Computer Modeling of Creep  for Hereditary Materials by Abel’s Kernel

Iskakbayev, Alibai; Teltayev, Bagdat; Yensebayeva, G. M.; Kutimov, K. S.

doi:10.32014/2018.2518-170x.36

Cited by 4 publications

(9 citation statements)

References 8 publications

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“…The improved methods for determination of the parameters λ, α, β have been developed in the works [49,50], and it is shown that the unsteady-state creep for an asphalt concrete can be approximated with a high accuracy using the Rabotnov'slinebreak fractionexponential function.…”

Section: Creep Kernelmentioning

confidence: 99%

“…The works [38,50] show the possibility for description of the unsteady-state creep of an asphalt concrete with a high accuracy by more simple expression than Equation (3).…”

Section: Creep Kernelmentioning

confidence: 99%

“…Equation ( 5) contains three unknown parameters: ε 0 , α and δ. The works [36,50,51] propose to consider α as the known parameter, and the parameters ε 0 and δ are calculated according to the expressions:…”

Section: Determination Of Parameters ε 0 α δmentioning

confidence: 99%

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Unsteady-State Creep of an Asphalt Concrete

Teltayev¹,

Iskakbayev

Rossi

et al. 2022

Applied Sciences

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This paper reports the experimental investigation of the unsteady-state creep process for road hot fine-grained asphalt concrete within the variation for a stress (from 0.0081 to 3 MPa) and a temperature (from +60 to −24 °C) at uniaxial tension. It is found out that unsteady-state creep for the asphalt concrete is approximated with a high accuracy at all the considered temperatures and stresses by the power function (with 3 parameters: ε0, α, δ) obtained from the Rabotnov’s fraction-exponential function; at temperatures from −12 to +12 °C the parameter α has the mean value of 0.5; unsteady-state creep duration for the asphalt concrete depends strongly on the stress and the temperature. It is satisfactorily described by the mathematical expression in the form of multiplication of the exponential and the power functions. Mathematical expressions have been obtained which describe the unsteady-state creep and the steady-state creep rates for the asphalt concrete. It was found that the strain rate is varied sharply in the initial time moments from t≈0 to 500–600s (theoretically from ∞ at t = 0 to ≈1–2×10−3%/s at t = 500–600 s); then it decreases monotonously in the following time moments, approximately according to a straight-line dependence. An asphalt concrete creep as a physical process can be similar to the viscous liquid flow: it is proposed to call the sites of the unsteady-state and the steady-state creeps as the sites of the transient and the constant viscosities respectively; a mechanical (rheological) model is represented which describes the sites of the transient and the constant viscosities for the creep curve of the asphalt concrete through Trouton and Newton viscosities respectively. Meanwhile, it has been stated that the viscosity of the asphalt concrete can reach 26,000 and 45,000 MPa at the temperatures of +24 and +36 °C respectively at the end of the unsteady-state creep.

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Section: Creep Kernelmentioning

confidence: 99%

“…The works [38,50] show the possibility for description of the unsteady-state creep of an asphalt concrete with a high accuracy by more simple expression than Equation (3).…”

Section: Creep Kernelmentioning

confidence: 99%

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Unsteady-State Creep of an Asphalt Concrete

Teltayev¹,

Iskakbayev

Rossi

et al. 2022

Applied Sciences

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“…The works [5][6][7][8] suggest the parameter to consider as the specified one, and the remaining two other parameters to determine using the least squares method. In the work [9] the above method has been improved: the determining ratios have been changed by introducing the so-called experimental rheological parameter.…”

Section: Relaxation Kernel Parametersmentioning

confidence: 99%

“…Creep and relaxation are important characteristics of hereditary materials. The creep has been studied for an asphalt concrete and other materials in the works [5][6][7][8][9][10][11][12][13]. The present work is devoted to the modeling of the process for relaxation of a number of hereditary materials.…”

Section: Introductionmentioning

confidence: 99%

Modeling of Hereditary Materials Relaxation by Abel Kernel

Zhurinov¹,

Iskakbayev²,

Teltayev³

et al. 2020

SERIES OF GEOLOGY AND TECHNICAL SCIENCES

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The present work is devoted to mathematical modeling of the process of the hereditary materials relaxation. Nonlinear integral equation of a hereditary type is proposed. The Abel kernel with two unknown parameters is adopted as the kernel of the integral equation: α∈(0,1),δ>0. Two new characteristics were introduced: 1) experimental rheological parameter of relaxation; 2) calculated (model) rheological parameter of relaxation. Using the least squares method, expressions are obtained to determine unknown parameters of the Abel kernel. A mathematical expression is given to approximate the process of the hereditary materials relaxation. Using examples of rheonomic materials different in structure (polyurethane matrix, propellant, polyoxymethylene, fiberglass), it is shown that the proposed methods allow to determine Abel kernel parameters with a high accuracy and to model the process of relaxation of rheonomic materials different in structure during a long period of time: from 102 to 1.8·106 seconds (500 hours).

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Modeling of unsteady-state creep of asphalt concrete

Iskakbayev,

Teltayev,

Aitbayev

et al. 2024

Vib. proced.

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The article experimentally investigated unsteady-state creep of a hot fine-grained dense asphalt concrete under uniaxial tension at temperatures of 22-24 °C. 61 samples of the asphalt concrete in the form of a rectangular beam with dimensions of 50×50×150 mm were tested to complete failure at seven different stresses (from 0.084 MPa to 0.3053 MPa) in a special installation with a heat chamber. Based on the test results, unsteady-state creep curves were constructed, which were normalized and approximated with high accuracy by a power function. Reliable dependences of the limiting time of hardening, the limiting strain of hardening, and the hardening rate on stress have been established.

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Computer Modeling of Creep for Hereditary Materials by Abel’s Kernel

Cited by 4 publications

References 8 publications

Unsteady-State Creep of an Asphalt Concrete

Unsteady-State Creep of an Asphalt Concrete

Modeling of Hereditary Materials Relaxation by Abel Kernel

Modeling of unsteady-state creep of asphalt concrete

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