Comparative study of analytical expressions for the modelling of stainless steel behaviour. Real, E., Arrayago, I., Mirambell, E. and Westeel, R.

Transcription

1 Comparative tdy of analytical expreion for the modelling of tainle teel behavior Real, E., Arrayago, I., Mirambell, E. and Weteel, R. Forth International Expert Seminar Acot, UK 6-7 December 212

2 2/22 1. INTRODUCTION Stainle teel: nonlinear tre-train behavior decribed by analytical material model. Different material model baed on Ramberg-Ogood expreion:.2 E Material model e parameter (E,, n, ) fitting experimental tet. n Parameter obtainment: - Experimental data - Standard - table - expreion Different vale: for different material model Standard: table and analytical expreion for different tainle teel grade

3 3/22 1. INTRODUCTION Reearch ignificance: obtain the main parameter for each material model compare different material model, determine bet approach The aim of thi paper i 1.- to preent a program which provide (from the experimental data): the mechanical propertie the nonlinear coefficient which better fit different material model 2.- to analyze the difference between crrent material model to: determine the mot appropriate approach gget ome expreion for the material parameter

4 4/22 2. EXISTING MATERIAL MODELS Material Model Definition Parameter One tage model Ramberg-Ogood p to % proof tre E,, n Mirambell -Real p to ltimate train E,, n,, * p, m Two tage model Ramen p to ltimate train E,, p Gardner p to 1% train E,, n -, 1., * p1., n -1. Qach p to ltimate train E,, n - Three tage model Hradil et al. p to ltimate train E,, n -, 1., * p1., n -1.,, * p, n 1.-

5 5/22 2. EXISTING MATERIAL MODELS EN , Annex C.2 E E n m for for E 2 GPa for atenitic and atenitic-ferritic exclding , , (195 GPa) 22 GPa for ferritic σ and σ Table 2.1 n ln 2 n ln.1 or Table 4.1 m m 1 3.5

6 6/22 3. TEST DATA 42 tainle teel tre-train crve Atenitic grade: (12 copon) (5 copon) (5 copon) (2 copon) Ferritic grade: 1.43 (3 copon) (6 copon) (6 copon) (3 copon) Stre Strain All copon were annealed and teted in rolling direction

7 7/22 4. DEVELOPED PROGRAM From any experimental tre-train crve throgh Office Excel heet with atomatic procee (VBA modle) Material propertie: E, σ, σ, ε, etc. Optimized nonlinear parameter n, m

8 8/22 4. DEVELOPED PROGRAM Material parameter obtainment: ÍNDICE - Yong modl determination: linear regreion Repreentative vale of E : importance of the elected et of point (MPa) 25 (MPa) Nonlinear branch 1 5 Conidered firt point 1,E+ 5,E-5 1,E-4 1,5E-4 Initial experimental data diperion,e+ 1,E-3 2,E-3 3,E-3 Importance and effect of the conidered lat point

9 9/22 4. DEVELOPED PROGRAM Material parameter obtainment: ÍNDICE - Yong modl determination - Simple calclation of the proof tree From E σ.1, σ, σ 1. σ E E Peqeño ajte

10 1/22 4. DEVELOPED PROGRAM Stre (MPa) Material parameter obtainment Nonlinear parameter optimization: Leat qare adjtment: minimizing the error between crve Error definition: e 2 i A C i min ka Error definition m( i ) ( k ).1 2 i k P model (σ) e(conidered) e(common) P(σ ) nearet to P(σ) P(σ) Analytical model Experimental Analytical model Experimental crve Strain (mm/mm)

11 1/22 4. DEVELOPED PROGRAM Stre (MPa) Material parameter obtainment Nonlinear parameter optimization: Leat qare adjtment: minimizing the error between crve Error definition: e 2 i A C i min ka Error definition m( i ) ( k ).1 2 i k P model (σ) e(conidered) e(common) P(σ ) nearet to P(σ) P(σ) Analytical model Experimental Analytical model Experimental crve Strain (mm/mm)

12 11/22 4. DEVELOPED PROGRAM Stre (MPa) Initial tre-train data: Ferritic 1.459: experimental data Program otpt: Strain (mm/mm) Tet: material parameter MPa E MPa.5 33 MPa.1 32 MPa 17.6% 331 MPa MPa MPa

13 12/22 4. DEVELOPED PROGRAM Program otpt: Modelling: nonlinear parameter Ramberg-Ogood Mirambell-Real Ramen Gardner Hradil et al. n n n n n m 1.75 m 1.73 n n n E E E E E E Optimized for train p to % Optimized for train p to 1% Optimized for train p to 5%

14 13/22 4. DEVELOPED PROGRAM Program otpt: (MPa) Material model comparion Ferritic grade Tet (corrected) Ramberg-Ogood 15. Mirambell-Real 1. Ramen EN Gardner Three-tage..E+ 2.E-3 4.E-3 6.E-3 8.E-3 1.E-2

15 (MPa) 13/22 4. DEVELOPED PROGRAM Program otpt: 425. Material model comparion Ferritic grade Tet (corrected) Ramberg-Ogood Mirambell-Real 35. Ramen EN Gardner Three-tage 325..E+ 1.E-2 2.E-2 3.E-2 4.E-2 5.E-2

16 14/22 5. ANALYSIS OF RESULTS Nonlinear parameter from different material model are very imilar Conidering Ramen model : need only 3 parameter ε=f(σ) expreion i imilar to EN , Annex C Good agreement to experimental data for train p to 1%

17 14/22 5. ANALYSIS OF RESULTS Nonlinear parameter from different material model are very imilar Conidering Ramen model: need only 3 parameter ε=f(σ) expreion i imilar to EN , Annex C Good agreement to experimental data for train p to 1% Nonlinear parameter fitted from Ramen material model are conidered Analyi: - accracy of the claical expreion for n - applicability of σ /σ expreion to ferritic tainle teel - accracy of the original expreion for m

18 15/22 5. ANALYSIS OF RESULTS Stre (MPa) Nonlinear parameter n definition Experimental Strain (mm/mm)

19 15/22 5. ANALYSIS OF RESULTS Stre (MPa) Nonlinear parameter n definition claical expreion σ,2 ln 2 n ln σ,1.1 Experimental Strain (mm/mm)

20 15/22 5. ANALYSIS OF RESULTS Stre (MPa) 4 35 Nonlinear parameter n definition claical expreion n ln 2 ln Experimental n=1 (original expreion) Strain (mm/mm)

21 15/22 5. ANALYSIS OF RESULTS Stre (MPa) 4 Nonlinear parameter n definition new propoal σ,5 σ,2 n ln ln Experimental Strain (mm/mm)

22 15/22 5. ANALYSIS OF RESULTS Stre (MPa) 4 35 Nonlinear parameter n definition new propoal n ln ln Experimental n=1.7 (new propoal) Strain (mm/mm)

23 Ferritic Nonlinear parameter n Atenitic Nonlinear parameter n 16/22 5. ANALYSIS OF RESULTS Ditribtion of nonlinear parameter n Optimized Original expreion Propoal

24 Ferritic Atenitic 17/22 5. ANALYSIS OF RESULTS σ /σ 1. Ditribtion of σ /σ parameter Experimental.75 Original expreion for atenitic Original expreion for all alloy.5 5 σ /σ E 185 E 1.375(n 5) for atenitic and dplex for all alloy

25 18/22 5. ANALYSIS OF RESULTS Ditribtion of σ /σ parameter for Ferritic Stainle Steel σ /σ y = x Experimental ferritic σ /E 185 E (n 5) Original expreion E Propoal linear expreion

26 18/22 5. ANALYSIS OF RESULTS Ditribtion of σ /σ parameter for Ferritic Stainle Steel σ /σ Experimental Original expreion for atenitic Original expreion for all alloy Propoal E (n 5) Original expreion E Propoal linear expreion

27 Stre (MPa) 19/22 5. ANALYSIS OF RESULTS Original expreion: m Nonlinear parameter m Strain (mm/mm) m=3.5 (original expreion) m=1.71 (experimental vale) Experimental

28 Stre (MPa) 19/22 5. ANALYSIS OF RESULTS Original expreion: m Nonlinear parameter m m=3.5 (original expreion) m=1.71 (experimental vale) Experimental Strain (mm/mm) New propoal: m m 1 Atenitic Ferritic

29 Atenitic Ferritic 2/22 5. ANALYSIS OF RESULTS Nonlinear parameter m Nonlinear parameter m Ditribtion of nonlinear parameter m Optimized Original expreion Propoal

30 21/22 6. CONCLUSIONS Parameter propoed in EN are not accrate enogh. Optimized nonlinear parameter: imilar relt for all analyzed material model. new expreion for determining n and m are propoed. m ln n ln for atenitic 4.5 New linear approximation for σ /σ for ferritic tainle teel i alo propoed. 185 E E m 1 for atenitic for ferritic for ferritic

31 22/22 7. FUTURE WORK New propoal obtained from a limited nmber of tet data. Frther reearch in order to: adjt the new propoal extend their applicability to cold-formed tainle teel

32 Comparative tdy of analytical expreion for the modelling of tainle teel behavior Real, E., Arrayago, I., Mirambell, E. and Weteel, R. Forth International Expert Seminar Acot, UK 6-7 December 212

33 .1 ln 2 ln n.5 ln 4 ln n m m 1 m E E 185 EN , Annex C Propoal for atenitic and dplex tainle teel 5).375(n 1 E 185 E 185 for all alloy for atenitic for ferritic for atenitic for ferritic for for m n E.2 E