Multilevel character of deformation of polymers

The inhomogeneity in the creep rate of polymers on different scales of deformation has been studied by laser interferometry. The main results have been obtained for the amorphous-crystalline polymer polytetrafluoroethylene. The deformation characteristics are the oscillation periods of the rate (jumps of deformation), oscillation amplitudes of the rate, and the scatter of these quantities. Application of computer methods for processing of the results has made it possible to determine the difference and similarity between jumpwise deformations on different structural levels, including the nanolevel. For a more distinct separation of deformation levels, the measurements have been made in a magnetic field and outside the magnetic field. Deformation jumps have been found on five levels: from 4 nm to more than 10 μm. Introduction of a sample into a magnetic field changes the characteristics of jumps; in this case, the scatter in the values of jumps always increases, whereas their average value varies differently on different scale levels. The measurement of the parameters of deformation jumps on different scales allows one to study the laws of the development of the deformation process and the evolution of structural inhomogeneities.     

Step deformation of solid amorphous polymers

The variation of step deformation kinetics in solids is studied as a function of morphological factors. Oscillations of creep rate at micrometer increments of the amount of deformation, which reflect the step nature of the process, are investigated from an interferogram. It is shown that the plasticization of polymethyl methacrylate by dibutyl phthalate blurs the steps, while their height varies insignificantly. The results are explained using the concept of the netlike structure of amorphous polymers. The data obtained confirm the universal nature of jumps as a mode of evolution of deformation in various solids. The jumps reflect the cooperative nature of motion of kinetic units, and the regular variation of the characteristics of the jumps lends support to the definition of creep as a process of structural self-organization.     

Micro- and nanoscale instabilities of deformation in polymers

The rate and magnitude of the deformation in polymers under constant compressive stresses at room temperature have been measured. The use of laser interferometer has made it possible to perform measurements at small intervals of variations in the specimen length Δl = 0.325 μm, and the analysis of the form of beats has made it possible to estimate oscillations of the strain rate in nanoscale displacements. It has been shown that the average strain rate of polymers continuously varies and no creeping interval with a constant rate is observed. At all stages of smooth variations in the average rate, jumps of its current values corresponding to Δl from several nanometers to a hundred and more nanometers have been found. Changes in the structure with an increase in the deformation manifest themselves in an increase in the size of nanoscale jumps and in a complication of their shape.     

Activation parameters of stepped deformation of polymers

Creep rates on short deformation base lines before and after a change in temperature and stresses were measured by interferometry to determine the activation energies and activation volumes of the process. It is shown that the activation parameters of polymer creep vary not only at a macroscopic level but also within the micron-size deformation steps. The largest potential barrier corresponds to the lowest rate in a step and plays the role of a “physical node.” The results confirm the supposition that micron-size jumps (steps) of polymer deformation are caused by the nonmonotonic nature of intermolecular interactions in microvolumes of this level. Fiz. Tverd. Tela (St. Petersburg) 40, 1635–1638 (September 1998)     

Structural factors in deformation of crystalline polymers

The multiple α absorption of bulk-crystallized polyethylene (PE) was separated into the α₁ and the α₂ absorptions on the assumption that this α₂ absorption is associated with shear deformation of lamellar crystals, i.e., has the same characteristics as in single crystal mats. The separated α₁ mechanism is related to the molecular motions in the intermosaic block region. The α₁ process is very sensitive to static and dynamic deformation, whereas the α₂ process is not affected. Plastic deformation of bulk crystallized PE was analyzed in terms of true stress and true strain. The temperature dependence of the critical yield stress below 60°C showed the same magnitude of activation energy (26 kcal/mole) as that of α₁. The leading mechanism of deformation at lower temperatures is the breakdown of lamellar crystals into mosaic blocks. Compressive deformation of solid-state extrudates along the molecular axis, giving rise to kink bands, was analyzed with X-ray goniometry and in terms of the strain-rate dependence of the yield stress. The deformation of the crystals in the kink bands occurred by superposition of intercrystallite slip (α₁) and uniform shear deformation (α₂). It was concluded that consideration of intermosaic slip mechanisms (α₁), in addition to the shear deformation (α₂) and the interlamellar deformation (β), is effective and helpful to understand the deformation process of crystalline polymers.     

Chevron morphology in deformed semicrystalline polymers

Chevron morphology was observed using transmission electron microscopy in various semicrystalline polymers deformed in tensile experiments. The morphological and mechanical prerequisites for chevron structure formation in semicrystalline polymers were revealed. It was demonstrated that chevron folding is a common deformation mode which can appear in real, i.e. globally unoriented or partially oriented samples, in areas where the lamellar stacks are oriented perpendicular to the deformation direction. Similarities with the behaviour of other layered systems were found. The mechanism of chevron formation is discussed in the light of the fundamental statements of the folding theories and is related to the specific microstructure of the polymers. The effect of boundary conditions, deformation temperature and macroscopic strain on the characteristics of the chevron structure is described.     

The development of spherulite morphology in polymers

Morphology of polyethylene spherulites has been investigated by the low-dose technique using transmission electron microscopy (TEM) in a scanning mode for dark field and microdiffraction. Specimens were prepared by solvent casting and subsequent recrystallization at different temperatures. The dark-field studies provide spatial information on the lamellar morphology. Two major types of spherulite morphology have been observed: At high temperatures (low crystallization rate) the dark fields show a preferred orientation of the lamellae along the 020 axis. At low temperatures the preferred orientation is 110. The microdiffraction patterns confirm the dark-field results and also show that for intermediate temperatures, regular alteration of regions with 020 and 110 growth planes is responsible for the ringed spherulite appearance. The twisted lamellae model cannot be excluded, but it is shown that it is not responsible for the regular changes in contrast. A model of dendritic growth of spherulite lamellae is used in which the plane of crystal growth is temperature dependent and, for intermediate temperatures, results in regular fluctuation in the mode of crystal growth, branching, and ringed spherulites appearance.     

Mechanisms of reversible thermal deformation of oriented polymers

Reversible thermal deformation coefficients (TDCs) of oriented samples of a flexible-chain polymer (polyethylene) and of a number of rigid-chain polymers were measured in the longitudinal and transverse directions near room temperature. The same samples were used to measure the TDCs of crystallites by x-ray diffraction. The magnitudes of the TDCs of macroscopic oriented samples and of constituting crystallites and the characteristics of the thermal deformation of flexible-chain and rigid-chain polymers are compared. A conclusion is made that the mechanisms that determine thermal deformation in the longitudinal and transverse directions for the flexible-chain and rigid-chain polymers are different.     

Electric fields in polymers during dynamic deformation

The transverse vibrations of a beam and the propagation of tension, compression, and shear deformation waves along the axis of a rod are studied by recording the electric field that appears under these conditions near the rod. Experiments are performed on samples made of various plastic materials in order to compare the effect of the properties of a material on the electric response during dynamic deformation, all other things being equal. Dynamic Young’s moduli are determined during bending vibrations and the propagation of longitudinal waves. It is shown that the location and type of antenna should be taken into account to adequately interpret a recorded signal and a dynamic mechanical process.     

Structural conditions of deformation and fracture of oriented crystalline polymers

Deformation of supermolecular structure elements of oriented crystalline polymers and nucleation of initial submicroscopic cracks induced by stress have been studied by the small-angle x-ray scattering technique. It is shown that the intrafibrillar amorphous interlayers have low strength and high deformability. The rupture of the weakest amorphous interlayers leads to nucleation of initial submicrocracks. The influence of submicrocracks on deformation around such cracks is revealed. The micromechanics of deformation and fracture of polymers is discussed.     

Structural heterogeneity and jumplike deformation of polymers on the mesoscopic level

This paper reports on the results of research into the jumplike deformation of two polymers based on poly(oxymethylene) (POM) with structural aggregates (spherulites) of different micrometer-scale sizes at a temperature of 290 K, as well as of polyimide (PI) and a PI + graphite composite at temperatures of 290 and 690 K. The creep rate under compression is measured with a laser interferometer in 0.3-μm deformation increments. It is found that, in the course of deformation on the micrometer scale, the creep rate varies nonmonotonically. Periodic variations of the creep rate correspond to a jumplike (stepwise) behavior of the creep. It is shown that the mean jumps in the microdeformation correspond to the mean sizes of poly(oxymethylene) grains and graphite particles in polyimide. The results obtained are in agreement with previously drawn conclusions: the deformation jumps are determined by the scale of ordered microaggregates typical of the structure under investigation.     

On the micromechanisms of plastic deformation in semicrystalline polymers

Many different molecular processes that cause plastic deformation in polymers can be investigated by transmission electron microscopy (TEM). A short review of those deformation mechanisms is given in this paper using model morphologies and correlating them to the corresponding mechanical behavior.     

Discontinuous deformation of Ni3Fe alloy single crystals in various states of atomic order

The conditions conducive to discontinuous deformation of alloy single crystals in various states of order were studied in experiments. An equation defining the minimum temperature for deformation discontinuities to develop was obtained. The possible reasons for the influence of order upon discontinuous deformation were analyzed.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 12, pp. 65–71, December, 1977.     

Effect of the magnetic field on nanometer-scale deformation jumps in polymers

The effect of a constant magnetic field on the rate of jumplike creep under compression is investigated for vitreous polymers with a globular structure. The interferometric method used for recording the creep makes it possible to measure deformation jumps from 300 nm and larger. It is demonstrated that the sizes of deformation jumps in polyester and epoxy resins decrease in the magnetic field (B = 0.2 T). Taking into account that the deformation jump size corresponds to the size of structural inhomogeneities, it is assumed that macroglobules under the action of a constant magnetic field are separated into smaller structural units on the nanometer level.     

Distinction between two molecular mechanisms for deformation of glassy amorphous polymers

During deformation of glassy amorphous polymers the rotation of rigid chain segments around skeletal bonds is restricted simultaneously by configurational (intramolecular) and chain-chain (intermolecular) energy barriers. These barriers are modeled in a self-consistent manner for six polymers by use of an approximate analytical treatment. The comparative contribution of these barriers to the small-strain modulus of the bulk solid is used as a basis for distinguishing between two mechanisms of stiffening. With polycarbonate, polyphenylene oxide, and an aromatic polyimide, in which the rigid chain segment is relatively long, the modulus derives its value primarily from the resistance to displacements across chains due to intermolecular barriers. With vinyl polymers such as polystyrene, poly(vinyl chloride) and poly(methyl methacrylate), however, in which the rigid chain segment is short, resistance to displacements along the main chain due to intramolecular barriers contributes equally significantly to the modulus. Our calculations also show that the length of the rigid chain segment, acting as a mechanical moment arm, affects the resistance to intramolecular displacements much more than does the height of the rotational energy barrier.     

Environmental effects on the tensile deformation of polymers at low temperatures

General experimental results are presented on the environmental effect exerted by nitrogen and argon on the tensile deformation of polymers in the neighborhood of 80° K. The primary features are the large dependence of tensile strength on strain rate and the occurrence of crazing, both of which are absent in helium and vacuum environments. The fracture stress in N₂ and Ar may be less or greater than that in He and vacuum in accordance with the strain rate being low or high, respectively. A brief theory for the low-temperature environmental crazing is presented. A central part of the theory is related to the fact that the adsorption of N₂ and Ar on all polymers around 80° K substantially reduces their surface free-energy by about 25 to 75%.     

Role of the entangled amorphous network in tensile deformation of semicrystalline polymers

Being composed of crystalline lamellae and entangled amorphous polymeric chains in between, semicrystalline polymers always show a complicated deformation behavior under tensile deformation. In recent years, the process of tensile deformation was found to exhibit several regimes: intralamellar slipping of crystalline blocks occurs at small deformation whereas a stress-induced crystalline block disaggregation-recrystallization process occurs at a strain larger than the yield strain. The strain at this transition point is related to the interplay between the amorphous entanglement density and the stability of crystal blocks. We report experimental evidence from true stress-strain experiments that support this argument. It is emphasized that tie molecules, which connect adjacent lamellae, are of lesser importance with respect to the deformational behavior.     

Fracture and mechanical behavior of rubber-like polymers under finite deformation in biaxial stress field

A study on the mechanical properties of rubbery polymers under finite deformation is presented here using the biaxial stress relaxation method for the experimental study. In the first part the gradient functions of the strain energy density function are determined as functions of I₁ and I₂, which are the invariants of the deformation sensor, by biaxial stress relaxation testing. The following results were found for both vulcanized natural rubber and SBR.

1. Each ?W/?I₁ and ?W/?I₂ is a function of both I₁ and I₂, especially in the small deformation region. However, the functions take on almost constant values and become flat for relatively large deformations.

2. The temperature dependence of these functions are such that ?W/?I₁ is proportional to the absolute temperature in the rubbery region whereas ?W/?I₂ is almost independent of temperature.

3. The relaxation properties of both functions are very close and have almost the same relaxation rate.

In the second part some discussion on the cause of the functional forms of these functions are presented using a structural model composed of 16 stretchable elements. The result is that ?W/?I, can be related to the energy required for the elongation of these elements, and aW/aI, corresponds to the energy required for the expansion of surfaces which are formed by the elements. This implies that ?W/?I₂ corresponds to an intramolecular energy, such as entropy elasticity, and ?W/?I₁ to the energy caused by intermolecular forces in the body. This estimation is also supported by an experiment in which ?W/?I₂ took a negative value in the small deformation region.

Finally, the fracture properties of the rubber-like polymers are observed by using both the biaxial tensile tester and the thin film inflation method. The fracture criterion of constant stretch ratio is proposed. This simple criterion can be deduced from the structural model presented here. It is also shown, using plasticized polyvinyl chloride, that if the material changes its property from rubbery to glassy, this simple relation is no longer applicable.     

Discontinuous perturbations

Perturbations of quantum systems ranging from oscillators to fields can be either continuous or discontinuous functions of the coupling. The system under consideration is the familiar harmonic oscillator in one degree of freedom. Previous studies have shown that when the harmonic oscillator is subjected to a perturbation with a power law singularity, a permanent change in the system characteristics is observed for a specific range of power law values. The introduction of a logarithmic singularity into the power law potential fine tunes the singularity power.