Effect of fillers on the sensitivity of epoxide compositions to stress concentrations in the glassy state

The results are presented of a study of the effect of mica and annealed and unannealed quartz on the strength characteristics of epoxide compositions and on their sensitivity to stress concentrations in the glassy state. It was established that the positive effect of the fillers on the properties of the polymeric compositions in the glassy state becomes apparent in a reduction of the sensitivity of these materials to stress concentrations.Institute of Physical Chemistry, Academy of Sciences of the USSR, Moscow. Translated from Mekhanika Polimerov, No. 5, pp. 929–931, September–October, 1973.     

Effect of temperature on the fracture surfaces of filled systems based on SKS-85 butadiene-styrene copolymer

The tear fracture surfaces of mixtures of SKS-85 butadiene — styrene copolymer (85% styrene) with ordinary (carbon black, chalk) and polymeric (Kapron and cellophane powder) fillers have been investigated on the interval from –60 to +40°C. As the temperature varies within the limits of the glassy state (T_g SKS-85=+24°C) of the filled polymer, the nature of the fracture surface of specimens of filled mixtures, like that of the unfilled polymer, changes; in the region of the temperature transition of the copolymer associated with the mobility of the phenyl groups (–10±5°C) there is a slowing of the fracture process. At temperatures below the T_g of the copolymer the tear fracture surfaces of specimens of mixtures containing ordinary and polymeric fillers differ sharply. The introduction of fillers (20 vol. %) with a coefficient of thermal expansion different from that of the filled polymer considerably reduces the resistance of the material to fracture and leads to a sharp increase in the rate of crack propagation; the introduction of polymeric fillers with coefficients of thermal expansion similar to that of the filled polymer leads to an increase in the resistance of the material to fracture and to a decrease in the rate of crack propagation.Moscow Technological Institute of the Meat and Dairy Industry; State Institute of Polymer Adhesives, Kirovakan. Translated from Mekhanika Polimerov, No. 5, pp. 819–826, September–October, 1969.     

Calculation of elastic characteristics and creep functions of hollow-sphere plastics by the effective medium method

Conclusion Solutions for the elastic characteristics and the creep functions of a composite containing hollow spherical fillers as applies to the four-phase nucleus/jacket/binder/equivalent-homogeneous-material model are obtained in the study when the method of self-correspondence is used. It is demonstrated that if the two-stage approach (when the elastic characteristics of the nucleus + jacket system, and the composite are calculated in the first and second stages, respectively) yields an exact solution for the bulk modulus K_* of the composite, it is highly approximate when the shear modulus G_* of the composite is determined. The error of determination of G_* increases considerably (by a factor of 2–2.5 when = 0.4) when Kerner's approximate solution (2) is used in lieu of solution (8) for the three-phase model within the framework of the two stage approach. Dzenis and Maksimov [5] establish by comparison with experimental data that the four-phase model provides a rather exact solution for the elastic modulus of a composite when the bulk content of hollow spheres 0.4. It is also demonstrated that use of Kerner's approximate solution (2) within the framework of the two-stage approach in predicting the creep of a composite yields an inadmissibly high error in the region of the principal relaxation transition of the binder from the glassy to the highly elastic state.This work was sponsored at the Iberoamericana University in 1993 by the Mexican National Council of Science and Technology (CONACYT).Translated from Mekhanika Kompozitnykh Materialov, Vol. 30, No. 2, pp. 177–188, March–April, 1994.     

Relation between the mechanical properties of polymers and the kinetic flexibility of the macromolecules

Nuclear magnetic resonance combined with extension of the specimens in the NMR spectrometer on the reversible deformation range has been used to study the cooperative modes of motion of the macromolecules in polymers, specifically polycaprolactam and polyethylene terephthalate. For each of these polymers there are two temperatures near which the nature of the molecular motion changes sharply. At low temperatures there is a transition from independent hindered vibrations of the repeating units to correlated vibrations, as a result of which the chains in the amorphous regions acquire limited kinetic flexibility within the glassy state; at high temperatures there is a transition to segmental motion. The question of how changes in the modes of molecular motion are reflected in the macroscopic mechanical properties of polymers is examined.Ioffe Physicotechnical Institute, Academy of Sciences of the USSR, Leningrad. Translated from Mekhanika Polimerov, No. 1, pp. 24–29, January–February, 1971.     

Effect of fibrous filler on the mechanical properties of polystyrene and polymethyl methacrylate in the glassy state

The authors have investigated the effect of introducing fiberglas into polystyrene and polymethyl methacrylate films on the transition temperatures and on the intervening glassy-state temperature intervals within which the polymers possess different physicomechanical properties. The variation in a number of the mechanical characteristics of these polymers has been studied as a function of filler concentration within all the subregions of the glassy state bounded by the transition temperatures obtained. Temperature inversion of the reinforcing action of the fibrous filler within the glassy state has been detected. Attention is drawn to the existence at a given temperature of a large number of filled polymer systems with the same reinforcing effect and the same strength at different contents of the same filler in the same polymer.Mekhanika Polimerov, Vol. 3, No. 3, pp. 517–523, 1967     

Effect of strain rate on the mechanical properties and transition temperatures of glass-reinforced polystyrene and polymethyl methacrylate

The effect of strain rate on the mechanical properties and transition temperatures and the subregions of the glassy state that the latter define has been investigated for polystyrene and polymethyl methacrylate films containing various amounts of fiberglas. An inversion of the reinforcing effect of the filler is observed as the strain rate is varied at fixed temperature. Varying the temperature can also lead to an inversion of the nature of the strain-rate dependence of the strength of the reinforced polymer within the glassy state. In the low-temperature region the strength increases with decrease, and in the high-temperature region with increase in strain rate. The transition temperatures of the reinforced polymers are more sensitive than those of the unreinforced polymers to changes of strain rate. The subregions of the glassy state are almost independent of the strain rate, except that as the latter increases they are shifted into the high-temperature region.Mekhanika Polimerov, Vol. 4, No. 3, pp. 462–466, 1968     

RIGIDITY IN GLASSES AND PROTEINS

We review recent progress in applying the theory of rigidity to glassy networks and to proteins. These three dimensional systems require a generalization of Laman's theorem, which we have used to develop a technique called the Pebble Game which allows the rigid regions (containing both isostatic and overconstrained parts) and the flexible joints between them, to be found. We show that a flexibility index, which measures the local density of floppy modes, is useful in characterizing the network. A sampling of recent results is given for network glasses, where we show how the glass structure can self-organize to produce an intermediate phase that is stress-free and contains a percolating isostatic cluster. In proteins, we show how maps of the rigid regions and flexible joints, as well as maps of the flexibility index, can help to elucidate the connection between structure and function. This revised version was published online in August 2006 with corrections to the Cover Date.     

Failure of particulate reinforced polymers

In this presentation, a review is given on the main effects of mineral particulate fillers (with an aspect ratio of about unity) on the deformation and fracture of amorphous and semicrystalline thermoplastic and thermosetting polymers. Elastomeric modifiers, polymer blends, and filled elastomers are not considered here. Fillers are generally used to reduce cost as well as the thermal sensitivity of mechanical properties of the matrix material and to improve, if possible, the strength and toughness. The addition of particulate fillers influences all stages of the fabrication and use of the resulting composites. We focus on the effects of a stiff second phase on elastic moduli, matrix structure, and on deformation, creep, and failure mechanisms. As the main mechanisms, particle-matrix debonding, void formation, and matrix microshear yielding are identified. Toughness is less sensitive to the quality of adhesion since particle-matrix debonding and formation of voids can be tolerated. If well controlled, debonding contributes to deformation (formation of voids should be well distributed in space and time). Reference is also made to the surprising and positive effect of CaCO₃ particles on the toughness and impact resistance of HDPE, which increases at small interparticle distances due to interfacial effects on lamellar growth in the ligament area. Submitted to the 11th International Conference on Mechanics of Composite Materials (Riga, June 11–15, 2000). Published in Mekhanika Kompozitnykh Materialov, Vol. 36, No. 3, pp. 305–316, March–April, 2000.     

Effect of physicalstate on tearing of filled systems based on linear amorphous polymers

A study has been made of the temperature dependence of the service behavior, deformation, and tear rate of filled systems based on SKS-85. It is established that the introduction of fillers which enhance the strength of systems in the high-elastic state effect a loss of strength in the vitreous state. The observed reversal of the strengthening effect from positive to negative is explained by weakening of the adhesive strength of the bond between polymer and filler particles caused by the increase and concentration of shrinkage stresses during cooling of the specimens. This effect is called temperature inversion of the reinforcing action of fillers.Mekhanika Polimerov, Vol. 1, No. 6, pp. 98–102, 1965     

Temperature reversal of the reinforcing effect of fillers

A previous investigation [4] of the tear strength of filled systems based on SKS-85 butadiene-styrene copolymer over a broad temperature interval revealed a reversal of the reinforcing effect of fillers with a coefficient of thermal expansion different from that of the filled polymer. At Tg the strength of mixtures containing polymer fillers [Kapron (polycaprolactam) and cellophane powder] exceeds that of mixtures containing chalk and carbon black. The temperature reversal effect is attributed to the severe weakening of the adhesion of the polymer to the surface of the filler particles as a result of the concentration of shrinkage stresses in the polymer-filler contact zone. The presence of shrinkage stresses around the filler particles at Tg is qualitatively demonstrated on model systems using a photoelastic technique. Moreover, it is shown that the unbalance, and hence the residual stresses, in filled systems at temperatures below the glass transition temperature of the filled polymer is determined by the difference in the coefficients of thermal expansion.Moscow Technological Institute of the Meat and Dairy Industry. Translated from Mekhanika Polimerov, No. 4, pp. 579–583, July–August, 1969.     

The effect of fullerene fillers on the mechanical properties of polymer nanocomposites

The effect of fullerene and carbon fillers on the mechanical properties of polymer nanocomposites based on thermoreactive (epoxy resin) and thermoplastic (polyamide-12) matrices was investigated. It was found that the introduction of these fillers did not affect the properties of the thermoreactive blends, but Young’s modulus and the tensile strength of the thermoplastic ones increased by about 30-40% upon addition of 0.02-0.08 wt.% fullerene materials. The best results were obtained for a mixture of C ₆₀/C ₇₀.     

Damage detection approach based on the second derivative of flexibility estimated from incomplete mode shape data

The presence of damage in a structural member causes local and global deterioration of structural performance. The stiffness and flexibility can be predicted using the measured mode shapes. The stiffness and flexibility are estimated because it is not easy to collect the complete modal data corresponding to full modes and degrees of freedom (DOFs). The prediction using the lowest few modes provides a more accurate flexibility prediction compared with the stiffness. This work indicates that the updated flexibility matrix can extract more information concerning the state of the structural health compared with the stiffness matrix. Additionally, incomplete measurement data should be expanded to construct the flexibility matrix at damaged state. This study derives the analytical methods used to update the flexibility matrix based on an expanded full set of DOFs and to detect damage using the updated flexibility curvature. The validity of the proposed method is evaluated using a numerical experiment, and the method's effectiveness depending on the number of truncated modes is investigated.     

A Formal,Decision-Theoretic Approach to Flexibility and Robustness

Traditional decision-making techniques only deal with a limited type of uncertainty: that which can be foreseen sufficiently to be expressed as a number of alternate moves between which nature will choose. A plan is formulated which specifies how the decision-maker should respond to nature's moves. Such a plan makes no allowance for uncertainty which could not be foreseen. Unforeseeable uncertainty can only be dealt with if the decision-maker's response to nature's moves is not fixed in advance but is itself uncertain. Flexibility is then defined as the entropy of that uncertainty. It is a measure of both the number of alternative sequences of moves which are open to the decision-maker and his attitude to them. Robustness is a way of trading off flexibility against expected value as estimated under foreseeable uncertainty. The cost of flexibility may be estimated and controlled.     

A Unique Theory of Gravity and Matter

The author has previously suggested that the ground state for 4-dimensional quantumgravity can be represented as a condensation of non-linear gravitons connected by Dirac strings.In this note we suggest that the low-lying excitations of this state can be described by a quasi-topological action of the form ∫d ¹³ z F₄∧F₅∧F₄ , corresponding to a trilinear coupling of solitonic 8-branes and 7-branes. It is shownthat when the excitations associated with F₅ are neglected, the effective action can beinterpreted as a theory of conformal gravity in four dimensions. This in turn suggests that ordinarygravity as well supersymmetric matter and phenomenological gauge symmetries arise from thespontaneous breaking of topological invariance. The possibly deep mathematical significance ofthis theory is also noted. 1999 Elsevier Science Ltd.     

Theory of filled polymers and the problem of modifying the structure and properties of polymers with fillers

An attempt is made to explain the effect of fillers on the structure and properties of polymers. The effect of fillers on the state of thermodynamic equilibrium and the stability of polymer structure and properties is also considered.Kiev Shevchenko State University. Translated from Mekhanika Polimerov, No. 6, pp. 1031–1041, November–December, 1970.     

Anisotropy of torsional rigidity of sheet polymer composite materials

Wide application of polymer composite materials (PCM) in modern technology calls for detailed evaluation of their stress-strain properties in a broad temperature range. To obtain such information, we use the dynamic mechanical analysis and with the help of a reverse torsion pendulum measure the dynamic torsional rigidity of PCM bars of rectangular cross section in the temperature range up to 600 K. It is found that the temperature dependences of the dynamic rigidity of the calculated values of dynamic shear moduli are governed by the percentage and properties of the binder and fibers, the layout of fibers, the phase interaction along interfaces, etc. The principles of dynamic mechanical spectrometry are used to substantiate and analyze the parameters of anisotropy by which the behavior of a composite can be described in the temperature range including the transition of the binder from the glassy into a highly elastic state. For this purpose, the values of dynamic rigidity are measured under low-amplitude vibrations of the PCM specimens with a fiber orientation angle from 0 to 90°. It is shown that for unidirectional composites the dependence between the dynamic rigidity and the fiber orientation angle is of extreme character. The value and position of the peak depend on the type of the binder and fibers and change with temperature. It is found that the anisotropy degree of PCM is dictated by the molecular mobility and significantly changes in the temperature range of transition of the binder and reinforcement from the glassy into a highly elastic state (in the case of SVM fibers). The possibility of evaluating the anisotropy of composites with other reinforcement schemes, in particular, of orthogonally reinforced PCMs, is shown.Translated from Mekhanika Kompozitnykh Materialov, Vol. 35, No. 3, pp. 291–308, May–June, 1999.     

Homogenization of Linear Elastic Properties of Silicon Nitride

The effective linear elastic properties of silicon nitride (Si₃N₄) are estimated based on first–, third–, and fifth–order bounds of the strain energy density. This specific type of material is a mixture of two linear elastic materials with different material symmetries. The β-Si₃N₄ grains have a hexagonal symmetry with significant amount of anisotropy, whereas the glassy phase is approximately isotropic. The results are as follows: i) The fifth–order upper and lower bounds are almost identical. Therefore, these bounds are sufficient for estimating the effective elastic properties. ii) For fixed elastic constants of the hexagonal β-Si₃N₄ grains, the effective properties of Si₃N₄ are determined as a function of properties of the glassy phase and its volume fraction. The corresponding diagrams allow for the inverse identification of the elastic properties of the glassy phase. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Temperature dependence of E and tg δ for polymethylmethacrylate and polystyrene with different kaolin contents

The temperature dependence of the dynamic modulus of elasticity E and the loss tangent tg has been investigated for polymethylmethacrylate (PMMA) and polystyrene (PS) with different contents of kaolin filler (K), in the glassy state and in the region of incipient devitrification. It is concluded that supermolecular reinforcing structures appear in filled polymers in which the intermolecular forces are sufficiently strong.Mekhanika Polimerov, Vol. 3, No. 5, pp. 854–857, 1967     

Crumpled Cube and Solid Horned Sphere Space Fillers

We construct two classes of wildly embedded space fillers of R³. First, every crumpled cube is shown to have an embedding in R³ that admits a monohedral tiling of R³. Second, a solid Alexander horned sphere with a topologically trivial interior is shown to admit a monohedral tiling of a cube and hence R³. By joining a solid horned sphere with compact polyhedral 3-submanifolds of R³ with one boundary component, we construct space fillers homeomorphic to the polyhedral submanifolds but of different embedding types. Using the suitably embedded crumpled cubes instead of a solid horned sphere, space fillers of even more different topological types can be produced.     

Temperature and Rate effects in Finite Viscoplasticity of Glassy Polymers at Different Deformation Modes: Experiments and Simulations

The non–linear inelastic response of glassy polymers is highly influenced by the three–dimensional deformation state, the temperature and the strain rate at which they are deformed. The contribution presents new experiments for different deformation modes which are carried out at different temperatures and rates on commercial bis–phenol A polycarbonate. Emphasis is put not only on the experimental results by themselves but also on the setup and the technique employed in the obtention of the data. The effect of temperature on the velocity with which the neck propagates along the gaged section of a flat specimen under tension is studied means a facility based on photogrammetry. From the homogeneous compression experiments a single set of material parameters appearing in a constitutive model based on the distributed free volume theory under the frame work of additive kinematics will be identified. The inhomogeneous experimental results serve then as a validation for 3–D simulations since the non–uniform strain distribution on the surfaces of both, simulations and experiments, can be compared. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)