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. 2. Normalized accumulation damage curve for steel 12Cr18Ni10Ti: experimental data (points) and its approximation (line) ( a ); experimental data (points) and approximation (line) in logarithmic coordinates ln( t * ) – ln(σ) ( b ) a b Comparative analysis of deformation modes Let’s consider the uniaxial stretching of a rod made of steel 12Cr18Ni10Ti to a given strain value 0 c ε for two deformation modes. For mode 1 from (20) we have ( ) 0 0 0 0 0 0 ( ) , sh( / ) g c c A B B c ω σ σ ω σ = ω ε σ = ε σ . (23) For mode 2 in view of the time 0 0 0 0 sh( / ) c c A t B c ε ε = = η σ and solving (21), (22) we find numerically ( ) 0 0 0 ( ) , c η ω σ = ω ε σ . (24) The creep rates η 0 = 8.85·10 –4 ; 1.5·10 –3 ; 2.57·10-3; 7.39·10 –3 h –1 corresponds to the stresses σ 0 = 39.2; 49; 58.8; 78.4 MPa at the steady-state stage. Lines 1–4 in Fig. 3, a are dependences ( ) t σ obtained from the solution of the system (21), (22) for these four kinematic deformation modes 0 const η = . It can be seen that the stage of steady-state creep in Fig. 1, a is very short, as a result, the curves in Fig. 3, a haven’t horizontal part and immediately begin to fall. Up to the fracture in mode 2, it is actually impossible to perform calculations. This can be explained by the fact that at low stress values, the fracture strain begins to increase significantly. For example, according to (15) at 0 20 σ = MPa the strain is % * 0 ( ) 35 c ε σ = , and at 0 15 σ = MPa the fracture strain is already 60 %. The mode close to relaxation mode begins to be observed (Fig. 3, a ) at such low values of stresses. However, there are no experimental data at such stresses, so it can be assumed that the model adequately describes the deformation in the stress range of 40 MPa 80 ≤ σ ≤ MPa. For a more accurate description of the deformation in a wider stress range, it may be necessary to enter a second scalar parameter or additional coefficients.