PSI - Issue 32

Yuriy Bayandin et al. / Procedia Structural Integrity 32 (2021) 26–31 Author name / Structural Integrity Procedia 00 (2019) 000–000

30

5

and (12) at different times independently of each other and solely from empirical laws. In the present paper, it is shown that obtained equations (9)-(10) allow the describing of fatigue curve and damage accumulation in material. 3. Fatigue curve simulation results According to the meth od proposed in this paper, the unknown model parameters Γ δ and σ c from formulas (9) − (10) are determined by solving the problem of minimizing the residuals between the experimental and the calculated fatigue curves. The experimental data are used from work presented by Aidi (2016). The values of obtained constants are Γ δ = 7,96 ∙10 -9 Pa -1 ; σ c = 0,076 σ B . The result is shown in Fig. 1.

Fig. 1. The fatigue curve. Solid line − calculation, dots − experiment , obtained by Aidi (2016).

The work presented by Aidi (2016) also shows experimental data on the elastic modulus degradation under different stresses. The calculation was carried out with the identified constants. The numerical result agrees well with the elastic modulus evolution for sample under fatigue loading (Fig. 2).

Fig. 2. Elastic modulus degradation at different stress amplitudes. Solid line - calculation, dots - experiment, obtained by Aidi (2016).

4. Conclusion Based on the proposed kinetic equation of damage accumulation, the mathematical model of cyclic loading of composite material was developed, which allows to describe the degradation of the effective elastic modulus. Identification of the model parameters was performed and well correspondence between the numerical results and the experimental data was obtained. The developed mathematical model made it possible to describe qualitatively