Enhancement of Lemaitre Model to Predict Cracks at Low and Negative Triaxialities in Sheet Metal Forming

Abstract:

Advanced high strength steels are still one of the best alternatives for light weight design in the automotive industry. Due to their good performances like high strength and high energy absorption, those steel grades are excellent for body in white components. Because of their restricted ductility, which sometimes leads to the formation of cracks without or low necking during forming operations, conventional forming limit diagrams may fall short. As a remedy, an enhanced variant of the Lemaitre continuum mechanical damage model (CDM) is presented in this work.Previous model extensions of the Lemaitre model improved the damage prediction for the shear and compression dominated stress states by introducing an additional weighting factor for the influence of compression on damage evolution, the so called crack closure parameter h. However, the possible range of the fracture behavior predicted by such models for low and negative stress triaxialities is limited. In this work, the Lemaitre CDM has been enhanced by considering the maximal shear stress to predict the fracture occurrence under shear. Previous models for the effect of void closure on damage evolution are reviewed and a novel model enhancement taking into account the maximal shear stresses is described. The determination of the damage model parameters is presented for a dual phase steel. For this particular material, the response of model enhancement on the failure prediction is discussed for a test part.

• Periodical: Key Engineering Materials (Volume 639)
• Pages: 427-434
• DOI: https://doi.org/10.4028/www.scientific.net/KEM.639.427
• Online since: March 2015
• Authors: Kerim Isik, Maria Doig, Helmut Richter, Till Clausmeyer, A. Erman Tekkaya
• Keywords: Damage, Finite Element Method (FEM), Parameter Identification

References

[1] F.A. McClintock, A criterion of ductile fracture by growth of holes. Journal of Applied Mechanics 35 (1968), 363-371.

DOI: 10.1115/1.3601204

[2] J.R. Rice, D.M. Tracey, On the ductile enlargement of voids in triaxial stress fields. Journal of Mechanics and Physics of Solids 17 (1969), 201-217.

DOI: 10.1016/0022-5096(69)90033-7

[3] J.W. Hancock, A.C. Mackenzie, On the mechanisms of ductile failure in high-strength steels subjected to multi-axial stress-states. Journal of Mechanics and Physics of Solids 24 (1976), 147-160.

DOI: 10.1016/0022-5096(76)90024-7

[4] Y. Bao, T. Wierzbicki, On fracture locus in the equivalent strain and stress triaxiality space. International Journal of Mechanical Sciences 46 (2004), 81-98.

DOI: 10.1016/j.ijmecsci.2004.02.006

[5] B. -A. Behrens, M. Vucetic, I. Peshekhodov, Calibration of fracture initiation models for advanced high-strength sheet steels in a wide range of stress states using a uniaxial tensile testing machine. Proceedings of IDDRG 2014, Paris, France, 252-257.

[6] Y. Bai, T. Wierzbicki, Application of extended Mohr-Coulomb criterion to ductile fracture. International Journal of Fracture (2010) 161, 1-20.

DOI: 10.1007/s10704-009-9422-8

[7] K. Nahshon, J.W. Hutchinson, Modification of the Gurson model for shear failure. European Journal of Mechanics A/Solids 27 (2008), 1-17.

DOI: 10.1016/j.euromechsol.2007.08.002

[8] T. -S. Cao, J. -M. Gachet, P. Montmitonnet, P. -O. Bouchard, A Lode-dependent enhanced Lemaitre model for ductile fracture prediction at low stress triaxiality. Engineering Fracture Mechanics 124-125 (2014), 80-96.

DOI: 10.1016/j.engfracmech.2014.03.021

[9] Y. Lou, H. Huh, S. Lim, K. Pack, New ductile fracture criterion for prediction of fracture forming limit diagrams of sheet metals. International Journal of Solids and Structures 49 (2012), 3605-3615.

DOI: 10.1016/j.ijsolstr.2012.02.016

[10] J. Lemaitre, A Course on Damage Mechanics, Springer-Verlag, Berlin, (1992).

[11] K. Isik, C. Soyarslan, Continuum damage mechanics (CDM) based local approach to the sheet-bulk metal formability prediction. Advanced Materials Research 769 (2013), 205-212.

DOI: 10.4028/www.scientific.net/amr.769.205

[12] M. Doig, K. Isik, C. Soyarslan, H. Richter, A.E. Tekkaya, Towards ductile damage prediction of advance high strength steels. Tools and Forming 2013, Graz, Austria.