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Research Papers

On the Application of Stress Triaxiality Formula for Plane Strain Fracture Testing

[+] Author and Article Information
Yuanli Bai1

Impact and Crashworthiness Laboratory, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Room 5-218, Cambridge, MA 02139byl@alum.mit.edu

Xiaoqing Teng2

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 02139

1

Corresponding author. Present address: General Electric Global Reseach Center, Room KW-C273, 1 Research Cir, Niskayuna, NY 12309.

2

Present address: HESS Corporation, Houston, TX.

J. Eng. Mater. Technol 131(2), 021002 (Mar 06, 2009) (10 pages) doi:10.1115/1.3078390 History: Received September 28, 2007; Revised November 13, 2008; Published March 06, 2009

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.

Copyright © 2009 by American Society of Mechanical Engineers
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References

Figures

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Figure 1

Three types of coordinate system in the space of principal stresses

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Figure 2

A general 3D fracture locus newly postulated by Bai and Wierzbicki (11)

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Figure 3

Necking in a round bar specimen

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Figure 4

A sketch of a flat-grooved plane strain specimen(left), and the cross section of the specimen (right)

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Figure 5

Verification and correction of Bridgman’s formula of stress triaxiality in the center of a round notch bar, after Wierzbicki and Bao (22)

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Figure 6

Finite element models of flat-grooved specimens with different groove radii

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Figure 7

Stress triaxiality versus equivalent strain in the center of flat-grooved specimens from numerical simulations

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Figure 8

Comparison of initial stress triaxialities from the analytical solution and numerical simulations

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Figure 9

1045 steel round bar specimens with different notches

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Figure 10

Force displacement response of 1045 steel smooth and notched round bar specimens

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Figure 11

Stress versus plastic strain curve of 1045 steel used in numerical simulations

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Figure 12

1045 steel plane strain flat specimens with different notches

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Figure 13

Finite element model of flat-grooved specimen, t=1.55 mm, R=3.97 mm

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Figure 14

Force displacement response of 1045 steel plane strain flat specimens with groove notch=3.97 mm

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Figure 15

Dimension of torsional tubing specimen (a) and fractured specimens (b)

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Figure 16

The torque-rotation curves of tubes under torsional loading

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Figure 17

Comparison of the fracture loci of 1045 steel measured from two groups of classical specimen in the plane of equivalent strain to fracture and initial stress triaxiality, which clearly shows the effect of the Lode angle parameter on ductile fracture locus

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Figure 18

Fracture locus of steel 1045 from numerical simulations using average stress triaxiality. The evolution of stress triaxiality for round bars (dash curves) and flat-grooved specimens (solid curves), together with the average values (squares or circles), are also plotted

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Figure 19

A comparison of fracture loci constructed on the basis of the initial stress triaxiality (direct method, solid line) and average triaxiality (inverse method, dash line)

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Figure 20

Fracture locus of DH36 steel from experimental measurements using initial stress triaxiality

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Figure 21

Fracture locus of DH36 steel from numerical simulations using average stress triaxiality. The evolution of stress triaxiality for round bars (dash curves) and flat-grooved specimens (solid curves), together with the average values (squares or circles), are also plotted.

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Figure 22

3D fracture loci of 1045 steel and DH36 steel, data from experimental measurements, assuming symmetric fracture locus (ϵ̂f(+)=ϵ̂f(−))

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