and one unfilled). At a certain strain amplitude683 strain softening occurs, which leads to a significant decrease684 in the storage modulus in conjunction with a measurable in-685 crease in the loss modulus. It was further observed that the loss686 modulus exhibits a local maximum and that a cross-over in the687 storage and loss moduli was present at high strain. This is in688 contrast to the control sample which, being firmly bonded to689 the parallel-plate geometry, exhibited nearly linear viscoelastic690 behavior over the entire applied strain range (up to the maxi-691 mum torque limit of the rheometer). From this it is concluded692 that the strain softening noted in both pre-prepared materials is693 indeed related to wall slip. 694 It is proposed that wall slip is caused by an adhesive failure695 at the specimen-plate interface. This is therefore a result of the696 critical stress required to overcome the adhesive forces caused697 by static friction between the sample and measuring plates be-698 ing attained. It starts to occur at the point of highest stress699 which, due to the parallel-plate configuration, is nominally at700 the outer rim of the sample. It is hypothesized that associated701 with the adhesive failure is a local stick-slip or pure slip be-702 havior and, therefore, dynamic friction conditions. Regardless703 of this physical mechanism, slip leads to a pronounced dissi-704 pation of energy that can be observed as an increase in the loss705 modulus. Therefore, this change in the loss modulus (in unfilled706 elastomeric systems) is an indicator of the onset of wall slip. As opposed to the serrated rotor configuration, where slip is found to occur at the serrated surface only, a more complex response707 is present in the smooth (rotor and base) plate geometry. However, qualitatively similar divergences in the response, namely708 the strain softening and evolution of the complex moduli, is still709 710 observed. Evaluating the system response for a single steady state de-711 formation cycle, it was noted that wall slip leads to an asym-712 metric stress response and a pronounced additional contribution713 to the phase shift. The energy dissipated due to the imperfect714 force transfer associated with dynamic friction leads to a signif-715 icant increase of the area within Lissajous figures as compared716 to experiments in which the effects of slip were negated. Contrary to the general observation in viscoelastic fluids 717 (such as polymer melts) where wall slip is considered to be associated with the presence of even harmonics, fast-Fourier-718 transformation analysis of the oscillatory data showed that in719 the investigated case and for the listed testing apparatus only720 odd harmonics are present. This might be explained by the dif-721 722 ferent physical mechanisms of wall slip that arise for different723 categories of media. The occurrence of these odd harmonics724 was found to be closely related to slip of elastomeric materials.725 The relation between higher harmonics and slip is supported by726 727 the observation that there are no higher harmonics present in the728 in situ cured control experiments. It was further shown that the729 applied strain deviates from the sinusoidal waveform if slip is730 present. This feature is related to the use of a stress-controlled731 732 rotational rheometer in conjunction with the DSO mode, where733 the real-time strain position control is disturbed by wall slip. 734

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Acknowledgement

The support of this work by the European Research Council (ERC) through the Advanced Grant 289049 MOCOPOLY is gratefully acknowledged by the authors from the Chair of Applied Mechanics. The authors would like to thank Prof. Dr. H. Münstedt and Dr. Z. Starý for their comments and discussions related to this work. The authors would also like to thank Ms. J. Reiser and Ms. M. Hofmann for respectively performing the laser scans and the swelling experiments to detect the cross-link density. References [1] R. L. Warley, D. L. Feke, I. Manas-Zloczower, Transient effects in dynamic modulus measurement of silicone elastomers 1. Zero mean strain measurements, Journal of Applied Polymer Science 98 (3) (2005) 1001– 1009. [2] A. P. Meera, S. Said, Y. Grohens, S. Thomas, Nonlinear viscoelastic behavior of silica-filled natural rubber nanocomposites, The Journal of Physical Chemistry C 113 (42) (2009) 17997–18002. [3] M. Klüppel, Evaluation of viscoelastic master curves of filled elastomers and applications to fracture mechanics, Journal of Physics: Condensed Matterl 21 (3) (2009) 035104. [4] J. L. Leblanc, C. de la Chapelle, Updating a torsional dynamic rheometer for Fourier transform rheometry on rubber materials, Rubber Chemistry and Technology 76 (2) (2003) 287–298. [5] F. Clément, L. Bokobza, L. Monnerie, Investigation of the Payne effect and its temperature dependence on silica-filled polydimethylsiloxane networks. Part I: Experimental results, Rubber Chemistry and Technology 78 (2) (2005) 211–231.

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[31] K. Hyun, M. Wilhelm, C. O. Klein, K. S. Cho, J. G. Nam, K. H. Ahn, S. J. Lee, R. H. Ewoldt, G. H. McKinley, A review of nonlinear oscillatory shear tests: Analysis and application of large amplitude oscillatory shear (LAOS), Progress in Polymer Science 36 (12) (2011) 1697–1753. [32] R. H. Ewoldt, P. Winter, J. Maxey, G. H. McKinley, Large amplitude oscillatory shear of pseudoplastic and elastoviscoplastic materials, Rheologica Acta 49 (2) (2010) 191–212. [33] J. Läuger, H. Stettin, Differences between stress and strain control in the non-linear behavior of complex fluids, Rheologica Acta 49 (9) (2010) 909–930. [34] S. G. Hatzikiriakos, J. M. Dealy, Wall slip of molten high density polyethylene. I. Sliding plate rheometer studies, Journal of Rheology 35 (4) (1991) 497–523. [35] M. D. Graham, Wall slip and the nonlinear dynamics of large amplitude oscillatory shear flows, Journal of Rheology 39 (4) (1995) 697–712. [36] C. Klein, H. W. Spiess, A. Calin, C. Balan, M. Wilhelm, Separation of the nonlinear oscillatory response into a superposition of linear, strain hardening, strain softening, and wall slip response, Macromolecules 40 (12) (2007) 4250–4259. [37] J. M. Dealy, K. F. Wissbrun, Melt Rheology and its Role in Plastics Processing, Springer Netherlands, 1990. [38] A. J. Giacomin, J. M. Dealy, Large-Amplitude Oscillatory Shear, Springer Netherlands, 1993, Ch. 4, pp. 99–121. [39] C. M. Roland, Dynamic mechanical behavior of filled rubber at small strains, Journal of Rheology 34 (1) (1990) 25–34. [40] M.-J. Wang, The role of filler networking in dynamic properties of filled rubber, Rubber Chemistry and Technology 72 (2) (1999) 430–448. [41] A. S. Yoshimura, R. K. Prud’homme, Wall slip effects on dynamic oscillatory measurements, Journal of Rheology 32 (6). [42] A. S. Yoshimura, R. K. Prud’homme, Response of an elastic bingham fluid to oscillatory shear, Rheologica Acta 26 (5) (1987) 428–436. [43] C. Carotenuto, M. Grosso, P. L. Maffettone, Fourier transform rheology of dilute immiscible polymer bends: A novel procedure to probe blend morphology, Macromolecules 41 (12) (2008) 4492–4500.

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[6] M. Aloui, S.and Klüppel, Magneto-rheological response of elastomer806 composites with hybrid-magnetic fillers, Smart Materials and Structures807 24 (2) (2015) 025016. 808 [7] T. F. Tian, W. H. Li, J. Ding, G. Alici, H. Du, Study of shear-stiffened809 elastomers, Smart Materials and Structures 21 (12) (2012) 125009. 810 [8] T. F. Tian, W. H. Li, G. Alici, H. Du, Y. M. Deng, Microstructure and mag-811 netorheology of graphite-based MR elastomers, Rheologica Acta 50 (9-812 10) (2011) 825–836. 813 [9] T. F. Tian, W. H. Li, G. Alici, Study of magnetorheology and sensing814 capabilities of MR elastomers, Journal of Physics: Conference Series815 412 (1) (2013) 012037. 816 [10] T. F. Tian, X. Z. Zhang, W. H. Li, G. Alici, J. Ding, Study of PDMS based817 magnetorheological elastomers, Journal of Physics: Conference Series818 412 (1) (2013) 012038. 819 [11] I. Agirre-Olabide, J. Berasategui, M. J. Elejabarrieta, M. M. Bou-Ali,820 Characterization of the linear viscoelastic region of magnetorheological821 elastomers, Journal of Intelligent Material Systems and Structures 25 (16)822 (2014) 2074–2081. 823 [12] I. Agirre-Olabide, M. J. Elejabarrieta, M. M. Bou-Ali, Matrix dependence824 of the linear viscoelastic region in magnetorheological elastomers, Jour-825 nal of Intelligent Material Systems and Structures. 826 [13] H. A. Barnes, A review of the slip (wall depletion) of polymer solutions,827 emulsions and particle suspensions in viscometers: Its cause, character,828 and cure, Journal of Non-Newtonian Fluid Mechanics 56 (3) (1995) 221–829 251. 830 [14] S. G. Hatzikiriakos, Slip mechanisms in complex fluid flows, Soft Matter831 11 (40) (2015) 7851–7856. 832 [15] B. K. Aral, D. M. Kalyon, Effects of temperature and surface roughness833 on time-dependent development of wall slip in steady torsional flow of834 concentrated suspensions, Journal of Rheology 38 (4) (1994) 957–972. 835 [16] W. B. Russel, M. C. Grant, Distinguishing between dynamic yielding and836 wall slip in a weakly flocculated colloidal dispersion, Colloids and Sur-837 faces A: Physicochemical and Engineering Aspects 161 (2) (2000) 271–838 282. 839 [17] R. Buscall, Letter to the Editor: Wall slip in dispersion rheometry, Journal of Rheology 54 (6) (2010) 1177–1183. [18] H. J. Walls, S. B. Caines, A. M. Sanchez, S. A. Khan, Yield stress and wall slip phenomena in colloidal silica gels, Journal of Rheology 47 (4) (2003) 847–868. [19] M. J. Reimers, J. M. Dealy, Sliding plate rheometer studies of concentrated polystyrene solutions: Nonlinear viscoelasticity and wall slip of two high molecular weight polymers in tricresyl phosphate, Journal of Rheology 42 (3) (1998) 527–548. [20] S. G. Hatzikiriakos, Wall slip of molten polymers, Progress in Polymer Science 37 (4) (2012) 624–643. [21] L. Ma, G. V. Barbosa-Cánovas, Rheological characterization of mayonnaise. Part I: Slippage at different oil and xanthan gum concentrations, Journal of Food Engineering 25 (3) (1995) 397–408. [22] C. S. Nickerson, J. A. Kornfield, A “cleat” geometry for suppressing wall slip, Journal of Rheology 49 (4) (2005) 865–874. [23] K. A. Grosch, The relation between the friction and visco-elastic properties of rubber, in: Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences, Vol. 274, The Royal Society, 1963, pp. 21–39. [24] B. N. J. Persson, Theory of rubber friction and contact mechanics, The Journal of Chemical Physics 115 (8) (2001) 3840–3861. [25] I. B. Kazatchkov, S. G. Hatzikiriakos, Relaxation effects of slip in shear flow of linear molten polymers, Rheologica Acta 49 (3) (2010) 267–274. [26] M. Ebrahimi, M. Ansari, S. G. Hatzikiriakos, Wall slip of polydisperse linear polymers using double reptation, Journal of Rheology 59 (3) (2015) 885–901. [27] H. M. Laun, C. Gabriel, C. Kieburg, Wall material and roughness effects on transmittable shear stresses of magnetorheological fluids in plate–plate magnetorheometry, Rheologica Acta 50 (2) (2011) 141–157. [28] J. Läuger, K. Wollny, S. Huck, Direct strain oscillation: A new oscillatory method enabling measurements at very small shear stresses and strains, Rheologica Acta 41 (4) (2002) 356–361. [29] M. Wilhelm, D. Maring, H. W. Spiess, Fourier-transform rheology, Rheologica Acta 37 (4) (1998) 399–405. [30] J. L. Leblanc, Fourier transform rheometry on gum elastomers, Journal of Applied Polymer Science 89 (4) (2003) 1101–1115.

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Shown in fig. I is the wear pattern observed on the sample’s865 upper surface (that is in contact with the serrated plate) after experiments conducted using pre-prepared samples and the standard protocol (serrated rotor, smooth stator). This demonstrates that the surface pattern observed after these experiments (see fig. 4 in the main document) are indeed related to wear caused by the rotor tips.

(γ0 ≈ 10−3 ) in the standard procedure and again leads to strain softening, a gradual decrease in G0 and an increase in G00 . Furthermore, the evolution of σ0 , G0 and G00 differs from that obtained with the standard protocol using the serrated rotor. 10

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Figure II: Comparison of the oscillatory strain sweep experiments using the standard protocol (RTV-2; smooth rotor and stator) with the control protocol.

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Figure I: Surface profile of LSR sample upper surface, measured using a laser881 scanner, after testing at γ0 = 1 and γ0 = 4 with the standard protocol (serrated882 rotor, smooth stator). Measurements were performed with an UBM Profilome-883 ter with a resolution of 0.06 µm. 884 885

The onset of slip is shifted to smaller excitation amplitudes and a second, more pronounced peak is present in the loss modulus together with an significant decrease of the storage modulus. This could be explained by the surface properties of the plates. Whereas wall slip was observed to commence at the serrated surface only (see fig. 4 and its related discussion in the main document), there is no preferred surface for slip in the smooth rotor configuration (as both the rotor and base plate have identical surface finishes). Slip therefore is initiated on either or simultaneously both interfaces leading to a more complex total system response. The second peak in G00 could be due to the onset of sample buckling10 . This phenomenon was observed in complementary experiments performed by means of the DHR-3 rheometer in conjunction with a custom made disposable smooth parallel-plate configuration using a high speed camera. Due to the complex slipping behavior, possible buckling and sample dislocation, the overall reproducibility for this experimental configuration above a threshold strain is not as good as that of the serrated rotor configuration. Within the applied strain range no cross-over in G0 and G00 was observed.

Experiments conducted with a smooth rotor To fully assess the influence of geometrical properties of the plate surface, pre-prepared samples are also characterized utilizing a smooth rotor (smooth stator). With this configuration, the experimental results at small strains fit those obtained with the in situ cured control procedure. As is shown in fig. II, the smooth surface of the rotor removes the error in the reported modulus observed previously for the serrated rotor, indicating that the gap setting has been correctly established. The overall reproducibility of the data from both sets of experiments is also very good. Therefore, for small strain experiments a smooth rotor can be used to obtain reliable experimental data. However, wall slip starts to appear at moderately low shear strains

10 In preliminary studies it was observed that the specimen was occasionally dislodged from the geometry if the deformation was sufficiently large and a low static normal force (less than 3 N) was used in combination with the smooth rotor configuration.

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Different cross-linking densities of samples: Although the945 materials and curing conditions are the same (25 ◦C946 for RTV-2 and 120 ◦C for LSR), the final stages of the947 preparation process for the in situ samples is slightly different to that used for the pre-prepared samples (which948 may vary marginally in thickness). From swelling exper-949 iments (conducted using toluene as the solvent) we have950 determined that the average cross-linking density of all951 samples is the same within 5 % (noting that this value is952 sensitive to the shape of the sample). Furthermore, similar953 results are obtained from both preparation procedures at954 low strain when using the smooth rotor, for which the gap955 setting is correctly established by the rheometer. 956 957

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Delamination of the in situ cured sample: Although the possibility of delamination is present, there exist two methods to demonstrate that this does not occur in the tested system. After the experiments are concluded, the sample remains firmly bonded to the geometry and can only be removed though a process of soaking in toluene. The point of initiation for delamination would be at the sample rim (the point of highest stress), but no separation of the sample from the rotor or base plate was observed. Furthermore, dissipative nonlinearities (namely an increase in the loss modulus, such as was shown in the conclusive cases of wall slip) were not observed in any tested scenario.

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Apparatus resolution: At very small deflections together with low measured torque, the system is close to the limits of resolution. A non-sinusoidal strain is applied to the specimen and therefore an apparent nonlinear behavior is measured. Focusing on experimental data recorded above this regime (γ0 > 10−4 ) results in the removal of these artificial higher harmonics.

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System inertial effects: The inertia of the apparatus’ drive 958 mechanism, including the motor and rotor, plays an in959 creasing role in the system response as the frequency and excitation amplitude increase. This may lead to an overestimation of the elastic stress response. As a preventative measure, we adopt an excitation frequency commonly used in the literature (10 rad s−1 ) much less than the maximum that can be provided by the system (628 rad s−1 ). Confirmation that inertial effects are not dominant in this system at the tested frequency is given by the fact that, for the in situ cured control protocol, no apparent shear stiffening at high strains is detected.

Internal interactions of polymers with complex composition: Typically commercial elastomers are reinforced with fillers (such as carbon black or fumed silica). In the case of magnetic field-responsive elastomers, they are also filled with magnetizable particles. To prevent effects related to any additional particles (sedimentation and agglomeration, both causes of material inhomogeneity, and interparticle interactions that lead to further nonlinearities), for this study we exclude them from the material composition. Furthermore, as it may be difficult to distinguish between material (viscoelastic behavior) and system dissipation (caused by wall slip), a minimally dissipative viscoelastic material composition is preferred.

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displaces during the preload stage, leading to a consistent underestimation of the sample thickness. All further computations are affected by this systematic error. Confirmation of the problem is achieved by comparing small-strain results with those obtained using the smooth rotor configuration. Boundary effects, such as stress inhomogeneities and a changing contact area between the rotor and sample, may also be caused by the serrations.

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Possible sources of error 940 The following list presents some of the possible sources of941 systematic error in the tested system, and indicates the methods942 used to minimize their influence on the documented results: 943

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Effect of serration: It was assumed that the surface geometry of the serrated rotor may influence the results. The process of detecting the sample thickness is complicated by the serrations located on this rotor’s surface. Additional volume is present between the grooves into which the material 2