Determination of Nonlinear Creep Parameters for Hereditary Materials

Abstract

This work proposes an effective algorithm for description of nonlinear deformation of hereditary materials based on Rabotnov's method of isochronous creep curves. The notions have been introduced for experimental and model rheological parameters and similarity coefficients of isochronous curves. It has been shown how using them, one can find instantaneous strains at various stress levels for description of nonlinear deformation of hereditary materials at creep. Relevant equations have been determined from the nonlinear integral equation of Yu. N. Rabotnov for the application cases of Rabotnov's fractional exponential kernel and Abel's kernel for nonlinear deformation of hereditary materials at creep. The improved methods have been given for determination of creep parameters α, ε 0 , δ, β, and λ. By processing and using test results for material Nylon 6 and glass-reinforced plastic TC 8/3-250, the process has been shown for sequential implementation of the developed methods for description of linear and nonlinear deformation of these materials at creep. From the results of the experimental investigation performed by the authors of this paper, it has been determined that fine-grained, dense asphalt concrete at the temperature of 20 ± 2 • C and stresses up to 0.183 MPa at direct tension is deformed considerably in a nonlinear way. It has been shown in an illustrative way by construction of isochronous creep curves at various load durations and curves of experimental rheological parameter at various stresses. Nonlinear deformation of asphalt concrete at creep is adequately described by the proposed methods.

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

“…As it has been said above, in the right part it contains known Abel's function with parameter of singularity α, which has the value within the interval (0, 1). In the works [7,[9][10][11] it was proposed to consider the parameter α as known and to determine the unknown parameters ε 0 and δ with the use of least square method. According to the least square method the values of parameters ε 0 and δ should meet the following condition:…”

“…In the expressions (11) and (12) k e (t) represents by itself the so called experimental rheological parameter [11], determined under formula: Experimental rheological parameter k в (t) represents by itself normalized time function in relation to experimental instantaneous strain. It has the value equal to 1 at t=0 and more than 1 at time values of t>0.…”

“…Short calculation method. Using approach developed in the authors' work [11], one can determine model (theoretical, calculated) values for creep strain in the following sequence:…”

“…It is known that the selection of kernel of the integral equation and determination of its parameters is one of the most responsible actions in description of mechanical behavior of viscoelastic materials. In the works [6][7][8][9][10][11] Rabotnov's fractional exponential kernel and Abel's kernel have been used for description of creep procedure of various materials.…”

“…In Kazakhstan complex experimental and theoretical research for deformation and strength of asphalt concretes is carried out [9][10][11][12][13][14][15][16][17][18][19][20]. The current paper is continuation of the above works and it considers the matters of computer modeling for creep procedure of hereditary materials using nonlinear integral equation of Yu…”