13th International Conference on Fracture June 16–21, 2013, Beijing, China -4- ( ) Δσ ρ β − ν = c 1 2 A T0 1 , ( ) 2 2 0 2 c 1 2 4 T A ⎟⎟ Δσ ⎠ ⎞ ⎜⎜ ⎝ ⎛ ρ β − ν = , (3) Analysis of the relations (2), (3) leads to the conclusion that in the classical case amplitude of the first and second harmonics does not depend on frequency and are linear functions of stress amplitude and the square of the stress amplitude, respectively. At the present time been suggested that the effect of thermoelasticity is strongly nonlinear [6]. Significant contribution to the temperature dependence of the time makes the process of changing the elastic properties of the material on temperature. Assuming the dependence of the elastic modules of the material on the temperature ( Tλ , Tμ ), the temperature change is described by the equation: ( ) sin2 t (3 2 ) c ) (1.5 2 2(3 2 ) c t cos (3 2 ) c ) (1.5 2 2 (3 2 ) c c 1 2 LogT 2 2 2 2 2 T 2 T 2 2 2 2 0 T 2 0 T t ⎟ Δσ ω ω ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ μ λ+ μ ρ λ + λμ+μ +μ λ+ μ ρ λ + ⎟ Δσω ω + ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ μ λ+ μ ρ σ λ + λμ+μ + μ λ+ μ ρ σ +λ ρ β − ν = − (4) At the tip of fatigue crack occurs intensive energy dissipation due to the localization of plastic deformation. The characteristic size of the zone of energy dissipation in framework of linear fracture mechanics, determined by the value of stress intensity factor. The magnitude of the stress intensity factor taking into account geometry of the sample can be estimated using the expression: 1 2 ⎟ ⎠ ⎞ ⎜ ⎝ ⎛π =σ π W a aSec K , (5) where W – wide of specimen, a– half-length of crack.The radius of the zone of plastic deformation on the surface of the plate is: 2 2 y p K r k σ = , (6) where k – coefficient depending on the type of stress state and accepted model of plastic deformation, σy – flow stress. The form of the zone of plastic deformation at the crack tip under quasi-static tension can be described by the relations: taking into account Mises criterion ( ) ( ) ( ) ( ) θ + θ + π σ θ = 2 2 2 3sin 1 cos 4 1 y p K r , (7) taking into account Tresca Saint Venant criterion ( ) 2 2 2 2 2 1 sin 2 cos 2 1 ⎟⎟ ⎠ ⎞ ⎜⎜ ⎝ ⎛ ⎟ ⎠ ⎞ ⎜ ⎝ ⎛θ ⎟ + ⎠ ⎞ ⎜ ⎝ ⎛θ π σ θ = y p K r . (8)
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