4 – Constitutive Modeling of High Strain-Rate Elastomeric Polymers

Phase-separated segmented copolymers composed of hard and soft segments can be tailored to offer hybrid mechanical performance including a highly dissipative yet resilient large strain behavior. The phase-separated morphology provides multiple relaxation processes which lead to a rate-dependent stress–strain behavior with a transition in rate sensitivity. In addition to the viscoelastic-viscoplastic dissipation pathways, stretch-induced softening due to microstructural breakdown provides a significant source of dissipation as evident in the hysteresis observed during cyclic loading. Extensive shape recovery is observed upon unloading, showing a highly resilient behavior in tandem with extensive dissipation. Here a microstructurally informed three-dimensional constitutive model is developed to capture the remarkable features of the large strain behavior of the segmented copolymers. The model employs multiple microrheological mechanisms to capture the time-dependent nonlinear constitutive responses of both hard and soft domains as well as the stretch-induced softening of the hard domains. In direct comparison to experimental data, the model is found to successfully capture the behavior of an exemplar polyurea copolymer over least six orders of magnitude in strain rate (10−3– 103 s−1). The model is also shown to be predictive of the highly dissipative yet resilient stress–strain behavior under a variety of cyclic loading conditions. The microstructurally informed nature of the model provides insights into tailoring copolymeric microstructures to provide tunable energy storage and dissipation mechanisms in this important class of material. This chapter reviews the literature on long-term performance of emerging polymer materials and introduces environmental test methodology to predict their life cycle behavior. A multifunctional weathering system has been designed and developed to create extreme environments for materials testing and to reproduce service environments for development and validation of emerging defense structural components as well as to conduct accelerated tests for their life cycle performance. The environmental chamber will apply not only to characterization of common polymer materials, but to the development of a wide range of applications of advanced materials and components in defense applications, such as smart helmets and body armors, protective coatings, structural adhesives, and building envelope materials. The accelerated performance test mechanisms and dimensional analysis of structural model testing are introduced for multiscale characterization of polymer materials and structures using the environmental chamber. A case study of long-term performance of an adhesive anchor system demonstrates the environmental test methodology of polymers. The present test methodology and instrument will provide comprehensive tool for design and development of novel advanced organic matrix composites using polyuria, epoxy, polyethylene, and asphalt among others. The deviation of the description of viscoelastic solids from linear behavior is examined. It is demonstrated that the incorporation of dilatational effects into the time-scale reduction of the physical properties through a multiplying factor similar to and including the typical time–temperature reduction process (dilatation clock model) leads to physically observed nonlinear behavior for the example of poly(methyl)methacrylate. On the other hand, for situation where shear deformations dominate, a molecular mechanics model following Eyring “reaction rate” principles is developed that also leads to a stress or strain dominated time multiplying factor to develop “yield-like” characteristics of an otherwise linearly viscoelastic solid under sufficiently large deformations or octahedral shear. It is held that under highly compressive deformation scenarios typical of explosive environments these concepts elucidate the description of elastomeric solids being driven into the glassy domain under very short time scales, commensurate with the behavior of the glassy poly(methyl)methacrylate. No account has been taken of temperature increase derived from the energy dissipation associated with such extreme loading scenarios, but there is reasonable support that such an inclusion is accomplished through the standard time–temperature reduction process once the dissipation characterization is understood more clearly.