In this paper, we present a new model to predict the fracture in brittle materials from a geometrical weakness presenting an arbitrary stress concentration. The main idea is to combine the strain gradient elasticity with a cohesive model that includes both the displacement and the rotation jumps between the cohesive surfaces in the separation law. Three material parameters were used in the establishment of the fracture criterion. The first two parameters are the commonly used σc, the ultimate stress, and Gc, the critical energy release rate. The third parameter is the characteristic length l as in most of the strain gradient models. The proposed three-parameter model enables to take the different stress concentration levels into account, thus providing a criterion to predict fractures for any stress concentration, whether it is singular or not. Experimental results were selected to verify the accuracy and efficiency of the criterion. It was shown that the proposed model is physically reasonable, highly accurate, and easy to apply. It can be used in crack initiation prediction of engineering structures made of brittle materials.

1.
Bazant
,
Z. P.
, 1976, “
Instability, Ductility and Size Effect in Strain Softening Concrete
,”
J. Engrg. Mech. Div.
0044-7951,
102
, pp.
331
344
.
2.
Irwin
,
G.
, 1968, “
Linear Fracture Mechanics, Fracture Transition and Fracture Control
,”
Eng. Fract. Mech.
0013-7944,
1
, pp.
241
257
.
3.
McClintock
,
F. A.
, 1958, “
Ductile Fracture Instability in Shear
,”
J. Appl. Mech.
0021-8936,
10
, pp.
582
588
.
4.
Ritchie
,
R.
,
Knott
,
J.
, and
Rice
,
J.
, 1973, “
On the Relation Between Critical Tensile Stress and Fracture Toughness in Mild Steel
,”
J. Mech. Phys. Solids
0022-5096,
21
, pp.
395
410
.
5.
Seweryn
,
A.
, and
Lukaszewicz
,
A.
, 2002, “
Verification of Brittle Fracture Criteria for Elements With V-shaped Notches
,”
Eng. Fract. Mech.
0013-7944,
69
, pp.
1487
1510
.
6.
Leguillon
,
D.
, 2002, “
Strength or Toughness? A Criterion for Crack Onset at a Notch
,”
Eur. J. Mech. A/Solids
0997-7538,
21
, pp.
61
72
.
7.
Barenblatt
,
G.
, 1959, “
The Formation of Equilibrium Cracks During Brittle Fracture
,”
J. Appl. Math. Mech.
0021-8928,
23
, pp.
434
444
.
8.
Dugdale
,
D.
, 1960, “
Yielding of Steel Sheets Containing Slits
,”
J. Mech. Phys. Solids
0022-5096,
8
, pp.
100
104
.
9.
Li
,
J.
, and
Zhang
,
X. B.
, 2006, “
A Criterion Study for Non-Singular Stress Concentrations in Brittle or Quasi-Brittle Materials
,”
Eng. Fract. Mech.
0013-7944,
73
, pp.
505
523
.
10.
Toupin
,
R. A.
, 1962, “
Elastic Materials With Couple Stresses
,”
Arch. Ration. Mech. Anal.
0003-9527,
11
, pp.
385
414
.
11.
Mindlin
,
R. D.
, and
Tiersten
,
H. F.
, 1962, “
Effects of Couple-Stresses in Linear Elasticity
,”
Arch. Ration. Mech. Anal.
0003-9527,
11
, pp.
415
448
.
12.
Aifantis
,
E. C.
, 1987, “
The Physics of Plastic Deformation
,”
Int. J. Plast.
0749-6419,
3
, pp.
211
247
.
13.
Fleck
,
N. A.
, and
Hutchinson
,
J. W.
, 1993, “
A Phenomenological Theory for Strain Gradient Effects in Plasticity
,”
J. Mech. Phys. Solids
0022-5096,
41
, pp.
1825
1857
.
14.
Fleck
,
N. A.
,
Muller
,
G. M.
,
Ashby
,
M. F.
, and
Hutchinson
,
J. W.
, 1994, “
Strain Gradient Plasticity: Theory and Experiments
,”
Acta Metall. Mater.
0956-7151,
42
, pp.
475
487
.
15.
Ma
,
Q.
, and
Clarke
,
D. R.
, 1995, “
Size Dependent Hardness of Silver Single Crystals
,”
J. Mater. Res.
0884-2914,
10
, pp.
853
863
.
16.
Lam
,
D. C. C.
, and
Chong
,
A. C. M.
, 1999, “
Indentation Model and Strain Gradient Plasticity Law for Glassy Polymers
,”
J. Mater. Res.
0884-2914,
14
, pp.
3784
3788
.
17.
Lam
,
D. C. C.
,
Yang
,
F.
,
Chong
,
A. C. M.
,
Wang
,
J.
, and
Tong
,
P.
, 2003, “
Experiments and Theory in Strain Gradient Elasticity
,”
J. Mech. Phys. Solids
0022-5096,
51
, pp.
1477
1508
.
18.
Yang
,
F.
,
Chong
,
A. C. M.
,
Lam
,
D. C. C.
, and
Tong
,
P.
, 2002, “
Couple Stress Based Strain Gradient Theory for Elasticity
,”
Int. J. Solids Struct.
0020-7683,
39
, pp.
2731
2743
.
19.
Siegmund
,
T.
, and
Brocks
,
W.
, 2000, “
A Numerical Study on the Correlation Between the Work of Separation and Dissipation Rate in Ductile Fracture
,”
Eng. Fract. Mech.
0013-7944,
67
, pp.
139
154
.
20.
Camacho
,
G. T.
, and Ortiz M., 1996, “
Computational Modelling of Impact Damage in Brittle Materials
,”
Int. J. Solids Struct.
0020-7683,
33
, pp.
2899
938
.
21.
Xu
,
X. P.
, and
Needleman
,
A.
, 1994, “
Numerical Simulation of Fast Crack Growth in Brittle Solids
,”
J. Mech. Phys. Solids
0022-5096,
42
, pp.
1397
1434
.
22.
Foulk
,
J. W.
,
Allen
,
D. H.
, and
Helems
,
K. L. E.
, 2000, “
Formulation of a Three-Dimensional Cohesive Zone Model for Application to a Finite Element Algorithm
,”
Comput. Methods Appl. Mech. Eng.
0045-7825,
183
, pp.
51
66
.
23.
Lennard-Jones
,
J. E.
, 1924, “
The Determination of Molecular Fields I: From the Variation of the Viscosity of a Gas With Temperature
,”
Proc. R. Soc. London
0950-1207,
106A
, pp.
441
462
.
24.
Mohammed
,
I.
, and
Liechti
,
K. M.
, 2000, “
Cohesive Zone Modelling of Crack Nucleation at Bimaterial Corners
,”
J. Mech. Phys. Solids
0022-5096,
48
, pp.
735
64
.
25.
Hutchinson
,
J. W.
, and
Evans
,
A. G.
, 2000, “
Mechanical of Materials: Top-Down Approaches to Fracture
,”
Acta Mater.
1359-6454,
48
, pp.
125
35
.
26.
Herrmann
,
L. R.
, 1983, In
Hybrid and Mixed, Finite Element Methods
, (edited by
Atluri
,
S. N.
,
,
Gallagher
,
R. H.
, and
Zienkiewicz
,
O. C.
,
Wiley
,
New York
.
27.
Xia
,
Z. C.
, and
Hutchinson
,
J. W.
, 1996, “
Crack Tip Fields in Strain Gradient Plasticity
,”
J. Mech. Phys. Solids
0022-5096,
44
, pp.
1621
1648
.
28.
Timoshenko
,
S. P.
, and
Goodier
,
J. N.
, 1970,
Theory of Elasticity
,
3rd ed.
,
Mc Graw-Hill
,
New York
.
29.
Rice
,
J. R.
, 1968, “
A Path Independent Integral and Approximate Analysis of Strain Concentration by Notches and Cracks
,”
ASME J. Appl. Mech.
0021-8936,
35
, pp.
379
86
.
30.
Chen
,
Y.
,
Lee
,
J. D.
, and
Eskandarian
,
A.
, 2003, “
Examining the Physical Foundation of Continuum Theories from the Viewpoint of Phonon Dispersion Relation
,”
Int. J. Eng. Sci.
0020-7225,
41
, pp.
61
83
.
31.
Chen
,
Y.
,
Lee
,
J. D.
, and
Eskandarian
,
A.
, 2004, “
Atomistic Viewpoint of the Applicability of Micro Continuum Theories
,”
Int. J. Solids Struct.
0020-7683,
41
, p
2085
2097
.
32.
Shibutani
,
Y.
,
Vitek
,
V.
, and
Bassani
,
J. L.
, 1998, “
Nonlocal Properties of Inhomogeneous Structures by Linking Approach of Generalized Continuum to Atomistic Model
,”
Int. J. Mech. Sci.
0020-7403,
40
, pp.
129
137
.
33.
Reid
,
A. C. E.
, and
Gooding
,
R. J.
, 1992, “
Inclusion Problem in a Two-Dimensional Nonlocal Elastic Solid
,”
Phys. Rev. B
0163-1829,
46
, pp.
6045
6049
.
34.
Sharma
,
P.
, and
Ganti
,
S.
, 2004, “
Size-Dependent Eshelbys Tensor for Embedded Nano-Inclusions Incorporating Surface/Interface Energies
,”
J. Appl. Mech.
0021-8936,
71
, pp.
663
671
.
35.
Ravi-chadar
,
K.
, and
Yang
,
B.
, 1997, “
On the Role of Microcracks in the Dynamic Fracture of Brittle Materials
,”
J. Mech. Phys. Solids
0022-5096,
45
, pp.
535
563
.
36.
McCormack
,
B.
,
Walsh
,
C.
,
Wilson
,
S.
, and
Prendergast
,
P.
, 1998, “
A Statistical Analysis of Microcrack Accumulation in PMMA Under Fatigue Loading: Applications to Orthopaedic Implant Fixation
,”
Int. J. Fatigue
0142-1123,
20
, pp.
581
593
.
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