Self-reinforcement of liquid-crystal polymers at static and dynamic loading

The self-reinforcement effect of a solid uniaxially oriented SVM-K liquid-crystal polyamide and a copolyester of hydroxybenzoic and hydroxynaphthoic acids has been investigated by tensile-strength, stress-relaxation, and dynamic methods. The samples were prepared by spinning from lyotropic solution (SVM-K) and from a thermotropic melt (polyester). The tensile-strength and stress-relaxation tests were performed on complex fibers and the dynamic test on single fibers. The set of stress-strain curves, changing from a convex shape with two linear sections (at room temperature) to a concave shape (at high temperatures) is shown for both materials in Fig. 1. There is a pronounced difference between the deformation mechanisms at low and high strains in the stability of rigidity. At high temperatures the rigidity becomes less than the initial one during deformation and the current modulus at high strains has the same value within large ranges of temperatures and strains (Fig. 2). A low-deformation transition of another physical parameter than the yield-stress has been found. The stress-strain diagram for both investigated polymers has been generalized by using the constant value of the current modulus for the normalization of the stress value (Fig. 3). The stress-relaxation phenomena are shown to be anomalous. At high temperatures the stress-relaxation intensity decreases with increasing deformation, i.e., after deformation the polymer is characterized by a stability of rigidity which is higher than the initial value (Fig. 4). The dynamic modulus appears to increase with increasing deformation rate (Fig. 5). Due to these peculiarities the liquid-crystal polymers must be considered not only as normal high-modulus reinforcements for composite materials but also as materials, self-reinforcing under loading.Translated from Mekhanika Kompozitnykh Materialov, Vol. 30, No. 4, pp. 435–441, July–August, 1994.     

Structural damage accumulation and stable postcritical deformation of composite materials

The macroscopic failure of composite materials is preceded by complex multilevel processes accompanied by accumulation and localization of damaged centers and formation of a failure cluster. Therefore, the study of these mechanisms is one of the basic problems for the mechanics of modern composite materials used in aerospace engineering. The formation of a theory of the stable postcritical deformation of the work-softening media is considered. The pseudo-plastic deformation affected by structural damage of granular composites is investigated within the framework of the considered two-level structurally phenomenological model of heterogeneous media. The stable evolution of the interconnected processes is accompanied by stress redistributions, partial or complete unloading, and strain or damage localization that are one of the main causes of implementation of the postcritical deformation stage. The numerical calculation results of inelastic deformation and failure of the periodic unidirectional fiber-reinforced composites are presented under conditions of the displacement-controlled transverse proportional loading mode. The main mechanisms of the work-softening behavior for the indicated type of materials are described in the macro-homogeneous stress-strain states. Macroscopically, the failure of heterogeneous media as a result of postcritical deformation and the loss of stability of damage accumulation depends on the stiffness of the loading system. When a deformable body is fixed on the closed surface with sufficiently but not infinitely large coefficients of stiffness, it is possible to observe the equilibrium development of the localized volumes of work-softening and damage. The constitutive equations for the work-softening isotropic, transverse isotropic, and orthotropic media are presented. The effect of the loading system on the stability of deformation, damage accumulation, and failure under monotone and nonmonotone triaxial loading was studied. The growth of failure strains with increase in stiffness of the loading system and unequal resistance of heterogeneous body are registered and investigated. A preventive unloading method is offered for the mathematical modeling of the damage accumulation during the testing of the materials on the servo-controlled systems. The displacement-controlled mode is simulated by a series of soft loading and unloading cycles. The detected phenomenon of failure where the unloading leads to stress-strain diagrams with a negative slope of the descending branch was not found either in the displacement or stress-controlled monotone loading mode.Submitted to the 10th International Conference on Mechanics of Composite Materials, April 20–23, 1998, Riga, Latvia.Perm' State Technical University, Russia. Translated from Mekhanika Kompozitnykh Materialov, Vol. 34, No. 2, pp. 234–250, March–April, 1998.     

Reaction of sloping spherical shells of glass-fiber-reinforced plastic during nonstationary loading

The behavior of spherical shells of glass-fiber-reinforced plastic under the action of exponentially changing dynamic loading was studied in a nonlinear formulation. The method of finite differences, used in the form of an explicit difference scheme, was used to solve the differential equations of the dynamics of sloping shells based on the Kirchhoff-Love hypotheses. The characteristic features of the deformation process and the influence of the degree of anistropy of the shell material operating under conditions of dynamic loading are noted.Moscow. Translated from Mekhanika Polimerov, No. 2, pp. 311–314, March–April, 1975.     

Deformation of cylindrical composite shells under combined dynamic loading

Conclusions A procedure has been shown for calculating the stress-strain state of cylindrical multilayer shells made from composite materials under the combined action of dynamic axial compression and dynamic external pressure, as well as with different variants of combined loading with static and dynamic forces. An investigation has been made of the effect on the mode of the buckled shell surface of the ratio of the application rate of dynamic loads; ranges of loading rates have been established in which stresses predominate caused either by axial compression or external pressure. It has been shown that, as a result of preliminary static loading, a marked change occurs in the initial imperfections of the shell mode which affects subsequent dynamic buckling. To calculate the time when the first defect occurs and its location in the shell body, a procedure has been devised for layer-by-layer strength analysis employing a tensor-polynomial criterion. It was demonstrated that the level of preliminary static loading noticeably affects the time until the first failure of the layer, not only a reduction of this time being possible with an increase in the static loads, but also an increase in it.We should also point out the work in [10] where it is shown that it is possible to weaken the susceptibility of the shell to initial imperfections when internal pressure is applied.Translated from Mekhanika Kompozitnykh Materialov, No. 3, pp. 461–473, May–June, 1981.     

Nonaxisymmetric thermal stress state of laminated rotational bodies of orthotropic materials under nonisothermic loading

A procedure for numerical investigation of nonaxisymmetric temperature fields and the elastic stress-strain state of laminated rotational bodies of cylindrically and rectilinearly orthotropic materials under nonisothermal loading is proposed. The deformation of orthotropic materials is described by the equations of anisotropic elasticity theory. The equations of state are written in the form of Hookes law for homogeneous materials, with additional terms which take into account the thermal deformation, changes in the mechanical properties of materials in the circumferential direction, and their dependence on temperature. A semianalytic finite-element method in combination with the method of successive approximations is used. An algorithm for numerical solution of the corresponding nonlinear boundary problem is elaborated, which is realized as a package of applied FORTRAN programs. Some numerical results are presented.Translated from Mekhanika Kompozitnykh Materialov, Vol. 40, No. 6, pp. 731–752, November–December, 2004.     

Physical nonlinearity with microstructural transitions

A physical model of a deformable body with a network structure composed of individual elements linked by valence bonds is considered. The effect of dissociated valence bonds on the irreversible deformation is investigated using Fermi-Dirac statistics. The physical stress-strain relation obtained is a generalization of certain known constitutive equations.Bulgarian Academy of Sciences, Sofia. Translated from Mekhanika Polimerov, No. 1, pp. 36–44, January–February, 1973.     

Effect of relaxation parameters on the behavior of rigid polymers in pure shear

The authors have investigated the effect of the relaxation parameters of a rigid polymer corresponding to the individual terms of the relaxation spectrum on the nature of the theoretical curves calculated for creep, strain relaxation and loading at constant strain rate in pure shear on the assumption that the stress-strain relation is described by the generalized Maxwell equation.Institute of Chemical Physics, Academy of Sciences of the USSR, Moscow. Translated from Mekhanika Polimerov, No. 3, pp. 431–436, May–June, 1969.     

Stress relaxation in polyethylene as a dislocation process

The deformation of high-pressure polyethylene at different intervals of the stress-strain curve has been investigated by the stress relaxation method. The results are interpreted in terms of the motion and multiplication of dislocations.Mekhanika Polimerov, Vol. 4, No. 2, pp. 375–377, 1968     

Inelastic deformation and fracture of disordered fiber-reinforced composites

Conclusions Simulation of the process of nonlinear deformation and failure in the structure of a unidirectional epoxy glass plastic under transverse loading has indicated that equilibrium regions of failure receiving only hydrostatic compressive loading may form. The development of this region explains the high (up to 40%) nonlinearity of deformation diagrams under transverse biaxial compressive loading. The regions of nonlinear deformation of the epoxy matrix affect less markedly the nonlinearity of the macroscopic s* diagrams. This fact and also the formation and avalanchelike propagation of regions of complete failure explain the linear form of many diagrams corresponding to tensile and shear loading in the transverse plane. The relations of the nonlinear theory of elasticity make it possible to describe with sufficient accuracy the entire set of the calculated diagrams.Translated from Mekhanika Kompozitnykh Materialov, Vol. 29, No. 5, pp. 621–628, September–October, 1993.Translated from Mekhanika Kompozitnykh Materialov, Vol. 29, No. 5, pp. 621–628, September–October, 1993.     

Deformability modelling of foam elongation

The relationships concerning the deformation of rigid cellular foams during elongation are reviewed under the conditions of a monotonous load increase. The cellular structure behavior is modelled by the operation of a certain piston structure. The proposed equation leads to a satisfactory approximation of the experimental stress-strain diagram for polystyrene and poly(vinyl chloride) foams.V. A. Kucherenko Central Scientific-Research Institute of Building Constructions, Moscow. Translated from Mekhanika Polimerov, No. 1, pp. 154–157, January–February, 1972.     

Deformation of thermoplastic materials at low-cycle loading

The possibility is discussed of deducing analytical equations for evaluating the deformation of polymer materials at a low-cycle periodic loading on the basis of the linear prehistory theory. Finite expressions are given for the case of loading by rectangular and triangular pulses. Comparison of the results of the experimental study of the deformation of low- and high-pressure polyethylenes (LPP and HPP, respectively) with the conclusions of the theory shows satisfactory agreement for tests of up to 5·10³ loading cycles.Leningrad Institute of Aviation Instrument Engineering. Translated from Mekhanika Polimerov, No. 2, pp. 230–234, March–April, 1976.     

Strength and deformability of reinforced polymers in tension normal to the fibers

The strength and deformability of reinforced polymers in tension across the fibers is investigated. It is assumed that the polymer deforms as an ideal elastoplastic body. Relations are obtained for the nature of the deformation of the polymer between the fibers and the strength and deformability of the composite with allowance for the structural distribution of the components. Theoretical stress-strain diagrams are presented for composites with different reinforcement densities and resin elasticities. The theoretical values of the strength and deformation of reinforced polymers with the load applied across the fibers are compared with the results of experiments on model specimens of epoxy-Thiokol polymers.Leningrad Mechanical Institute. Translated from Mekhanika Polimerov, No. 4, pp. 682–687, July–August, 1970.     

Micromechanical investigation of osteons with crossed lamellae

A micromechanical investigation of osteons with crossed lamellae has shown that they can be regarded as orthogonally reinforced material. The stress-strain curve has a break at low stresses. This effect can be explained by reference to the mechanical behavior of orthogonally reinforced laminates. It is assumed that a stress concentration develops at the fiber-matrix interface in the lamellae with transverse fibers oriented at 90° to the direction of loading, and that microfractures can develop in the osteon before the proportionality limit of the fibers parallel to the loading axis is reached.Study No. 73.00430.04 of the Italian National Research Council. Paper presented at the First All-Union Conference on Engineering and Medical Biomechanics, Riga, October, 1975.Rome University. Translated from Mekhanika Polimerov, No. 4, pp. 669–673, July–August, 1975.     

Evolution of structural damage and macrofailure of inhomogeneous media at the supercritical stage of deformation

The article deals with the evolution of structural damage of an inhomogeneous body as a function of the properties of the loading system whose characteristics are taken into account by supplementing the boundaryvalue problem (1), (2) with the boundary conditions of the third kind (3) and (4). With the numerical solution by the finite-element method these boundary conditions are satisfied in accordance with the Eqs. (6) and (7) by changing the rigidity matrix of the discretized body (8). The material loses its load-bearing capacity at some point of the descending branch of the stress-strain diagram (Fig. 1a) at the instant the conditions of stability (9) are infringed. Normalized correlation functions of a damaged structure plotted for different equilibrium states of a granular composite (Fig. 2) make it possible to identify characteristic stages of failure. Macroscopic failure of material is regarded as the concluding stage of the processes of the onset, localization of structural disruptions, and formation of a macrodefect. Increased rigidity of the loading system makes it possible to stabilize the process of damage calculation, and this leads to an increase of limit deformations. The realization of the supercritical stage of deformation, together with energy dissipation upon structural destruction is the mechanism of adaptation of an inhomogeneous body to the loading conditions.Perm State Technical University, Russia. Translated from Mekhanika Komozitnykh Materialov, Vol. 33, No. 3, pp. 329–339, May–June, 1997.     

Quasilinear theory of viscoelasticity

By postulating equal contributions the number of kernels in the principal cubic theory of viscoelasticity and in the theory with regular kernels of two arguments is reduced to three. For certain quasilinear relations all the kernels and functions are determined from creep, relaxation, and simple loading and deformation tests. In the case of simple loading and deformation the problems for a viscoelastic incompressible material reduce to problems of the theory of small elastoplastic deformations of an incompressible material. Several problems relating to this case are considered.Moscow M. V. Lomonosov State University. Translated from Mekhanika Polimerov, No. 4, pp. 603–611, July–August, 1969.     

Calorimetric investigation of the tensile deformation of polyethylene

A calorimetric apparatus for investigating the thermal effects associated with tensile deformation is described. The results of calorimetric measurements made on high- and low-density polyethylene during the deformation process are presented. It is shown that on the interval of strains and loading rates investigated the deformation of polyethylene is energetic in character.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 4, pp. 579–584, July–August, 1970.     

Variation of the elasticoviscous characteristics of a heavily filled rubber after periodic shear deformation

The results of an investigation of the recovery of the elasticoviscous characteristics after thixotropic reduction by periodic deformation in the nonlinear zone are reported. The rate of recovery of the mechanical properties depends on the deformation frequency and the previous history of dynamic deformation is shown to affect the dependence of the elasticoviscous characteristics on the shear rate gradient. The effects of stationary and dynamic deformation regimes on the relaxation spectrum of the material are compared.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 3, pp. 528–533, May–June, 1969.     

Strength of cylindrical shells of laminar composites under dynamic loading

Conclusion The methods described in the present review paper for the computation of cylindrical shells of laminar composites under various types of dynamic loads make it possible to calculate the stress-strain state at any point of the body of the shell at an arbitrary time and to determine the time of the first failure of a layer (including fatigue failure) using strength criterion of an anisotropic body for the case of a plane stressed state, and also the location of the first flaw in the shell. This makes it possible to determine the magnitude of the applied pulse (the amplitude of a pulsed loading), or the amplitude of a vibratory loading for which the first centers of failure appear in the design.Presented at the Second Soviet-American Symposium on the Problem Failure of Composite Materials (Bethlehem, Pa., USA, March, 1981).Translated from Mekhanika Kompozitnykh Materialov, No. 3, pp. 460–467, May–June, 1982.     

The relationship between stress and deformation of polymers in the linear stress state

The relation between stress, strain and strain rate is proposed as a means of describing the deformation properties of polymers. The equation describes the stress-strain curve, aftereffect, and stress relaxation in polymers. The theoretical conclusions are in good agreement with the results of creep tests on kapron (nylon-6).Mekhanika Polimerov, Vol. 1, No. 5, pp. 25–29, 1965