13th International Conference on Fracture June 16–21, 2013, Beijing, China -3- diamond suspension from 3 to 1 microns sizes. Table 1. Chemical compound of the etching: HNO3 2%, HF 2% H2O 96% After polishing materials was etching by compound with shown in table 1, time of etching – 10 seconds. a) b) c) Fig. 3.Structure of the Ti Grade 4 samples to study influence of grain size on fatigue strength and its dissipation properties a) initial stage with grain size ~25 µm b) Stage under Equichannel angular extrusion in condition 1 c) Stage under Equichannel angular extrusion in condition 2 High cycle testing was carried out on BOSE testing machine in laboratory of Bordeaux with frequencies 50 Hz and 10 Hz with symmetric conditions (R=-1). Test was started from stress 200 MPa. During fatigue processing, the temperature of specimen was measured by infrared camera CEDIP. When the temperature of specimen surface is reach stable value, test stopped and stress increased on 20 MPa until we get sharp rise in temperature which means reaching fatigue limit 3. Theoretical description of changes in temperature of the metal during cyclic deformation Evolution of temperature during cyclic deformation ( )t A σ=σ +Δσ ω sin under the assumption of homogeneity of its distribution, the absence of structural transitions and plastic deformation can be described by the Kelvin equation: ( ) t cos c 1 2 LogTt Δσ ω ρ β − ν ω =− , (1) where β- coefficient of thermal expansion, ρ - density, c – specific heat capacity, ν - Poisson's ratio, ω - the angular frequency of loading, t (.) - time derivative. The solution of equation (1) has the form: ( ) sin t] c 1 2 T T exp[ 0 Δσ ω ρ β − ν − = , (2) series expansion of (2) taking into account the smallness of the ratio, which stands in the exponent, gives the following relations for the first and second harmonic:
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