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.

Copyright © 2017 by ASME
Your Session has timed out. Please sign back in to continue.


Christensen, R. M. , 2016, “ Perspective on Materials Failure Theory and Applications,” ASME J. Appl. Mech., 83(11), p. 111001. [CrossRef]
Neuber, H. , 1958, Theory of Notch Stress, Springer, Berlin, Germany.
Novozhilov, V. , 1969, “ On a Necessary and Sufficient Condition for Brittle Strength,” Prikl. Mat. Mekh., 33(2), pp. 212–222.
Pugno, N. , and Ruoff, R. , 2004, “ Quantized Fracture Mechanics,” Philos. Mag. A, 84(27), pp. 2829–2845. [CrossRef]
Taylor, D. , 2004, “ Predicting the Fracture Strength of Ceramic Materials Using the Theory of Critical Distances,” Eng. Fract. Mech., 71(16–17), pp. 2407–2416. [CrossRef]
Lazzarin, P. , and Berto, F. , 2005, “ Some Expressions for the Strain Energy in a Finite Volume Surrounding the Root of Blunt V-Notches,” Int. J. Fract., 135(1), pp. 161–185. [CrossRef]
Cornetti, P. , Pugno, N. , Carpinteri, A. , and Taylor, D. , 2006, “ Finite Fracture Mechanics: A Coupled Stress and Energy Failure Criterion,” Eng. Fract. Mech., 73(14), pp. 2021–2033. [CrossRef]
Carpinteri, A. , Cornetti, P. , and Sapora, A. , 2011, “ Brittle Failures at Rounded V-Notches: A Finite Fracture Mechanics Approach,” Int. J. Fract., 172(1), pp. 1–8. [CrossRef]
Mohammadipour, A. , and Willam, K. , 2016, “ Lattice Approach in Continuum and Fracture Mechanics,” ASME J. Appl. Mech., 83(7), p. 071003. [CrossRef]
Seweryn, A. , 1994, “ Brittle Fracture Criterion for Structures With Sharp Notches,” Eng. Fract. Mech., 47(5), pp. 673–681. [CrossRef]
Ritchie, R. O. , Knott, J. F. , and Rice, J. R. , 1973, “ On the Relation Between Critical Tensile Stress and Fracture Toughness in Mild Steel,” J. Mech. Phys. Solids, 21(6), pp. 395–410. [CrossRef]
Taylor, D. , 2007, The Theory of Critical Distances: A New Perspective in Fracture Mechanics, Elsevier Science and Technology, London.
Leguillon, D. , 2002, “ Strength or Toughness? A Criterion for Crack Onset at a Notch,” Eur. J. Mech. Phys. A/Solids, 21(1), pp. 61–72. [CrossRef]
Taylor, D. , Cornetti, P. , and Pugno, N. , 2005, “ The Fracture Mechanics of Finite Crack Extension,” Eng. Fract. Mech., 72(7), pp. 1021–1038. [CrossRef]
Sih, G. C. , and Macdonald, B. , 1974, “ Fracture Mechanics Applied to Engineering Problems-Strain Energy Density Fracture Criterion,” Eng. Fract. Mech., 6(2), pp. 361–386. [CrossRef]
Lazzarin, P. , and Zambardi, R. , 2001, “ A Finite-Volume-Energy Based Approach to Predict the Static and Fatigue Behavior of Components With Sharp V-Shaped Notches,” Int. J. Fract., 112(3), pp. 275–298. [CrossRef]
Lazzarin, P. , and Tovo, R. , 1996, “ A Unified Approach to the Evaluation of Linear Elastic Stress Fields in the Neighborhood of Cracks and Notches,” Int. J. Fract., 78(1), pp. 3–19. [CrossRef]
Lindner, D. , Mathieu, F. , Francois, H. , Olivier, A. , Cuong, H.-M. , and Olivier, P.-C. , 2015, “ On the Evaluation of Stress Triaxiality Fields in a Notched Titanium Alloy Sample Via Integrated Digital Image Correlation,” ASME J. Appl. Mech., 82(7), p. 071014. [CrossRef]
Gross, R. , and Mendelson, A. , 1972, “ Plane Elastostatic Analysis of V-Notched Plates,” Int. J. Fract. Mech., 8(3), pp. 267–276. [CrossRef]
Leguillon, D. , and Yosibash, Z. , 2003, “ Crack Onset at a V-Notch. Influence of the Notch Tip Radius,” Int. J. Fract., 122(1), pp. 1–21. [CrossRef]
Gearing, B. P. , and Anand, L. , 2004, “ Notch-Sensitive Fracture of Polycarbonate,” Int. J. Solids Struct., 41(3–4), pp. 827–845. [CrossRef]
Lazzarin, P. , and Filippi, S. , 2006, “ A Generalized Stress Intensity Factor to be Applied to Rounded V-Shaped Notches,” Int. J. Solids Struct., 43(9), pp. 2461–2478. [CrossRef]
Torki, M. E. , Benzerga, A. A. , and Leblond, J.-B. , 2015, “ On Void Coalescence Under Combined Tension and Shear,” ASME J. Appl. Mech., 82(7), p. 071005. [CrossRef]
Liu, B. , Huang, Y. , Jiang, H. , Qu, S. , and Hwang, K. C. , 2004, “ The Atomic-Scale Finite Element Method,” Comput. Methods Appl. Mech. Eng., 193(17–20), pp. 1849–1864. [CrossRef]
Liu, B. , Jiang, H. , Huang, Y. , Qu, S. , Yu, M. F. , and Hwang, K. C. , 2005, “ Atomic-Scale Finite Element Method in Multiscale Computation With Applications to Carbon Nanotubes,” Phys. Rev. B, 72(3), p. 035435. [CrossRef]
Balamane, H. , Halicioglu, T. , and Tiller, W. A. , 1992, “ Comparative Study of Silicon Empirical Interatomic Potentials,” Phys. Rev. B, 46(4), pp. 2250–2079. [CrossRef]
Bolding, C. B. , and Anderson, C. H. , 1990, “ Interatomic Potential for Silicon Clusters, Crystals, and Surfaces,” Phys. Rev. B, 41(15), p. 10568. [CrossRef]
Tada, H. , Paris, P. C. , and Irwin, G. R. , 1985, The Stress Analysis of Cracks Handbook, 3rd ed., ASME Press, New York.
Bazant, Z. P. , 1984, “ Size Effect in Blunt Fracture: Concrete, Rock, Metal,” J. Eng. Mech., 110(4), pp. 518–535. [CrossRef]
Bazant, Z. P. , and Kazemi, M. T. , 1990, “ Size Effect in Fracture of Ceramics and Its Use to Determine Fracture Energy and Effective Process Zone Length,” J. Am. Chem. Soc., 73(7), pp. 1841–1853.
Bazant, Z. P. , Ozbolt, J. , and Eligehausen, R. , 1994, “ Fracture Size Effect: Review of Evidence for Concrete Structures,” J. Struct. Eng., 120(8), pp. 2377–2398. [CrossRef]
Bazant, Z. P. , and Chen, E. P. , 1997, “ Scaling of Structural Failure,” ASME Appl. Mech. Rev., 50(10), pp. 593–627. [CrossRef]
Bazant, Z. P. , 2000, “ Size Effect,” Int. J. Solids Struct., 37(1–2), pp. 69–80. [CrossRef]
Bazant, Z. P. , 2004, “ Scaling Theory for Quasibrittle Structural Failure,” Proc. Natl. Acad. Sci., 101(37), pp. 13400–13407. [CrossRef]
Gao, H. J. , and Huang, Y. G. , 2003, “ Geometrically Necessary Dislocation and Size-Dependent Plasticity,” Scr. Mater., 48(2), pp. 113–118. [CrossRef]
ABAQUS, 2014, “ ABAQUS Theory Manual and Users Manual, Version 6.14,” ABAQUS Inc., Providence, RI.
Peterson, R. E. , 1959, “ Notch-Sensitivity,” Metal Fatigue, G. Sines , and J. L. Waisman , eds., McGraw-Hill, New York, pp. 293–306.
Christensen, R. M. , 2015, “ Evaluation of Ductile/Brittle Failure Theory and Derivation of the Ductile/Brittle Transition Temperature,” ASME J. Appl. Mech., 83(2), p. 021001. [CrossRef]
Aboudi, J. , and Volokh, K. Y. , 2015, “ Failure Prediction of Unidirectional Composites Undergoing Large Deformations,” ASME J. Appl. Mech., 82(7), p. 071004. [CrossRef]
Bouklas, N. , Landis, C. M. , and Huang, R. , 2015, “ Effect of Solvent Diffusion on Crack-Tip Fields and Driving Force for Fracture of Hydrogels,” ASME J. Appl. Mech., 82(8), p. 081007. [CrossRef]


Grahic Jump Location
Fig. 8

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

Grahic Jump Location
Fig. 9

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

Grahic Jump Location
Fig. 5

Two similar holed atomic plate models composed of discrete atoms

Grahic Jump Location
Fig. 2

Schematics of two different components with defects

Grahic Jump Location
Fig. 7

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

Grahic Jump Location
Fig. 6

Failure loadings of a series of similar atomic models from simulations

Grahic Jump Location
Fig. 10

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

Grahic Jump Location
Fig. 4

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

Grahic Jump Location
Fig. 3

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

Grahic Jump Location
Fig. 11

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

Grahic Jump Location
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

Grahic Jump Location
Fig. 1

Schematic of an infinite body containing a long hole

Grahic Jump Location
Fig. 13

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

Grahic Jump Location
Fig. 23

Schematic of the imaginary crack method

Grahic Jump Location
Fig. 24

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

Grahic Jump Location
Fig. 16

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

Grahic Jump Location
Fig. 17

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

Grahic Jump Location
Fig. 18

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

Grahic Jump Location
Fig. 19

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

Grahic Jump Location
Fig. 20

Schematic of the point method

Grahic Jump Location
Fig. 21

Two FEM models with different notch shapes

Grahic Jump Location
Fig. 22

Schematic of the line method



Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In