Modeling of the viscoelastic behavior of a polyimide matrix at elevated temperature

RESUME L'utilisation de composites a matrice polymere (CMPs) s'est grandement repandue dans l'industrie du transport au cours des dernieres decennies. Ces materiaux offrent un rapport rigidite/masse superieur a celui des metaux et permettent d'alleger les vehicules et d'augmenter leur efficacite energetique. Pour ces raisons, les principales compagnies aeronautiques et aerospatiales ont commence a utiliser les CMPs dans des applications structurelles telles que les ailes, le fuselage et meme les moteurs d'avion. L'utilisation des CMPs dans des applications telles que les moteurs d'avions necessitent des materiaux capable de resister a des conditions d'utilisation extremes, entre autres des temperatures elevees, ainsi que des chargements mecaniques importants et un environnement oxydant. Dans de telles conditions, la matrice polymere est susceptible de posseder un comportement viscoelastique dependant de son chargement et de la temperature. De plus, a proximite des moteurs, la combinaison des hautes temperatures et de l'environnement accelere les vieillissements physiques et chimiques. Tous ces parametres doivent etre pris en consideration afin de pouvoir predire le comportement du materiau tout au long de son utilisation. Le principal objectif de cette these etait d'etudier le comportement viscoelastique d'une telle matrice et de developper une loi de comportement capable de tenir compte de tout type de conditions d'utilisation. Ce modele devait ensuite etre implemente dans un logiciel commercial d'elements finis tel que ABAQUS ou ANSYS. Premierement, le vieillissement chimique de la matrice a la temperature d'utilisation a ete etudie. A cette fin, une analyse thermogravimetrique fut realisee sur des echantillons de poudre dans une atmosphere d'air. Deux types de tests furent menes a bien : i) des tests cinetiques durant lesquels la poudre est chauffee a un rythme constant jusqu'a sa sublimation complete ; ii) des test isothermes durant lesquels les echantillons sont maintenus a une temperature unique pendant 24 heures. Le premier type de tests fut utilise pour developper un modele de degradation reproduisant avec grande precision les resultats experimentaux. La prediction des resultats des essais isothermes a rencontre beaucoup moins de succes, en particulier pour les basses temperatures. A ces temperatures, une phase d'oxydation precede la phase de degradation chimique. Or le modele developpe est incapable de representer ce phenomene. D'autres essais de degradation isothermes furent conduits sur des echantillons de traction plutot que sur de la poudre. Ces tests furent menes a la temperature de service, pour des periodes de temps bien superieures. Les masses, volumes et proprietes mecaniques furent mesures apres 1, 4, 9 et 17 mois. Les resultats ont montre qu'apres 17 mois, la matrice avait perdue pres de 5% de sa masse et jusqu'a 19%, 30% et 10% de son module d'Young, contrainte a la rupture et deformation a la rupture, respectivement. La seconde etape a consiste a etudier le comportement viscoelastique de la matrice dans diverses conditions d'utilisation afin de developper une loi de comportement. Cette loi fut developpee a partir du travail accompli par Schapery en 1964, base sur les principes de la Thermodynamique des Procedes Irreversibles. L'avantage principal des lois de comportement de type Schapery reside dans la prise en charge des effets des differents parametres, tels que les contraintes, la temperature ou le vieillissement physique, par des fonctions nonlineaires explicites. Des echantillons de traction du materiau furent testes a la temperature de service.----------ABSTRACT The use of Polymer Matrix Composite Materials (PMCMs) has steadily increased in the transport industry over the past few decades. These materials offer a higher stiffness/mass ratio than their metallic counterparts and therefore allow for a reduction in the mass of the vehicle, which leads to an increased energy efficiency. Leading aerospace and aeronautics companies progressively using PMCMs for structural applications, such as wings, fuselage and more recently, aircraft engines. Use of PMCMs in aircraft engines requires materials able to withstand extreme service conditions, such as elevated temperatures, high mechanical loadings and an oxidative environment. In such an environment, the polymer matrix is likely to exhibit a viscoelastic behaviour dependent on the mechanical loading and temperature. In addition, the combined effects of elevated temperature and the environment near the engines are likely to increase physical as well as chemical ageing. These various parameters need to be taken into consideration for the designer to be able to predict the material behaviour over the service life of the components. The main objective of this thesis was to study the viscoelastic behaviour of a high temperature polyimide matrix and develop a constitutive theory able to predict the material behaviour for every of service condition. Then, the model had to have to be implemented into commercially available finite-element software such as ABAQUS or ANSYS. Firstly, chemical aging of the material at service temperature was studied. To that end, a thermogravimetric analysis of the matrix was conducted on powder samples in air atmosphere. Two kinds of tests were performed: i) kinetic tests in which powder samples were heated at a constant rate until complete sublimation; ii) isothermal tests in which the samples were maintained at a constant temperature for 24 hours. The first tests were used to develop a degradation model, leading to an excellent _t of the experimental data. Then, the model was used to predict the isothermal data but which much less success, particularly for the lowest temperatures. At those temperatures, the chemical degradation was preceded by an oxidation phase which the model was not designed to predict. Other isothermal degradation tests were also performed on tensile tests samples instead of powders. Those tests were conducted at service temperature for a much longer period of time. The samples masses, volume and tensile properties were recorded after 1, 4, 9 and 17 months. The results of those tests showed that after 17 months, the matrix lost about 5% of its mass and volume and as much as 19%, 30% and 10% of its Young's modulus, stress and strain at break, respectively. The second step consisted in studying the viscoelastic behaviour of the matrix under various conditions and develop a constitutive theory to model its mechanical behaviour. That theory was developed using the framework laid out by Schapery in 1964, using the Thermodynamics of Irreversible Processes. The main advantage of Schapery-type constitutive theories is that the effects of various parameters such as stresses, temperature and physical ageing can be taken into account by using user-defined explicit nonlinearizing functions. Tensile samples of the material were tested at service temperature using strain gages rosettes in order to study the matrix 3D behaviour. It was found that the Poisson's ratio was time-independent, meaning that its retardation times spectrum was the same as the compliance function.