薄板プレス成形の高精度変形解析手法と割れ予測
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1 Finite Element Simulation of Deformation and Breakage in Sheet Metal Forming Noritoshi Iwata, Masao Matui 3 4J2G Stören & Rice FEM In the analysis of sheet metal forming, constitutive equations are examined for the prediction of breakage strains. Breakage initiation is numerically evaluated by Gotoh's method in which the onset of the localized necking is adopted as a breakage condition. The commercial elastic-plastic FEM code is improved by using J2-Gotoh's corner theory and biquadratic anisotropic yield function. The evaluation function for breakage is also introduced into this code. The friction coefficient on dies are measured by a model test, and the actual pressure distribution on the blank-holder is considered. The square-cup drawing process is numerically analyzed using the improved code. Numerical results with respect to the distribution of displacement and strain along the die surface, the punch load, the breakage location, and the punch stroke at the onset of breakage are in good agreemen with the experimental results. The ring-shaped cup press working process is also numerically analyzed. The yield function is modified so as to consider the effect of the pressure on breakage. Numerical results for the strain, the breakage site, and the breakage depth are in good agreement with the experimental results. R&D Vol. 32 No. 1 ( )
2 CAD ( computer aided design ) / CAE ( computer aided engineering ) CAE 2 ) ) FEM ) ) FEMJNIKE3D 20% FEM FEM FEMJNIKE3D JNIKE3D von MisesJ2F An example of mechanical properties of mild steel sheet ( thickness:t = 0.7mm ). Tensile direction α / Yield stress σy / MPa Tensile stress Ts / MPa Total elongation δ / % n-value r-value mean R&D Vol. 32 No. 1 ( )
3 Uniaxial yield stressσ /MPa r-value Hill2 4 Hill Bassani ) FEM Hill24 15% r (1) 4 φ *4 = σ *4 = σ 4 X 2.77σ 3 Xσ Y σ 2 Xσ 2 Y 2.76σ X σ 3 Y σ 4 Y + ( 5.79σ 2 X 7.32σ X σ Y σ 2 Y ) τ 2 XY τ 4 XY(1) J2G 4J2G (14) (2) φ *4 = σ 4 = σ 4 X + A 2 σ 3 Xσ Y + A 3 σ 2 Xσ 2 Y + A 4 σ X σ 3 Y + A 5 σ 4 Y + ( A 6 σ 2 X + A 7 σ X σ Y + A 8 σ 2 Y )τ 2 XY + A 9 τ 4 XY 2 ( σ 3 X + σ 3 Y)σ' Z + 3(σ 2 X + σ 2 Y)σ' 2 Z 2( σ X + σ Y ) σ' 3 Y + σ' 4 Zσ' Z = σ Z / X (2) A 2 A 9 X =2 Biquadratic Old Hill's Experimental 2.4 r-value σ Tensile direction in degree from roll direction Uniaxial yield stress and r-value at nominal strain 15% ( experiment and theory ). Model test for friction condition in deep drawing. R&D Vol. 32 No. 1 ( )
4 (1) (2) FEM J2F 4 J2G Stören & Rice ( ) ( ) J2G g ( g 1 g 2 ) 4 (3) Ag Bg 3 1 g 2 + Cg 2 1 g Dg 1 g Eg 4 2 = 0 (3) AE 4 (3) ( ) Table 1 0.7mm ( SPCD ) 8 ( ) JIS5 σ ε p Swiftσ ε ε p n Fig. 2 F : Punch force P : Blankhold Punch(150150) force(80kn) P Blank holder Die Blank(340340) Conditions of square-cup drawing. Friction coefficient measured by model test. Part of tool Flange Die shoulder Punch shoulder Friction coefficient h : Punch travel R&D Vol. 32 No. 1 ( )
5 Pressure p / MPa Fig. 4 h = 25mm 20mm 20mm25mm 0.013mm : p = k ( t t min ) (4) Y p / MPa t : t min : t max 0.013mm k : Fig. 6(a)h = 25mm Fig. 6(b) h = 34.5mm 4J2G 4J2F von Mises O X Pressure distribution on blank-holder in square-cup drawing ( h = 25mm ). h = 25mm Thickness / mm (b) h=34.5mm Relationship between sheet thickness and pressure on blank-holder in square-cup drawing. Calculated distribution of thickness strain in square-cup drawing. R&D Vol. 32 No. 1 ( )
6 Punch load F / kn J2F25mm Relationship between punch load and. punch travel in square-cup drawing ( Y.F. : Yield function, C.E. : Constitutive equation ). Y. F. C. E. Biquadratic J2G Biquadratic J2F von Mises J2F Experimental Punch travel h / mm Fig. 6 ε r h34.5mm von Mises L 0 = 95mm ε r L 0 140mm 4J2GJ2F von Mises 130 L 0 160mm ε t von Mises L 0 = 95mm ε t L 0 100mm 4 J2GJ2Fvon Mises 40L 0 70mm J2GJ2F ε r Original distance from center L 0 / mm Thickness strain t ε t h=34.5mm Punch L Die Y. F. Biquadratic Biquadratic von Mises Experimental Original distance from center L 0 / mm C. E. J2G J2F J2F Meridional strain distribution along diagonal direction in square-cup drawing. Thickness strain distribution along diagonal direction in square-cup drawing. R&D Vol. 32 No. 1 ( )
7 Rolling direction 4 (a) 33.5mm Fig. 10(b) ( : 35mm ) 14 Fig. 10(b) 1mmFig. 10 φ37mm64mm ( Y ) 10mm65mm Picture of specimen after ring-shaped cup press working. 420 Y A La 150 X Notch Breakage position in square-cup drawing. Geometry of specimen in ring-shaped cup press working. R&D Vol. 32 No. 1 ( )
8 2mm 590MPaJIS13B 0mm ( Fig. 11 ) 1/4 ( 2 1/2 JIS13B Swiftσ ε ε p n 4 (2)4 X ( 2 1 ) 2r Mechanical properties of workpiece in ringshaped cup press working. Tensile Yield Tensile Total direction stress stress elongation α / σy / MPa Ts / MPa δ / % n-value r-value mean A half section of press working in ring-shaped cup press working. Initial pressure distribution on inner blankholder in ringshaped cup press working. R&D Vol. 32 No. 1 ( )
9 Thickness strain ( ) S = 40mm ( B ) Fig. 12XA 40mm 20 30mm Fig. 11La = 19mm A A A Fig. 11 ( 40mm ) 37mm 1mm h = 40mm Necking La: Arc from point A / mm Calculation, S=20mm Calculation, S=30mm Calculation, S=40mm Experimental, S=20mm Experimental, S=30mm Experimental, S=40mm Thickness strain around inner edge ringshaped cup press working. Thickness strain distribution in ring-shaped cup press working ( h : punch travel ). Calculated location of breakage intiation in ring-shaped cup press working ( h = 36mm ). R&D Vol. 32 No. 1 ( )
10 (3) ( ) mm 32mm 1/10 FEM ()1 Punch travel of breakage initiation in ringshaped cup press working. Out-plane stress Punch travel Calculation Neglected 32.0 Calculation Considered 36.0 Experiment ),, :, -275(1983), ),, :, (1995), 62 3),, :, (1992), 97 4),,, :, -63(F)(1993), 113 5), :, -340(1989), 625 6) Nakamachi, E. and Wagoner R. H. : SAE Tech. Pap. Ser., No (1988), 12p. 7) Proc. of NUMISHEET'93, Ed. by Makinouchi, A., Nakamachi, E., Onate, E. and Wagoner, R. H., (1993) 8) : A, -458 (1984), ) Hill, R : Plasticity, (1950), 317, Oxford. 10) :, -208(1978), ) Hill, R : Math. Proc. Camb. Phil. Soc., (1979), ) Bassani, J. L. : Int. J. Mech. Sci., (1977), ) :, -210(1978), ) Gotoh, M. : Int. J. Solids & Struct., -11(1985), ) Duncan, J., Shabel, B. S., Gerbase Filho, J. : SAE Tech. Pap. Ser. No (1978). 16) : A, -437(1982), 92 17) Stören, S., Rice, J. R. : J. Mech. & Phys. Solids, -6 (1975), 42 18),, :, -381 (1992), 1202 R&D Vol. 32 No. 1 ( )
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