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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
Authority(S/NRA/R),
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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Figures

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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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