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1 Application of Plastics CAE: Focusing on Impact Analysis Sumitomo Chemical Co., Ltd. Plastics Technical Center Masaaki TSUTSUBUCHI Tomoo HIROTA Yasuhito NIWA Tai SHIMASAKI To review recent topics on impact analysis in the field of plastics, this report outlines the application trends and analysis techniques followed by an explanation of the characteristic physical properties of resins which may be the key points for their practical application. First we introduce how we predict yield stress under a wide range of temperatures and strain rates. Second, for the elastic-plastic model, we explain that it may be appropriate to consider dependence of yield stress on stress state and volume increase due to craze generation. Finally, we show how fracture behavior depends on temperature and strain rate. CAE Computer Aided Engineering ) 98Dr. Jason R. Lemon CAE 2) CAE CAE CAE CAE 98 CAE 3) 6) 7), 8) 9) Fig. a Fig. b CAE 2 CAO Computer Aided OptimizationCAO CAE 2) CAO CAE ) CAE CAE Fig. 2 2-

2 Fig. (a) Semi-anechoic chamber (b) Impact testing machine Experimental facilities for Plastics CAE Plastics CAE (Product/Material design and product performance evaluation) < CAE for Polymer Design > Structure & Composition of Materials Fig. 2 CAE CAO Physical properties of Materials * CAE : Computer Aided Engineering CAO : Computer Aided Optimization Plastics CAE system < CAE for Product Design > CAE CAO Performance & Processability of Products ) 6) 7) 8), 9) 2) 23) 24), 25) ) 27) 29) 3) 3) 32), 33) 34) LS-DYNA LS-DYNA 976 DYNA3D

3 Courant Courant u Δt C = Δx C CourantuΔ t Δx u ρe u = E/ρ 2 Δt Δx ρ/e () (2) E =.5GPa ρ = 9kg/m 3 Δx =.m Δ t.77 Δt Courant 35) LS-DYNA 2 Δ x Courant 3 Fluid Structure Interaction: FSI Lagrange Lagrange Euler ALE Arbitrary Lagrangian Eulerian ALE 2-

4 Euler ALE Lagrange 3 36) n σ 2 ε. =, σ ε. 2 ε 2 ε. = ε ε. 2 n (3) σ σ 2 ε ε 2 ε ε 2 n Stress (MPa) 5 5 Strain (a) Original data Stress (MPa) (b) Superposed data by the scaling rule Fig Strain.5s.s.2s.5s s 2s 5s s 2s 5s s 2s 5s.5s s 2s 5s s 2s 5s s 2s 5s Tensile testing results: Relationship between nominal stress and nominal strain 3 Fig. 3.5s ) σθεε E w h σ(ε,ε.,θ) = E (ε.,θ) [ e w(ε.,θ)ε ]e h(ε.,θ)ε 2 w(ε.,θ) 4 Fig. 3 Fig. 3 a E w h ) Cowper-Symonds 5 σ y = σ y [ + (ε. /C ) /p ] σ y σ y ε C p (4) (5) 2-

5 Eyring 6 39) Eyring Eyring V p *σ y V p *σ y 6 PC, PMMA, PP R σ y = Σ sinh T p=α,β V ε.* p *,p ε. *,p = ε.,p exp ΔU p RT σ y ε ε,p TRV p * ΔU p ε. (6) 6 Fig. 4 Fig. 4 6 Yield Stress (MPa) C 3 C 2 C C C C 23 C {(σ xx σ yy ) 2 +(σ yy σ zz ) 2 +(σ zz σ xx ) 2 +6(τ 2 xy + τ 2 yz + τ 2 zx)} σ 2 y 2 (7) σ y σ xx σ yy σ zz τ xy τ yz τ zx 4) von Mises 25) : ε L : ε T Fig. 5 d ε T /d ε L, Fig. 5 Digital Image Correlation Method; DICM 4) Fig. 5 42) Fig. 4.. Strain Rate (s ) Plots: Experimental data Curves: Eq.6 Dependence of yield nominal stress on temperature and nominal strain rate von Mises 7 von Mises Transverse true strain Parallel part length of the specimen: 57mm Fig Slope:.42.2mm/s.m/s Longitudinal true strain Relationship between transverse true strain and longitudinal true strain 2-

6 43) ε pt ε pl ε pt /ε pl.5 Fig. 6 F S S S v σ d σ p 8 F = σ d S = σ p (S S v ) d ΔV V 9 44) d = σ d /σ p = (S S v )/S = /( + ΔV/V ) Tensile Direction F = σ d S = σ p (S S v ) S (8) (9) 3 Fig. 7 A D Table Strain at break A B C D Fig. 7 Table Region C D Break under uniform deformation (A) Break immediately after start of necking (B) Break under propagation of necking (C) Break at the shoulder part of the specimen (D) B Break behavior of the specimen at tensile testing Break behavior Break under uniform deformation Break immediately after start of necking Break under propagation of necking Break at the shoulder part of the specimen C... Strain rate (s ) Relationship between nominal strain at break and nominal strain rate Temperature Low High Nominal strain rate High Low A Fig. 8 a T WLF 45) A B A 23 C 3 C S v C log a T = (T T ref ) C2 + (T T ref ) () Fig. 6 Stress of damaged material Cross-section TTref C C 2 2-

7 Strain at break 4 C 3 C 2 C C C C 23 C log at 5 Exp Temperature ( C) 99 Fig. 9.. Strain rate (s ) Plastics part Fig. 8 Results of time-temperature superposition in region A 23.2 Fig. 7 46) 99 CAE Acceleration (m/s 2 ) 2 Fig. 9 Time (s) Free Motion Headform Analysis (CAO) Analysis (Manual) Experiment Example of simulation of impact test for rib box parts CAO Response Surface Method Modified Method of Feasible Directions 47) CAO. 2-

8 48) 2 Fig. Yield Stress (MPa) Strain rate (s ) (a) Dependence of nominal yield stress on nominal strain rate Strain at break C 4 C 45 C 35 C 4 C 45 C.4 Strain rate (s ) Predicted unstable or unmeasurable condition for tensile test (b) Dependence of nominal strain at break on nominal strain rate Fig. Determination of failure characteristics Fig. Example of drop impact analysis for the standing-pouch A Table A 6 Fig. a Fig. b 35 Fig. 2 Blown off door (a) with poor material properties Fig. 2 Properly opened door (b) with good material properties Airbag cover deployment test analysis result 2-

9 3 Fig 3 Model A von Mises.5 Model B Fig. 4 Model B Model A Upper clamp Lower clamp Fig. 3 Force (N) Fig mm 5mm Dart with hemispherical tip weight: 6.5kg Plate specimen 3mm Schematic diagram of CAE analysis model for the falling weight impact test Drop height : 4cm Displacement (mm) Exp. CAE (Model A) CAE (Model B) Comparison of experimental result and CAE predictions for the falling weight impact test 49) 5) Gough-Joule 5) 52), 53) XFEM 54) 55) CAE CAECAE ) J. R. Lemon, S. K. Tolani and A. L. Klosterman, CAD-Fachgespräch, 98, 6 (98). 2),,,, 5 (24). 3),,,,,, 984-@, 7 (984). 4),,,,,, 992-@, 68 (992). 5),,,,,, 995-!, 75 (995). 6),,,, 2-@, 3 (2). 7) M. Tsutsubuchi, T. Kitayama, Y. Togawa, T. Nishio and, H. Kutschera, Intern. Polym. Process., 5(3), 33 (2). 8),,, 98, 998, 39. 9),,,, 29-!, 4 (29). 2-

10 ),, 22(), 53 (2). ) M. Walter, H. Chladek and A. Huß, 4th European LS-DYNA Users Conference, 23, G--5. 2) I. Lupea, J. Comier and S. Shah, 8th International LS-DYNA Users Conference, 24, ) T. Yeo and J. Park, 23 ABAQUS Users Conference, 23. 4) T. Goel and N. Stander, Comput. Methods Appl. Mech. Engrg., 98, 237 (29). 5) M. Keranen, S. Krishnaraj, K. Kulkarni, L. Lu, R. Thyagarajan and V. Ganesan, SAE Technical Paper, (25). 6) C. J. Ribeiro, J.C. Viana, F.Vilaça and J. Azenha, Plastics, Rubber and Composites, 35, 253 (26). 7) A. Malladi, Saifuddin and G. Gadekar, SAE Technical Paper, (2). 8),,,,,, No.99-98, 9 (998). 9),,, No.3-99, 3 (999). 2),,,,,, 26, 27. 2),, 32, 5 (26). 22) J. M. Lorenzo, SAE Technical Paper, (999). 23) K. Lee, T. Yeo, S. Park, H. A. Gese and H. Dell, SAE Technical Paper, (28). 24) P.A. Du Bois, M. Koesesters, T. Frank and S. Kolling, 3. LS-DYNA Anwenderforum, 24, C-I-. 25) P.A. Du Bois, S. Kolling, M. Koesters and T. Frank, International Journal of Impact Engineering, 32, 725 (26). 26) M. C. H. Lee and G. E. Novak, SAE Technical Paper, (26). 27),,,,,,, 2, ) D. Yu, J. B. Kwak, S. Park and J. Lee, Microelectronics Reliability, 5, 28 (2). 29) K. H. Low, A. Yang, K.H. Hoon, X. Zhang, J. K. T. Lim and K. L. Lim, Advances in Engineering Software, 32, 683 (2). 3) T. Allen, J. Hart, J. Spurr, S. Haake and S. Goodwill, Procedia Engineering, 2, 3275 (2). 3) A. W. Pugh, R. Hamilton, D. H. Nash and S. R. Otto, Procedia Engineering, 2, 323 (2). 32),,, C, 76(772), 3343 (2). 33) W. Petersen and J. McPhee, Sports Eng., 2(2), 77 (2). 34), C, 65(638), 389 (999). 35),,, 25(4), 34 (26). 36),,,, (995), p ) W. Michaeli, M. Glißmann, Polymer Testing, 2(5), ),, 57(3), 29 (28). 39) E.T.J. Klompen, L.E. Govaert, Mech. Time-depend. Mater., 3, 49 (999). 4),, 5(9), 968 (2). 4) F. Grytten, H. Daiyan, M. Polanco-Loria and S. Dumoulin, Polymer Testing, 28(6), 653 (29). 42) V. Delhaye, A. H. Clausen, F. Moussy, R.Othman and O.S.Hopperstad, International Journal of Impact Engineering, 38(4), 28 (2). 43),, 5, 25, ) M. Nutini and M. Vitali, 7. LS-DYNA Anwenderforum, 28, D-I-. 45),,, 5(6), 25 (22). 46),,,, 26, ),,,,, 2, ),,,, 6, 26, ) R. N. Haward, J. Polym. Sci. Part B:Polymer Physics, 45, 9 (27). 5),, 77(), 2 (24). 5),,,, 3, (983), p ) I. Doghri, Mechanics of Deformable Solids, Linear and Nonlinear Analytical and Computational Aspects, Springer (2), p ),,, A, 77(778), 92 (2). 54) N. Moës, J. Dolbow, and T. Belytschko, International Journal for Numerical Methods in Engineering, 46(), 3 (999). 55),, A, 67 (659), 93 (2). 2-

11 PROFILE Masaaki TSUTSUBUCHI Yasuhito NIWA Tomoo HIROTA Tai SHIMASAKI 2-

薄板プレス成形の高精度変形解析手法と割れ予測

薄板プレス成形の高精度変形解析手法と割れ予測 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