Research Papers

An Exploration Toward a Unified Failure Criterion

[+] Author and Article Information
S. Xiao

State Key Laboratory of Optoelectronic
Materials and Technologies,
School of Physics,
Sun Yat-sen University,
Guangzhou 510275, China
e-mail: xiaos6@mail.sysu.edu.cn

B. Liu

Department of Engineering Mechanics,
Tsinghua University,
Beijing 100084, China
e-mail: liubin@tsinghua.edu.cn

Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received October 23, 2016; final manuscript received November 29, 2016; published online January 12, 2017. Editor: Yonggang Huang.

J. Appl. Mech 84(3), 031004 (Jan 12, 2017) (9 pages) Paper No: JAM-16-1517; doi: 10.1115/1.4035366 History: Received October 23, 2016; Revised November 29, 2016

For components with different defects, selecting a proper criterion to predict their failure is very important, but sometimes this brings confusion to engineers. In this paper, we explore to establish a unified failure criterion for defects with various geometries. First, a fundamental and universal law on failure that all criteria should follow, so-called the zeroth law of failure, is introduced, and the failure is completely governed by the local status of failure determining zone (FDZ), such as the stress distribution, material properties, and geometrical features. Failure criteria lacking a local dimension parameter within FDZ may have limited applicability, such as the traditional strength and fracture criteria. We choose the blunt V-notch as an example to demonstrate how to establish a unified failure criterion for quasi-brittle materials, and a series of experiments are carried out to verify its applicability. The proposed unified failure criterion and some existing failure criteria are also discussed and compared. The failure criteria that only include a single critical constant are incapable of reflecting the whole stress field information and local geometrical features of the FDZ. Our proposed unified failure criterion is expressed with a two-parameter function and has a wider applicability.

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Fig. 1

Schematic of an infinite body containing a long hole

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Fig. 2

Schematics of two different components with defects

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Fig. 3

Schematics of two similar plates with different-sized central circular holes subjected to uniaxial tensions

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Fig. 4

Schematics of (a) a larger circular hole and (b) a smaller circular hole with the failure determining zones

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Fig. 5

Two similar holed atomic plate models composed of discrete atoms

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Fig. 6

Failure loadings of a series of similar atomic models from simulations

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Fig. 7

Schematics of two cracklike defects with the same length but different root radii

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Fig. 8

Atomic models with cracks by removing (a) one layer of atoms and (b) three layers of atoms

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Fig. 9

Atomic models with different-sized cracklike defects but the same root radii

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Fig. 10

Simulation results on the nominal critical stress intensity factors of different models

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Fig. 11

Schematic of a component with a blunt V-notch subjected to tension

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Fig. 12

Stress contours of components (a) with a longer notch under tension, (b) with a shorter notch under tension, and (c) with a shorter notch under bending

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Fig. 13

Simulation results of the stress distributions along the symmetrical plane for models with (a) different notch depth and (b) different overall size

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Fig. 16

A standard tensile specimen (a) before and (b) after uniaxial tension

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Fig. 17

(a) Schematic and (b) photograph of a V-notched specimen

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Fig. 18

The critical stress value σmaxc from the tensile tests on different V-notched specimens

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Fig. 19

Schematic of a failure surface in the space of (ρ,α,σmaxc) representing the unified failure criterion

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Fig. 20

Schematic of the point method

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Fig. 21

Two FEM models with different notch shapes

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Fig. 22

Schematic of the line method

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Fig. 23

Schematic of the imaginary crack method

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Fig. 24

Schematics of two notched models with the same notch depth but different notch root radii




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