David T. Grubb

Single-fibre polymer composites

We have used Raman spectroscopy to measure the axial stress distribution along a fibre during a quasi-static single fibre pull-out test. The stress distribution at the debonding front during the progress of debonding gives the maximum interfacial shear strength τs directly. In addition, the stress distribution along the fibre after debonding can be used to evaluate the interfacial normal stress and the frictional coefficient. For the plasma treated high modulus polyethylene (PE) fibres used here, τs is found to be 28 MPa by this method, while the apparent mean interfacial shear strength τa obtained from the regular single fibre pull-out test varies from 3 to 15 MPa with the fibre embedded length Ie. Stress distributions derived from the shear-lag theory fit the experimental data for fully bonded fibres well, giving values for the shear-lag constant K and the stress transfer length 1/β [1]. According to the shear-lag theory, τs = βleτacoth(βle). If β can be found for a given system from Raman spectroscopy, τs can be evaluated from the pull-out test using this equation.The regular pull-out tests, corrected for residual stress and interfacial friction, give the same τs but not the same β or pull-out load as the slower Raman test. The shear-lag constant K can be expressed as a function of the matrix shear modulus and geometric terms. One of these terms is the effective interfacial radius, re, the radius at which the strain in the matrix equals the average matrix strain. Raman measurements indicate that re is small, only four times the fibre radius. This result is supported by polarizing optical microscopy. The model of Greszczuk [2], which assumes a uniform shear within an effective interaction thickness bi, gives a similar result. We find that bi = 20 μm, about twice the fibre radius. Using the pull-out test data, as for other fibre composites, bi and re predicted by shear-lag theories do not agree with the results of microscopy to this extent. In these cases τs is much larger than the yield strength of the matrix and as neither treatment considers plastic deformation of the matrix agreement should not be expected.

Small-angle X-ray diffraction of Kevlar using synchrotron radiation

Abstract A synchrotron source of X-rays has been used to obtain high-resoultion small-angle X-ray scattering (SAXS) patterns from commercial poly( p -phenylene terephthalamide) (Kevlar) fibres. In Kevlar 49, detailed analysis of the equatorial streak, often called the ‘void scattering’, shows that it comes from the crystals in the fibre and not from any voids. The scattering objects producing the SAXS pattern have the same length, width and orientation distribution as the crystals. In Kevlar 149, there is less scatter overall, a bimodal distribution of sizes and orientation, and an off-axis streak at ±25° to the equator. Similar off-axis small-angle scattering has recently been seen in other rigid-rod polymer fibres, but the fibre structure producing it is not understood.

Gel-drawn fibres of poly(vinyl alcohol)

Semi-crystalline gels of several samples of poly(vinyl alcohol) were made from solutions in which the polymer concentration varied from 2.0 to 15.0%. Entanglement density in the material was in this way reduced from the melt entanglement density. When gels were partially dried and drawn isothermally the maximum draw ratio increased with drawing temperature up to 11 to 14 at 140 to 180‡ C. A meltcast film could be drawn to 6.8 times at 140‡ C. Drawn material had a crystallinity of 55 to 80%, while that of isotropic material was 20 to 55%. Gels of lower initial concentration (lower entanglement density) could be drawn to greater extensions at a given draw temperature and had better mechanical properties. Youngs modulus increased with draw ratio to values very close to those for polyethylene fibres drawn by the same amount. Youngs modulus was independent of drawing temperature or degree of crystallinity, but on comparing drawn gels of the same draw ratio, crystallinity and crystalline orientation, those of lower entanglement density had a higher Youngs modulus.

The annealing of solution grown crystals of alpha and gamma poly(vinylidene fluoride)

Single crystals of poly(vinylidene fluoride) PVF2 have been grown from dilute solution and sedimented to form oriented mats. The product was α‐PVF2 or a mixture of α‐ and γ‐PVF2 and different morphologies were observed for the two phases. Annealed mats exhibited complex melting behavior, due in part to melting and recrystallization. Plots of melting temperature against reciprocal lamellar spacing indicate equilibrium melting points of 443.5 and 457.3 K for rapidly crystallized α‐ and γ‐PVF2 after 1‐h anneal, and fold surface free energies of 15.6 and 27.2 mJm−2 for α‐PVF2 from different solvents, 24.8 mJm−2 for γ‐PVF2. Long annealing times or high annealing temperatures tend to increase the melting point without changing the lamellar thickness probably due to rejection of head‐to‐head defects.

Measurement of stress concentration in a fiber adjacent to a fiber break in a model composite

The axial stress in a continuous fiber adjacent to a broken fiber has been measured directly. The model composites used are hybrid and comprise of a single fiber of either Nicalon or carbon flanked by two Kevlar fibers and embedded in a large cross-section of epoxy resin. The center fiber breaks cleanly at small strains, and the axial stress in Kevlar fibers can be measured within the transparent matrix by using a Raman microprobe. The laser probe was focused to about 10 μm, so this was the spatial resolution of the stress measurement. The stress transfer length of about 200 μm agrees with theory and photoelastic measurements, but the stress concentration factor does not agree with theoretical predictions. A significant amount of load is transferred to the matrix in the geometry used here. Load transfer models based on the concept of an effective radial interaction distance are proposed which give a better agreement with the measured stress concentration factors.

Fiber interactions in the multi-fiber composite fragmentation test

The single-fiber fragmentation test has been extended to a multi-fiber fragmentation test that demonstrates the fiber/fiber interactions that are present in real composites. The model composites are of Nicalon fibers embedded in an epoxy resin and have a controlled inter-fiber separation. An important qualitative result is that the interfacial failure in each fiber in an array is correlated with that of its neighbors, even when the individual fiber breaks are not at the same location. The fiber bundle as a whole thus has well defined regions of interfacial failure. Quantitatively, fibers in an array have a larger mean fragment length than a single fiber, and the fragment length increases with smaller inter-fiber separation or more embedded fibers. Shear-lag theory predicts the opposite effect. The results suggest that the presence of neighboring fibers prevent failure at some flaws. The flaw density function changes as a result of fiber/fiber interactions and this affects the fiber fragmentation process. Multi-fiber fragmentation tests show that the embedded single fiber test is insufficient to model fiber behavior within real composites.

Molecular stress distribution and creep of high-modulus polyethylene fibres

Abstract Raman spectroscopy has been used to measure the molecular stress distribution in high-modulus, high-strength polyethylene fibres (Allied Spectra 1000 and Spectra 900) at low temperature and as a function of time during creep at room temperature. Increase in band width or change of band shape is interpreted as due to a distribution of stress or strain in molecules in the all-trans configuration. Fibres loaded at 77 K show two peaks in the stress distribution, as was found by van Eijk et al. at 240 K. About one-sixth of the all-trans molecules in a Spectra 1000 fibre as produced carry little load. The rest carry from half to twice the mean load. Spectra 1000 fibres loaded at over 1 GPa for a few minutes at room temperature show two well defined peaks in each of the C-C stretching Raman bands at 1064 and 1130 cm−1 and thus a sharp bimodal distribution of stress. At long creep times, the higher stress peak increases in width while keeping the same area. Eventually, the stress distribution has a single peak with a broad tail on the high-stress side. This result unifies the previous two observations, one of which found only a single asymmetric peak and the other only two peaks in the stress distribution. As the tail broadens, the number of very highly strained molecules increases, and a significant number reach strains of 10%. It is not surprising that this leads to fracture of the fibre. After loading for less than a minute at room temperature or for a few minutes at 273 K, there is only a single peak in the stress distribution. The fibre structure is thus undergoing complex changes during creep, and the stress distribution seen at room temperature is not simply related to the original structure.

Craze behaviour in isotactic polystyrene: 1. Craze-spherulite interaction

Abstract The deformation of isotactic polystyrene (i-PS) in uniaxial tension at room temperature has been studied in detail by transmission electron microscopy. Quantitative analysis reveals that crazes in amorphous i-PS are similar to crazes formed in atactic polystyrene (a-PS) under the same conditions, except for a higher stress concentration at the craze tip. Fully spherulitic i-PS films contain crazes with very irregular paths which often nucleate at spherulite triple points. Craze-spherulite interactions have been observed in films which contain spherulites isolated in an amorphous matrix. Lamellae with their c -axis perpendicular to the tensile axis generally yield a higher craze fibril draw ratio than in the amorphous matrix. Lamellae with their c -axis parallel to the tensile axis cause a decrease in both λ and craze width. When the c -axis is in the plane of the film but oblique to the tensile axis, the craze deviates toward the centre of the spherulite. The entanglement network approach applied to crystalline i-PS predicts the correct anisotropic behaviour of λ when neutron scattering data on chain conformation in i-PS crystals are used.

Solution grown crystals of poly(vinylidene fluoride): The effect of ionic species on growth

Abstract For a range of solvents it is found that the addition of ionic impurities to PVF2 solutions causes polar phases to form. Single crystals of gamma phase grown from dilute (0.01%) solution of commercial polymer have a folded ribbon morphology, but from pure radiation polymerized PVF2 both alpha and gamma crystals are pseudo-hexagonal lamellae. Concentrated (1%) solutions of PVF2 in dimethyl-acetamide (DMA) give thin films on evaporation. The usual product is a mixture of alpha and gamma phase, and the addition of salts such as KBr causes more gamma to form. Care must therefore be taken when casting films on salt disks for IR analysis as KBr dissolves readily in DMA. LiCl causes growth in the gamma phase and also in the beta phase at above 3 ppm LiCl in solution. At LiCl levels of 10 ppm in solution the film is beta + gamma, with no alpha detectable. Simple models of polar gamma crystals indicate that ions are strongly attracted to their polar faces. The electrostatic energy of a growing crystal is ...

Short‐term isothermal annealing of polyethylene single crystals

Polyethylene single‐crystal mats 20 μm thick were heated to the annealing temperatures (120–132 °C) in less than 1 s. The Cornell High Energy Synchrotron Source (CHESS) and a TV detector system were used to obtain wide‐ and small‐angle x‐ray scattering patterns from these mats during annealing with a time resolution of 0.3 s. Both whole polymer and a molecular weight fraction showed rapid melting and recrystallization, with a minimum crystallinity at 2–4 s after reaching the annealing temperature. Recrystallization was essentially complete in 60–90 s and most curves could be fitted to the Johnson–Mehl–Avrami equation with exponent n=1. Two‐thirds of the material could be molten before there was any loss of the original crystal orientation. The increase in long period was discontinuous at high annealing temperature. The original small‐angle long‐spacing peak quickly lost intensity as crystallinity fell and a new peak appeared at larger long spacing. This new long spacing increased with time for the whole p...