Theoretical and experimental studies have shown that stress triaxiality is the key parameter controlling the magnitude of the fracture strain. Smooth and notched round bar specimens are mostly often used to quantify the effect of stress triaxiality on ductile fracture strain. There is a mounting evidence (Bai and Wierzbicki, 2008, “A New Model of Metal Plasticity and Fracture With Pressure and Lode Dependence,” Int. J. Plast., 24(6), pp. 1071–1096) that, in addition to the stress triaxiality, the normalized third deviatoric stress invariant (equivalent to the Lode angle parameter) should also be included in characterization of ductile fracture. The calibration using round notched bars covers only a small range of possible stress states. Plane strain fracture tests provide additional important data. Following Bridgman’s stress analysis inside the necking of a plane strain specimen, a closed-form solution is derived for the stress triaxiality inside the notch of a flat-grooved plane strain specimen. The newly derived formula is verified by finite element simulations. The range of stress triaxiality in round notched bars and flat-grooved specimens is similar, but the values of the Lode angle parameter are different. These two groups of tests are therefore very useful in constructing a general 3D fracture locus. The results of experiments and numerical simulations on 1045 and DH36 steels have proved the applicability of the closed-form solution and have demonstrated the effect of the Lode angle parameter on the fracture locus.
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e-mail: byl@alum.mit.edu
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April 2009
Research Papers
On the Application of Stress Triaxiality Formula for Plane Strain Fracture Testing
Yuanli Bai,
Yuanli Bai
Impact and Crashworthiness Laboratory,
e-mail: byl@alum.mit.edu
Massachusetts Institute of Technology
, 77 Massachusetts Avenue, Room 5-218, Cambridge, MA 02139
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Xiaoqing Teng,
Xiaoqing Teng
Impact and Crashworthiness Laboratory,
Massachusetts Institute of Technology
, 77 Massachusetts Avenue, Room 5-218, Cambridge, MA 02139
Search for other works by this author on:
Tomasz Wierzbicki
Tomasz Wierzbicki
Impact and Crashworthiness Laboratory,
Massachusetts Institute of Technology
, 77 Massachusetts Avenue, Room 5-218, Cambridge, MA 02139
Search for other works by this author on:
Yuanli Bai
Impact and Crashworthiness Laboratory,
Massachusetts Institute of Technology
, 77 Massachusetts Avenue, Room 5-218, Cambridge, MA 02139e-mail: byl@alum.mit.edu
Xiaoqing Teng
Impact and Crashworthiness Laboratory,
Massachusetts Institute of Technology
, 77 Massachusetts Avenue, Room 5-218, Cambridge, MA 02139
Tomasz Wierzbicki
Impact and Crashworthiness Laboratory,
Massachusetts Institute of Technology
, 77 Massachusetts Avenue, Room 5-218, Cambridge, MA 02139J. Eng. Mater. Technol. Apr 2009, 131(2): 021002 (10 pages)
Published Online: March 6, 2009
Article history
Received:
September 28, 2007
Revised:
November 13, 2008
Published:
March 6, 2009
Citation
Bai, Y., Teng, X., and Wierzbicki, T. (March 6, 2009). "On the Application of Stress Triaxiality Formula for Plane Strain Fracture Testing." ASME. J. Eng. Mater. Technol. April 2009; 131(2): 021002. https://doi.org/10.1115/1.3078390
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