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Lightweight deformation gage attached to a polymer specimen determines the thickness changes undergone by the specimen during the testing of its tensile and elongation properties. Mechanical noise from outside sources is dampened when the assembly is hung on a light rubber band.
The self-assembly of colloidal nanoparticles into ordered superlattices typically uses dynamic interactions to govern particle crystallization, as these non-permanent bonds prevent the formation of kinetically trapped, disordered aggregates. However, while the use of reversible bonding is critical in the formation of highly ordered particle arrangements, dynamic interactions also inherently make the structures more prone to disassembly or disruption when subjected to different environmental stimuli. Thus, there is typically a trade-off between the ability to initially form an ordered colloidal material and the ability of that material to retain its order under different conditions. Here, we present a method for embedding colloidal nanoparticle superlattices into a polymer gel matrix. This encapsulation strategy physically prevents the nanoparticles from dissociating upon heating, drying, or the introduction of chemicals that would normally disrupt the lattice. However, the use of a gel as the embedding medium still permits further modification of the colloidal nanoparticle lattice by introducing stimuli that deform the gel network (as this deformation in turn alters the nanoparticle lattice structure in a predictable manner). Moreover, encapsulation of the lattice within a gel permits further stabilization into fully solid materials by removing the solvent from the gel or by replacing the solvent with a liquid monomer that can be photopolymerized. This embedding method therefore makes it possible to incorporate ordered colloidal arrays into a polymer matrix as either dynamic or static structures, expanding their potential for use in responsive materials.
Deformation process and structure of crystalline polymers
The Zimm plot has been widely used to characterize the molecular dimensions of polymers from small-angle scattering experiments, where the reciprocal intensity is analyzed as a function of the square of the magnitude of the scattering wavevector Q. Here, this work explores the benefits of analyzing the reciprocal scattering intensity from deformed polymers, extending the original Zimm plot to anisotropic materials. In the small-angle limit, a tensorial extension of the Guinier law is found for the gyration tensor and the reciprocal single-chain structure factor. In the high-Q limit, application of the spherical harmonic expansion technique to the reciprocal structure factor permits direct model-independent analysis of spatially dependent molecular deformation of polymers. Additionally, the contributions from high-order spherical harmonics become insignificant in the reciprocal-intensity representation. The proposed generalized Zimm plot approach is demonstrated computationally with the affine deformation model and the Rouse model, and experimentally with small-angle neutron scattering measurements of deformed polystyrene melts.
Procedures for modeling the effect of high strain rate on composite materials are needed for designing reliable composite engine cases that are lighter than the metal cases in current use. The types of polymer matrix composites that are likely to be used in such an application have a deformation response that is nonlinear and that varies with strain rate. The nonlinearity and strain rate dependence of the composite response is primarily due to the matrix constituent. Therefore, in developing material models to be used in the design of impact-resistant composite engine cases, the deformation of the polymer matrix must be correctly analyzed. However, unlike in metals, the nonlinear response of polymers depends on the hydrostatic stresses, which must be accounted for within an analytical model. An experimental program has been carried out through a university grant with the Ohio State University to obtain tensile and shear deformation data for a representative polymer for strain rates ranging from quasi-static to high rates of several hundred per second. This information has been used at the NASA Glenn Research Center to develop, characterize, and correlate a material model in which the strain rate dependence and nonlinearity (including hydrostatic stress effects) of the polymer are correctly analyzed. To obtain the material data, Glenn s researchers designed and fabricated test specimens of a representative toughened epoxy resin. Quasi-static tests at low strain rates and split Hopkinson bar tests at high strain rates were then conducted at the Ohio State University. The experimental data confirmed the strong effects of strain rate on both the tensile and shear deformation of the polymer. For the analytical model, Glenn researchers modified state variable constitutive equations previously used for the viscoplastic analysis of metals to allow for the analysis of the nonlinear, strain-rate-dependent polymer deformation. Specifically, we accounted for the effects of hydrostatic stresses. An important discovery in the course of this work was that the hydrostatic stress effects varied during the loading process, which needed to be accounted for within the constitutive equations. The model is characterized primarily by shear data, with tensile data used to characterize the hydrostatic stress effects.
designing reliable composite engine cases that are lighter than the metal cases in current use. The types of polymer matrix composites that are likely to be used in such an application have a deformation response that is nonlinear and that varies with strain rate. The nonlinearity and the strain-rate dependence of the composite response are due primarily to the matrix constituent. Therefore, in developing material models to be used in the design of impact-resistant composite engine cases, the deformation of the polymer matrix must be correctly analyzed. However, unlike in metals, the nonlinear response of polymers depends on the hydrostatic stresses, which must be accounted for within an analytical model. By applying micromechanics techniques along with given fiber properties, one can also determine the effects of the hydrostatic stresses in the polymer on the overall composite deformation response. First efforts to account for the hydrostatic stress effects in the composite deformation applied purely empirical methods that relied on composite-level data. In later efforts, to allow polymer properties to be characterized solely on the basis of polymer data, researchers at the NASA Glenn Research Center developed equations to model the polymers that were based on a non-associative flow rule, and efforts to use these equations to simulate the deformation of representative polymer materials were reasonably successful. However, these equations were found to have difficulty in correctly analyzing the multiaxial stress states found in the polymer matrix constituent of a composite material. To correct these difficulties, and to allow for the accurate simulation of the nonlinear strain-rate-dependent deformation analysis of polymer matrix composites, in the efforts reported here Glenn researchers reformulated the polymer constitutive equations from basic principles using the concept of an associative flow rule. These revised equations were characterized and validated in an experimental program carried out through a university grant with the Ohio State University, wherein tensile and shear deformation data were obtained for a representative polymer for strain rates ranging from quasi-static to high rates of several hundred per second. Tensile deformation data also were obtained over a variety of strain rates and fiber orientation angles for a representative polymer matrix composite composed using the polymer.
The results presented here are part of an ongoing research program to develop strain rate dependent deformation and failure models for the analysis of polymer matrix composites subject to high strain rate impact loads. State variable constitutive equations originally developed for metals have been modified in order to model the nonlinear, strain rate dependent deformation of polymeric matrix materials. To account for the effects of hydrostatic stresses, which are significant in polymers, the classical 5 plasticity theory definitions of effective stress and effective plastic strain are modified by applying variations of the Drucker-Prager yield criterion. To verify the revised formulation, the shear and tensile deformation of a representative toughened epoxy is analyzed across a wide range of strain rates (from quasi-static to high strain rates) and the results are compared to experimentally obtained values. For the analyzed polymers, both the tensile and shear stress-strain curves computed using the analytical model correlate well with values obtained through experimental tests. The polymer constitutive equations are implemented within a strength of materials based micromechanics method to predict the nonlinear, strain rate dependent deformation of polymer matrix composites. In the micromechanics, the unit cell is divided up into a number of independently analyzed slices, and laminate theory is then applied to obtain the effective deformation of the unit cell. The composite mechanics are verified by analyzing the deformation of a representative polymer matrix composite (composed using the representative polymer analyzed for the correlation of the polymer constitutive equations) for several fiber orientation angles across a variety of strain rates. The computed values compare favorably to experimentally obtained results.
Polymer matrix composites (PMCs) are increasingly being used in aerospace structures that are expected to experience complex dynamic loading conditions throughout their lifetime. As such, a detailed understanding of the high strain rate behavior of the constituents, particularly the strain rate, temperature, and pressure dependent polymer matrix, is paramount. In this paper, preliminary efforts in modeling experimentally observed temperature rises due to plastic deformation in PMCs subjected to dynamic loading are presented. To this end, an existing isothermal viscoplastic polymer constitutive formulation is extended to model adiabatic conditions by incorporating temperature dependent elastic properties and modifying the components of the inelastic strain rate tensor to explicitly depend on temperature. It is demonstrated that the modified polymer constitutive model is capable of capturing strain rate and temperature dependent yield as well as thermal softening associated with the conversion of plastic work to heat at high rates of strain. The modified constitutive model is then embedded within a strength of materials based micromechanics framework to investigate the manifestation of matrix thermal softening, due to the conversion of plastic work to heat, on the high strain rate response of a T700Epon 862 (T700E862) unidirectional composite. Adiabatic model predictions for high strain rate composite longitudinal tensile, transverse tensile, and in-plane shear loading are presented. Results show a substantial deviation from isothermal conditions; significant thermal softening is observed for matrix dominated deformation modes (transverse tension and in-plane shear), highlighting the importance of accounting for the conversion of plastic work to heat in the polymer matrix in the high strain rate analysis of PMC structures.
There has been significant interest in the engineering of polymer topology to control rheology and mechanical stability in dilute solutions for applications involving extreme shear rate flows. However, methods to experimentally probe properties at relevant shear rates (≈ 10 4 –10 6 s –1 ) have remained ex situ, obscuring access to measures of polymer deformation and rheology that would otherwise provide mechanistic insight into the topology-dependent properties that control their behavior in extreme shear flows. In this study, we used novel in situ small angle neutron scattering measurements in a capillary rheometer (capillary rheo-SANS) to simultaneously measure solution viscosities and polymer deformations in high shear on a series of chemically homologous topology-defined polymers including linear, randomly branched, and star-shaped molecules. We demonstrate that differences in the onset of chain stretching and shear thinning of these polymers in dilute solution are controlled primarily by differences in their molecular relaxation time. These differences correlate with differences in chain scission inferred from ex situ measurements at more extreme shear rates. Together, the results demonstrate a direct coupling between chain deformation and scission, and suggest that the dominant effect of branching as a means to impart resilience against mechanical degradation is through differences in relaxation dynamics due to branching. We anticipate that these results will provide key insights to engineer topology-controlled polymers for rheological modification, mechanical stability, and controlled mechano-chemistry.
Bond rupture and fracture in semicrystalline polymers, noting agreement with random length molecular tie chain scission model
There has been no accurate procedure for modeling the high-speed impact of composite materials, but such an analytical capability will be required in designing reliable lightweight engine-containment systems. The majority of the models in use assume a linear elastic material response that does not vary with strain rate. However, for containment systems, polymer matrix composites incorporating ductile polymers are likely to be used. For such a material, the deformation response is likely to be nonlinear and to vary with strain rate. An analytical model has been developed at the NASA Glenn Research Center at Lewis Field that incorporates both of these features. A set of constitutive equations that was originally developed to analyze the viscoplastic deformation of metals (Ramaswamy-Stouffer equations) was modified to simulate the nonlinear, rate-dependent deformation of polymers. Specifically, the effects of hydrostatic stresses on the inelastic response, which can be significant in polymers, were accounted for by a modification of the definition of the effective stress. The constitutive equations were then incorporated into a composite micromechanics model based on the mechanics of materials theory. This theory predicts the deformation response of a composite material from the properties and behavior of the individual constituents. In this manner, the nonlinear, rate-dependent deformation response of a polymer matrix composite can be predicted.
A previously developed analytical formulation has been modified in order to more accurately account for the effects of hydrostatic stresses on the nonlinear, strain rate dependent deformation of polymer matrix composites. State variable constitutive equations originally developed for metals have been modified in order to model the nonlinear, strain rate dependent deformation of polymeric materials. To account for the effects of hydrostatic stresses, which are significant in polymers, the classical J2 plasticity theory definitions of effective stress and effective inelastic strain, along with the equations used to compute the components of the inelastic strain rate tensor, are appropriately modified. To verify the revised formulation, the shear and tensile deformation of two representative polymers are computed across a wide range of strain rates. Results computed using the developed constitutive equations correlate well with experimental data. The polymer constitutive equations are implemented within a strength of materials based micromechanics method to predict the nonlinear, strain rate dependent deformation of polymer matrix composites. The composite mechanics are verified by analyzing the deformation of a representative polymer matrix composite for several fiber orientation angles across a variety of strain rates. The computed values compare well to experimentally obtained results.
Stimuli-responsive microgels, composed of small beads with soft, deformable polymer networks swollen through a combination of synthetic control over the polymer and its interaction with water, form a versatile platform for development of multifunctional and biocompatible sensors. The interfacial structural variation of such materials at a nanometer length scale is essential to their function, but not yet fully comprehended. Here, we take advantage of the plasmonic response of a gold nanorod embedded in a thermoresponsive microgel (AuNR@PNIPMAm) to monitor structural changes in the hydrogel directly near the nanorod surface. By direct comparison of the plasmon response against measurements of the hydrogel structure from dynamic light scattering and nuclear magnetic resonance, we find that the microgel shell of batch-polymerized AuNR@PNIPMAm exhibits a heterogeneous volume phase transition reflected by different onset temperatures for changes in the hydrodyanmic radius (R H ) and plasmon resonance, respectively. The new approach of contrasting plasmonic response (a measure of local surface hydrogel structure) with R H and relaxation times paves a new path to gain valuable insight for the design of plasmonic sensors based on stimuli-responsive hydrogels.
Recently applications have exposed polymer matrix composite materials to very high strain rate loading conditions, requiring an ability to understand and predict the material behavior under these extreme conditions. In this first paper of a two part report, background information is presented, along with the constitutive equations which will be used to model the rate dependent nonlinear deformation response of the polymer matrix. Strain rate dependent inelastic constitutive models which were originally developed to model the viscoplastic deformation of metals have been adapted to model the nonlinear viscoelastic deformation of polymers. The modified equations were correlated by analyzing the tensile/ compressive response of both 977-2 toughened epoxy matrix and PEEK thermoplastic matrix over a variety of strain rates. For the cases examined, the modified constitutive equations appear to do an adequate job of modeling the polymer deformation response. A second follow-up paper will describe the implementation of the polymer deformation model into a composite micromechanical model, to allow for the modeling of the nonlinear, rate dependent deformation response of polymer matrix composites.
New theory calculates anisotropies induced by large deformations in polymers. Theory was developed primarily for calculating anistropy of thermal expansivity, but is also applicable to thermal conductivity, elastic moduli and other properties. Theory assumes that in isotropic state, long polymer chains are randomly coiled and not oriented in particular direction. They acquire an orientation when material is deformed. As average molecular orientation increases with deformation, properties of bulk material exhibit averaging of the microscopic anistropies of the oriented molecular segments.
Yield criteria for plastic deformation on glassy high polymers induced by stress field, noting crazing and shear yielding dependence on first stress invariant
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