Predicting ductile failure of advanced high strength steel with shell element models

Transcription

1 Predicting ductile failure of advanced high strength steel with shell element models Keunhwan Pack 1, Christian C. Roth 2, Maysam B. Gorji 1 and Dirk Mohr 2 1 ICL - Impact and Crashworthiness Laboratory Massachusetts Institute of Technology, Cambridge MA, USA 2 MAVT - Department of Mechanical and Process Engineering, ETH Zürich, Switzerland GDIS2017

2 Fracture in Automotive Applications Shear induced fracture (Courtesy of ThyssenKrupp) FLD Bending under tension (Courtesy of US Steel) 2 Fractures on tight radii during stamping cannot be predicted by Forming Limit Diagram (FLD) Usually termed as shear fracture, presents little necking, shows slant fracture

3 Industrial Fracture Consortium PHASE I ( ) Effect of stress state on ductile fracture Multi-axial testing Plasticity modeling MMC Fracture Model PHASE II ( ) Effect of strain rate Effect of anisotropy Loading history Edge fracture HC Fracture Model PHASE III ( ) Implementation into commercial software Simplified experimental techniques Fracture model for shell elements Consortium members from automotive and steel industry: 3

4 Basic Hosford-Coulomb Model Shear localization σ N τ f Equivalent plastic strain to fracture Mohr-Coulomb τ + cσ N = k crit Lode parameter Stress triaxiality 4 [Bai & Wierzbicki, 2010] [Stoughton & Yoon, 2011] [Marcadet & Mohr, 2015] (void shape change) (void growth)

5 Basic Hosford-Coulomb Model 3D View f 2D View f plane stress plane stress f [, ] f cos 2 3 5

6 Damage Accumulation f [, ] f Example: uniaxial tension Define damage indicator d p D 0 D [, ] D 1 f (initial) (fracture) 6

7 Damage Accumulation f [, ] f Define damage indicator d p D 0 D [, ] D 1 Example: uniaxial compression followed by tension f (initial) (fracture) 7

8 Damage Accumulation f [, ] f Define damage indicator d p D 0 D [, ] D 1 Example: uniaxial compression followed by tension f (initial) (fracture) Non-linear loading path effect! 8

9 Industry-friendly Calibration Experiments Focus on simplicity and robustness of experimental technique: [Roth & Mohr, 2016] All experiments can be performed in a uniaxial testing machine Strains to fracture can be directly measured on specimen surface (no FEA needed) I. Shear test II. V-bending III. Mini-Punch 20mm 60mm 9

10 V-bending 10

11 Punch test 11

12 Basic HC Model Calibration SHEAR BENDING SHEAR PUNCH PUNCH BENDING 12 Non-linearity in loading paths is negligible!!!

13 Basic HC Model Calibration Excel program for calibration HC parameters Identified model parameters 13

14 Application of the Basic HC Model [Marcadet & Mohr, 2016] f f f DP780 DP590 TRIP780 CH PU SH CH PU NT20 NT6 SH CH PU SH NT20 NT6 NT20 NT6 a=1.47 b= c=0.008 a=1.89 b=522.2 c=0.001 a=1.29 b= c=

15 Full HC Fracture Model Hosford-Coulomb (HC) Model provides equivalent plastic strain to fracture as a function of: STRESS STATE & LOADING PATH Lode Proportional parameter Reverse & Stress orthogonal triaxiality loading ANISO TROPY Material orientation STRAIN RATE Equivalent plastic strain rate temperature SHELL ELEMENT Domain of Shell-to-Solid Equivalence 3 parameters +3 parameters +2 parameters +1 parameter [Roth & Mohr, 2014] 15

16 High strain rate testing Setup for high and intermediate strain rate testing Unfiltered (raw) exp. data [Roth et al., 2015] LOAD INVERSION DEVICE

17 High strain rate fracture experiment 17

18 Rate-dependent HC model EXPERIMENTAL RESULTS (DP780) FRACTURE MODEL [Roth & Mohr, 2014] 18 Strain to fracture increases as a function of strain rate

19 Full HC Fracture Model Hosford-Coulomb (HC) Model provides equivalent plastic strain to fracture as a function of: STRESS STATE & LOADING PATH Lode parameter Stress parameter triaxiality Stress triaxiality Proportional Reverse & orthogonal loading ANISO TROPY Material orientation STRAIN RATE Equivalent plastic strain rate temperature SHELL ELEMENT Domain of Shell-to-Solid Equivalence 3 parameters +3 parameters +2 parameters +1 parameter [Pack & Mohr, 2017] 19

20 Two structural examples Comparison between Solid vs Shell Picture removed from distributed version 20

21 Domain of Shell-to-Solid Equivalence Localized necking criterion for arbitrary loading conditions e.g. combination of bending and membrane loading Picture removed from distributed version 21

22 What if localized necking does not occur? Ductile fracture without necking Picture removed from distributed version 22

23 Structural validation #1. 2 nd Sandia Fracture Challenge [Pack & Roth, 2016] Blind prediction of crack initiation and propagation Slow loading mm/s F C A E D G B Experiment Simulation Fast loading 25.4 mm/s [Li et al., 2010] 23

24 Structural validation #2. Three point bending of hot stamped martensitic hat section [Pack & Marcadet, 2016] 24

25 Structural validation #3. Triangular cup drawing [Gorji et al., 2016] Picture removed from distributed version Picture removed from distributed version Picture removed from distributed version 25

26 Conclusions Developed HC ductile fracture model accounting for (a) stress state, (b) strain rate, (c) anisotropy, and (d) loading history Basic version of HC model requires results from three calibration experiments only All calibration experiments can be performed in a uniaxial testing frame and fracture strain is directly measured using digital image correlation Presented SHPB technique for oscillation-free measurements at intermediate and high strain rates 26 By combining the Domain of Shell-to-Solid Equivalence and HC model, ductile failure is conveniently predicted with shell finite elements

27 Research team Acknowledgements Main sponsors Picture removed from distributed version Picture removed from distributed version Picture removed from distributed version Picture removed from distributed version Tom Wierzbicki Dirk Mohr Christian Roth Maysam Gorji Picture removed from distributed version Picture removed from distributed version Picture removed from distributed version Picture removed from distributed version 27 Keunhwan Pack Colin Bonatti Rami Abi Akl Thomas Tancogne-Dejean