Kinetic equations of creep and damage for description of materials with non-monotonic dependence of fracture strain on stress

OBRABOTKAMETALLOV MATERIAL SCIENCE Vol. 23 No. 3 2021 Fig. 1. Experimental data (points) and approximation dependences (lines) 1–4 for steel 12Cr18Ni10Ti at temperature 850 T = °C and σ = 39.2; 49; 58.8; 78.4 MPa. Dashed lines – approximation at steady-state creep; solid lines – approximation with considering the damage ( a ); experimental data (points) and approximation (line) in the coordinates “ ln (η) – σ” corresponding to the steady-state creep ( b ) a b 39,2; 49; 58,8; 78,4 σ = MPa. In Fig. 1, b these data are rebuilt in the coordinates ln( ) η − σ to find the coefficients of the second creep stage. It can be seen that the experimental points are located near a straight line ln( ) a b η = σ + . The coefficients a and b were found using the least squares method. Then the coefficients 1 / c a = and 2 exp( ) A B b = were determined. As a result, the values of 4 2,183 10 A B − = ⋅ h –1 and 18, 6 c = MPa were obtained; the dashed lines in Fig. 1, a is an approximation by the dependence sh( / ) A B c η = σ with the found values A B and c . Pearson’s correlation coefficient (linear pair correlation coefficient) is 0, 987 p k = . In Fig. 2, a , the experimental data are rebuilt in the normalized coordinates ω − τ  * * ( / , / c t t τ = ω = ε ε  , 0 1 ≤ τ ≤  ). The solid line is an approximation of this data by a “single curve” (4) using the least squares method. Coefficient m = 1.8 was obtained with the correlation index of nonlinear regression k r = 0.979. The straight line in Fig. 2, b is an approximation of the experimental data of steel 12Cr18Ni10Ti, obtained by the method of least squares in coordinates * ln( ) ln( ) t − σ . The coefficients g = 3.165 and B ω = 6.231·10 –8 MPa –g h –1 were determined from (18). Pearson’s correlation coefficient is 0, 998 p k = . Thus, all the parameters of equations (12)–(14) have been found. Solid lines 1–4 in Fig. 1, a are an approximation of experiments using equations (12)–(14), where ( ) sh( / ) c A f B c σ = σ ⋅ σ and ( ) g c B ω ϕ σ = σ in view of coefficients found. The values * ñ ε = 12.9, 10.9, 10.4, 12.0 % are fracture strains calculated according to (15) at σ = 39.2; 49; 58.8; 78.4 MPa.