Physical Mechanism-based Constitutive Models Of Amorphous Glassy Polymers

Amorphous glassy polymers have been widely used in different engineering fields such as automobiles,aerospace,communication,optical and medical instruments.Under certain external loads,polymers can undergo large irreversible deformation while the strain may reach or exceed 100%.After the initial elastic response,amorphous glassy polymers exhibit highly nonlinearity,i.e.,the significant macro-yield peak(including the pre-yield nonlinearity,the yield peak point and the post-yield softening)and the subsequent post-yield strain hardening.This finite deformation process is very sensitive to rate,temperature and deformation state.Therefore,it is necessary to establish a constitutive model that can describe and predict the complex behavior of amorphous glassy polymers.Fruitful efforts have been carried out on the finite deformation constitutive model of amorphous polymers.However,most of them adopted a phenomenological evolution equation to represent the intermolecular deformation,and the effect of material's microstructures and their evolution on the post-yield strain softening has not been thoroughly discussed.Meanwhile,for the strain hardening behavior of amorphous polymer,most works assumed a crosslinked molecular network,and the entropy elastic models were employed to describe the strain hardening.Those works considered only the effect of orientation alignment of molecular chains but not the phenomena such as the slippage of molecular chains/chain packages and the interaction of the entanglement points during the hardening process.To discuss the relationship between macroscopic deformation of amorphous glassy polymers and the underlying microstructures and their evolution,this dissertation has carried out the following works:(1)After analyzing and summarizing the existing experimental results,a new micro-mechanism is proposed to interpret the formation of macro-yield peak of amorphous glassy polymers based on the concept of molecular chain entanglement.It is assumed that,in addition to the topological entanglement formed by the knotting of molecular chains which determines material's benchmark properties,another class of microstructure,i.e.,sub-entanglement formed by the interaction of local segments of adjacent molecular chains,exists.The sub-entanglement and its evolution are the intrinsic cause for the macro-yield peak.Using the entanglement microstructures as internal variables,an elastic-viscoplastic finite deformation constitutive model is constructed.This constitutive model can not only reasonably describe the deformation response of the macro-yielding process,but also has the capability to consider the influences of thermo-mechanical history and deformation state.(2)Based on the concept of sub-entanglement and topological entanglement,the effects of strain rate and temperature on the macro-yield behavior of amorphous glassy polymers are well explained.With the consideration of the influence of rate on the glass-transition temperature(_gT),an elastic-viscoplastic finite deformation constitutive model is proposed to describe the rate-/temperature-dependent macro-yield behavior.By comparing the theoretical results with corresponding experimental ones,it is verified that the proposed model can,using the same set of material parameters,reasonably simulate and predict the macro-yield behavior in a temperature range from room temperature to _gT and a strain rate range from quasi-static to 0.1s^-1.(3)During the strain hardening of amorphous glassy polymers,the occurrence of molecular chain orientation along the principle stretch direction is complemented by the slippage of topological entanglement which forms a new class of microstructure,i.e.,cluster entanglement.The topological entanglements within the cluster entanglement cannot slip anymore.The initial isotropic molecular network dominated by topological entanglement will gradually transform to an anisotropic molecular network dominated by cluster entanglement,accompanying with energy dissipation induced by the slippage of molecular chains/chain packages etc.The Edwards-Vilgis molecular network model is adopted and extended by considering the effects of deformation and temperature on the microstructure-related variables such as the slippage of entanglement points and entanglement density etc.,to describe the evolution of molecular network during the strain hardening.A finite deformation constitutive model is then proposed to describe the strain hardening.By comparing the theoretical and experimental results,it is verified that the proposed model can effectively describe and predict the influences of strain rate,temperature and loading deformation state on the strain hardening behavior of amorphous glassy polymers.