OBRABOTKAMETALLOV MATERIAL SCIENCE Том 23 № 3 2021 EQUIPMEN . INSTRUM TS Vol. 6 No. 2 2024 If the stress-strain state at each stage of molding a porous blank is known, the stress and strain intensity can be determined. Since in the plastic state the stress intensity is constant σi = σs and the increment of strain work [20–22]: d s i dA dV = σ ⋅ ε ⋅ ∫∫∫ , (3) where dV is the volume increment of the displaced metal; σs is the yield strength of the porous blank material; εi is the strain intensity. Fig. 9 shows, as an example, the strain intensity distribution of the top and middle layer of the blank, calculated using the following equation: ( )2 2 2 3 3 2 i xx yy xy ε = ε − ε + γ . (4) Fig. 9. Dependence of strain intensity εi of thin sections with Kh = 0.5 (3, 4) and 0.85 (1, 2) of the sintered blank on its reduced radius Kr, determined: 1 and 3 – experimentally; 2 and 4 – by simulation The incremental work of contact friction forces was generally represented as follows: f c c dA dF = τ ⋅ , (5) where τc is the tangential stresses on the contact surfaces; dFc is the increment of the contact area “toolblank”. If the contact friction stress is known, the following formula has been proposed to determine the work of contact friction forces [20]: 2 2 2 f c À u v w dF = τ + + ∫∫ . (6) The specific deformation force of the porous blank was determined from the simulation results and according to the formula [22]: ( ) 1 3 s c D d p h − = σ + ⋅ τ ⋅ , (7) where σs is the material yield strength; τc is the tangential stresses on the contact surfaces; D and d are the bushing outer and inner diameters. The equation for determining the stress τc on the tangent surface of the tool and the porous blank has the following form [9, 23]: ( )3 1 c c s τ = µ ⋅ σ ⋅ − Θ , (8) where μc is the contact friction coefficient; ϴ is the relative density of the blank.
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