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. 3 . Steel 12Cr18Ni10Ti, 850 ºС. Lines 1–4 dependences σ( t ) for the kinematic mode η 0 = B A sh(σ 0 / c ) = = const for σ 0 = 39.2; 49; 58.8; 78.4 MPa ( a );dependences ω(σ 0 ): solid lines 1, 3 – static deformation mode; dashed lines 2, 4 – kinematic deformation mode; lines 1, 2 correspond ε 0 = 6 %, , lines 3, 4 – ε 0 = 4 %, lines 5, 6 – ε 0 = 2 % ( б ) a b Solid lines 1, 3, 5 in Fig. 3, b are numerical calculation of 0 ( ) ω σ according to the formula (23); dashed lines 2, 4, 6 are calculation of 0 ( ) ω σ according to the formula (24); lines 1, 2 correspond to the strain % 0 6 c ε = , lines 3, 4 correspond to the strain % 0 4 c ε = , lines 5, 6 correspond to the strain % 0 2 c ε = . It can be seen from the analysis of the graphs that for both modes the accumulation of damage at 0 65 σ ≈ MPa is almost the same; mode 2 is preferable at 0 65 σ < MPa, since η σ ω < ω ; and mode 1 is the best at 0 65 σ > MPa, since . σ η ω < ω It can be assumed that for alloys with a maximum of function * ( ) c ε σ in diagrams with creep curves ( ) c t ε [23, 29–31], deformation modes with rates corresponding to stresses from the interval at which this maximum is reached, on the contrary, will give the least accumulation of damage, while strains will be maximum. In fact, such modes can be classified as modes close to superplasticity. Conclusions 1. The research showed the possibility of using creep equations with a scalar damage parameter in Sosnin-Gorev approach for alloys with a non-monotonic dependence of fracture strain on stress in diagrams with creep curves. The damage parameter is equated to the normalized strain, namely, to the ratio of the current strain to the fracture strain. 2. To determine the coefficients of the kinetic creep equations, it is necessary to check the geometric similarity of the experimental creep curves in the normalized values “normalized strain – normalized time”, i.e. the presence of a single normalized damage accumulation curve. The determination of the coefficients using the “single curve” method is demonstrated by the example of experimental data for steel 12Cr18Ni10Ti at 850°C, which has a minimum of fracture strain in diagrams with creep curves at constant stress. 3. For steel 12Cr18Ni10Ti, which has a minimum of fracture strain on creep diagrams, the damage parameter was calculated for two modes of uniaxial deformation: when the stress in the cross section is constant and when the strain rate corresponding to these stresses at the steady-state creep stage is constant. The analysis of the deformation modes for the material under study showed that the accumulation of damage