Creep Kernels Research Articles

Statistical Methods for Parameter Identification of Temperature Dependent Viscoelastic Models

AbstractA fully fractional stochastic model for linear viscoelastic materials is proposed. Time dependent stress‐strain response for creep tests is described through Adaptive Links theory as a random process of successive micro‐stretching events due to disentanglements between groups of material fibers. The process is modeled by a Continuous Time Random Walk (CTRW) that tends in average to power‐law function, which corresponds to the creep kernel of the usual fractional model for viscoelasticity. Thermal effects are explained through changes in waiting time and jump compliance distribution parameters. Simulated CTRWs are compared with experimental results of specimens of epoxy resin. It was observed that simulated mean function approaches to measurements in long term during the creep phase. Additionally, parameter averages decrease for higher temperatures, representing more frequent jumps of fiber creep strain and faster development of creep process.

The averaged model of layered elastic-creeping composite materials

Composite materials consisting of several phases are widely used in modern construction. The mechanical characteristics of elastic-creeping layered composite materials are considered in the article. Each of the constituent phases has the properties of elasticity, viscosity or creep. Numerous experiments have shown that the properties of structurally heterogeneous materials can differ significantly from those of the individual components making up the composition. Besides, rapidly changing coefficients of differential equations describing such composite materials greatly complicate the solution of boundary value problems even with the help of computer calculation methods. Therefore, the homogenization method is used to solve such problems. Creep kernels are given by the sum of a finite number of decreasing exponential functions. The use of creep kernels of this type is experimentally justified. In this paper, it is shown that an effective (averaged) model for a composite material with the indicated properties is a homogenized medium that is described by a creep kernel, also represented by a sum of exponential functions. An algorithm for the rapid and accurate calculation of averaged creep kernels of a homogenized material is proposed.

Contact problem for a solid indenter and a viscoelastic half-space described by the spectrum of relaxation and retardation times

The mechanical properties of a material which is modeled by an exponential creep kernel characterized by a spectrum of relaxation and retardation times are studied. The research is carried out considering a contact problem for a solid indenter sliding over a viscoelastic half-space. The contact pressure, indentation depth of the indenter, and the deformation component of the friction coefficient are analyzed with respect to the case of half-space material modeled by single relaxation and retardation times.

Combined Numerical and Analytical Determination of Poisson’s Ratio for Viscoelastic Isotropic Materials

The Laplace–Carson integral transform method and numerical inversion of the solutions are used to establish the relationship between hereditary kernels that define the scalar properties of isotropic linear viscoelastic materials in combined stress state. The hereditary creep kernel characterizing the behavior of the viscoelastic Poisson’s ratio with time is identified. The calculation of shear creep strains and transverse creep under uniaxial loading with allowance for the time-dependent Poisson’s ratio are experimentally validated.

Problem of modelling a layered medium taking into account the creep of its materials

Problems for heterogeneous materials arise in many areas of construction. This article deals with elastic-creeping layered composite materials. Relations of the theory of linear heredity of Boltzmann-Volterra are accepted. Creep kernels are given by the sum of a finite number of decreasing exponential functions. Such sum of several exponential functions can be used to approximate the experimental data for the creep and relaxation kernels with a given accuracy. It is obtained that the resulting homogeneous medium is described by a creep kernel, which is also a sum of decreasing exponential functions. Algorithm for the rapid and accurate calculation of averaged creep kernels of a homogenized material is proposed. Some qualitative properties of the received homogenized model are analyzed.

Contact Problem for a Viscoelastic Half-Space and a Rough Rigid Cylinder under the Conditions of Hydrodynamic Lubrication

A model has been proposed for use in studying the combined effect of the roughness of a rigid punch and the viscous properties of a base separated by a thin lubricant layer exerted on the characteristics of contact interactions and the sliding friction force. The problem of the motion of a thin a lubricant layer between a fixed rigid cylinder with a regular relief, as well as the surface of a moving viscoelastic half-space, the rheological properties of which are described by an integral operator with an exponential creep kernel, has been considered. The pressure and thickness of the lubricating layer, as well as the deformation component of the frictional force depending on the sliding velocity, have been analyzed. A comparison of the results of solutions of contact problems for viscoelastic and elastic rough bodies in the presence of a lubricant has been presented.

Effective characteristics of a layered tube consisting of elastic-creeping materials

The article suggests a method for modelling the stress-strain state of layered elastic-creeping tube. This method is based on a combination of the theory of averaging and creep theory. This theory takes into account the previous stress state and its effect on the subsequent deformation period. Creep kernels for the averaged problem are found in the explicit analytical form. These formulas can be used to estimate displacement and stress fields during long-term loading of a composite tube.

Method of approximate calculation of the stress tensor in layered elastic-creeping environments

The paper deals with the problem of constructing an effective model of a layered composite material. The layers consist of elastic-creeping materials, the creep kernels of which are exponents. The characteristics of the averaged model are given in explicit form. Some qualitative properties of the homogenized model are analyzed. Estimates of the closeness of the displacement and stress fields for the initial and averaged models are given. An example of numerical modeling of the characteristics of an averaged material is presented. The exact number of constants required for a complete description of the averaged model is given.

On the Modeling of Creep Layered Structures with Nonlinear Constitutive Relations

A layered creep medium with nonlinear stress-strain relations is studied. The Boltzmann-Volterra hereditary theory with creep kernels of the Abel type is used for creep modeling. Using time discretization, linear motion equations with memory terms are derived on each time step. Then, the homogenization technique is applied to these equations. An estimate of error in terms of a small parameter is derived and an algorithm for numerical implementation of the suggested approach is presented.

THE RHEOLOGICAL MODEL OF LIMITED CREEP OF WOOD

Rheological properties of wood and deformation features depending on different conditions of temperature, humidity, and mechanical stress are used to improve existing and develop new technologies of hydrothermal and mechanical treatment. The solution of this task is complicated as wood belongs to the class of physically nonlinear, natural heterogeneous polymers, characterized by high hydrophilic and a wide range of physical and mechanical characteristics. Therefore, the research of rheological behaviour of wood depending on directions of anisotropy, determination of the characteristics of creep or relaxation functions is an actual task. In the course of study the authors have defined the function of creep and have also got dependences of time relaxation of wood. Firstly, studies of the rheological behaviour of wood concerning the structural anisotropy under conditions of limited creep are presented. Then the authors have obtained the rheological model of high-elastic deformation with stress. The built algorithms of determination of descriptions of rheological conduct of pine and fir wood are based on approximation of experimental information. Moreover, the ratio between instantaneous and protracted modulus of elasticity for pine and fir wood in tangential direction of the deformation was determined. Regularities of creep deformation of wood were investigated. For the approximation of experimental curves of creep we used the method of interpolation function as a sum of exponentials. To define the analytical form of the kernel of creep required to calculate the strain-relaxation properties of wood we used experimental data of creep deformation of the material. Thus, the choice of a creep kernel is determined by the features of rheological behaviour of wood. The authors have presented comparison of theoretical researches to the approximated experimental curves of high-elasticity deformation of pine and fir wood in the case of determination of rheological descriptions in the conditions of aftereffect.

Stress Distribution in Layered Elastic Creeping Array with a Vertical Cylindrical Shaft

Construction should be taking into account the influence of time factor on the stability of the structures. In the paper hereditary creep and homogenization theories are used to determine stresses in the layered elastic creeping array with a vertical shaft. Volterra correspondence principle was applied. As a result, the reduction of a time-dependent elastic creeping problem to a corresponding elastic problem became possible. The method proposes a way to determine average (effective) elastic creeping properties and homogenized stress field from known properties of the layers’ components. Creep kernels are of a convolution type and are taken in the exponential form. The problem of heterogeneous elastic creeping environment is reduced to a problem of homogeneous transversely isotropic medium. Different boundary conditions on the cylindrical shaft’s surface were considered. An analytical solution was obtained. These explicit expressions can be useful for the necessary calculations in the construction practice.

Identification of the Hereditary Kernels of Isotropic Linear Viscoelastic Materials in Combined Stress State. 2. Proportional deviators

The relationships between the hereditary and creep kernels are established. The hereditary kernels define the scalar properties of isotropic linear viscoelastic materials in a combined stress state. The creep kernels are obtained in uniaxial-tension and pure-torsion tests. The constitutive equations are chosen so as to meet the hypothesis of proportional deviators. The problems of analyzing the creep deformation and stress relaxation of thin-walled tubular specimens under combined tension and torsion are solved and tested experimentally

Identification of the Hereditary Kernels of Isotropic Linear Viscoelastic Materials in Combined Stress state. 1. Superposition of Shear and Bulk creep

Relations between the shear and bulk creep kernels of an isotropic linear viscoelastic material in combined stress state and the longitudinal and shear creep kernels constructed from data of creep tests under uniaxial tension and pure torsion are formulated. The constitutive equations of viscoelasticity for the combined stress state are chosen in the form of a superposition of the equation for shear strains and the equation for bulk strains. The hereditary kernels are described by Rabotnov’s fractional-exponential functions. The creep strains of thin-walled pipes under a combination of tension and torsion or tension and internal pressure are calculated

Determination of the Creep Parameters of Linear Viscoelastic Materials

Creep process of linear viscoelastic materials is described by the integral equation of Boltzmann-Volterra in which creep kernel is approximated by Rabotnov’s fractional exponential function. The creep equation contains four unknown parameters:α, singularity parameter;β, fading parameter;λ, rheological parameter; andε0, conditionally instantaneous strain. Two-stage determination method of creep parameters is offered. At the first stage, taking into account weak singularity properties of Abel’s function at the initial moment of loading, parametersε0andαare determined. At the second stage, using already known parametersε0andα, parametersβandλare determined. Analytical expressions for calculating these parameters are obtained. An accuracy evaluation of the offered method with using experimentally determined creep strains of material Nylon 6 and asphalt concrete showed its high accuracy.

Numerical-graphical method for describing the creep of damaged highly filled polymer materials

A method for describing the creep behavior until fracture of a highly filled polymer material previously damaged in preliminary tests is proposed. The constitutive relations are the relations of nonlinear endochronic theory of aging viscoelastic materials (NETAVEM) [1]. The numerical-graphical method for identifying the functions occurring in NETAVEM, which was proposed in [2] for describing loading processes at a constant strain rate, is used here for the first time in creep theory. We use the results of experiments with undamaged and preliminary damaged specimens under the action of the same constant tensile loads. The creep kernel is determined in experiments with an undamaged specimen. The reduced time function contained in NETAVEM is determined from the position of points corresponding to the same values of strain on the creep curves of the damaged and undamaged specimens. An integral equation is solved to obtain the aging function, and then the viscosity function is determined. The knowledge of all functions contained in the constitutive relations permits solving the creep problem for products manufactured from a highly filled polymer material.

Analytical solution for estimating the stand-up time of the rock mass surrounding tunnel

The term “stand-up time” is used first time in Lauffer’s rock mass classification (1958) in relation to the so called “effective unsupported span” and then modified by Barton et al. (1975) and Bieniawski (1993). Until now stand-up time is a useful parameter in rock mechanics and tunnel design. It affects the selection of excavation method, excavation cycle and rock reinforcement method and time to install rock support. In other words, the stand-up time is a function not only of rock mass properties but also of excavation technique. Because classification methods are based on rock mass quality empirical evaluation through specific parameters, however, the determination of the rock mass properties to evaluate rock mass quality and also the stand-up time is very difficult in in-situ. Therefore, the development of a mathematical model is necessary and have great meaningful to estimate the stand-up time in the tunneling. The objective of the paper is to develop an analytical solution to predict stand-up time of the rock mass surrounding tunnel based on the rheological deformation model using Abel’s creep kernel and allowable displacement of the tunnel wall. The results of numerical example shown in good agreement with Bieniawski’s suggested method.

Experimental Evaluation of The Durability of A Composite-Composite Pasted Assembly Under Quasistatic Loading

Optimization of composite structures for the design and repair through, in particular, the use of pasted junctions in lieu of bolted or riveted junctions for different applications. The object of this work is to model the durability of a pasted assembly of composite structures under quasistatic loads by the hereditary Rabotnov approach. To do this, it took on the one hand, an experimental analysis of the damage of the adhesive in shear behavior subjected to different loading rates. On the other hand, the establishment of the model required experimental identification of the parameters of the creep kernels in formulating expressions for determining the durability and long-term strength limit in the shear of glued composite assembly. Special attention is paid to the prediction of the strength characteristics of the material under long loading periods up to 10 6 h (approximately 100 years of operation) by laboratory tests carried out for 10 3 h. The results could be useful, in particular, when designing and assembling the elements in composite structures located in bridge decks and walkways (beams, spacers, etc.) and also in shipbuilding.

Energy version of the kinetic equations of isothermal creep and long-term strength

Energy-type kinetic equations of inelastic rheological deformation are proposed in which the elastic, plastic, and creep strains are the additive components of the total strain, and the damage parameter is taken into account. A model of viscoelastic material with a creep kernel of exponential type is considered. The Lyapunov stability of solutions under constant stress is studied. The stability range of the solutions of the differential equations of the mathematical model corresponding to asymptotically bounded creep is established. It is shown that the instability range of the solutions corresponds to the onset of the third stage of creep. The relationship is determined between the Lyapunov stability of the solutions and the stability of the computational algorithm for the numerical solution of the system of equations. The proposed model is experimentally verified. It is shown that the calculated and experimental data are in good agreement.

Determining the Parameters of the Hereditary Kernels of Nonlinear Viscoelastic Materials in Tension

A method of determining the parameters of the hereditary kernels in a viscoelastic model with time-independent nonlinearity is tested. The parameters are determined by fitting the discrete values of the kernels that are obtained considering the similarity of isochronous creep curves and instantaneous deformation curve. The discrete values of the kernels in the zone of singularity are found using weight functions. The Abel function, a combination of power and exponential functions, and fractional-exponential functions are used as hereditary kernels. The method is tested by analyzing the creep, creep recovery, and stress relaxation in laminated composites, polymeric binders, and fiber reinforcements under uniaxial tension Introduction. The main difficulties faced in determining the parameters of the hereditary kernels of nonlinear viscoelastic materials are associated with the selection of the most adequate nonlinear viscoelastic model and with the inadequate accuracy of measurements in short-term tests in which dynamic effects are manifested. The most effective approaches to and methods of resolving such challenges are reviewed in (6, 9, 10, 15, 22, 25). In (2), a method was proposed for determining the parameters of the hereditary kernels in a Rabotnov-type nonlinear theory of viscoelasticity with time-independent nonlinearity. The method is based on the unified isochronous deformation curve that reflects the similarity of isochronous creep curves to the instantaneous deformation curve. The nonlinearity of the constitutive equations is determined by the nonlinearity of the instantaneous deformation curve. We will use the creep kernel rather than the relaxation kernel because creep tests are easier to conduct than relaxation tests. The parameters of creep kernels are determined by fitting their discrete values obtained by differentiating the average similarity function. The discrete values of the kernels in the zone of singularity occurring in short-term tests are obtained using weight functions. Here the method of determining the parameters of the hereditary kernels of nonlinear viscoelastic materials outlined in (2) is tested by calculating creep strains at constant stresses, creep recovery under complete unloading, and stress relaxation. 1. Problem Formulation. Subject of Analysis. We will test the method of determining the parameters of the hereditary kernels of nonlinear viscoelastic materials in the hereditary theory of viscoelasticity with time-independent nonlinearity. We start with the following one-dimensional constitutive equations (3, 5, 15, 23):

The Test Study of Genetic Creep Kernel Function of Artificial Frozen Clay and its Parameters

The test study the creep property of artificial frozen clay at different frozen temperature by independently developed uniaxial creep testing machine WDT-100, the test result indicated that the nonlinear creep property of deep artificial frozen clay can be described by the function as ε=atb. It is found that the creep of deep frozen clay can be calculated by genetic theory through contrastive study, analysis of parameters of genetic creep kernel function shows that the parameter a and creep stress are exponential relationship while linear correlation with test temperature, parameter b is only related to creep stress.