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Predicting fracture at non-isothermal forming conditions: A temperature dependent extension of the LS-DYNA GISSMO fracture indicator framework

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Abstract

Hot stamping processes are becoming increasingly important in the manufacturing of sheet metal parts for body-in-white applications. However, the non-isothermal nature of these processes leads to challenges in evaluating the forming limits, since established methods such as Forming Limit Curves (FLC) only allow the assessment of critical forming strains for steady temperatures. For this reason, a temperature-dependent extension of the well-established GISSMO fracture indicator framework is developed by the authors to predict forming failures under non-isothermal conditions. In this paper, the general approach to combining several isothermal FLCs within the temperature-extended GISSMO model into a temperature-dependent forming limit surface is investigated. The general capabilities of the model are tested in a coupled thermo-mechanical FEA and compared with state-of-the-art evaluation methods.
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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, 342373. 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, 841875. 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, 841875. 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, 21032118. 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, 342373. 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 541547
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, 841875. 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
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