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39th IDDRG ANNUAL CONFERENCE, virtual l October 26-30, 2020
A TEMPERATURE DEPENDENT EXTENSION OF THE LS-DYNA GISSMO
FRACTURE INDICATOR FRAMEWORK
NON-ISOTHERMAL FORMING CONDITIONS
PREDICTING FRACTURE AT
Alan A. Camberg1, Tobias Erhart2, Thomas Tröster1
MOTIVATION: Ductile failure prediction at non-isothermal forming conditions.
PREDICTING FRACTURE
AT NON-ISOTHERMAL FORMING CONDITIONS
Predicting fracture at non-isothermal forming conditions: A temperature dependent extension of LS-DYNA GISSMO fracture indicator framework | IDDRG 2020 2
▪Hot stamping of aluminum alloys:
Mohamed et al. (2018)
Camberg et al. (2018)
▪Flash Forming Process for SPD aluminum sheets:
Common industrial simulation approach:
•Non-isothermal plasticity model
•Non-isothermal stamping simulation
•Post-processing failure evaluation
▪Isothermal worst-case FLC (PHS ~ 700 °C)
▪or critical thinning (~ 20 %)
▪Press hardening of boron steels:
Karabasian & Tekkaya (2010)
Jocham et al. (2014)
STATE OF THE ART: Ductile failure prediction at non-isothermal conditions.
Predicting fracture at non-isothermal forming conditions: A temperature dependent extension of LS-DYNA GISSMO fracture indicator framework | IDDRG 2020 3
PREDICTING FRACTURE
AT NON-ISOTHERMAL FORMING CONDITIONS
FLCs at multiple elevated temperatures are often available from
experimental tests or theoretical plastic instability models
Abedrabbo et al. (2006) Int J Plast 22, 342–373. doi:10.1016/j.ijplas.2005.03.006
Formability evaluation with only one “worst-case” FLC:
Temperature gradients are relevant, even for warm forming:
But which FLC is the “worst-case” and how to make
use of the information of multiple FLCs?
STATE OF THE ART: Ductile failure prediction at non-isothermal conditions.
Predicting fracture at non-isothermal forming conditions: A temperature dependent extension of LS-DYNA GISSMO fracture indicator framework | IDDRG 2020 4
PREDICTING FRACTURE
AT NON-ISOTHERMAL FORMING CONDITIONS
Theoretical FLC models like M-K or MMFC with
temperature dependency in differential form
Krauer & Hora (2011) eMMFC with temperature dependencyCui et al. (2015) temperature dependent 3D FLC
Combination of several isothermal FLC at different
temperatures to a temperature dependent 3D FLC
►Neglection of non-linear strain and non-constant temperature paths of the
material during hot stamping → elements pre-strained at higher temperatures can
be evaluated as “failed” just by cooling down
►For most industrial applications “too complex”,
experimental data cannot be used directly, model calibration
necessary, user subroutines
STATE OF THE ART: Ductile failure prediction at non-isothermal conditions.
Predicting fracture at non-isothermal forming conditions: A temperature dependent extension of LS-DYNA GISSMO fracture indicator framework | IDDRG 2020 5
PREDICTING FRACTURE
AT NON-ISOTHERMAL FORMING CONDITIONS
Johnson-Cook (1983) fracture initiation model:
Buyuk (2013) –a general tabulated form of the J-C model:
Stress-state invariant
temperature scaling
Predicting fracture at non-isothermal forming conditions: A temperature dependent extension of LS-DYNA GISSMO fracture indicator framework | IDDRG 2020 6
PREDICTING FRACTURE
AT NON-ISOTHERMAL FORMING CONDITIONS
GOAL: Implementation of a generalized temperature dependent fracture indicator framework.
Considering multiple isothermal FLCs at
elevated temperatures with arbitrary
characteristics
Incremental evaluation to consider
non-linear strain and non-constant
temperature paths
Accessing a generalized stress state and
temperature dependent fracture framework
APPROACH: A generalized temperature dependent fracture framework.
Predicting fracture at non-isothermal forming conditions: A temperature dependent extension of LS-DYNA GISSMO fracture indicator framework | IDDRG 2020 7
GISSMO: Generalized Incremental Stress State Dependent Failure Model
▪Damage accumulation, arbitrarily selectable damage exponent:
▪Instability measure accumulation:
▪Stress tensor degradation, arbitrarily selectable fading exponent:
Fracture
Coupling of damage to stress tensor
“T-GISSMO”: Generalized Incremental Stress State and Temp. Dependent Failure Model
▪Damage accumulation, arbitrarily selectable damage exponent:
▪Instability measure accumulation:
▪Stress tensor degradation, arbitrarily selectable fading exponent:
Fracture
Coupling of damage to stress tensor
, temperature dependency
*The damage exponent DMGEXP as well as the fading exponent FADEXP, are assumed to be
temperature independent
PREDICTING FRACTURE
AT NON-ISOTHERMAL FORMING CONDITIONS
Predicting fracture at non-isothermal forming conditions: A temperature dependent extension of LS-DYNA GISSMO fracture indicator framework | IDDRG 2020 8
PREDICTING FRACTURE
AT NON-ISOTHERMAL FORMING CONDITIONS
Multiple isothermal FLCs
APPROACH: Implementation of a generalized temperature dependent fracture framework.
Multiple isothermal fracture
curves
FORMABILITY STUDY: Comparative assessment between three different approaches.
Predicting fracture at non-isothermal forming conditions: A temperature dependent extension of LS-DYNA GISSMO fracture indicator framework | IDDRG 2020 9
PREDICTING FRACTURE
AT NON-ISOTHERMAL FORMING CONDITIONS
Comparison between:
Temperature-dependent 3D-FLD
Starting point:
►various isothermal FLCs at different elevated
temperatures (theoretical or experimental)
JC-like approach
GISSMO with temp. dependency
FORMABILITY STUDY: Non-isothermal stamping of EN-AW 5182-O, initial blank temperature 260 °C.
Predicting fracture at non-isothermal forming conditions: A temperature dependent extension of LS-DYNA GISSMO fracture indicator framework | IDDRG 2020 10
PREDICTING FRACTURE
AT NON-ISOTHERMAL FORMING CONDITIONS
FORMABILITY STUDY: Temperature and strain rate dependent hardening + temperature dependent Barlat89 .
Predicting fracture at non-isothermal forming conditions: A temperature dependent extension of LS-DYNA GISSMO fracture indicator framework | IDDRG 2020 11
PREDICTING FRACTURE
AT NON-ISOTHERMAL FORMING CONDITIONS
Implemented using LS-DYNA standard material model library: *MAT_036, HR = 9
Material data adapted from Abedrabbo et al. (2007) Int J of Plast 23, 841–875. doi:10.1016/j.ijplas.2006.10.005
FORMABILITY STUDY: Temperature and strain rate dependent hardening + temperature dependent Barlat89 .
Predicting fracture at non-isothermal forming conditions: A temperature dependent extension of LS-DYNA GISSMO fracture indicator framework | IDDRG 2020 12
PREDICTING FRACTURE
AT NON-ISOTHERMAL FORMING CONDITIONS
The thermal extension of GISSMO presented in this work is available in: LS-DYNA R11.1.0 (R11.139588)
Material data adapted from: Abedrabbo et al. (2007) Int J of Plast 23, 841–875. doi:10.1016/j.ijplas.2006.10.005, Rahmaan et al. (2015) EPJ Web Conf 94. doi:10.1051/epjconf/20159401033
Transformation from the principal strain space to
the mixed strain-stress space:
Strain ratio:
Triaxiality:
Equivalent
plastic strain:
+
adapted from Rahmaan et al. (2015)
and scaled in a JC-like manner
FORMABILITY STUDY: 3D FLD evaluation.
Predicting fracture at non-isothermal forming conditions: A temperature dependent extension of LS-DYNA GISSMO fracture indicator framework | IDDRG 2020 13
PREDICTING FRACTURE
AT NON-ISOTHERMAL FORMING CONDITIONS
Critical drawing depth: 20 mm
Critical element
FORMABILITY STUDY: 3D FLD evaluation.
Predicting fracture at non-isothermal forming conditions: A temperature dependent extension of LS-DYNA GISSMO fracture indicator framework | IDDRG 2020 14
PREDICTING FRACTURE
AT NON-ISOTHERMAL FORMING CONDITIONS
FORMABILITY STUDY: Johnson-Cook like evaluation.
Predicting fracture at non-isothermal forming conditions: A temperature dependent extension of LS-DYNA GISSMO fracture indicator framework | IDDRG 2020 15
PREDICTING FRACTURE
AT NON-ISOTHERMAL FORMING CONDITIONS
Critical drawing depth: 25 mm
Critical element
D = 1
FORMABILITY STUDY: Johnson-Cook like evaluation.
Predicting fracture at non-isothermal forming conditions: A temperature dependent extension of LS-DYNA GISSMO fracture indicator framework | IDDRG 2020 16
PREDICTING FRACTURE
AT NON-ISOTHERMAL FORMING CONDITIONS
FORMABILITY STUDY: GISSMO with temperature dependency.
Predicting fracture at non-isothermal forming conditions: A temperature dependent extension of LS-DYNA GISSMO fracture indicator framework | IDDRG 2020 17
PREDICTING FRACTURE
AT NON-ISOTHERMAL FORMING CONDITIONS
Critical drawing depth: 24 mm
Critical element
D = 1
FORMABILITY STUDY: GISSMO with temperature dependency.
Predicting fracture at non-isothermal forming conditions: A temperature dependent extension of LS-DYNA GISSMO fracture indicator framework | IDDRG 2020 18
PREDICTING FRACTURE
AT NON-ISOTHERMAL FORMING CONDITIONS
FORMABILITY STUDY: Comparison of evaluation approaches.
Predicting fracture at non-isothermal forming conditions: A temperature dependent extension of LS-DYNA GISSMO fracture indicator framework | IDDRG 2020 19
PREDICTING FRACTURE
AT NON-ISOTHERMAL FORMING CONDITIONS
Critical drawing depth 3D FLD approach: 20 mm J-C approach: 25 mm GISSMO: 24 mm
∆- + 25% + 20%
FORMABILITY STUDY: Johnson-Cook like approach vs. GISSMO with temperature dependency.
Predicting fracture at non-isothermal forming conditions: A temperature dependent extension of LS-DYNA GISSMO fracture indicator framework | IDDRG 2020 20
PREDICTING FRACTURE
AT NON-ISOTHERMAL FORMING CONDITIONS
JC-like approach:
stress state-invariant temperature
scaling
GISSMO with temp. dependency:
Arbitrary stress state-dependent
temperature scaling
(tabulated input)
Comparison: Temperature-invariant FLC scaling (JC-like) vs. actual temperature dependent FLC.
Predicting fracture at non-isothermal forming conditions: A temperature dependent extension of LS-DYNA GISSMO fracture indicator framework | IDDRG 2020 21
PREDICTING FRACTURE
AT NON-ISOTHERMAL FORMING CONDITIONS
►In the sheet metal forming relevant “biaxial valley”, the difference between a JC-like FLC and the
actual temperature dependent 3D-FLC ranges up to
for the exemplary investigated material
CONCULISONS & OUTLOOK.
Predicting fracture at non-isothermal forming conditions: A temperature dependent extension of LS-DYNA GISSMO fracture indicator framework | IDDRG 2020 22
Temperature dependent
fracture framework
Non-isothermal
formability evaluation
Temperature dependent
yield locus
Temperature dependent
FLC data
The thermal extension of the GISSMO fracture indicator framework:
▪Allows to consider arbitrary FLCs for different temperatures
▪The FLCs can further be enhanced by temperature dependent fracture curves
▪In this way a closed fully non-isothermal evaluation of warm / hot stamping processes is possible
▪Ductile fracture characterization at several elevated temperatures is currently being performed
▪An implementation and validation with experimental data will follow
PREDICTING FRACTURE
AT NON-ISOTHERMAL FORMING CONDITIONS
Temperature and strain rate
dependent hardening rule
REFERENCES.
Predicting fracture at non-isothermal forming conditions: A temperature dependent extension of LS-DYNA GISSMO fracture indicator framework | IDDRG 2020 23
PREDICTING FRACTURE
AT NON-ISOTHERMAL FORMING CONDITIONS
Karbasian H, Tekkaya A E 2010 A review on hot stamping. Journal of Materials Processing Technology 210, 2103–2118. doi:10.1016/j.jmatprotec.2010.07.019
Mohamed M, Norman D, Petre A, Melotti F, Szegda D 2018 Advances in FEM Simulation of HFQ®AA6082 tailor welded blanks for automotive applications. IOP Conf. Series: Materials
Science and Engineering 418 012036 doi:10.1088/1757-899X/418/1/012036
Camberg A A, Bohner F, Tölle J, Schneidt A, Meiners S, Tröster T 2018 Formability enhancement of EN AW-5182 H18 aluminum alloy sheet metal parts in a flash forming process:
testing, calibration and evaluation of fracture models. IOP Conf. Series: Materials Science and Engineering 418 012018; DOI: 10.1088/1757-899X/418/1/012018
Jocham D, Sunderkötter C, Helmholz R, Marusch H E, Volk W 2014 Failure prediction in direct press hardening through virtual forming limit curves based on measurable material
properties, in: Hora, P. (Ed.), Proceedings of the 7th Forming Technology Forum, University of Twente, Faculty of Engineering Technology, Enschede
Abedrabbo N, Pourboghrat F, Carsley J, 2006 Forming of aluminum alloys at elevated temperatures –part 2: Numerical modeling and experimental verification. International Journal of
Plasticity 22, 342–373. doi:10.1016/j.ijplas.2005.03.006
Johnson G R and Cook W H 1983 A constitutive model and data for metals subjected to large strains, high strain rates and high temperatures. Proceedings of the 7th International
Symposium on Ballistics, pp 541–547
Buyuk M 2013 Development of a Tabulated Thermo-Viscoplastic Material Model with Regularized Failure for Dynamic Ductile Failure Prediction of Structures Under Impact Loading.
Dissertation, George Washington University, Ashburn
Andrade F X C, Feucht M, Haufe A, Neukamm F 2016 An incremental stress state dependent damage model for ductile failure prediction. International Journal of Fracture, 200:127-150
Abedrabbo N, Pourboghrat F, Carsley J 2007 Forming of AA5182-O and AA5754-O at elevated temperatures using coupled thermo-mechanical finite element models. International
Journal of Plasticity 23, 841–875. doi:10.1016/j.ijplas.2006.10.005
Barlat F, Lian K, 1989 Plastic behavior and stretchability of sheet metals. part I: A yield function for orthotropic sheets under plane stress conditions. International Journal of Plasticity 5, 51–
66. doi:10.1016/0749-6419(89)90019-3.
Rahmaan T, Butcher C, Abedini A, Worswick M 2015 Effect of strain rate on shear properties and fracture characteristics of DP600 and AA5182-O sheet metal alloys. EPJ Web of
Conferences 94, 01033. doi:10.1051/epjconf/20159401033
THANK YOU FOR
YOUR ATTENTION!
Alan A. Camberg
Paderborn University
Faculty of Mechanical Engineering
Insititute of Lightweight Design with Hybrid Systems (ILH)
Chair of Automotive Lightweight Design (LiA)
alan.camberg@uni-paderborn.de
www.leichtbau-im-automobil.de