Material parameter identification for the numerical simulation of deep-drawing drawing of aluminium alloys B.M. Chaparro, J.M. Antunes, A.J. Baptista, D.M. Rodrigues,, J.V. Fernandes, L.F. Menezes M2D'26 - PORTO, 24-26 JULY University of Coimbra CENTRO DE ENGENHARIA MECÂNICA DA UNIVERSIDADE DE COIMBRA I. Introduction II. III. IV. Constitutive models Inverse Analysis Demeri Test V. Conclusions OUTLOOK 2
Multiplicity of constitutive models F ( σ X L ) σ ( σ X M ) Y ( ) ',, = ',, = k k1 k 2 Equivalent stress associated with the yield criteria Equivalent stress associated with the work hardening law In this study, an automatic procedure for the identification of material parameters according to several phenomenological elastoplastic constitutive models was developed. Introduction 3 Hill, 1948 (Hill48) ( ) ( ) ( ) 2 2 2 2 2 2 2 yy zz + zz xx + xx yy + 2 yz + 2 zx + 2 xy = F σ σ G σ σ H σ σ Lτ Mτ Nτ K Barlat, 1991 (YLD91) m m m 1 2 + 1 3 + 2 3 = 2 S S S S S S K m Plastic surface s = L :σ (Isotropic Equivalent Stress) ( ) c2 + c3 / 3 c3 / 3 c2 / 3 c3 / 3 ( c3 + c1 ) / 3 c1 / 3 c2 / 3 c1 / 3 ( c1 + c2 ) / 3 L = c4 c5 c6 m=6 for BCC materials m=8 for FCC materials Constitutive Models - Yield Criteria 4
Isotropic hardening - Voce Law σ = Y + R sat (1 e p n v ε ) Y - Initial yield stress R sat - saturation stress n - constant isotropic hardening Kinematic hardening - Lemaitre & Chaboche model X& = Cx X sat ( σ X ) p σ X & ε C x and X sat are material parameters kinematic hardening Constitutive Models Work hardening law 5 The calculation methodology is based on the best fit between each model and the full set of available experimental results. 2 2 σ r erroryield _ criteria = w1 1 w exp + 2 1 exp σ r σ r exp error exp σ is the yield stress in tension for a specific orientation () with the rolling direction (RD) σ and r denotes the corresponding values obtained from the yield criteria wi exp is the r-ratio obtained in tension performed at a specific angle with the RD are weighting factors work hardening σ = 1 exp σ is the experimental equivalent stress 2 σ denotes the corresponding values obtained from the hardening law. Inverse Analysis 6
Materials: EN AW-5182-H111 EN AW-612-T4 Inverse analysis - Results 7 Experimental curves obtained in the tensile, shear and Baushingers shear tests for the EN AW-5182-H111 aluminium alloy Stress [MPa] σ11 / τ11 4 3 2 1 -.4 -.2.2.4.6.8-1 -2-3 Strain ε 11 / γ 12 5182_T_ 5182_T_15 5182_T_3 5182_T_45 5182_T_6 5182_T_75 5182_T_9 5182_S_ 5182_S_15 5182_S_3 5182_S_45 5182_S_6 5182_S_75 5182_S_9 5182_B_1 5182_B_2 5182_B_3 8
Experimental yield stresses and r values for the EN AW-5182-H111 aluminium alloy Angle with RD [º] r values Yield stress [Mpa].77 18. 15.688 17.8 3.741 18.3 45.859 14. 6.77 18.4 75.799 19.6 9.87 111.9 2 2 σ r erroryield _ criteria = w1 1 w exp + 2 1 exp σ r Hill48 F G N.531.5888 1.4252 YLD91 c 1 c 2 c 3 c 6 m 1.184 1.556.9484.986 8 Material parameters identified for the Hill48 and YLD91 yield criteria 9 Comparison between experimental and numerical results Yield stresses 1.4 1.2 Txy=. Txy=.25 Txy=.433 Txy=.5 EXP 1.4 1.2 Txy=. Txy=.25 Txy=.433 Txy=.5 EXP 1 1.8.8 Sy.6 Sy.6.4.4.2.2 -.2 -.2.2.4.6.8 1 1.2 Sx -.2 -.2.2.4.6.8 1 1.2 Sx Hill48 YLD91 1
Comparison between experimental and numerical results r-values 1..9 r.8.7.6 EXP HILL48 YLD91.5.4 15 3 45 6 75 9 Angle with RD 11 Isotropic work hardening parameters identified using the von Mises, Hill48 and YLD91 yield models error work hardening σ = 1 exp σ 2 Yield model R sat [MPa] nv Von Mises 221.1 11.4 Hill48 212. 11.52 YLD91 232.9 1.91 12
Experimental and numerical equivalent stress-strain curves considering the von Mises yield criterion and pure isotropic work hardening 4 35 3 25 2 15 1 5.1.2.3.4.5 5182_T_ 5182_T_15 5182_T_3 5182_T_45 5182_T_6 5182_T_75 5182_T_9 5182_S_ 5182_S_15 5182_S_3 5182_S_45 5182_S_6 5182_S_75 5182_S_9 DD3MAT Voce Iso 13 Experimental and numerical equivalent stress-strain curves considering the Hill 48 yield criterion and pure isotropic work hardening 4 35 3 25 2 15 1 5.1.2.3.4.5 5182_T_ 5182_T_15 5182_T_3 5182_T_45 5182_T_6 5182_T_75 5182_T_9 5182_S_ 5182_S_15 5182_S_3 5182_S_45 5182_S_6 5182_S_75 5182_S_9 DD3MAT Voce Iso 14
Experimental and numerical equivalent stress-strain curves considering the YLD91 yield criterion and pure isotropic work hardening 4 35 3 25 2 15 1 5.1.2.3.4.5 5182_T_ 5182_T_15 5182_T_3 5182_T_45 5182_T_6 5182_T_75 5182_T_9 5182_S_ 5182_S_15 5182_S_3 5182_S_45 5182_S_6 5182_S_75 5182_S_9 DD3MAT Voce Iso 15 Isotropic and Kinematic work hardening parameters identified using the von Mises, Hill48 and YLD91 yield models error work hardening σ = 1 exp σ 2 Yield model R sat [MPa] nv C x X sat [MPa] Mises 174.9 1.3 32.3 43.8 Hill48 162.9 11. 25. 44.7 YLD91 196.8 9.1 53. 4. 16
Experimental and numerical equivalent stress-strain curves considering the von Mises yield criterion and isotropic and kinematic work hardening 4 3 2 1 -.2 -.1-1.1.2.3.4-2 -3-4 5182_T_ 5182_T_15 5182_T_3 5182_T_45 5182_T_6 5182_T_75 5182_T_9 5182_S_ 5182_S_15 5182_S_3 5182_S_45 5182_S_6 5182_S_75 5182_S_9 5182_B_1 5182_B_2 5182_B_3 DD3MAT_B_1 DD3MAT_B_2 DD3MAT_B_3 17 Experimental and numerical equivalent stress-strain curves considering the Hill 48 yield criterion and isotropic and kinematic work hardening 4 3 2 1 -.2 -.1-1.1.2.3.4-2 -3-4 5182_T_ 5182_T_15 5182_T_3 5182_T_45 5182_T_6 5182_T_75 5182_T_9 5182_S_ 5182_S_15 5182_S_3 5182_S_45 5182_S_6 5182_S_75 5182_S_9 5182_B_1 5182_B_2 5182_B_3 DD3MAT_B_1 DD3MAT_B_2 DD3MAT_B_3 18
Experimental and numerical equivalent stress-strain curves considering the YLD91 yield criterion and isotropic and kinematic work hardening 4 3 2 1 -.2 -.1-1.1.2.3.4-2 -3-4 5182_T_ 5182_T_15 5182_T_3 5182_T_45 5182_T_6 5182_T_75 5182_T_9 5182_S_ 5182_S_15 5182_S_3 5182_S_45 5182_S_6 5182_S_75 5182_S_9 5182_B_1 5182_B_2 5182_B_3 DD3MAT_B_1 DD3MAT_B_2 DD3MAT_B_3 19 Experimental curves obtained in the tensile, shear and Baushingers shear tests for the EN AW-612-T4 aluminium alloy Results - EN AW- 612 T4 2
Experimental yield stresses and r values for the EN AW-612 T4 aluminium alloy Angle with RD [º] r value Yield stress [MPa].691 14.5 15.69 16.4 3.557 16.1 45.476 14.1 6.53 15.6 75.654 13.1 9.692 98.3 2 2 σ r erroryield _ criteria = w1 1 w exp + 2 1 exp σ r Hill48 F G N.618.58 1.186 YLD91 c1 c2 c3 c6 m 1.79 1.66.97.941 8 Material parameters identified for the Hill48 and YLD91 yield criteria Results - EN AW-612 T4 21 Comparison between experimental and numerical results Yield stresses 1.4 1.2 Txy=. Txy=.25 Txy=.433 Txy=.5 EXP 1.4 1.2 Txy=. Txy=.25 Txy=.433 Txy=.5 EXP 1 1.8.8 Sy.6 Sy.6.4.4.2.2 -.2 -.2.2.4.6.8 1 1.2 Sx -.2 -.2.2.4.6.8 1 1.2 Sx Hill48 YLD91 Results - EN AW-612 T4 22
Comparison between experimental and numerical results r-values 1..9 r.8.7.6 EXP HILL48 YLD91.5.4 15 3 45 6 75 9 Angle with RD Results - EN AW-612 T4 23 Isotropic work hardening parameters identified using the von Mises, Hill48 and YLD91 yield models error work hardening σ = 1 exp σ 2 Yield model R sat [MPa] nv Mises 164. 13.3 Hill48 156.4 11.9 YLD91 17.4 12.9 Results - EN AW-612 T4 24
Experimental and numerical equivalent stress-strain curves considering the von Mises yield criterion and pure isotropic work hardening 3 25 2 15 1 5.1.2.3.4.5 612_T_ 612_T_15 612_T_3 612_T_45 612_T_6 612_T_75 612_T_9 612_S_ 612_S_15 612_S_3 612_S_45 612_S_6 612_S_75 612_S_9 DD3MAT Voce Iso Results - EN AW-612 T4 25 Experimental and numerical equivalent stress-strain curves considering the Hill 48 yield criterion and pure isotropic work hardening 3 25 2 15 1 5.1.2.3.4.5 612_T_ 612_T_15 612_T_3 612_T_45 612_T_6 612_T_75 612_T_9 612_S_ 612_S_15 612_S_3 612_S_45 612_S_6 612_S_75 612_S_9 DD3MAT Voce Iso Results - EN AW-612 T4 26
Experimental and numerical equivalent stress-strain curves considering the YLD91 yield criterion and pure isotropic work hardening 3 25 2 15 1 5.1.2.3.4.5 612_T_ 612_T_15 612_T_3 612_T_45 612_T_6 612_T_75 612_T_9 612_S_ 612_S_15 612_S_3 612_S_45 612_S_6 612_S_75 612_S_9 DD3MAT Voce Iso Results - EN AW-612 T4 27 Isotropic and Kinematic work hardening parameters identified using the von Mises, Hill48 and YLD91 yield models error work hardening σ = 1 exp σ 2 Yield model R sat [MPa] nv von Mises 138.2 9.8 68.2 35.5 Hill48 114.8 9.2 31.7 43.7 YLD91 142.9 9.4 69.4 37.2 C x X sat [MPa] Results - EN AW-612 T4 28
Experimental and numerical equivalent stress-strain curves considering the von Mises yield criterion and isotropic and kinematic work hardening 4 3 2 1 -.2 -.1.1.2.3.4-1 -2-3 612_T_ 612_T_15 612_T_3 612_T_45 612_T_6 612_T_75 612_T_9 612_S_ 612_S_15 612_S_3 612_S_45 612_S_6 612_S_75 612_S_9 612_B_1 612_B_2 612_B_3 DD3MAT_B_1 DD3MAT_B_2 DD3MAT_B_3 Results - EN AW-612 T4 29 Experimental and numerical equivalent stress-strain curves considering the Hill 48 yield criterion and isotropic and kinematic work hardening 4 3 2 1 -.2 -.1-1.1.2.3.4-2 -3 612_T_ 612_T_15 612_T_3 612_T_45 612_T_6 612_T_75 612_T_9 612_S_ 612_S_15 612_S_3 612_S_45 612_S_6 612_S_75 612_S_9 612_B 1 612_B 2 612_B 3 DD3MAT_B_1 DD3MAT_B_2 DD3MAT_B_3 Results - EN AW-612 T4 3
Experimental and numerical equivalent stress-strain curves considering the YLD 91 yield criterion and isotropic and kinematic work hardening 4 3 2 1 -.2 -.1-1.1.2.3.4-2 -3-4 612_T_ 612_T_15 612_T_3 612_T_45 612_T_6 612_T_75 612_T_9 612_S_ 612_S_15 612_S_3 612_S_45 612_S_6 612_S_75 612_S_9 612_B 1 612_B 2 612_B 3 DD3MAT_B_1 DD3MAT_B_2 DD3MAT_B_3 Results - EN AW-612 T4 31 Springback evaluation Demeri Test 1 25 a) Drawn cup b) Ring cutting c) Ring specimen d) Ring springback Difference between the ring diameters, before and after splitting, gives a direct measure of the springback effect Formability Analysis 32
Benchmark experimental apparatus Final stage of the stamping operation After the stamping operation Formability Analysis 33 NUMERICAL SIMULATIONS PROCEDURE DD3IMP DD3TRIM Blank discretization Full model used in the simulations Formability Analysis 34
Punch force during the stamping operations Force [kn] 9 8 7 6 5 4 3 EXP EN AW-5182-H111 NUM EN AW-5182-H111 2 EXP EN AW-612-T4 1 NUM EN AW-612-T4 1 2 3 4 5 6 Displacement [mm] Formability Analysis 35 Springback results Difference between the ring diameters, before and after splitting Material Experimental ring opening Numerical ring opening EN AW-5182-H111 79.8 mm 87.4 mm EN AW-612-T4 46.8 mm 47.4 mm Formability Analysis 36
Independently of the constitutive model considered, the material parameter identification error reported was always less than 5%. For the EN AW-5182 alloy, the YLD91 criteria enable an accurate description of the plastic behaviour of this alloy for all the testing directions. For the EN AW-612 alloy, none of the plasticity criteria enables the correct description of the entire range of stress-strain curves. This can be related with the strong variation of the plastic anisotropy coefficients in the sheet plane. A more flexible criterion is needed to improve the description of the plastic behaviour of this material. The numerical program developed for the material parameter identification tasks proved to be an efficient tool that can be used to select the best phenomenological model. Conclusions 37