OBRABOTKAMETALLOV technology Vol. 24 No. 1 2022 Ta b l e 1 Mechanical characteristics and physical properties of heat-resistant alloys required for temperature calculation Material grade Ultimate strength su, MPa Percentage elongation %EL, % Thermalconductivity coefficient λ, W/m·K Volumetric heat capacity СV, kJ/ m3·K Thermal diffusivity coefficient w, m2/s Density ρ, kg/m3 56% Ni-Cr-W-Mo-Co-Al 1,050 17 10.53 4.39 2.858ˑ10-6 8,400 The 56% Ni-Cr-W-Mo-Co-Al heat-resistant alloy was chosen for the study. The physical and mechanical properties of this material are presented in Table 1 [17, 18] The calculations are based on the dependences of the change in the actual ultimate strength on temperature during high-temperature tensile tests of heat-resistant alloys (Figure 2), as well as information on the effect of strain and strain rate on the change in the yield strength of the selected alloys [19]. Based on these data, a constitutive equation was built to determine the yield strength, which is suitable for any alloy shown in Figure 2: 0 exp( ) p m p q b A K B T S ε τ ′ = ε − ∆ , (5) 1 3 3 ln(1 ) m z A − = + ε , (6) where 0 p b S τ is the ratio of the value of the actual ultimate strength at the test temperature to the value of the ultimate strength at room temperature, m p A ⋅ ε is the equation of the material to be hardened (simple loading), m is the strain hardening coefficient, Kε is an empirical constant characterizing the effect of strain rate on the yield strength, q B is an empirical constant characterizing the effect of temperature softening of the material, T ∆ ′ is the increment of the homological temperature. In the literature there are similar models of the change in the yield strength depending on the strain, strain rate and temperature, for example, the Johnson-Cook model [20] ( )(1 ln )(1 ) n p m A B C T s = + ⋅ ε + ⋅ ε − . (7) But both the defining equation (5) and the Johnson-Cook model (7) have drawbacks. For example, in both equations, temperature acts as an independent factor, i.e. one can change the temperature by simply heating the material. In order to take into account the dependence of the combined effect of temperature, strain and strain rate during milling, it is necessary to replace in the constitutive equation (5) the ratio of the actual ultimate strength at the test temperature to the value of the actual ultimate strength at room temperature on the ultimate resilience [15]: 0 p w b p dA S d τ = ε , (8) 0 0 u p w b A d S ε τ = ε ∫ . (9)
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