Despite real applications having complex triaxial loading, current physical test methods to predict component behaviour are mainly uniaxial. But previous work has indicated that there may be substantial differences between the rubber's uniaxial and biaxial behaviour and hence through incompressibility, its triaxial properties. In order to quantify these differences equipment was developed to assess the biaxial performance of selected rubber compounds using inflated circular diaphragms. Although allowing higher extensions than stretching a sheet in its own plane, such tests do not allow stress and strain to be measured directly, requiring careful marking of the sample, or calculation through simulation. On the grounds of perceived accuracy, the latter was chosen, requiring accurate, general, elastic constants to high extensions. In this thesis the development of this apparatus, along with the associated techniques is described, along with the development of a new elastic theory. The tests on this new apparatus indicated significant differences between the uniaxial and biaxial strength and fatigue of rubber. In a unimdal test natural rubber (NR) is much stronger than styrene butadiene rubber (SBR) below 35pphr of carbon black. In a biaxial test though the converse is true, although there is some evidence of crystallinity in NR during the biaxial test. Distinct differences were also found in fatigue between the two load cases. When plotted against extension ratio the biaxial life of SBR was found to increase, while the converse is true for NR. However if life is plotted against a function of strain energy, the biaxial life of both polymers increases for a given energy.

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Ballistic fabrics made from high performance polymeric fibers such as Kevlar®, Twaron® and Spectra® fibers and composites utilizing these fabrics are among the leading materials for modern body armor systems. Polymeric fibers used to produce ballistic fabrics often behave viscoelastically and exhibit time- and rate-dependent stress-strain relations. This necessitates the study of the constitutive behavior of composites filled by ballistic fabrics. Rheological models based on discrete rheological components (including spring and dashpot) have been widely used to study the viscoelastic behavior of polymeric fabrics. Such rheological (or viscoelasticity) models are qualitatively useful in understanding the effects of various micro-mechanisms and molecular features on the macroscopic responses of ballistic fabrics. In the present work, the constitutive behavior of Twaron CT709® fabric/natural rubber (Twaron®/NR) composite is studied using three viscoelasticity models (i.e., a four-parameter Burgers model, a three-parameter generalized Maxwell (GMn=1) model, a five-parameter generalized Maxwell (GMn=2) model) and a newly developed para-rheological model. The new model utilizes a three-parameter element to represent the Twaron® fabric and the affine network based molecular theory of rubber elasticity to account for the deformation mechanisms of the NR constituent. The uniaxial stress-strain relation of the Twaron®/NR composite at two constant strain rates is experimentally determined. The values of the parameters involved in all the models are extracted from the experimental data obtained in this study. The stress-relaxation response (under a uniaxial constant strain) and the creep deformation (under a uniaxial constant stress) of the composite are also experimentally measured. The three viscoelasticity models considered here are capable of predicting the viscoelastic constitutive behavior of the composite with different levels of accuracy. The stress-strain relation at each strain rate predicted by the newly developed para-rheological model is seen to be in good agreement with the measured stress-strain curve over the entire strain range studied. It is shown that the new model also predicts the elastic moduli and ultimate stress of the Twaron®/NR composite well. All the four models are found to predict the initial relaxation response of the composite fairly well, while the long-term stress relaxation is more accurately represented by the para-rheological model. An implicit solution provided by the para-rheological model is shown to predict the creep response of the composite more accurately than all the other models at both the primary and secondary stages. The mathematical complexity that arises from including an additional Maxwell element to the GMn=1 model to obtain the GMn=2 model with enhanced predictability is traded with the use of simple characteristic time functions in the para-rheological model. These functions are found to greatly improve the predictability of the newly developed model for the stress relaxation modulus and creep compliance. This study also explores the utility of the para-rheological model as a tool to probe the micromechanisms and molecular features that are causally related to the macroscopically observed viscoelastic behavior of the composite. The relaxation and creep trends predicted by the para-rheological model indicate that the long time viscoelastic response of the composite lies between that of a crosslinked polymer and a semi-crystalline thermoplastic.

<p>U radu su prvi put za proveru teorija nastajanja i gumolike elastičnosti polimernih mreža primenjeni modelni poliuretanski sistemi čiji su čvorovi veoma stabilni izocijanurat(heksahidro-1,3,5-triazin- 2,4,6-trion) prstenovi. Rad obuhvata: (1) Sintetezu nekoliko serija homogenih poli(uretan-izocijanuratnih) mreža, na bazi 2.4-TDI i poli(oksipropilen)diola, dvoetapnim postupkom u masi, tj. ciklotrimerizacijom teleheličnih diizocijanata uz katalizator Polycat 41. (2) Sintezu manje savr&scaron;enih mreža sa nekom definisanom koncentracijom visećih lanaca koja je postignuta uvodenjem monoola dietilenglikol- monometiletra u toku pripreme prepolimera. (3) Odredivanje povoljnih reakcionih uslove svih etapa sinteze uz primenu i modifikaciju postojećih analitičkih postupaka za karakterizaciju svojstava reakcionih komponenti i praćenja reakcija umrežavanja. (4) Procenu mogućih bočnih reakcija u toku nastajanja mreža jer one mogu značajno uticati na raspodelu različitih fragmenata u mrežama praćenjem koncentracija reakcionih proizvoda kod modelnih reakcija u rastvoru uz isti diol i isti katalizator i odgovarajuće mono-funkcionalne izocijanatne komponente. (5) Karakterizaciju svojstava i strukturnih parametara modelnih mreža i to primenom postupaka ekstrakcije i bubrenja, diferencijalne skanirajuće kalorimetrije, fotoelastičnih merenja, dinamičko-mehaničke spektroskopije i merenja napon-istezanje. Izborom nominalne Mn diola od 400 do 4000 postigne gustina umreženja 0.1x10^-4mol/cm³ do 10x10^-4mol/cm³ sa rasponom temperatura staklastog prelaza od -60&deg;C do +30&deg;C. Za procenu strukturnih parametara mreža primenjena je teorija granajućih procesa sa kaskadnom zamenom za slučaj nastajanja mreža ciklotrimerizacijom i dvoetapni postupak. U zavisnosti od konverzije NCO grupa u mrežama izračunate su masa po monomernoj jedinici, maseni udeo, broj po monomernoj jedinici, koncentracija po jedinici zapremine, Mn, Mw, Mz i Mw/Mn kako za elastično aktivne, osnovne i viseće lance tako i zamolekule sola. Ključni ekspehmentalni podaci koji su kori&scaron;ćeni za proveru teorija nastajanja bio sadržaj gela dobijen vi&scaron;estrukim ekstrakcijama, a za teorije gumolike elastičnosti ravnotežni modul dobijen iz fotoelastičnih merenja. Provera teorija gumolike elastičnosti se zasnivala se u nalaženje vrednosti pred- faktora 3 (tzv. faktora pamćenja) u jednačini koja daje vezu ravnotežnog modula elastičnosti i koncentracije elastično aktivnih lanaca mreže koji ukazuje na način fluktuacije cvorova mreže. Fotoelastična merenja su omogućila da se preko njih parameter pred-faktor 3 proceni pri malim deformacijama. Potvrden je koncept stvarnih mreža sa delimično potisnutim fluktuacijama čvorova uz aditivni doprinos zapletenosti lanaca modulu elastičnosti prema Langley-Graesley konceptu zarobljenih prepletaja.</p> / <p>In this thesis polymer network formation theories and rubber elasticity of polymer networks on model polyurethane systems having as a junction very stable isocyanurate(hexahidro-1,3,5-tгiazin-2,4,6- trion) rings are for the first time investigated. The work contains: (1) Synthesis of homogenious series of several poly(urethane-isocyanurate) networks based on poly(oxypropylene)diol and 2.4-TDI by two stages procedures in bulk i.e. cyclotrimerization of telechelic diisoicyanates with Polycat 41 as catalyst. (2) Synthesis of less perfect networks with some concentration of dangling chains obtained by introduction of monofunctional component diethyleneglycolmonomethylether during prepolymer formation. (3) Determination of optimal reaction conditions for both stages of the synthesis. (4) Estimation of possible side reaction during network formation because of theirs important influence on nework fragment distribution. (5) Caracterization of networks structure and properties by swelling and multiply extraction, differential scanning calorimetry, photoelastical measurements, dynamic-mechanical spectroscopy and stress-strain measurements. By using the different Mn of diols (400 - 4000) the network density from<br />0.1x10^-4mol/cm³ to 10x10^-4mol/cm³ and glass transition temperatures from -60&deg;C to +30&deg;C was achieved. For network structure determinations the theory of branching processes with cascade substitution was used. Mass per monomer unit, mass fraction, number per monomer unit, concentration per unit volume, Mn, Mw, Mz and Mw/Mn for elastically active network chains, backbone chains, dangling chains and sol molecules In the dependence on NCO groups conversion are calculated. Crucial experimental data for examination of network formation theories was the gel content and for rubber<br />elasticity theories the equilibrium modulus received from photoelastical measurement. The estimation of rubber elasticity theories was based on the analysis of the front factor 3 in the equation which gives the relation between the equilibrium modulus and concentration of elastically active network chains. It is estimated the additive contribution of chain entanglements to the equilibrium modulus, especially in the case of high networks density according to Langley-Graesley theory of trapped entanglements.</p>

Une analyse du comportement thermomécanique du caoutchouc naturel est réalisée en combinant deux techniques d'imagerie quantitative. La corrélation d'images visibles sert à estimer les déformations puis l'énergie de déformation alors que des images infrarouges permettent d'estimer, via l'équation de diffusion, les quantités de chaleur mise en jeu. La construction de bilans d'énergie montre alors l'importance relative des mécanismes dissipatifs et de couplage thermomécanique. A basse fréquence pour de faibles déformations, les résultats permettent de retrouver le fameux effet d'inversion thermoélastique. A déformation plus importante, les résultats montrent une compétition sur le plan énergétique entre élasticité entropique et mécanismes de cristallisation/fusion sous contrainte. Aucun effet dissipatif significatif n'est détecté à basse comme en haute fréquence alors que dans chaque cas, sur le plan mécanique, une aire d'hystérésis caractérise la réponse cyclique du matériau. / An analysis of the thermomechanical behavior of the natural rubber is carried out by combining two quantitative imaging techniques. The digital image correlation of visible images is used to estimate the strain and then the deformation energy whereas infrared images make it possible to estimate, via the heat equation, the amounts of heat involved in the material transformation. The construction of energy balance enables us to determine the relative importance of the dissipative and thermomechanical coupling mechanisms. For low frequency and low extension ratio, the results show the famous thermoelastic inversion effect. From an energy standpoint, a competition between entropic elasticity and stress-induced crystallization/fusion mechanisms is observed for more significant extension ratios. No significant dissipative effect can be detected at low or high loading frequency whereas in each case, a stress-strain hysteresis characterizes the cyclic response of the material.