Research Papers: Materials and Fabrication

Consideration of a Stress-Based Criterion for Local Failure and Its Implementation in a Damage Mechanics Model

[+] Author and Article Information
Hitoshi Nakamura

Regulatory Standard and Research Department,
Secretariat of Nuclear Regulation
1-9-9, Roppongi, Minato-ku,
Tokyo 106-8450, Japan
e-mail: hitoshi_nakamura@nsr.go.jp

Contributed by the Pressure Vessel and Piping Division of ASME for publication in the JOURNAL OF PRESSURE VESSEL TECHNOLOGY. Manuscript received April 16, 2018; final manuscript received April 5, 2019; published online May 15, 2019. Assoc. Editor: San Iyer.This work was prepared while under employment by the Government of Japan as part of the official duties of the author(s) indicated above, as such copyright is owned by that Government, which reserves its own copyright under national law.

J. Pressure Vessel Technol 141(4), 041405 (May 15, 2019) (9 pages) Paper No: PVT-18-1078; doi: 10.1115/1.4043544 History: Received April 16, 2018; Revised April 05, 2019

Analyses of the notched tension tests of carbon steel show that ductile failure is initiated when the sum of flow stress and mean stress reaches the limit for the material, regardless of stress triaxiality. Therefore, this explicit critical stress condition could be a candidate criterion for local failure. An equation expressing the relation between stress triaxiality and critical strain was derived from the critical stress condition, and it was found that the critical strain diagram obtained by the equation nearly overlapped with that obtained by the conventional empirical equation. This suggests that the critical stress condition can be approximately determined if the critical strain diagram was obtained for a particular steel. The critical stress condition was consistent with the classical void nucleation theory, and the theory was incorporated into the void nucleation term of stress control in the Gurson–Tvergaard (GT) model—a well-known damage mechanics model for ductile failure. Since only the strain-controlled term is used in the recent GT model, herein, a finite element method (FEM) code was newly developed to implement the GT model with the stress-controlled term. Notched tension tests were analyzed with the critical stress condition using the developed code, and the analyses reproduced the failure behaviors and critical strains of the tests considerably well. These results strongly support the practicality of the stress-based criterion and demonstrate that ductile failure could be appropriately predicted by combining the GT model using the void nucleation term of stress control with the critical stress condition.

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ASME, 2015, “ ASME Boiler & Pressure Vessel Code, Section III, Division 1-Subsection NE, Article NE-3213.8 Primary stress,” The American Society of Mechanical Engineers, New York.
U.S. Nuclear Regulatory Commission, 2000, “ Design, Instrumentation, and Testing of a Steel Containment Vessel Model,” Sandia National Laboratories, Livermore, CA, Report No. NUREG/CR-5679,SAND 98-2701.
U.S. Nuclear Regulatory Commission, 2006, “ Containment Integrity Research at Sandia National Laboratories,” Sandia National Laboratories, Livermore, CA, Report No. NUREG/CR-6906,SAND2006-2274P.
ASME, 2015, “ ASME Boiler & Pressure Vessel Code, Section VIII, Division 2 Alternative Rules, Article 5.3 Protection Against Local Failure,” The American Society of Mechanical Engineers, New York.
Connelly, F. M. , and Davis, E. A. , 1959, “ Stress Distribution and Plastic Deformation in Rotating Cylinders of Strain-Hardening Material,” ASME J. Appl. Mech., pp. 25–30.
Hancock, J. W. , and Mackenzie, S. C. , 1976, “ On the Mechanisms of Ductile Failure in High-Strength Steel Subjected to Multi-Axial Stress-States,” J. Mech. Phys. Solid, 24(2–3), pp. 147–169. [CrossRef]
Manjoine, M. J. , 1982, “ Creep-Rapture Behavior of Weldments,” Weld. Res. Suppl., pp. 50S–57S.
Otsuka, A. , Miyata, T. , Sakurai, T. , and Iida, H. , 1985, “ Effect of Stress Triaxiality on Ductile Fracture,” J. Soc. Mater. Sci., Jpn., 34(381), pp. 622–626. [CrossRef]
Dameron, R. A. , Dunham, R. S. , Rashid, Y. R. , and Tang, H. T. , 1991, “ Conclusions of the EPRI Concrete Containment Research Program,” Nucl. Eng. Des., 125(1), pp. 41–55. [CrossRef]
Bridgman, P. W. , 1952, Studies in Large Plastic Flow and Fracture, Mc-GRAWHill, New York, pp. 9–37.
Enami, K. , and Nagai, H. , 2005, “ Evaluation of Plastic Deformation Limit by Circumferentially Notched Tension Test,” Tetsu-to-Hagane, 91(2), pp. 285–291. [CrossRef]
Argon, A. S. , IM, J. , and Needleman, A. , 1975, “ Distribution of Plastic Strain and Negative Pressure in Necked Steel and Copper Bars,” Metall. Trans. A, 6A, pp. 815–824. [CrossRef]
Tsuchida, N. , Inoue, T. , and K, E. , 2012, “ Estimations of the True Stress and True Strain Until Just Before Fracture by the Stepwise Tensile Test and Bridgman Equation for Various Metals and Alloys,” Mater. Trans., 53(1), pp. 133–139. [CrossRef]
Yoshinari, H. , Enami, K. , Koseki, T. , and Shimanuki, H. , 2001, “ Ductile and Brittle Fracture Initiation Behavior for Compressively Prestrained Steel,” Conference Proceedings the Society of Naval Architects of Japan, Tokyo, Japan, pp. 559–567.
Enami, K. , and Yoshinari, H. , 2002, “ On the Mechanics of Ductility-Decreasing of Compressively Prestrained Steel,” The Society of Naval Architects of Japan, Kure, Japan, pp. 493–498.
Argon, A. S. , IM, J. , and Safoglu, R. , 1975, “ Cavity Formation From Inclusions in Ductile Fracture,” Metall. Trans., 6(4), pp. 825–837. [CrossRef]
Gurson, A. L. , 1977, “ Continuum Theory of Ductile Rupture by Void Nucleation and Growth—Part 1: Yield Criteria and Flow Rules for Porous Ductile Media,” ASME J. Eng. Mater. Technol., 99(1), pp. 2–15. [CrossRef]
Chu, C. C. , and Needleman, A. , 1980, “ Void Nucleation Effects in Biaxially Stretched Sheets,” ASME J. Eng. Mater. Technol., 102(3), pp. 249–256. [CrossRef]
Tvergaard, V. , 1982, “ On Localization in Ductile Materials Containing Spherical Voids,” Int. J. Fract., 18(4), pp. 237–252.
Tvergaard, V. , 1990, “ Material Failure by Void Growth to Coalescence,” Adv. Appl. Mech., 27, pp. 83–151. [CrossRef]
Tvergaard, V. , and Needleman, A. , 1984, “ Analysis of the Cup-Cone Fracture in a Round Tensile Bar,” Acta Metal, 32(1), pp. 157–169. [CrossRef]
Oh, C.-S. , Kim, N.-H. , Kim, Y.-J. , Baek, J.-H. , Kim, Y.-P. , and Kim, W.-S. , 2011, “ A Finite Element Ductile Failure Simulation Method Using Stress-Modified Fracture Strain Model,” Eng. Fract. Mech., 78(1), pp. 124–137. [CrossRef]
Kami, A. , Dariani, B. M. , Sadough Vanini, A. , Comsa, D. S. , and Banabic, D. , 2015, “ Numerical Determination of the Forming Limit Curves of Anisotropic Sheet Metals Using GTN Damage Model,” J. Mater. Process. Technol., 216, pp. 472–483. [CrossRef]
Kikuchi, M. , and Takahashi, A. , 2001, “ Dimple Fracture Simulation Under Differenr Loading Conditions,” Jpn. Soc. Mech. Eng. A, 67(656), pp. 665–671. [CrossRef]
Dassault Systèmes, 2016, “ SIMULIA User Assistance 2017, Abaqus,” Dassault Systèmes, Vélizy-Villacoublay, France.
ITOCHU Techno-Solutinos Corporation, 2017, “ FINAS/STAR Version2015r170210, User Manual,” ITOCHU Techno-Solutions Corporation, Tokyo, Japan.
Argon, A. S. , and IM, J. , 1975, “ Separation of Second Phase Particles in Spheroidized 1045 Steel, Cu-0.6Pct Cr. Alloy, and Maraging Steel in Plastic Straining,” Metall. Trans. A, 6A, pp. 839–851. [CrossRef]
Needleman, A. , and Rice, J. R. , 1978, “ Limits to Ductility Set by Plastic Flow Location,” Mech. Sheet Met. Forming, pp. 237–267.
Tvergaard, V. , 1981, “ Influence of Voids on Shear Band Instability Under Plane Strain Conditions,” Int. J. Fract., 17(4), pp. 389–407. [CrossRef]
Murakami, S. , 2008, “ Constitutive Equations for Ductile Damage of Void Materials,” Continuum Damage Mechanics (Japanese), Morikita Publishing Co., Ltd., Tokyo, Japan.
Hughes, T. J. , 1980, “ Generalization of Selective Integration Procedures to Anisotropic and Nonlinear Media,” Int. J. Numer. Methods Eng., 15(9), pp. 1413–1418. [CrossRef]
Enami, K. , Hagiwara, Y. , and Mimura, H. , 2004, “ Assessment Method of Ductile and Brittle Fracture Initiation in High Strength Steels,” J. Soc. Nav. Archit. Jpn., 195, pp. 263–270. [CrossRef]
Shimanuki, H. , Inoue, T. , and Toyoda, M. , 1999, “ Effect of Stress Triaxiality and Strain Rate on Ductile Fracture Initiation in Steel,” The Society of Naval Architects of Japan, Nagasaki, Japan, pp. 475–483.
Anderson, T. L. , 2011, “ Ductile Fracture,” Fracture Mechanics: Fundamentals and Application, 3rd ed., Morikita Publishing Co., Ltd., Tokyo, p. 234 (Japanese).
Fujita, M. , Kawabe, Y. , and Nishimoto, N. , 1977, “ Role of Oxide and Sulfide Particles on Charpy Impact Properties in 10Ni-8Co Alloy Steels,” Tetsu to Hagane, 63(10), pp. 1709–17018. [CrossRef]
Franklin, A. , 1969, “ Comparison Between a Quantitative Microscope and Chemical Methods for Assessment of Non‐Metallic Inclusions,” J. Iron Steel Inst., 207, pp. 181–186.


Grahic Jump Location
Fig. 1

Circumferentially notched tension specimen of the test by Enami and Nagai [11]

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Fig. 2

Schematic of circumferentially notched tension specimen used in Bridgman's equation [10]

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Fig. 3

The true stress and true strain curves of various notched tension tests by Enami and Nagai [11]

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Fig. 4

FE meshes for circumferentially notched tension specimens: (a) specimen of the initial notch radius of 15 mm and (b) specimen of the initial notch radius of 2 mm

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Fig. 5

Comparison between FE analyses and experiments: diagram of tensile load and diameter of the notched section

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Fig. 6

Comparison between FE analyses and experiments: diagram of true stress and true strain

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Fig. 7

Transitions of void volume fraction on notch section right before and after the initiation of failure: (a) the specimen of R0 = 15 mm and (b) the specimen of R0 = 2 mm

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Fig. 8

Comparison between the critical strain diagrams derived from the stress-based criterion and the experimental curve



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