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Register a new userA generalized mechanical model using stress-strain duality at large strain for amorphous polymers
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Ca Bernard
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Numerous models have been developed in the literature to simulate the thermomechanical behavior of amorphous polymer at large strain. These models generally show a good agreement with experimental results when the material is submitted to uniaxial loadings (tension or compression) or in case of shear loadings. However, this agreement is highly degraded when they are used in the case of combined load cases. A generalization of these models to more complex loads is scarce. In particular, models that are identified in tension or compression often overestimate the response in shear. One difficulty lies in the fact that 3D models must aggregate different physical modeling, described with different kinematics. This requires the use of transport operators complex to manipulate. In this paper, we propose a mechanical model for large strains, generalized in 3D, and precisely introducing the adequate transport operators in order to obtain an exact kinematic. The stress strain duality is validated in the writing of the power of internal forces. This generalized model is applied in the case of a polycarbonate amorphous polymers. The simulation results in tension/compression and shear are compared with the classical modeling and experimental results from the literature. The results highly improve the numerical predictions of the mechanical response of amorphous polymers submitted to any load case.
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Molecular dynamic simulation enables one to correlate the evolution of the micro-structure with anisotropic stress when a material is subject to strain. The anisotropic stress due to a constant strain-rate load in a cross-linked polymer is primarily dependent on the mean-square bond length and mean-square bond angle. Excluded volume interactions due to chain stacking and spatial distribution also has a bearing on the stress response. The bond length distribution along the chain is not uniform. Rather, the bond lengths at the end of the chains are larger and uniformly decrease towards the middle of the chain from both ends. The effect is due to the presence of cross-linkers. As with linear polymers, at high density values, changes in mean-square bond length dominates over changes in radius of gyration and end-to-end length. That is, bond deformations dominate over changes in size and shape. A large change in the mean-square bond length reflects in a jump in the stress response. Short-chain polymers more or less behave like rigid molecules. Temperature has a peculiar effect on the response in the sense that even though bond lengths increase with temperature, stress response decreases with increasing temperature. This is due to the dominance of excluded volume effects which result in lower stresses at higher temperatures. At low strain rates, some relaxation in the bond stretch is observed from $epsilon=0.2$ to $epsilon=0.5$. At high strain rates, internal deformation of the chains dominate over their uncoiling leading to a rise in the stress levels.
We have created a flat piling of disks in a numerical experiment using the Distinct Element Method (DEM) by depositing them under gravity. In the resulting pile, we then measured increments in stress and strain that were associated with a small decrease in gravity. We first describe the stress in terms of the strain using isotropic elasticity theory. Then, from a micro-mechanical view point, we calculate the relation between the stress and strain using the mean strain assumption. We compare the predicted values of Youngs modulus and Poissons ratio with those that were measured in the numerical experiment.
Thermal conductivities (TCs) of the vast majority of amorphous polymers are in a very narrow range, 0.1 $sim$ 0.5 Wm$^{-1}$K$^{-1}$, although single polymer chains possess TC of orders-of-magnitude higher. Entanglement of polymer chains plays an important role in determining the TC of bulk polymers. We propose a thermal resistance network (TRN) model for TC in amorphous polymers taking into account the entanglement of molecular chains. Our model explains well the physical origin of universally low TC observed in amorphous polymers. The empirical formulae of pressure and temperature dependence of TC can be successfully reproduced from our model not only in solid polymers but also in polymer melts. We further quantitatively explain the anisotropic TC in oriented polymers.
The structural properties of a linear polymer and its evolution in time have a strong bearing on its anisotropic stress response. The mean-square bond length and mean bond angle are the critical parameters that influence the time-varying stress developed in the polymer. The bond length distribution along the chain is uniform without any abrupt changes at the ends. Among the externally set parameters such as density, temperature, strain rate, and chain length, the density as well as the chain length of the polymer have a significant effect on the stress. At high density values, changes in mean-square bond length dominates over changes in radius of gyration and end-to-end length. In other words, bond deformations dominate as opposed to changes in size and shape. Also, there is a large change in the mean-square bond length that is reflected as a jump in the stress. Beyond a particular value of the chain length, $n = 50$, called the entanglement length, stress-response is found to have distinctly different behavior which we attribute to the entanglement effects. Short chain polymers more or less behave like rigid molecules. There is no significant change in their internal structure when loaded. Further, temperature and rate of loading have a very mild effect on the stress. Besides these new results, we can now explain well known polymeric mechanical behavior under dynamic loading from the point of view of the evolution of the molecular dynamics and the derived structural properties. This could possibly lead to polymer synthesis with desired mechanical behavior.
A full factorial design of experiments was used to study the effect of blend shear strain on the compaction process, relative density and strength of pharmaceutical tablets. The powder blends were subjected to different shear strain levels (integral of shear rate with respect to time) using an ad hoc Couette shear cell. Tablets were compressed at different compaction forces using an instrumented compactor simulator, and compaction curves showing the force-displacement profiles during compaction were obtained. Although the die-fill blend porosity (initial porosity) and the minimum in-die tablet porosity (at maximum compaction) decreased significantly with shear strain, the final tablet porosity was surprisingly independent of shear strain. The increase in the in-die maximum compaction with shear strain was, in fact, compensated during post-compaction relaxation of the tables, which also increased significantly with shear strain. Therefore, tablet porosity alone was not sufficient to predict tablet tensile strength. A decrease in the work of compaction as a function of shear strain, and an increase in the recovered elastic work was observed, which suggested weaker particle-particle bonding as the shear strain increased. For each shear strain level, the Ryskewitch Duckworth equation was a good fit to the tensile strength as a function of tablet porosity, and the obtained asymptotic tensile strength at zero porosity exhibited a 60% reduction as a function of shear strain. This was consistent with a reduced bonding efficiency as the shear strain increased.
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