Physical Aging Of Polymers Studied By The Fractional Model

Polymers and other polymer materials have a wide range of applications in many fields of civil and defense. Aging characterization of these materials will occur throughout the service lifetime of the component. During this long period of time, its structure will change, leading to the aging-time dependent mechanical, thermal and dielectric properties such as creep compliance, tensile strength, thermal conductivity, specific volume, dielectric permittivity and etc. During practical service, chemical or biological aging might be accompanied, involving permanent modification and rupture of primary chemical bonds. Physical aging occurs when a polymer is in the glassy state and is caused by molecular relaxations that are biased in the direction required to drive the material closer to equilibrium. Statistics and dissipative dynamics of glassy state has been an important research subject in physics.Physical aging changes the structure,and at the same time it affects the mechanical properties of materials. Viscoelasticity is the typical property of mechanical properties of the polymer.The introduction of fractional calculus provides new tool and methods for studying viscoelasticity, and the viscoelasticity theory has a breakthrough development. Moreover, fractional-order derivatives and integrals provide a powerful instrument for the description of memory and hereditary properties of different substances. This is the most significant advantage of the fractional-order models and why fractional viscoelastic models get so many successful applications in reality. In this paper, based on experimental data, physical aging properties of polymers were studied by the fractional calculus model of viscoelastic materials. This study has the important theoretical value and practical significance for finding out the relation between property and structure of polymer.The stress relaxation curves and creep curves of PEEK and PPS at different aging temperatures and aging times were fitted using generalized fractional Maxwell model. Genetic algorithm and conjugate gradient method were employed to optimize the model parameters. The results show that this model can simulate the relaxation processes perfectly. The fractional ordersβandα(relaxation exponents) were determined by the material structures while the temperatures and aging times result in different relaxation timeτ(model parameter). When the time was scaled byτ, the stress relaxation curves and creep curves at all temperatures and aging times superpose naturally. It is to say that the time-aging time superposition and time-temperature superposition are well satisfied. Accordingly a reliable prediction to the long-term mechanical property of polymers can be obtained.