Predictions of limiting mechanical performance for anisotropic crystalline polymers

A four-stage synthesis of molecular, micromechanical, and macromechanical models is used to predict the dependence of the longitudinal and transverse Young's moduli and the axial and transverse shear moduli of anisotropic polyethylene on percent crystallinity and the state of molecular orientation. Variational methods are employed to establish the upper and lower limits for anisotropic elastic response. The difference between lower and upper bound limits is interpreted as the potential for improving mechanical performance. A modified form of the Tsai-Halpin equation is used to examine parametric ranging (via a contiguity factor, ξ) between the lower and Tupper bound limits. In this application, the contiguity factor is interpreted as a characteristic of the internal stress-strain distribution which is dependent upon the size, shape, packing geometry, and elastic properties of the crystalline and amorphous regions. The potential for achieving high modulus polymeric materials is illustrated by treating percent crystallinity, molecular orientation, and contiguity as materials design variables subject to control by processing conditions. Optimum property trade-offs, necessary for balancing the over all mechanical behavior of anisotropic materials, are illustrated through the control of orientation and contiguity, The theoretical predictions for the moduli of anisotropic polyethylene are in good agreement with values reported for material processed by traditional procedures as well as ultra-oriented polyethylene.     

Modeling the development of elastic anisotropy as a result of plastic flow for glassy polycarbonate

The development of anisotropy as a result of plastic deformation below the glass‐transition temperature is investigated and modeled for amorphous polycarbonate. Initially, isotropic polycarbonate was subjected to different extents of plastic flow in compression, and the development of its anisotropic wave speed moduli were studied using ultrasonic wave speed measurements. Longitudinal and shear wave speed measurements were performed both in the axial and transverse directions, with respect to the axis of compression. The moduli clearly indicated the development of a transversely elastic response as a result of the uniaxial compression. The measured moduli were used to model the elastic response of polycarbonate using a model for stress that depends both on the elastic and plastic parts of the deformation. POLYM. ENG. SCI., 2009. © 2009 Society of Plastics Engineers     

Mechanical properties of oriented polymers

The anisotropic mechanical behaviour of oriented polymers at low strains is discussed. In the case of amorphous polymers and polymers of low crystallinity, attempts to interpret the anisotropy in terms of an aggregate model are reviewed. This is followed by an account of recent work on the measurement of all the elastic constants for polymer films of orthorhombic symmetry. After a brief discussion of cold drawn crystalline polymers, where very high Young's moduli can be obtained, the behaviour of annealed oriented polymers is considered. It appears that the latter can be understood in terms of a composite solid model, combining the early notions of Takayanagi with more recent ideas of interlamellar shear.     

Ultrasonic determination of mechanical moduli of oriented semicrystalline polymers

Ultrasonics has been used for the determination of the mechanical properties of oriented semicrystalline polymers through time-of-flight measurements of elastic waves propagating in various directions within the material. While being nondestructive, such a method allows one to obtain more mechanical moduli with a better accuracy than the conventional tensile tests, especially regarding the shear properties and the Poisson's coefficients. Until now, the approach used to interpret the data was approximate and not rigorous. We present here a self-consistent rigorous approach for interpreting time-of-flight data based on the group velocity including allowance for lateral displacement of the transmitted beam. Results are presented for roll-drawn PET with various draw ratios. These samples are considered to have transversely isotropic symmetry. For the Young's moduli, comparisons are made with conventional tensile tests and the differences observed are interpreted in terms of viscoelastic efforts considering both the amorphous and crystalline phases.     

Effects of composition and phase relations on mechanical properties and crystallization of silicate glasses

Crystallization, mechanical properties, and workability are all important for the commercialization and optimization of silicate glass compositions. However, the inter-relations of these properties as a function of glass composition have received little investigation. Soda-lime-silica glasses with Na₂O-MgO-CaO-Al₂O₃-SiO₂ compositions relevant to commercial glass manufacture were experimentally studied and multiple liquidus temperature and viscosity models were used to complement the experimental results. Liquidus temperatures of the fabricated glasses were measured by the temperature gradient technique, and Rietveld refinements were applied to X-Ray powder diffraction (XRD) data for devitrified glasses, enabling quantitative determination of the crystalline and amorphous fractions and the nature of the crystals. Structural properties were investigated by Raman spectroscopy. Acoustic echography, micro-Vicker's indentation, and single-edge-notched bend testing methods were used to measure Young's moduli, hardness, and fracture toughness, respectively. It is shown that it is possible to design lower-melting soda-lime-silica glass compositions without compromising their mechanical and crystallization properties. Unlike Young's modulus, brittleness is highly responsive to the composition in soda-lime-silica glasses, and notably low brittleness values can be obtained in glasses with compositions in the wollastonite primary phase field: an effect that is more pronounced in the silica primary phase field. The measured bulk crystal fractions of the glasses subjected to devitrification at the lowest possible industrial conditioning temperatures indicate that soda-lime-silica glass melts can be conditioned close to their liquidus temperatures within the compositional ranges of the primary phase fields of cristobalite, wollastonite, or their combinations.     

Tensile yield in poly(chlorotrifluoroethylene) and poly(vinylidene fluoride)

Uniaxial tension tests to the yield point were performed on poly(chlorotrifluoroethylene) (PCTFE) and poly(vinylidene fluoride) (PVF2) from room temperature to near the melting point at a strain rate of 2 min^?1. At room temperature and at least two elevated temperatures, measurements were also made at strain rates from 0.02 to 8 min^?1. The properties of these polymers were found to be similar to those of other semicrystalline polymers. In the absence of other transitions, yield energy was found to be a linear function of temperature extrapolating to zero near the melting temperature. The ratio of thermal to mechanical energy to produce yielding is smaller than for glassy polymers. Yield stress is a linear function of log strain rate. The ratio of yield stress to (initial) Young's modulus is about 0.03 at room temperature for both polymers. Yield stress is a linear function of unstrained volume. Yield strain, elastic, and plastic strain all initially increase with temperature, but PCTFE shows a decrease with temperature starting at about 100°C, thus behaving like a glassy amorphous polymer in this region.     

Finite element modeling of polymer hot embossing using a glass‐rubber finite strain constitutive model

A hyperelastic–viscoplastic constitutive model for amorphous polymers was used in finite element simulations of micro‐hot embossing across the glass transition. The model was selected for its ability to capture finite strain temperature and rate dependence over a wide range of temperatures, including across the glass transition. The simulations focused on the glass transition temperature regime, and particularly probed the effects of time and temperature during cooling and mold release. The results show that strong temperature sensitivity of the material across the glass transition leads to a wide range of required embossing force and springback. The interplay between changes in material properties upon cooling and stress relaxation can lead to significant increases in embossing force during the cooling stage, especially when high cooling rates are employed. The effects of thermal expansion also complicate the problem during rapid cooling. Nonlinear material behavior is shown to affect results in parametric hot embossing studies. Careful tailoring of embossing temperature, cooling rate, and demolding temperature is critical in acceptable feature replication. The best results are found for moderate cooling rates, which allow adequate time for stress relaxation in the material prior to mold release. POLYM. ENG. SCI., 2009. © 2009 Society of Plastics Engineers     

Microindentation studies at the near surface of glassy polymers: Influence of molecular weight

The viscoelastic‐plastic properties of various amorphous, glassy polymers [polystyrene (PS), poly(styrene‐acrylonitrile) copolymer (SAN), poly(methyl methacrylate) (PMMA), poly(vinyl chloride) (PVC), polycarbonate (PC)] in the micron and submicron range were investigated by means of load‐displacement analysis from depth‐sensing experiments. Hardness and Young's modulus values decrease rapidly with increasing depth up to a few microns. New data on the glass transition temperature correlation with microhardness are presented. The influence of annealing below the glass transition temperature upon the microhardness for various glassy polymers is pointed out. For PS, the influence of the molecular weight variation and molecular weight distribution on the microhardness is reported. Results are discussed on the basis of an entanglement network model, recently developed to explain the fine structure of crazes in amorphous polymers. © 2004 Wiley Periodicals, Inc. J Appl Polym Sci 93: 1951–1956, 2004     

The amorphous contribution to the modulus of a semi-crystalline polymer

The amorphous contribution to the Young's modulus of a semi-crystalline polymer is calculated for two morphologies: the spherulite and the stacked lamellae structure. Four types of amorphous chains are considered: bridges (or tie molecules); cilia; loops; and floating, unattached chains. The statistics of a polymer chain between two, infinite, impenetrable, parallel walls are used in the modulus calculation. It is found that for each type of amorphous chain, the Young's modulus is greater in the stacked lamellae structure than in the spherulite. The Young's modulus of a cilium, loop and floating chain all increase with increasing chain contour length while the Young's modulus of a bridge passes through a minimum value. The behavior of the Young's modulus as a function of temperature is analogous. These results are discussed in terms of the relative importance of crystalline lamellar impenetrability and the inherent elastic nature of the amorphous chains, in the Young's modulus behavior.     

Characterization of textured ceramics containing mullite from phyllosilicates

Organized ceramics are obtained from kaolinite and muscovite suspensions and shaped by aqueous tape casting or centrifugation. These processes favor the preferential orientation of particles in the powder compact. After sintering at 1400 °C, this study analyzed sample microstructures using QTA to determine the degree of the mullite orientation. The analyses revealed two main texture components, a planar texture along the c-axis of the mullite and a preferred orientation along the a-axis, which were aligned parallel and perpendicular to the casting plane, respectively. The important role of processing parameters in the organization degree of the mullite was apparent during the study. The elastic properties at different measurement scales were obtained using US echography and nanoindentation and were closely related to the organization degree of the mullite crystals obtained from the QTA analyses that were consistent with the development of an interconnected mullite network. The Young's moduli due to the nanoindentations were also determined parallel and perpendicular to the layers, and indicated the samples' anisotropic behavior. Both the Young's modulus and the anisotropy of the Young's modulus were correlated with the texture index. In particular, the anisotropy of the Young's moduli was linearly related to the overall texture index, highlighting the microstructures' anisotropic nature.     

Elastic and swelling behavior of 2-hydroxyethyl methacrylate,diethylene glycol methacrylate,and methacrylic acid copolymers

The elastic and swelling behavior of copolymers of 2-hydroxyethyl methacrylate, diethylene glycol methacrylate, and methacrylic acid crosslinked with ethylene glycol dimethacrylate has been studied. In the range of copolymer composition studied, Young's modulus of the swollen networks increases with the content of methacrylic acid, and its dependence on the content of diethylene glycol methacrylate passes through a maximum. The concentrations of the elastic network chains and determined from Young's moduli of swollen networks are much higher than those calculated from stoichiometry. This effect is attributed to the presence of additional physical crosslinks due to water-induced ordering of the hydrophobic backbone chains. Both the elastic and swelling behavior of the polymers mentioned above are decisive for their application in the preparation of soft contact lenses. © 1997 John Wiley & Sons, Inc. J Appl Polym Sci 64: 2141–2148, 1997     

Elastic moduli of glassy polymers at low strains

The short time moduli of polystyrene, poly(methyl methyacrylate), and polycarbonate have been measured in the glassy state. The main methods used were as follows: (1) The Young's modulus of a strip was derived by extrapolating to infinite length. (2) A bidirectional strain gauge was used for Young's modulus and Poisson's ratio. (3) A unidirectional bulk modulus was measured by the method of Warfield. The results obtained made it possible to determine all the isotropic moduli including the bulk modulus, and these are compared with those reported in the literature. Poisson's ratio (v) was found to increase with temperature in all cases. For poly(methyl methacrylate), where results reported in the literature vary widely, our values agreed with the lower reported figures (v < 0.36). The Young's modulus of poly(methyl methacrylate) is found to be more dependent on temperature and frequency than with the other two polymers.     

Anisotropy Effects in the Shape-Memory Performance of Polymer Foams

Isotropic and anisotropic shape-memory polymer foams are prepared by supercritical carbon dioxide foaming from a multiblock copolymer (PDLCL) consisting of poly(ω-pentadecalactone) and poly(ε-caprolactone) segments. Analysis by micro-computed tomography reveals for the anisotropic PDLCL foam cells a high shape anisotropy ratio of R = 1.72 ± 0.62 with a corresponding Young's compression moduli ratio between longitudinal and transversal direction of 4.3. The experimental compression data in the linear elastic range can be well described by the anisotropic open foam model of Gibson and Ashby. A micro-morphological analysis for single pores using scanning electron microscopy images permits the correlation between the macroscopic stress-compression behavior and microscale structural changes.     

Fundamental properties of densified polymeric glasses

Glass forming high polymers have been densified by application of high hydrostatic pressure (～1.5 kbar) in the melt followed by cooling under pressure to ambient. A density increase of about 1% was induced in each of the following polymers: polyvinylchloride, polymethylmethacrylate, polystyrene, poly-4-chlorostyrene, poly-3-chlorostyrene, poly-4-methoxystyrene and poly-4-phenoxystyrene. Differential thermal analysis (DSC) and volume relaxation techniques were used to study the reversion of the densified glass to a more normal glass at a temperature ～T_g – 15 K in general. Enthalpy relaxation (a change from glass I to glass II) in this region gives a peak or diffuse hump on the DSC scan prior to a normal glass transition temperature. It is considered that although the densified glasses may become thermodynamically stable at a sufficiently low temperature they are inherently unstable at ambient. Reversion to a more normal glass is kinetically too slow to measure at ambient in all cases studied except polymethylmethacrylate. Changes of dynamic Young's moduli and dielectric constant with densification are reported in detail for some systems and in summary for others. The densified glasses exhibit moduli higher by ～6%, dielectric constant higher by ～2% and depressed secondary mechanical and dielectric relaxation processes. Ultimate property studies are reported for PVC.     

Elastic moduli of semicrystalline polyethylenes compared with theoretical micromechanical models for composites

A large collection of data on Young's modulus and density of unfilled polyethylenes at ambient conditions has been compared with various competing theoretical mixing rules developed for composite micromechanics. The objective was to see if such theories usefully predict the dependence of stiffness on crystalline content in an archetypal isotropic semicrystalline thermoplastic polymer above its glass trnsition temperature. It was found that the self-consistent scheme derived by Hill and Budiansky from continuum micromechanics appears to have valid application to this system. The scheme naturally and coherently incorporates information on bulk and shear moduli and Poisson's ratios, while giving a good account of the main trend in the Young's modulus data. Conversely, other theoretical models frequently invoked in the polymer literature were explicitly found to be unsuitable for representing principal features of modulus-density relationships dectated by the data.     

Modeling of the mechanical response and evolution of optical anisotropy in deformed polyaniline

The mechanical response under large deformation at room temperature of amorphous polyaniline (PANI) is simulated using an elastic‐viscoplastic model for large strain of glassy polymers. The evolution of optical anisotropy under deformation is also simulated by coupling the mechanical anisotropy due to molecular alignment to the optical properties. Several homogeneous deformation tests such as tension, compression and shear are considered. For the evolution of the mechanical anisotropy and the associated optical anisotropy, we compare the results from three network models. Our predicted results are compared to experimental observations and good agreement is found.     

Mechanical properties of oxynitride glasses

Oxynitride glasses combine a high refractoriness, with Tg typically >850°C, and remarkable mechanical properties in comparison with their parent oxide glasses. Their Young's modulus and fracture toughness reach 170 GPa and 1.4 MPa m^.5, respectively. Most reports show good linear relationships between glass property values and nitrogen content. There is a clear linear dependence of Young's modulus and microhardness on fractional glass compactness (atomic packing density). They also have a better resistance to surface damage induced by indentation or scratch loading. The improvements stem from the increase of the atomic network cross-linking—because of three-fold coordinated nitrogen—and of the atomic packing density, despite nitrogen being lighter than oxygen and the Si–N bond being weaker than the Si–O bond. For constant cation composition, viscosity increases by ∼3 orders of magnitude as ∼17 eq.% oxygen is replaced by nitrogen. For rare earth oxynitride glasses with constant N content, viscosity, Young's modulus, Tg, and other properties increase with increasing cation field strength (decreasing ionic radius). Research continues to find lighter, stiffer materials, including glasses, with superior mechanical properties. With higher elastic moduli, hardness, fracture toughness, strength, surface damage resistance, increased high temperature properties, oxynitride glasses offer advantages over their oxide counterparts.     

Anisotropic yielding of injection molded polyethylene: Experiments and modeling

The anisotropic yielding of injection molded polyethylene is discussed, specifically focusing on the differences between the tensile and compressive yield stress as a function of loading angle and strain rate. For the first time, it is demonstrated that a strong Bauschinger effect exists in polymers that possess molecular orientation due to melt-processing. A macroscopic constitutive model is proposed to capture the yielding phenomena observed in the experiments. This model features two sources of anisotropy, the physical significance of which is discussed: a frozen-in stress originating from the oriented elastic network, and an intrinsically anisotropic viscoplastic flow rule based on the yield function of Hill, extended to incorporate the asymmetry between the tensile and compressive response. Model simulations demonstrate that the constitutive relation proposed accurately captures the important features of the experimental data. Also, it is able to predict the anisotropy in the failure kinetics of injection molded polyethylene subjected to a constant tensile load in different directions without the requirement of additional parameters.     

Modeling the uniaxial rate and temperature dependent behavior of amorphous and semicrystalline polymers

Strain rate and temperature dependent constitutive equations are proposed for polymer materials based on existing isotropic formulations of viscoplasticity. The proposed formulations are capable of simulating some of the important features of deformation behavior of amorphous and semicrystalline polymers. The materials model is based on the assumption that the evolution of flow stress is dependent on the rate of deformation, temperature, and an appropriate set of internal variables. The proposed theory is capable of modeling yielding, strain softening, and the orientation hardening exhibited by amorphous polymers. It is also possible to model the initial viscoplastic and subsequent nonlinear hardening behavior shown by semicrystalline polymers at large strains. Uniaxial tensile tests with uniform and hourglass specimens are made at temperatures ranging from 23 to 100°C and under various crosshead speeds. Both amorphous polycarbonate and semicrystalline polypropylene sheet materials are tested to characterize the stress and strain behavior of these materials and to determine their appropriate material constants. Load relaxation experiments are also conducted to obtain the necessary material constants describing the rate and temperature dependent flow stress behavior of polypropylene. Simulation results compare favorably against experimental data for these polymer materials.     

Structure-property relationships of chlorinated polyethylenes

This experimental study of suspension-chlorinated linear polyethylenes (CPE), (degree of chlorination 25 to 48% Cl), covers dynamic mechancial behavior at 3.5 and 110 Hz in the temperature range ? 100 to 120°C. The semicrystalline samples, with a maximum degree of crystallinity of 25%, showed the main relaxations α and β. The effect of thermal treatment was examined. In the amorphous specimens, in addition to the Tg relaxation, other low temperature damping peaks were observed. The mechancial spectra indicate structure heterogeneity and increasing stiffness with increasing chlorine substitution. For the most prominent β relaxation, the apparent activation energy was determined from the frequency shift of tan δ and E″ maxima. The effect of structure, crystallinity and frequency on Young's moduli are also discussed. For the amorphous γ ray-Crosslinked elastomeric samples the photoelastic properties were examined at near equilibrium conditions between 30° and 80°C at various degrees of crosslinking. The polarizability anisotropy of the optical link and the Mooney-Rivlin elasticity constants were determined and an attempt was made to relate the result to the specimens' structure. A compatibility study was also made for a 42% Cl, CPE/high cis polybutadiene polyblend. The damping mechanical spectra indicate a noninteracting system whose Young's moduli can be correlated with those of the pure components using a phenomenological model proposed by Takayanagi.