Mechanical characterization of visco termo elastic properties of a polymer interlayer by dynamic tests Laura Andreozzi 1, Silvia Briccoli Bati 2, Mario Fagone 2 Giovanna Ranocchiai 2 Fabio Zulli 1 1 Department of Fisics Enrico Fermi, University of Pisa, Italy E-mail: anreozz@df.unipi.it, fabio.zulli@df.unipi.it 2 Department of Costruzioni e Restauro, University of Florence, Italy E-mail: silvia.briccolibati@unifi.it, mario.fagone@unifi.it, giovanna.ranocchiai@unifi.it, Keywords: Laminated glass, polymer, environmental degradation. SUMMARY. Experimental analysis of viscoelastic properties of materials is usually carried out with creep tests, relaxation tests (both addressed as transient tests) or periodic tests. The last method permits to perform the analysis of viscoelastic parameters at very short times, representing the effects of fast load conditions, usually hard to highligth by transient experiments. Moreover, experimental results of linear viscoelastic materials can be translated in the space of frequency and temperature, so to achieve information on material behaviour in a time domain wider than the experimental one. Here the first results are reported of an experimental analysis caried out with cyclic tests on composite glass specimens; some of them have been subjected to damage with exposure to solar radiation, moisture and thermal cycles. 1 INTRODUCTION Several kinds of polymers are employed as interlayers of laminated glass; these polymers are not crystalline, weakly cross-linked and consequently highly amorphous. Amorphous polymers are characterized by a slow transition from liquid to solid state passing through viscous behavior, without latent heat of phase transition. Viscoelastic behavior, that heavily depends on temperature, is typical of a specific temperature range that is called rubberlike domain. In composite glass, the interlayer exhibits rubberlike behaviour at room temperature, and, for this reason, in case of glass breakage it is able to produce a bridge ligament among glass fragments; in fact, glass fracture is not able to propagate within soft polymer interlayer, but deviates at the interface between glass and interlayer. Composite glass employed in architectural applications is subjected to various load conditions, which duration ranges from few seconds to several years; moreover, due to the great sensitivity from temperature, tests have to be performed at different temperatures in order to cover the possible climate range of the building life. Due to the variety of materials that progressively are entering the market, draft pren 13474-3 [1] provides an approximate method to account for the coupling capability of interlayer through a parameter that takes into account the stiffness of polymer as a function of time and temperature. Particularly, cyclic tests have been introduced in the draft rules, to evaluate the rheological properties of interlayer, which knowledge is necessary for the design of glass structures. In this paper, the results are reported of cyclic tests carried out on polymer interlayer
(polyvynil butyral) adhered to glass. The results are compared with those obtained on equal specimens previously damaged by environmental actions. 2 TERMO VISCO ELASTIC PROPERTIES OF INTERLAYER MATERIALS Polymers employed as interlayers are generally isotropic in the undeformed state; moreover, the viscous share of deformation is usually believed to be limited to the deviatoric part of strain. The Boltzmann superposition principle is generally accepted, that is the effects of mechanical history are linearly additive where the stress is described as a function of rate of strain history or, alternatively, the strain is described as a function of rate of stress history. This permits to assume constitutive equations of this kind: t t Jt t t dt (1a) t t Gt t γ t dt (1b) Generally, mechanical behaviours that depend on time are investigated by test methods that apply to specific ranges of load rates. A graph is reported in fig. 1 containing the different tests apt to catch the mechanical behaviour of a polymer in dependence of the load time you are interested at. As it is well known, the frequency scales of typical loads in engineering analysis range from 10-9 to 10-0 Hz. Higher frequencies are usefull in the study of impacts and explosions. forced vibrations resonance methods wave propagation transient experiments torsional pendulum 10-8 10-6 10-4 10-2 10 0 10 2 10 4 10 6 10 8 f (Hz) Figure 1: Frequency scales for different mechanical experimental techniques. 2.1 Transient experiments Transient experiments are performed, for example, imposing a sudden stress and recording the resulting strain that represents the description of the creep function (according to eq. 1a). On the contrary, imposing a sudden strain and recording the resulting stress, the description of the relaxation function is obtained (according eq. 1b). G(t) and J(t) are not inverse functions, because they represnt the responce to different experimental time patterns. The time law by which stress or strain has been applied, disturbs the successive results in term of creep and relaxation functions, until such effects become negligible, after some time interval,
long compared to the load time. For this reason specific experiments are to be preferred in order to investigate rheological behaviour at short actions. 2.2 Periodic experiments If stress (or strain) is varied periodically on a linear viscoelastic material (usually with sinusoidal law), after some cycles, due to Boltzman superposition principle, the strain (or stress) will also alternate with the same law and frequency, but it will be out of phase with the stress (or strain). The linearity of mechanical response, at each load level, can so be checked through the experiment. For example, if a strain is imposed according to γ γ0 (2) sin ωt it can be easely shown that the stress can be represented as: G ω and ω γ 0 G sin ωt G cos ωt (3) G are functions of frequencies and represent the shear storage modulus where and the shear loss modulus; G ω is the ratio of the stress in phase with the strain, to the strain and is proportional to the average storage of energy in a cycle of deformation; G ω is the ratio of the stress /2 out of phase with the strain, to the strain, and is proportional to the average dissipation of energy in a cycle of deformation. Periodic experiments are carried out imposing forced vibrations to specimens of various shape and subjected to various stress states [2] UNI EN ISO 6721-1 2.3 The method of reduced variables G ω and ω Given a certain frequency, different values of G can be found if periodic tests are performed at different temperatures. It was observed that, if one represents G() in a logaritmic scale, the experimental points obtained at a given temperature may be shifted to superimpose to experimental points obtained at different temperature [3]. The effect of a change from T to T 0 is to multiply G by T 0 0 /T and the frequency scale by a given constant a T. If a shift value log a T can be found that depends only on the temperature change, for all the viscoelastic variables a single composite curve can be obtained which represents the frequency dependence that would have been obtained over a much wider frequency range, at a single temperature (reference temperature). A general form for the description of a T as a function of (T-T 0 ), commonly accepted in the analysis of polymers, was proposed by William, Landel and Ferry (WLF equation): log a T 0 1 0 2 c T T0 c T T Once the mathematical constants c 1 0 e c 2 0 have been determined, as to obtain superposition of experimental points determined at various temperatures, it is possible to build the master curve at the reference temperature T 0 for all the viscoelastic constants and, with simple algebra, to represent master curves for different reference temperatures. 0 (4)
However, caution should be exercised in using a reduced viscoelastic function to predict properties at frequencies or times many decades removed from the range of experimental measurements, because of the accumulation of experimental errors and, also, because chemical changes may occur over long periods. 3 EXPERIMENTAL ANALYSIS Dynamic tests were carried out on composite glass specimens with PVB interlayer. MCR 301 rheometer Anton Paar was used to perform oscillatory rotational dynamic tests on composite glass. The rheometer is able to produce an oscillatory rotation on a specimen of various shapes, both in displacement and force control, and to record torque with a resolution of 0.1 nnm, and angular rotation with a resolution of 0.01rad. The specimen is contained in an environmental chamber able to keep the temperature constant during the test, and increase it. The application software supplied is able to perform all the necessary graphic and numerical processing of experimental data. Two composite glass plies 400 x 300 mm were laminated with PVB interlayer (Trosifol BG R20) by Roberglass (Calci, Pisa), with thickness 8-0.76-8 mm and 8-1.52-8 mm respectively. Cylindrical specimens ( button specimens ) with diameter 23.06 mm were drilled by a grass core bit. Some of them were intended for environmental damage. Particularly, some specimens were subjected to moisture action keeping them suspended over a covered thermostatic bath at the temperature of 50 [4] for 33 days (about 100% R.H.). Cylindrical specimens were glued to the rheometer accessoires, intended to be the load plates, with Vitralit 6128 Panacol-Elosol GmbH, and sinusoidal angular oscillation was produced of 0.141 mrad (Figure 2). Temperature and frequency of the tests are reported in tab. 1, 2, 3 and 4. 4 ANALYSIS OF DATA 4.1 Correction factor for specimens geometry For every frequency and test temperature, after reaching stationarity of dynamic response, the rheometer returns the values of torque, of phase angle and of the calculated G() and G(). These were calculated according to the procedure reported in par. 2.2, assuming uniform strain distribution and a radial linear stress distribution according to Coulomb theory of torsion of a cylindrical elastic solid, and assuming for the cylinder the height of the specimen and the base equal to the bottom load plate. The composite glass specimens were not homogeneous and the strain can be considered to be concentrated in the PVB interlayer only; for this reason, the values of G() and G(), computed by the software, were adapted to the real diameter of the button and to the effective width of interlayer by a geometric factor. 4.2 Master-curve The corrected values of G() and G() were calculated as a function of angular frequency and of test temperature. After that, the graphs were shifted on the logaritmic axe of G and G according to the parameter T 0 0 /T then the graphs were shifted on the logaritmic axe of frequency as to obtain superposition of adjoining edges, on the graph corresponding to the reference temperature of 30 C. In Figure 3 the master-curves are reported for 0.76 specimens and for 1.52 specimens.
1.52 interlayer Temperature ( C) Frequency (Hz) 30 0.00025-25 40 0.0001-100 50 0.0001-10 60 0.0001-100 70 0.0001-100 80 0.0001-100 Table 1: Temperatures and frequencies for 8+1.52+8 PVB specimens Moisture - 1.52 interlayer (U7B) Temperature Frequency ( C) (Hz) 25 0.0001-10 30 0.0001-10 50 0.0001-10 70 0.0001-10 80 0.0001-100 Table 2: Temperatures and frequencies for 8+1.52+8 PVB subjected to moisture. 0.76 interlayer Temperature ( C) Frequency (Hz) 30 0.01-100 40 0.01-100 50 0.0001-100 55 0.01-100 60 0.001-100 65 0.001-100 70 0.001-100 75 0.001-100 80 0.0001-100 80 0.0001-100 Table 3: Temperatures and frequencies for 8+0.76+8 PVB Moisture - 0.76 interlayer (U6A) Temperature Frequency ( C) (Hz) 30 0.0001-10 60 0.0001-10 Table 1: Temperatures and frequencies for 8+0.76+8 PVB subjected to moisture. Figure 2: A specimen in the test machine. Figure 3: Master-curves for 0.76 and 1.52 specimens.
4.3 WLF equation In order to determine the coefficients of WLF equation (eq.4) for the reference temperature of 30 C, the values of -(T-T 0 )/log a T, employed to obtain the master curves reported in Figure 3, were represented as a function of the corresponding (T-T 0 ), as reported in Figure 4. The slope and the constant term of the regression line enabled to determine the c 1 0 and c 2 0 constants of eq. 4. In Figure 4 the linear fit of the points and the values of a T are reported for 0.76 and 1.52 experiments, as a function of (T-T 0 ). The values of WLF equation coefficients determined in this way for the reference temperature T 0 = 30, are c 1 0 = 12.50 and c 2 0 = 89.01 for 0.76 mm interlayer and c 1 0 = 11.34 and c 2 0 = 74.80 for 1.52 mm interlayer. (a) (b) Figure 4: Evaluation of WLF coefficients via linear fit of experimental shift values (a) and comparison of experimental points with WLF equation (b). 4.4 Damaged specimens Two of the specimens subjected to moisture action (U6A and U7B) were intended to dynamic tests according to the procedure applied to the other specimens. Specimen U6A is characterized by 0.76 mm polymer interlayer and U7B is characterized by 1.52 mm polymer interlayer. After both specimens were subjected to the action of moisture (being suspended over a covered thermostatic bath at the temperature of 50 C for 33 days) they were submitted to a visual observation. The polymer interlayer was no more transparent as it was at the beginning of the moisture action, but it was getting opaque from the edge towards the center of the specimens (Figure 5). After the realization of dynamic tests, the master curves of the shear storage modulus and the shear loss modulus at the reference temperatures of 30 were realized and represented in Figure 6 as a comparison. Although the reading of G values on the logaritmic scale is quite difficult, it can be noted that the damaged specimens exhibit a quite higher value of the shear modulus, both on U6A and U7B specimens.
Figure 5: Specimen U6A before moisture action (above) and after moisture action (below). Figure 6: Comparison between untreated specimens and specimens subjected to moisture action (U6A and U6B).
5 REMARKS AND CONCLUSIONS Dynamic tests are a useful tool able to determine the visco termo elastic properties of interlayer. The use of reduced variables permits to extend the information obtained through a definite range of time scale and temperature, as to cover a wide range of time scale at a reference temperature and, vice versa, to have at disposal elastic properties at temperature different from the experimental one. The small button specimen, moreover, can be extracted as a sample of large laminated glass sheets devoted to the architectural applications, or it can be estracted from a laminated glass sheet subjected to the same lamination procedure. In so doing, the mechanical tests are able to ensure, as well, a control on the lamination procedure. Particular attention must be devoted to the evaluation of the distance of load plates (gap); in fact, it has been noted that the authomatic evaluation of this measure is affected by observational error that can produce, after the geometric correction of G values, up to 10% uncertanty. The procedure proposed in pren vwxyz Glass in building Laminted glass and laminated safety glass Determination of interlayer shear transfer coefficient [5], to which pren 13474-3 refers, requires the preparation of prismatic interlayer test specimens produced under normal manufacturing conditions, but not adhered to glass. Tensile modulus is then determined on such test specimens with various test temperature and at different frequencies ranging from 1 to 400 Hz. In so doing the production of test specimen is more complicated and the specimen is different from the real laminated interlayer. Moreover, further uncertainty is induced in calculating the shear modulus from the tensile modulus; this is usually made assuming a constant value of Poisson coefficient ( = 0.45) and introducing the hypothesis of linear isotropic elasticity. Transient experiments, moreover, are significantly useful to investigate polymer behaviour for engineering application, because the experimental time scales are more suited to structural life time and load duration. Obviously, processing tests results is necessary as to integrate transient and dynamic experiments and to obtain the maximum reliability of data. As for moisture damage, the very few specimens that were analized highlighted an increase in shear modulus of about 70%. Even if the tests are still inadequate, moisture seems to clearly modify both the transparency and the elastic properties of interlayer. These transformations can be due to structural modifications of the polymer and they can produce, as a consequence, variations of the thermal response and of the adhesion properties. References [1] pren 13474-3 Glass in building - Design of glass panes - Part 3: General basis of design, design of glass by calculation for non-fenestration use and design of glass by testing for any use, (2007). [2] UNI EN ISO 6721-1 Plastics - Determination of dynamic mechanical properties, General principles, (2003). [3] Ferry, J.D., Viscoelastic properties of polymers, John Wiley & Sons, New York (1980). [4] UNI EN ISO 12543-4 Glass in building - Laminated glass and laminated safety glass, Test methods for durability, (2000). [5] pren vwxyz Glass in building Laminted glass and laminated safety glass Determination of interlayer shear transfer coefficient (2008)