The statistical theory of the birefringence of an individual non‐Gaussian elastomer chain is used together with a chain network description of rubber elasticity to develop a relationship among the strain, birefringence, and stress in elastomers, valid for large deformations under generalized strain states. The result is a fully three‐dimensional internal variable based constitutive model of rubber elasticity in which measurement of the elastomeric birefringence during straining in one deformation state characterizes the optically anisotropic response of the elastomer. Simultaneous measurement of the stress vs. strain response provides the rubbery modulus and limiting network extensibility properties needed to completely characterize the mechanical anisotropy of the material. Once characterized using the single, large deformation experiment, the birefringence and stress responses of the elastomer in other deformation states may then be predicted without adjusting any model parameters. The theory is compared to experimental studies from the literature of large strain deformations of elastomers in uniaxial tension and compression for which the exhibited birefringence and stress responses of deforming elastomers have been simultaneously recorded.
The mechanical behavior, morphological characterization and constitutive modeling of plasticized poly(vinyl chloride) (or PVC) are studied in this paper. The plasticized PVC is tested to large strains over a broad range of strain rates. Uniaxial and plane strain compression data at various constant strain rates ranging from −0.001 to −10 s−1 are collected on a conventional servohydraulic test system. Additional uniaxial impact compression data at approximately constant strain rates ranging from −1160 to −5560 s−1 are obtained using an aluminum split Hopkinson pressure bar apparatus. The large strain load/unload response of the plasticized PVC is nonlinear, it contains hysteresis and plastic deformation, and the initial response is highly rate dependent when the strain rate spans the transition zone between quasi-static and impact strain rates at room temperature. The morphology of plasticized PVC is analyzed via differential scanning calorimetry (DSC) and dynamic mechanical analysis (DMA), and described as a physically entangled network. A three-dimensional rate dependent constitutive model for plasticized PVC is developed and shown to successfully predict its stress—strain behavior over a broad range of strain rates.
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