Cost-benefit conflict in material modeling Dr.-Ing. Birgit Reichert

Transcription

1 Cost-benefit conflict in material modeling 1 Dr.-Ing. Birgit Reichert

2 Content Introduction Modelling philosophies Material testing for data input FEM stress 3 strain Questions σ2, N/mm² σ 1, N/mm² 2

3 Cost-benefit conflict in material modeling Faurecia Seating Group Complete seat Frames Safety and comfort modules Mechanisms Foam and covers 3

4 Faurecia as global player

5 2 Leading commercial position & successful customer diversification % of sales Daimler Others Daimler 2 % 1 % Ford Others Renault Toyota 3 % Chrysler 4 % 2 % 28 % PSA VW PSA 8 % GM 13 % BMW % 26 % VAG Renault-Nissan * Excluding monoliths 28 Faurecia Group Presentation 5

6 The complex material landscape (steel sheet) EN - focus on yield strength - YS steps: 4MPa - specimen s length: 8mm JIS, JFS - focus on tensile strength - TS steps: no system - specimen s length: 5mm SAE, ASTM - focus on yield strength - YS steps: no system - specimen s length: 5mm EMS.ME - focus on yield strength - YS steps: 4MPa - specimen s length: 5mm 6

7 Best equivalence of sheet steel by norms Grade classes Europe Europe America Japan China India Deep drawing steel grades EN 113 SAE J2329 ASTM A 18M-7a JIS G 3141 JFS A 21 GB/T 5213 IS 513 cold rolled DC1 - CS SPCC JSC27C DC1 CR1 cold rolled DC3 CR3 DS SPCD JSC27D DC3 CR3 cold rolled DC4 CR4 DDS SPCE JSC27E DC4 CR4 cold rolled DC6 CR5 EDDS SPCG JSC26G DC6 CR5 Deep drawing steel grades EN 1111 SAE J2329 ASTM 111M-7 JIS G 3131 JFS A 11 GB 71-91/ GB IS 179 hot rolled DD SPHC - 8 D hot rolled DD12 HR2 HR CS Type B SPHD JSH27C - DD hot rolled DD SPHE JSH27D 8A1 EDD hot rolled DD14 HR3 HR DS Type B SPHF JSH27E - - High strength IF steel grades EN 1268 SAE J234 ASTM A 18M-7 JIS G 3135 JFS A 21 GB/T India HC18Y CR 18AT - SPFC34 JSC34W CR18IF cold rolled HC26Y CR 28AT - SPFC39 JSC39W CR26IF Microalloyed steel grades EN 1268 SAE J234 ASTM A 18M-7a JIS G 3135 JFS A 21 China IS HC26LA - CR SS Y HC3LA CR 3XF CR HSLAS31 Class Y cold rolled HC34LA CR 34XF CR HSLAS34 Class 2 - JSC44R 34Y HC38LA CR 38XF CR HSLAS38 Class Y HC42LA CR 42XF CR HSLAS41 Class Y Microalloyed steel grades EN 1149 SAE J234 ASTM 111M-7 JIS G 3134 JFS A 11 GB/T IS 5986 S315MC HR 3XF HR HSLAS31 Class 2 - JSH44R HR315F - S355MC HR 34XF HR HSLAS34 Class 2 - JSH49R HR355F Fe 49 S42MC HR 42XF HR HSLAS41 Class 2 - JSH54R HR42F - S46MC - HR HSLAS45 Class 2 - JSH59R HR46F - hot rolled SMC HR 49XF HR HSLAS48 Class HRF - S55MC HR 55XF HR HSLAS-F HR55F - S6MC - HR UHSS HR6F - S65MC HR65F - S7MC - HR UHSS HR7F - Dual phase steel grades draft EN 1338 SAE J2745 ASTM A 18M-7a JIS G 3135 JFS A 21 GB/T India HCT45X CR DP44T/25Y - SPFC44 JSC44W CR26/45DP - HCTX CR DP49T/29Y - SPFC49 - CR3/DP - cold rolled HCT6X CR DP59T/34Y - SPFC59 JSC59Y CR34/59DP - HCT78X CR DP78T/42Y - SPFC78Y JSC78Y CR42/78DP - HCT98X CR DP98T/55Y - SPFC98Y JSC98Y CR55/98DP - Dual phase steel grades draft EN 1338 SAE J JIS G 3134 JFS A 11 China - hot rolled HDT58X HR DP59T/3Y - SPFH59Y JSH59Y - - Complex phase steel grades draft EN 1338 SAE J2745 ASTM A 18M-7a JIS G 3135 JFS A 21 China India HCT6C cold rolled HCT78C HCT98C Complex phase steel grades draft EN 1338 SAE J2745 ASTM 111M-7 JIS G 3134 JFS A 11 China India HDT75C hot rolled HDT78C JSH78R - - HDT95C Often old short names in use In Europe EN standards obligatory In general only best equivalence to other standards possible (JIS, SAE, ASTM, JFS, ) For the newest steel developments standards do not exist, only companies information can be cited Martensite phase steel grades draft EN 1338 SAE J2745 ASTM 111M-7 JIS G 3134 JFS A 11 China India hot rolled HDT12M

8 Modeling philosophies Experimental data using the unprocessed al data (materials database) extrapolation by mathematical trend Empirical derived models e.g. flow stress functions parameter without physical meaning determination of parameters by fitting to al data of material Continuum mechanics models physical interpretable parameters fitting of model parameters to al data of material Microstructurally based models involving microstructure-related internal variables. determination of model parameter by certain set of s Ab initio modeling applying quantum mechanics parameter-free determination stress strain stress DATEN ZEIT <s>; KRAFT <N>; WEG <mm>;breitenaenderu.; e+2;.;..; e+2;.;..; e+2;.;..; e+2;.;..; e+2;.;..; e+2;.; e-2; e+2; e-5; e e-2; e+2; e-4; e e-1; e+2; e-4; e e+; e+2; e-4; e e+; e+2; e-3; e-4 Models represent macroscopic behaviour strain Models represent metal-physical mechanisms 8

9 Forming flow curve (quasi-static) forming limit diagram yield locus Youngs-Modulus Poisson ratio strain amplitude, % h HX34LAD true stress, N/mm² h anisotropy coefficient friction coefficient specific weight specific heat capacity Fatigue strain S-N curves fracture elastic portion plastic portion total strain S-N line Manson-Coffin S-N line Manson-Coffin elastic portion Manson-Coffin plastic portion friction,,,2,4,6,8 1, Experiment Input for FEM Estrin-Mecking Crash flow curves (dynamic) major strain, spring back, HX42LAD, 1.mm true stress, N/mm² H minor strain, - fracture bake hardening,.4s-1 at 296K 1s-1 at 296K 2s-1 at 296K 2s-1 at 296K fracture σ2, N/mm² σ 1, N/mm² cycle to failure N i 9

10 true stress, N/mm² h Empirical derived models for flow curves tensile test quasi-static Ludwik : k f ( ϕ ) = σ + CL Hollomon : k f ( ϕ) = CH 68 Swift : k f ( ϕ) = CS ( ϕi + ϕ) 63 Gosh : k ( ϕ) = C ( ϕ + ϕ) tensile test Hollomon (2 Parameter) Swift (3 Parameter) Gosh (4 Parameter) Voce (3 Parameter) Hockett-Sherby (4 Parameter) Estrin-Mecking (3 Parameter) Voce : k f f ( ϕ) = σ + ( σ σ ) Hockett Sherby : k Estrin Mecking: k S S f i f i ( ϕ) n ϕ n ϕ n n S S H S = C L D ϕ exp ϕr 2 ( C (199) (1945) (1952) 2 (1977) C m ) exp n ϕ ( ) = ( 2 ϕ σ ) exp S σ i σ S * ϕr microstructural interpretation of Voce for fine grain or precipitation hardened single phase microstructure 1 (1948) microstructurally interpreted by Kocks-Mecking for coarse grain and single phase microstructure (1981) HS HS ϕ (1975) (1984) Kocks-Mecking (Voce) and Estrin-Mecking are presented currently as modules of the One Internal Variable Model (OIVM) 1

11 Application of fitting functions to HX18YD hardening rate, MPa hardening rate, MPa 3 3 HX18YD tensile HX18YD bulge 2 Hollomon HX18YD tensile HX18YD bulge 2 Sw ift Differential quotient of tensile flow curve dσ/dε versus σ Minimising sum of flow curve and hardening rate: n ( yi_ Experiment yi _ Modell Σ= i 1 Constraints: - al tensile curve is of priority - stress at true plastic strain is not lower than R p.2 (25MPa) )

12 Application of fitting functions to HX18YD HX18YD Zug 3 HX18YD Zug 3 HX18YD Zug hardening rate, MPa HX18YD Bulge Ludw ik hardening rate, MPa HX18YD Bulge Voce hardening rate, MPa HX18YD Bulge Gosh

13 Application of fitting functions to HX18YD hardening rate, MPa hardening rate, MPa 3 3 HX18YD tensile HX18YD bulge 2 Estrin-Mecking HX18YD tensile 2 HX18YD bulge Hockett-Sherby Comments: - best simultaneous fit to flow curve and hardening rate for models with 4 parameters (Hockett- Sherby or Gosh) - best model working with 3 parameters is Estrin-Mecking; superior to Swift or Ludwik and similar to Gosh due to minimising criteria - application of model using two parameters is difficult (Hollomon) - if it comes to parameterise models for application of stochastic analysis then one may care for as less model parameters as possible 13

14 Cost assessment for basic testing Chemical composition Metallography Tensile tests on sheet specimens - longitudinal, transversal, diagonal - statistically reliable (e.g. according to SEP 124) Flow curve up to high strains for one material 14

15 Yield criteria families Yield criteria Hill's family σ σ 3 σ 45 σ 75 σ 9 σ b τ r r 3 r 45 r 75 r 9 r b A1 A2 Hill48 X X X X Hill79 X X X X Hill9 X X X X X X Hill93 X X X X X X X X Chu95 X X X X X X Lin, Ding96 X X X X X X X X Hu25 X X X X X X X X Hosford's family σ σ 3 σ 45 σ 75 σ 9 σ b τ r r 3 r 45 r 75 r 9 r b A1 A2 Hosford79 X X X X Barlat89 X X X X X Barlat91 X X X X X Karafillis, Boyce93 X X X X X X X X Barlat96 X X X X X X X X X BBC2 X X X X X X X X X Bron-Besson23 X X X X X X X X X Barlat23 X X X X X X X X X X BBC23 X X X X X X X X X X Aretz-Barlat24 X X X X X X X X X X A1: anomalous behavior of first kind A2: anomalous behavior of second kind 15

16 Other yield criteria approaches Budiansky (polar coordinates) Ferron (polar coordinates) Vegter (Bézier interpolation) σ σ σ1 σ1 λ λ λ σ = (1- ) + 2 (1- ) + σ 2 r i σ 2 /σ f equi bi-axial 2 h i λ 2 σ1 σ r 2 i+ 1 reference point plane strain Second order interpolation between the reference points i and i+1 (here i= 1, 2, 3, 4). Hinge points are the intersection points from the known slopes in these reference points. Orientation dependency described via cosine interpolation. hinge point pure shear uni-axial σ 1 /σ f 16

17 Experimental data for describing yield loci Uniaxial tension 9 5 σ 2 Strain plane Equibiaxial tension Uniaxial tension Strain plane σ 1 yield stress Tensile tests with different angle to rolling direction angle to rolling direction Lankford value angle to rolling direction Tensile tests: r, r 9, r 45, (r 15, r 3, r 6, r 75 ) σ, σ 9, σ 45, (σ 15, σ 3, σ 6, σ 75 ) Pure shear tension Hydraulic bulge test: σ b Point 1: σ Point 2: σ 1 = 2σ 2 (ε 2 = ) Point 3: σ 1 = σ 2 = σ b Point 4: σ 1 = σ 2 /2 (ε 2 = ) Point 5: σ 9 Point 6: σ 1 = -σ 2 = τ Biaxial tensile tests: σ b, further biaxial stress combinations (σ 1 = x σ 2 ) Shear test: τ 17

18 Determination of FLC Uniaxial tensile test (3) Hydraulic bulge test (5) Punch stretching test Keeler test (4) Hecker test Marciniak test.6 Nakajima test (2).4 Hasek test (1) ε ε 2 18

19 Forming seat tracks Bending (bending limit curve, ) Spring back (Chaboche, Backhaus, Yoshida, ) Failure (Gurson, EWK, CrachFEM, ) failure in deep drawing failure in bending grain boundaries 19

20 Cost assessment for advanced testing Chemical composition Metallography Tensile tests on sheet specimens - longitudinal, transversal, diagonal - statistically reliable (e.g. according to SEP 124) Flow curve up to high strains Plane strain and shear Forming limits Hole expansion and bending - 7 for one material 2

21 Dynamic tensile testing for crash Specific requirements needed for load measurement, direct measurement of strain and specimen geometry Schematic of Servo-hydraulic System Typical ranges of strain rate covered by conventional load frames, servo-hydraulic machines and bar testing systems Schematic of tensile Split Hopkinson Bar System 21

22 Johnson-Cook 6 DC6 85 HCT6X true stress, N/mm² H s-1 at 296K 1s-1 at 296K 2s-1 at 296K 25s-1 at 296K true stress, N/mm² H s-1 at 296K.91s-1 at 296K 13.14s-1 at 296K 81.7s-1 at 296K σ ( ) 1 ln + n & ε T T + room σ C ε C 1 (1983) m = 1 2 & ε Tmelt Troom 22

23 Tanimura true stress, N/mm² H DC σ =.4s-1 at 296K 1s-1 at 296K 2s-1 at 296K 25s-1 at 296K true stress, N/mm² H s-1 at 296K 55.91s-1 at 296K 13.14s-1 at 296K 81.7s-1 at 296K n m & ε k ( A + B ε ) + ( C Dε ) log + ( E& ε ) (1992) & ε true stress, N/mm² H HCT6X suggested fit by steel supplier.8s-1 at 296K.91s-1 at 296K 13.14s-1 at 296K 81.7s-1 at 296K

24 One Internal Variable Models (OIVM) 6 95 true stress, N/mm² H s-1at 296K 1s-1at 296K 2s-1at 296K 25s-1at 296K s-1at 296K true stress, N/mm² H ,8s-1 at 296K,91s-1 at 296K 13,14s-1 at 296K 81,7s-1 at 296K Estrin-Mecking extended by heat effects Hybrid model extended by dislocation self organisation, two-phase description and heat effects 24

25 Identifying family parameters for OIVM HX18YD 65 HX22YD 65 HX26YD HX18YD tensile HX22YD tensile HX26YD tensile 3 HX18YD bulge 3 HX22YD bulge 3 HX26YD bulge 25 HX18YD model 25 HX22YD model 25 HX26YD model Model constants: Taylor factor M: 3 Numerical constant α:.5 Shear modulus G: 8769 MPa HX18YD, HX22YD and HX26YD by Estrin-Mecking: Burgers vector b: 2.5 x1-1 m Normalising strain rate ε : 1s -1 Material parameters to adjust: Grain size d Recovery factor k 2 Exponent n Exponent m Family parameters determined: a and b for d c and d for k 2 e and f for n g and h for m and use of yield strength for each alloy 25

26 Application of family parameters true stress, N/mm² H true stress, N/mm² H 7 HX18YD HX22YD HX26YD,4s-1 at 296K 1s-1 at 296K 2s-1 at 296K 2s-1 at 296K ,4s-1 at 296K 1s-1 at 296K 2s-1 at 296K 2s-1 at 296K true stress, N/mm² H ,4s-1 at 296K 1s-1 at 296K 2s-1 at 296K 25s-1 at 296K Family parameters determined: a and b for d c and for k 2 e and f for n g and h for m and use of yield strengths for each alloy Heat conduction parameters: Heat transfer parameter β:.18s -1 Specific heat capacity c spec : 477 Nmkg -1 K -1 Material density d dens : 78 kgm -3 Heat dissipation factor χ: 1 26

27 Other models for strain rate dependence Extended Hollomon Cowper-Symonds 1 Parameter model Bergström Zerilli-Armstrong Mechanical Threshold (MTS) 27

28 Cost assessment complete process chain Formability testing: 7 Strain rate dependence of material for one material (plus joinability testing and evt. fatigue testing) 28

29 General questions How to come from the material testing to the models of choice? How to ensure reliable FEM input data worldwide? How to deal with the customer diversification? 29

30 Potential criteria for model choice Accuracy of model prediction proved by simulating standard material tests by FEM Number of model parameters Financial efforts for the material tests to determine the model parameters Number of materials the model chosen is applicable to Modular character of model Level of commercialisation 3