Creep Kernels Research Articles

Finite element modeling of integral viscoelastic properties of textile composites

The problem of modeling the effective integral viscoelastic properties of unidirectional composite materials is considered. To calculate the integral properties of viscoelasticity, the Fourier transform and the inverse Fourier transform are used, as well as the method of asymptotic averaging for composites with steady polyharmonic vibrations, and a finite element algorithm for solving local problems of the viscoelasticity theory on the periodicity cell of the composite. To obtain the material constants, a method of approximation of the Fourier images of the relaxation and creep kernels is proposed, which makes it possible to avoid the numerical error of the inverse Fourier transform.

Modeling of dynamic and spectral viscoelastic characteristics of composite materials

When designing products made of composite materials intended for use in difficult conditions of inhomogeneous deformations and temperatures, it is important to take into account viscoelastic, including spectral and dynamic, properties of the binder and fillers. The article considers dynamic characteristics (complex modulus, complex malleability, their real and imaginary parts, loss angle tangent) and spectral characteristics of relaxation and creep and their dependence on each other. The abovementioned characteristics were found for all known types of creep kernel and relaxation kernel. To find the spectral characteristics, one of the numerical methods of reversing the Laplace transformation was used - the method of quadrature formulas. Algorithms and computer programs have been compiled to implement this method.

Study of Energy Dissipation in a Two-Phase Soil System

The dependence of energy dissipation coefficient on filtration properties and on creep characteristics of soil skeleton is examined. The study was carried out on the basis of the general solution of the joint task of creep and consolidation theory for a two-phase soil system obtained on the basis of the generalized model of bulk forces, taking into account the interaction of soil phases, changes over time in the general stress state at any point of the soil and additional pressures in pore water, and incomplete transfer of external pressure to the pore water. Interactions between phases are taken into account in the solution of the one-dimensional joint task of the theory of creep and consolidation, and the creep kernel is taken in the form of an exponential function. The formula for the deformation of two-phase soils is presented as the sum of two syllables due to primary and secondary consolidation of the soil. The strain formula uses experimentally obtained values of filtration characteristics and creep parameters of the soil skeleton. Using the formulas obtained, hysteresis loops under sinusoidal stress changes can be plotted and the energy expended per deformation cycle and the dissipation coefficient for two-phase soil can be obtained.

Щодо розрахунку релаксації напружень в тонкостінних циліндричних оболонках із лінійно-в'язкопружних матеріалів

The problems of stress relaxation analysis in thin-walled cylindrical shells made of linear viscoelastic materials under uniaxial and biaxial loading have been solved. The analysis is based on a there-dimensional model of viscoelasticity starting from the hypothesis of the deviators proportionality. The viscoelastic properties of a material are given with relationships that establish the dependence between stress and strain intensities as well as between the mean stress and volumetric strain by the Bolzmann-Volterra type equation. The kernels of relaxation intensity and volumetric relaxation are given with the Rabotnov exponential-fractional functions. The parameters of relaxation kernels are determined from creep test result using the relationships between creep kernels under the complex stress state and creep kernels under the one- dimensional stress state. The problems of the analysis of normal and tangential stresses relaxation in thin-walled cylindrical shells made of high density polyethylene “ПЭВП” under uniaxial tension, pure torsion and combined tension with torsion loading have been solved and experimentally approved.

Calculation of elastic-creeping characteristics of a beam made of a layered composite material

Multilayer composite materials are often used in building structures. The direct calculation of layered structures requires large expenditures of computer time. Therefore, the homogenization method is used. This method reduces the problem of a layered material with isotropic layers to the problem of a homogeneous transversely isotropic medium. The material considered in the article is also elastic-creeping. In the equations of state of such a material, terms of the convolution type with difference creep (relaxation) kernels are added to the terms of the usual theory of elasticity. The creep (relaxation) kernels are represented by decreasing exponential functions depending on two parameters. This problem becomes a problem of the theory of elasticity with a parameter after applying the Laplace transform in time to it. The inverse Laplace transform can be done in a computer algebra package, for example, Wolfram Mathematica, Wolfram-alpha. The obtained characteristics of the material are used to solve the problem of a layered elastic-creeping beam with hinge support. Formulas are given for determining displacements in the case of layers parallel to the beam axis.

Обгрунтування застосування неліній-ної моделі в’язкопружності типу моделі Работнова в задачах повзучості

The relationship between the components of the strain tensor, stress tensor and time is given by the defining equations of the hereditary type, which are written based on the hypothesis of proportionality of the deviators. Thin-walled tubular low-pressure polyethylene elements are considered as the object of research. The scope of the model is substantiated based on the hypothesis of the existence of a single diagram of instantaneous deformation and a single diagram of long-term deformation. The invariance of the tensile and torsion diagrams with respect to the stress state is checked. The region of nonlinear elastic deformation is determined. The defining equations of the model contain a set of functions and coefficients determined from the basic experiments. A method for determining the parameters of heredity kernels of nonlinear viscoelastic materials under complex stress state has been developed. The nonlinearity of viscoelastic properties is given by equations of the Rabotnov's model type. The method is based on the relations between the creep kernels obtained under conditions of complex stress state and the creep kernels under one-dimensional stress state. The method is tested experimentally on the problems of calculating creep deformations under combined loading of thin-walled tubular elements made of low-pressure polyethylene.

Creep mathematical model on the example of early age concrete

The objective of the study is development of a creep kernel recording form, which allows obtaining representations for creep curves calculation. Based on the elastic-creeping body theory a possibility of the high-rate creep movement analytical study has been shown. A creep kernel, which contains a formula to describe the aging material properties, has been built. Essential stages of the proposed creep kernel formation have been given. The correspondence of the proposed calculations to real processes has been proved by a comparison with experimental data. In the numerical implementation, decomposition of integration elements into power series has been used. A possibility of calculating functions for a long time interval has been shown. Creep kernel parameters have been determined on the basis of experimental data of early age concrete samples by minimizing the standard deviation of theoretical and empirical values.

Deformation of composite plates with a layer of aging materials

The paper presents a calculation of the stress-strain state of composite plates. The mathematical model obtained by the authors earlier has been applied. In contrast to the previous results, the viscous-elastic properties of the material are taken into account in describing the behavior of the intermediate layer. The developed creep kernel of the layer material contains the expression that serves to describe the properties of the aging material. The compliance of the proposed formulas with actual processes has been proved by comparison with experimental data. In the numerical implementation decomposition of the expressions under integral sign into the Maclaurin series has been used. Based on the experimental data, the parameters of creep kernels have been determined. The parameters have been determined by minimizing the calculated data standard deviation from the experimental ones. The algorithm based on the random search method has been implemented. The results of the calculation according to the developed mathematical model have been given. The analysis of time variation in the stress-strain state of the joints between the layers of the composite structure has also been given.

Features of Inelastic Behavior of a Composite Under Cyclic Loading. Experimental and Theoretical Investigations

For a carbon-fiber-reinforced plastic made of an ELUR-P unidirectional tape and an ХТ-118 cold-cure binder, specimens with a ±45° stacking sequence were tested for cyclic tension. The total axial strain was considered as the sum of nonlinearly elastic, viscoelastic, and irreversible creep strains. Using the Abel creep kernel, it was found that, at instants of time shifted by values multiples of the loading period, the ratios between the viscoelastic strain components depended neither on the period of cyclic loading, nor the loading amplitude, nor the parameter determining the degree of viscosity of the material, but only on the parameter determining the decrease in the rate of the viscoelastic strain. To find parameters of the creep kernel, an identification method based on the use of a hypothesis that allows one to separate reversible and irreversible creep strains, as well as on the properties of Abel creep kernel was developed. The method is illustrated by an example of processing experimental results.

Effective modules of a layered elastic creep medium with power creep kernels

The paper considers the question of constructing the effective characteristics of a layered composite material when periodically repeating layers consist of an isotropic elastically creeping material. For the elastic composites, such characteristics are well known and can be obtained explicitly. In this paper, the effective characteristics of the layered elastic-creeping composite are obtained explicitly when the creep kernel are the power-law functions. The elements of the compliance matrix are presented as the sum of the terms corresponding to the instantaneous elastic compliance, unlimited and limited as the loading time increases due to the creep of the composite individual phases.

К ВОПРОСУ ОБ ОБОСНОВАННОЙ ФОРМЕ НАСЛЕДСТВЕННОЙ ВЯЗКОУПРУГОСТИ С ОДНИМ ЯДРОМ ПОЛЗУЧЕСТИ

К ВОПРОСУ ОБ ОБОСНОВАННОЙ ФОРМЕ НАСЛЕДСТВЕННОЙ ВЯЗКОУПРУГОСТИ С ОДНИМ ЯДРОМ ПОЛЗУЧЕСТИ

Forecast of settlement of single pile based on hereditary creep

The various calculation models are proposed in the literature for the purpose of description the creep behavior of soil bases. The objective of the paper is to develop an algorithm to predict long-term settlement of piles based on the rheological deformation model using Koltunov’s creep kernel. The paper discusses the results of single pile tests on weathered claystones and sandstones. Based on experimental results and theoretical study the author developed an automated algorithm for the calculation of settlement of pile on weathered claystones and sandstones. The following tasks are solved: 1) to describe the research technique; 2) to analyze the results of testing single piles; 3) to perform numerical calculation of settlement of piles; 4) to describe the capabilities of the developed algorithm for the calculation of pile settlement; 5) to compare the results of field tests, numerical simulation and calculation of the proposed method; 6) to state conclusions. The result shows that the proposed method is an excellent option for identifying the parameters of creep core for the prediction of long-term settlement of piles on claystones and sandstones.

About the mechanisms of fibre reinforced plastic behaviour under cycling loading

In order to study the peculiarities of the behavior of fiber reinforced plastics under cyclic loading, tests of specimens made of ELUR-P carbon tape and cold curing binder XT-118 with a stacking sequence 2 [+45°/−45°]2s (s - the number of laminas) for cyclic tension were carried out. It is established that stabilization of the secant modulus of elasticity is observed as the number of cycles increases. The experimental data were compared with the results of numerical modeling of the deformation processes under study. Based on numerical calculations and analytic solutions found, for a number of types of loads and creep kernels, the value of the secant modulus of elasticity does not depend on the load amplitudes, when using relations with the Abel creep kernel, the ratio of viscous parts of strain shifted by values, does not depend on the period of cyclic load, the amplitude of the load and the parameter that determines the degree of viscosity of the material, but depends only on the parameter that determines the degree of attenuation of the creeping process. By using the method of decomposing the load in a series of trigonometric functions with the same cyclic periods, it is shown that the effect is manifested in the general case of cyclic loading using relations with the Abel creep kernel. There is established the independence of secant and tangential moduli of elasticity from the absolute values of maximum and minimum stresses for any kinds of loads and creep kernels using the linear theory of hereditarily elastic body. A method has been developed for identifying creep kernel parameters, relations for viscoplastic and elastic strain based on the analysis of experimental data on cyclic loading. For the separation of hereditarily elastic and viscoplastic strain, the hypothesis was introduced that their rates at large times are very different. This made it possible, on the basis of theoretical results obtained for the Abel kernel, to obtain ratios from which, independently of other mechanical characteristics, one can find the attenuation parameter from the strain values, measured in the experiment in times shifted by an integer number of periods. The method is applied to processing the data of real experiments conducted by the authors.

Effective Characteristics of a Layered Hollow Cylindrical Body of Elastic Creeping Materials

The article deals with the problem of a layered composite pipe. The layers alternate in pairs and consist of elastic-creeping materials. The work is devoted to the study of the mechanical properties of the composite material with the help of its microstructure. Processes are studied with a typical pipe radius which is much more than the typical winding width. Heterogeneous layered material behaves as a certain “effective” material without layers in such processes. The method of calculation of effective moduli based on mathematical homogenization theory is described. Creep kernels are given by the sum of a finite number of decreasing exponential functions.

Determining the rheological properties of viscoelastic materials by the values of creep strain

Determination of creep strain arising due to stresses acting up to the moment of time t is considered. The phenomenon of constant-stress creep is described. A method is proposed to determine the parameters of the Arutyunyan creep kernel selected to describe the behavior of a material using two creep curves of a material with viscoelastic properties and nonlinear dependence of creep strain on the stress. In addition, the constant in the expression describing nonlinear dependence of creep strain on the stress is defined. The AMg6M alloy, widely used in the design of aerospace products, was chosen as the material to be analyzed. The tests were carried out on samples 3 mm thick at strains of 65MPa and 156.9MPa. According to the results of testing samples of materials on the test bench of Samara University creep curves were obtained. By determining the parameters of the approximation of the Arutyunyan kernel and the parameter included in the expression of nonlinear dependence of creep strain on the stress, it is possible to determine the value of the creep strain of the material for arbitrary values of stress and time. Comparison of the experimental and calculated creep curves for the AMg6M alloy confirms the validity of determination of the rheological characteristics of the tested material.

Theoretical-Experimental Method for Determining the Short- and Long-Term Creep Parameters of Technical Rubber in Shear

A technique is developed for identifying the hereditary properties of technical rubber in short-term shear creep from the experimental shift the center of damped flexural vibrations of a vertically fixed three-layer test specimens of symmetrical structure with a technical rubber midlayer after their preliminary holding in a static bent state. This technique is based on the finite element method and integral equations of the hereditary viscoelasticity theory with the Koltunov–Rzhanitsyn heredity kernel. For identifying the rheological parameters of this kernel an objective function is constructed. To minimize the function, the direct zero-order search is used, which does not require the calculation of its gradient. The rheological parameters found are compared with experimental data of the long-term shear creep of the rubber. Noted is the unfoundedness of the direction, developed by some researchers, where only equations of the theory of hereditary viscoelasticity is used to model the vibration processes and the energy dissipation. The parameters of rubber creep kernel were identified in a long-term regime at a constant shear stress, and results showed that this type of testing is inapplicable to studying the short-term creep of rubber in shear.

On the regularities of behavior of an elastic-viscoplastic composite under cyclic loading

Tests were performed on cyclic loading of the specimens made of ELUR-P carbon tape with the lay-up sequence [+45° / −45°]2s and cold-curing binder KhT-118. It has been established that when using viscoelasticity relations with Abel’s creep kernel, the ratio of viscous parts of strain at times shifted by values multiple to the load period does not depend on the amplitude and period of the cyclic load, the parameter that determines the degree of viscosity of the material, but depends only on the parameter determining the degree of attenuation of the creep process. The amount of energy absorbed in one loading cycle has the same property. It is shown that the independence of secant and tangent moduli from the absolute values of maximum and minimum stresses occurs for any kind of load and creep kernels using the linear theory of hereditary elasticity and a particular type of non-linear theory of viscoplastic flow with hardening. A method of sequential identification of creep kernel parameters, relations for viscoplastic and elastic strain based on the results of analysis of experimental data on cyclic loading is proposed. It is based on the hypothesis that at large creep times the rate of viscoplastic strain is much less than the rate of viscoelastic strain. This allows one, on the basis of theoretical results obtained for the Abel’s kernel, to obtain ratios from which it is possible, independently of other mechanical characteristics, to find the attenuation parameter from the strain values measured experimentally in times shifted by an integer number of periods. The method is illustrated by the example of data processing of real experiments conducted by the authors.

Creep of Textile-Reinforced Composite Under Static and Cyclic Loads

The paper considers the creep of a textile-reinforced thermoplastic composite with a glass filler under the action of a combined short-term cyclic and long-term static tensile loads at room temperature. The investigations were carried out on glass-fabric-reinforced polypropylene specimens, which were made by autoclave molding. The creep of the composite was experimentally investigated under a cyclic load at different amplitudes. The creep kernel has been calculated from experimental data according to the Boltzmann superposition principle. Other creep models of materials have been analyzed based on data from a review. The laws governing the short-term creep of polypropylene under the action of a static load have been determined. A behaviorial model of the composite under investigation under the considered conditions is proposed. Numerical calculations have been made with the aid of the proposed model using experimental results taken from other works, and a good agreement between them has been established. The peculiarities of the creep of textile-reinforced polypropylene under the considered conditions have been determined. The range of application of the model has been determined.

Про один метод визначення параметрів ядер спадковості нелінійно в’язкопржних матеріалів за умов складного напруженого стану

The deformation of viscoelastic medium given by means of constitutive equations of the hereditary type. These equations establish the relationship between the components of strain tensor, the components of stress tensor and the integral time operator, and contain the set of function and coefficients that are determined from the basic experiments. А method of the heredity kernel parameters determination of nonlinear viscoelastic materials is developed. As the visco-elastic model, the constitutive equations of the hereditary type are chosen in which the relationship between the components of the strain tensor and the stress tensor is given based on the hypothesis of the deviators proportionality. The nonlinearity of the viscoelastic properties is given by the equations of Ratotnov’s type. The method is based on the relations between the creep kernels under complex stress state and the creep kernels under one-dimensional stress state. The method verified experimentally for the problems of determination of creep deformations under combined loading applied to the thin-walled tubular elements made of polyethylene of high density.

Щодо розв'язку задач повзучості тонкостінних трубчастих елементів із ізотропних нелінійно-в'язкопружних матеріалів

A new approach to the creep strains analysis of thin-shelled tubular elements in isotropic nonlinear viscoelastic materials under combined loading with uniaxial tension and torsion has been proposed. The system of equations that is constructed according to the deviators proportionality hypothesis has been chosen as the creep constitutive equations the nonlinearity of viscoelastic properties in which is given with respect to the creep strain intensity and volumetric strain by the Rabotnov type models. The kernels of creep strain intensity and volumetric strain are given by the relations that establish the relationships between these kernels and one-dimensional creep kernels determined from a system of base experiments. One-dimensional tension with the measurement of longitudinal and transverse strains as well as one-dimensional tension and pure torsion with the measurement of longitudinal and shearing strains have been considered as base experiments. The functions of nonlinearity of viscoelastic properties are given by smoothing cubic splines. The problems of the analysis of longitudinal, transverse and shearing strains of thin-shelled tubular specimens made of “high density polyethylene PEHD” have been solved and experimentally approved.