Issue 49

M. Bannikov et alii, Frattura ed Integrità Strutturale, 49 (2019) 383-395; DOI: 10.3221/IGF-ESIS.49.38 392 where:   , σ , pl   , p are the corresponding components of the tensors ε  , σ , p ε  , p . At the first stage of identification, the problem of minimizing the discrepancy between the experimental and calculated stress-strain diagrams is solved. This determines the parameters   , p   , p  ; dimensionless strain rate 0 1 ε   (static loading), 1.15 δ const   . At the second stage, using the known values   , p   , p  the problem of minimizing the discrepancy between the experimental and calculated stress-strain diagrams at different strain rates is solved. This determines the parameters n  and p n , 1.15 δ const   . An illustration of optimization problem solving is presented in Tab. 3. Strain rate, s -1 Yield strength, MPa (the experiment, [25, 26]) Yield strength, MPa (the calculation) 0.0001 165 166 520 175 176 1210 210 213 Table 3 : The yield strength in the experiment [25, 26] and the calculation at different strain rates. The final step in identifying the parameters of the model is to determine the values of   and n  that are found using experimental fatigue loading data. Two characteristic points on the Wöhler curve were selected: (300,000 cycles, 190 MPa) and (300,000,000 cycles, 156 MPa). Parameters   and n  were chosen in such a way that at the loading amplitude of 190 MPa the material was destroyed after 300,000 cycles, and at 156 MPa - after 300,000,000 cycles, respectively. The frequency of loading in this case was equal to 20 000 Hz, as in the experiment. Thus, the complete set of constants for the AlMg6 alloy is as follows: Constants known from literature [24]: 2670 ρ  kg / m3, 41   GPa, 27 G  GPa. Constants that were defined: 529    (Pa·s) -1 , 38.5 p    (Pa·s) -1 , 2.9 p   (Pa·s) -1 , 3.46    (Pa·s) -1 , 0.967 p n n    , 1.985 n   . Numerical simulation results A numerical study of the behavior of a real structure and even a laboratory specimen in the very high cycle fatigue mode is not possible due to the requirement of huge computational and time resources. Therefore, instead of solving the boundary value problem, the problem of loading a representative material volume (24)-(28) with loading conditions in the form of applied cyclic stresses (29) with amplitude A  and frequency 20000   Hz, as well as initial conditions (21) is considered. ( ) sin(2 ) A t t     (29) 0 0 0 0 0 0, 0, 0, 1.15 p t t t t p δ δ            (30) The loading condition (19) can be written in terms of strain: ( ) ( )sin(2 ) A ε t ε σ t   (31) where ( ) ε σ is the function that converts stresses into strains for AlMg6 alloy. Differentiating (31) by time, we get: ( ) ( )2 cos(2 ) A ε t ε σ t     (32) The numerically constructed Wöhler curve and its comparison with experimental data of authors and experiment [27] with similar experiment conditions (AlMg-6, R=-1, frequency 10 kHz) are presented in Fig. 6.