The design of structures with a nonuniform stress field is of great industrial interest. The ability of the size effect law and critical distance theories to predict the nominal strength of notched and open hole specimens is analyzed in the present paper. The results obtained with these methods are compared with the solution of the problem computed, taking into account the material cohesive law. A conclusion of this paper is that the role of the critical fracture energy in determining the structural strength is negligible, except in large cracked structures. For unnotched structures of any size and for small cracked structures, the key parameter is the initial part of the softening cohesive law. This allows us to define design charts that relate the structural strength to a specimen size normalized with respect to a material characteristic length.

References

References
1.
Bažant
,
Z. P.
, and
Chen
,
E. P.
,
1997
, “
Scaling of Structural Failure
,”
ASME Appl. Mech. Rev.
,
50
(
10
), pp.
593
627
.10.1115/1.3101672
2.
Lubliner
,
J.
,
1990
,
Plasticity Theory
,
Collier-Macmillan
,
New York
.
3.
Timoshenko
,
S. P.
,
1953
,
History of Strength of Materials
,
Courier Dover
,
New York
.
4.
Griffith
,
A. A.
,
1921
, “
The Phenomena of Rupture and Flow in Solids
,”
Philos. Trans. R. Soc. London, Ser. A
,
221
, pp.
163
198
.10.1098/rsta.1921.0006
5.
Weibull
,
W.
,
1951
, “
A Statistical Distribution Function of Wide Applicability
,”
ASME J. Appl. Mech.
,
18
(
3
), pp.
293
297
.
6.
Bažant
,
Z. P.
,
2000
, “
Size Effect
,”
Int. J. Solids Struct.
,
37
(
1–2
), pp.
69
80
.10.1016/S0020-7683(99)00077-3
7.
Neuber
,
H.
,
1958
,
Theory of Notch Stresses: Principles for Exact Calculation of Strength With Reference to Structural Form and Material
,
2nd ed.
,
Springer-Verlag
,
Berlin
.
8.
Peterson
,
R. E.
,
1959
,
Notch-Sensitivity, Metal Fatigue
,
McGraw-Hill
,
New York
, pp.
293
306
.
9.
Taylor
,
D.
,
2007
,
The Theory of Critical Distances. A New Perspective in Fracture Mechanics
,
Elsevier
,
New York
.
10.
Bažant
,
Z. P.
, and
Planas
,
J.
,
1998
,
Fracture and Size Effect in Concrete and Other Quasibrittle Materials
,
CRC
,
Boca Raton, FL
.
11.
Whitney
,
J. M.
, and
Nuismer
,
R. J.
,
1974
, “
Stress Fracture Criteria for Laminated Composites Containing Stress Concentrations
,”
J. Compos. Mater.
,
8
, pp.
253
265
.10.1177/002199837400800303
12.
Waddoups
,
M. E.
,
Eisenmann
,
J. R.
, and
Kaminski
,
B. E.
,
1971
, “
Macroscopic Fracture Mechanics of Advanced Composite Materials
,”
J. Compos. Mater.
,
5
, pp.
446
454
.10.1177/002199837100500402
13.
Simo
,
J. C.
, and
Hughes
,
T. J. R.
,
1988
,
Computational Inelasticity
, Vol.
7
,
Springer
,
New York
.
14.
Bažant
,
Z. P.
, and
Belytschko
,
T. B.
,
1985
, “
Wave Propagation in a Strain-Softening Bar: Exact Solution
,”
J. Eng. Mech.
,
111
(
3
), pp.
381
389
.10.1061/(ASCE)0733-9399(1985)111:3(381)
15.
Belytschko
,
T.
,
Bažant
,
Z. P.
,
Yul-Woong
,
H.
, and
Ta-Peng
,
C.
,
1986
, “
Strain-Softening Materials and Finite-Element Solutions
,”
Comput. Struct.
,
23
(
2
), pp.
163
180
.10.1016/0045-7949(86)90210-5
16.
Oliver
,
J.
,
Huespe
,
A. E.
,
Pulido
,
M. D. G.
, and
Chaves
,
E.
,
2002
, “
From Continuum Mechanics to Fracture Mechanics: The Strong Discontinuity Approach
,”
Eng. Fract. Mech.
,
69
(
2
), pp.
113
136
.10.1016/S0013-7944(01)00060-1
17.
Rudnicki
,
J. W.
, and
Rice
,
J. R.
,
1975
, “
Conditions for Localization of Deformation in Pressure-Sensitive Dilatant Materials
,”
J. Mech. Phys. Solids
,
23
(
6
), pp.
371
394
.10.1016/0022-5096(75)90001-0
18.
Rice
,
J. R.
, and
Rudnicki
,
J. W.
,
1980
, “
A Note on Some Features of the Theory of Localization of Deformation
,”
Int. J. Solids Struct.
,
16
(
7
), pp.
597
605
.10.1016/0020-7683(80)90019-0
19.
Elices
,
M.
,
Guinea
,
G. V.
,
Gómez
,
J.
, and
Planas
,
J.
,
2002
, “
The Cohesive Zone Model: Advantages, Limitations and Challenges
,”
Eng. Fract. Mech.
,
69
(
2
), pp.
137
163
.10.1016/S0013-7944(01)00083-2
20.
Elices
,
M.
, and
Planas
,
J.
,
1996
, “
Fracture Mechanics Parameters of Concrete: An Overview
,”
Adv. Cem. Based Mater.
,
4
(
3–4
), pp.
116
127
.10.1016/S1065-7355(96)90080-2
21.
Ritchie
,
R. O.
,
1999
, “
Mechanisms of Fatigue-Crack Propagation in Ductile and Brittle Solids
,”
Int. J. Fract.
,
100
(
1
), pp.
55
83
.10.1023/A:1018655917051
22.
Ritchie
,
R. O.
,
2011
, “
The Conflicts Between Strength and Toughness
,”
Nature Mater.
,
10
(
11
), pp.
817
822
.10.1038/nmat3115
23.
Launey
,
M. E.
, and
Ritchie
,
R. O.
,
2009
, “
On the Fracture Toughness of Advanced Materials
,”
Adv. Mater.
,
21
(
20
), pp.
2103
2110
.10.1002/adma.200803322
24.
Li
,
H.
, and
Chandra
,
N.
,
2003
, “
Analysis of Crack Growth and Crack-Tip Plasticity in Ductile Materials Using Cohesive Zone Models
,”
Int. J. Plast.
,
19
(
6
), pp.
849
882
.10.1016/S0749-6419(02)00008-6
25.
Irwin
,
G.
,
1957
, “
Analysis of Stresses and Strains Near to the End of Crack Traversing a Plate
,”
ASME J. Appl. Mech.
,
24
, pp.
361
364
.
26.
Dugdale
,
D. S.
,
1960
, “
Yielding of Steel Sheets Containing Slits
,”
J. Mech. Phys. Solids
,
8
(
2
), pp.
100
104
.10.1016/0022-5096(60)90013-2
27.
Barenblatt
,
G. I.
,
1962
, “
The Mathematical Theory of Equilibrium Cracks in Brittle Fracture
,”
Adv. Appl. Mech.
,
7
(
C
), pp.
55
129
.10.1016/S0065-2156(08)70121-2
28.
Barenblatt
,
G. I.
,
1959
, “
The Formation of Equilibrium Cracks During Brittle Fracture. General Ideas and Hypotheses. Axially-Symmetric Cracks
,”
J. Appl. Math. Mech.
,
23
(
3
), pp.
622
636
.10.1016/0021-8928(59)90157-1
29.
Palmer
,
A. C.
, and
Rice
,
J. R.
,
1973
, “
Growth of Slip Surfaces in Progressive Failure of Over-Consolidated Clay
,”
Proc. R. Soc. London, Ser. A
,
332
(
1591
), pp.
527
548
.10.1098/rspa.1973.0040
30.
Rice
,
J. R.
,
1980
, “
The Mechanics of Earthquake Rupture
,”
Physics of the Earth's Interior
, Proceedings of the International School of Physics “Enrico Fermi” (Course 78),
A. M. Dziewonski, and E. Boschi
,
North Holland Publishing Co
.,
North-Holland, Amsterdam
, pp.
555
649
.
31.
Panasyuk
,
V. V.
,
2004
, “
Fracture Mechanics and Strength of Materials: Advances and Prospects
,”
Mater. Sci.
,
40
(
3
), pp.
305
319
.
32.
Bao
,
G.
, and
Suo
,
Z.
,
1992
, “
Remarks on Crack-Bridging Concepts
,”
ASME Appl. Mech. Rev.
,
45
(
8
), pp.
355
366
.10.1115/1.3119764
33.
Massabo
,
R.
, and
Cox
,
B. N.
,
1999
, “
Concepts for Bridged Mode II Delamination Cracks
,”
J. Mech. Phys. Solids
,
47
(
6
), pp.
1265
1300
.10.1016/S0022-5096(98)00107-0
34.
Yang
,
Q.
, and
Cox
,
B.
,
2005
, “
Cohesive Models for Damage Evolution in Laminated Composites
,”
Int. J. Fract.
,
133
(
2
), pp.
107
137
.10.1007/s10704-005-4729-6
35.
Hillerborg
,
A.
,
Modéer
,
M.
, and
Petersson
,
P. E.
,
1976
, “
Analysis of Crack Formation and Crack Growth in Concrete by Means of Fracture Mechanics and Finite Elements
,”
Cem. Concr. Res.
,
6
(
6
), pp.
773
781
.10.1016/0008-8846(76)90007-7
36.
Bažant
,
Z. P.
, and
Cedolin
,
L.
,
1979
, “
Blunt Crack Band Propagation in Finite Element Analysis
,”
ASCE J. Eng. Mech. Div.
,
105
(
2
), pp.
297
315
.
37.
Bažant
,
Z. P.
, and
Oh
,
B. H.
,
1983
, “
Crack Band Theory for Fracture of Concrete
,”
Mater. Constr.
,
16
(
93
), pp.
155
177
.10.1007/BF02486267
38.
Bažant
,
Z. P.
, and
Cedolin
,
L.
,
1983
, “
Finite Element Modeling of Crack Band Propagation
,”
J. Struct. Eng.
,
109
(
1
), pp.
69
92
.10.1061/(ASCE)0733-9445(1983)109:1(69)
39.
Wittmann
,
F.
,
Rokugo
,
K.
,
Brühwiler
,
E.
,
Mihashi
,
H.
, and
Simonin
,
P.
,
1988
, “
Fracture Energy and Strain Softening of Concrete as Determined by Means of Compact Tension Specimens
,”
Mater. Struct.
,
21
(
1
), pp.
21
32
.10.1007/BF02472525
40.
Guinea
,
G. V.
,
Planas
,
J.
, and
Elices
,
M.
,
1994
, “
A General Bilinear Fit for the Softening Curve of Concrete
,”
Mater. Struct.
,
27
(
2
), pp.
99
105
.10.1007/BF02472827
41.
Dávila
,
C. G.
,
Rose
,
C. A.
, and
Camanho
,
P. P.
,
2009
, “
A Procedure for Superposing Linear Cohesive Laws to Represent Multiple Damage Mechanisms in the Fracture of Composites
,”
Int. J. Fract.
,
158
(
2
), pp.
211
223
.10.1007/s10704-009-9366-z
42.
Bažant
,
Z. P.
,
Kim
,
J. H.
,
Daniel
,
I. M.
,
Becq-Giraudon
,
E.
, and
Zi
,
G.
,
1999
, “
Size Effect on Compression Strength of Fiber Composites Failing by Kink Band Propagation
,”
Int. J. Fract.
,
95
(
1–4
), pp.
103
141
.10.1023/A:1018640015465
43.
Gómez
,
F. J.
,
Elices
,
M.
, and
Valiente
,
A.
,
2000
, “
Cracking in PMMA Containing U-Shaped Notches
,”
Fatigue Fract. Eng. Mater. Struct.
,
23
(
9
), pp.
795
803
.10.1046/j.1460-2695.2000.00264.x
44.
Bažant
,
Z. P.
,
2004
, “
Scaling Theory for Quasibrittle Structural Failure
,”
Proc. Natl. Acad. Sci. U.S.A.
,
101
(
37
), pp.
13400
13407
.10.1073/pnas.0404096101
45.
Maimí
,
P.
,
Trias
,
D.
,
González
,
E. V.
, and
Renart
,
J.
,
2012
, “
Nominal Strength of Quasi-Brittle Open Hole Specimens
,”
Compos. Sci. Technol.
,
72
(
10
), pp.
1203
1208
.10.1016/j.compscitech.2012.04.004
46.
Pijaudier-Cabot
,
G.
,
Bažant
,
Z. P.
, and
Tabbara
,
M.
,
1988
, “
Comparison of Various Models for Strain-Softening
,”
Eng. Comput.
,
5
(
2
), pp.
141
150
.10.1108/eb023732
47.
Peerlings
,
R. H. J.
,
Geers
,
M. G. D.
,
de Borst
,
R.
, and
Brekelmans
,
W. A. M.
,
2001
, “
A Critical Comparison of Nonlocal and Gradient-Enhanced Softening Continua
,”
Int. J. Solids Struct.
,
38
(
44–45
), pp.
7723
7746
.10.1016/S0020-7683(01)00087-7
48.
Jirásek
,
M.
,
1998
, “
Nonlocal Models for Damage and Fracture: Comparison of Approaches
,”
Int. J. Solids Struct.
,
35
(
31–32
), pp.
4133
4145
.10.1016/S0020-7683(97)00306-5
49.
Lasry
,
D.
, and
Belytschko
,
T.
,
1988
, “
Localization Limiters in Transient Problems
,”
Int. J. Solids Struct.
,
24
(
6
), pp.
581
597
.10.1016/0020-7683(88)90059-5
50.
Ladevèze
,
P.
,
Allix
,
O.
,
Deu
,
J. F.
, and
Leveque
,
D.
,
2000
, “
A Mesomodel for Localisation and Damage Computation in Laminates
,”
Comput. Methods Appl. Mech. Eng.
,
183
(
1–2
), pp.
105
122
.10.1016/S0045-7825(99)00214-5
51.
Bažant
,
Z. P.
,
1984
, “
Size Effect in Blunt Fracture: Concrete, Rock, Metal
,”
J. Eng. Mech.
,
110
(
4
), pp.
518
535
.10.1061/(ASCE)0733-9399(1984)110:4(518)
52.
Bažant
,
Z. P.
,
1999
, “
Size Effect on Structural Strength: A Review
,”
Arch. Appl. Mech.
,
69
(
9–10
), pp.
703
725
.10.1007/s004190050252
53.
Bažant
,
Z. P.
,
1997
, “
Scaling of Quasibrittle Fracture: Asymptotic Analysis
,”
Int. J. Fract.
,
83
(
1
), pp.
19
40
.10.1023/A:1007387823522
54.
Bažant
,
Z. P.
,
1997
, “
Scaling of Quasibrittle Fracture: Hypotheses of Invasive and Lacunar Fractality, Their Critique and Weibull Connection
,”
Int. J. Fract.
,
83
(
1
), pp.
41
65
.10.1023/A:1007335506684
55.
Bažant
,
Z. P.
,
2003
, “
Asymptoric Matching Analysis of Scaling of Structural Failure Due to Softening Hinges—I: Theory
,”
J. Eng. Mech.
,
129
(
6
), pp.
641
650
.10.1061/(ASCE)0733-9399(2003)129:6(641)
56.
Bažant
,
Z. P.
, and
Yu
,
Q.
,
2009
, “
Universal Size Effect Law and Effect of Crack Depth on Quasi-Brittle Structure Strength
,”
J. Eng. Mech.
,
135
(
2
), pp.
78
84
.10.1061/(ASCE)0733-9399(2009)135:2(78)
57.
Östlund
,
S.
, and
Kärenlampi
,
P.
,
2001
, “
Structural Geometry Effect on the Size-Scaling of Strength
,”
Int. J. Fract.
,
109
(
2
), pp.
141
151
.10.1023/A:1011045510152
58.
Bažant
,
Z. P.
,
2002
, “
Concrete Fracture Models: Testing and Practice
,”
Eng. Fract. Mech.
,
69
(
2
), pp.
165
205
.10.1016/S0013-7944(01)00084-4
59.
Planas
,
J.
,
Guinea
,
G. V.
, and
Elices
,
M.
,
1997
, “
Generalized Size Effect Equation for Quasi-brittle Materials
,”
Fatigue Fract. Eng. Mater. Struct.
,
20
(
5
), pp.
671
687
.10.1111/j.1460-2695.1997.tb00300.x
60.
Morel
,
S.
,
2008
, “
Size Effect in Quasibrittle Fracture: Derivation of the Energetic Size Effect Law From Equivalent LEFM and Asymptotic Analysis
,”
Int. J. Fract.
,
154
(
1–2
), pp.
15
26
.10.1007/s10704-008-9291-6
61.
Morel
,
S.
,
2007
, “
R-Curve and Size Effect in Quasibrittle Fractures: Case of Notched Structures
,”
Int. J. Solids Struct.
,
44
(
13
), pp.
4272
4290
.10.1016/j.ijsolstr.2006.11.014
62.
Morel
,
S.
, and
Dourado
,
N.
,
2011
, “
Size Effect in Quasibrittle Failure: Analytical Model and Numerical Simulations Using Cohesive Zone Model
,”
Int. J. Solids Struct.
,
48
(
10
), pp.
1403
1412
.10.1016/j.ijsolstr.2011.01.014
63.
Bažant
,
Z. P.
,
Vořechovský
,
M.
, and
Novák
,
D.
,
2007
, “
Asymptotic Prediction of Energetic-Statistical Size Effect From Deterministic Finite-Element Solutions
,”
J. Eng. Mech.
,
133
(
2
), pp.
153
162
.10.1061/(ASCE)0733-9399(2007)133:2(153)
64.
Bažant
,
Z. P.
,
Pang
,
S. D.
,
Vořechovský
,
M.
, and
Novák
,
D.
,
2007
, “
Energetic-Statistical Size Effect Simulated by SFEM With Stratified Sampling and Crack Band Model
,”
Int. J. Numer. Methods Eng.
,
71
(
11
), pp.
1297
1320
.10.1002/nme.1986
65.
Bažant
,
Z. P.
, and
Pang
,
S. D.
,
2006
, “
Mechanics-Based Statistics of Failure Risk of Quasibrittle Structures and Size Effect on Safety Factors
,”
Proc. Natl. Acad. Sci. U.S.A.
,
103
(
25
), pp.
9434
9439
.10.1073/pnas.0602684103
66.
Le
,
J.-L.
,
Bažant
,
Z. P.
, and
Bažant
,
M. Z.
,
2011
, “
Unified Nanomechanics Based Probabilistic Theory of Quasibrittle and Brittle Structures: I. Strength, Static Crack Growth, Lifetime and Scaling
,”
J. Mech. Phys. Solids
,
59
(
7
), pp.
1291
1321
.10.1016/j.jmps.2011.03.002
67.
Le
,
J.-L.
, and
Bažant
,
Z. P.
,
2011
, “
Unified Nano-Mechanics Based Probabilistic Theory of Quasibrittle and Brittle Structures: II. Fatigue Crack Growth, Lifetime and Scaling
,”
J. Mech. Phys. Solids
,
59
(
7
), pp.
1322
1337
.10.1016/j.jmps.2011.03.007
68.
Bažant
,
Z. P.
,
Le
,
J. L.
, and
Bažant
,
M. Z.
,
2009
, “
Scaling of Strength and Lifetime Probability Distributions of Quasibrittle Structures Based on Atomistic Fracture Mechanics
,”
Proc. Natl. Acad. Sci. U.S.A.
,
106
(
28
), pp.
11484
11489
.10.1073/pnas.0904797106
69.
Carpinteri
,
A.
, and
Ferro
,
G.
,
1994
, “
Size Effects on Tensile Fracture Properties: A Unified Explanation Based on Disorder and Fractality of Concrete Microstructure
,”
Mater. Struct.
,
27
(
10
), pp.
563
571
.10.1007/BF02473124
70.
Carpinteri
,
A.
, and
Pugno
,
N.
,
2005
, “
Are Scaling Laws on Strength of Solids Related to Mechanics or to Geometry?
,”
Nature Mater.
,
4
(
6
), pp.
421
423
.10.1038/nmat1408
71.
Carpinteri
,
A.
,
Chiaia
,
B.
, and
Ferro
,
G.
,
1995
, “
Size Effects on Nominal Tensile Strength of Concrete Structures: Multifractality of Material Ligaments and Dimensional Transition From Order to Disorder
,”
Mater. Struct.
,
28
(
6
), pp.
311
317
.10.1007/BF02473145
72.
Carpinteri
,
A.
, and
Puzzi
,
S.
,
2009
, “
The Fractal-Statistical Approach to the Size-Scale Effects on Material Strength and Toughness
,”
Probab. Eng. Mech.
,
24
(
1
), pp.
75
83
.10.1016/j.probengmech.2008.01.003
73.
Bažant
,
Z. P.
, and
Yavari
,
A.
,
2005
, “
Is the Cause of Size Effect on Structural Strength Fractal or Energetic-Statistical?
,”
Eng. Fract. Mech.
,
72
(
1
), pp.
1
31
.10.1016/j.engfracmech.2004.03.004
74.
Taylor
,
D.
,
2008
, “
The Theory of Critical Distances
,”
Eng. Fract. Mech.
,
75
(
7
), pp.
1696
1705
.10.1016/j.engfracmech.2007.04.007
75.
Taylor
,
D.
,
2011
, “
Applications of the Theory of Critical Distances in Failure Analysis
,”
Eng. Failure Anal.
,
18
(
2
), pp.
543
549
.10.1016/j.engfailanal.2010.07.002
76.
Tan
,
S. C.
,
1988
, “
Effective Stress Fracture Models for Unnotched and Notched Multidirectional Laminates
,”
J. Compos. Mater.
,
22
(
4
), pp.
322
340
.10.1177/002199838802200402
77.
Tan
,
S. C.
,
1987
, “
Laminated Composites Containing an Elliptical Opening. I. Approximate Stress Analyses and Fracture Models
,”
J. Compos. Mater.
,
21
(
10
), pp.
925
948
.10.1177/002199838702101004
78.
Tan
,
S. C.
,
1987
, “
Laminated Composites Containing an Elliptical Opening. II. Experiment and Model Modification
,”
J. Compos. Mater.
,
21
(
10
), pp.
949
968
.10.1177/002199838702101005
79.
Wisnom
,
M. R.
,
Hallett
,
S. R.
, and
Soutis
,
C.
,
2010
, “
Scaling Effects in Notched Composites
,”
J. Compos. Mater.
,
44
(
2
), pp.
195
210
.10.1177/0021998309339865
80.
Rao
,
A. S.
,
Krishna
,
Y.
, and
Rao
,
B. N.
,
2004
, “
Comparison of Fracture Models to Assess the Notched Strength of Composite/Solid Propellant Tensile Specimens
,”
Mater. Sci. Eng. A
,
385
(
1–2
), pp.
429
439
.10.1016/j.msea.2004.07.041
81.
Kinloch
,
A. J.
, and
Williams
,
J. G.
,
1980
, “
Crack Blunting Mechanisms in Polymers
,”
J. Mater. Sci.
,
15
(
4
), pp.
987
996
.10.1007/BF00552112
82.
Kasiri
,
S.
, and
Taylor
,
D.
,
2008
, “
A Critical Distance Study of Stress Concentrations in Bone
,”
J. Biomech.
,
41
(
3
), pp.
603
609
.10.1016/j.jbiomech.2007.10.003
83.
Luca
,
S.
,
2008
, “
The Theory of Critical Distances: A Review of Its Applications in Fatigue
,”
Eng. Fract. Mech.
,
75
(
7
), pp.
1706
1724
.10.1016/j.engfracmech.2006.12.004
84.
Arajo
,
J. A.
,
Susmel
,
L.
,
Taylor
,
D.
,
Ferro
,
J. C. T.
, and
Ferreira
,
J. L. A.
,
2008
, “
On the Prediction of High-Cycle Fretting Fatigue Strength: Theory of Critical Distances vs. Hot-Spot Approach
,”
Eng. Fract. Mech.
,
75
(
7
), pp.
1763
1778
.10.1016/j.engfracmech.2007.03.026
85.
Taylor
,
D.
, and
Susmel
,
L.
,
2008
, “
Special Issue on Critical Distance Theories of Fracture
,”
Eng. Fract. Mech.
,
75
(
7
), p.
1695
.10.1016/j.engfracmech.2007.06.001
86.
Dyskin
,
A. V.
,
1997
, “
Crack Growth Criteria Incorporating Nonsingular Stresses: Size Effect in Apparent Fracture Toughness
,”
Int. J. Fract.
,
83
(
2
), pp.
191
206
.10.1023/A:1007304015524
87.
Leguillon
,
D.
,
2002
, “
Strength or Toughness? A Criterion for Crack Onset at a Notch
,”
Eur. J. Mech. A/Solids
,
21
(
1
), pp.
61
72
.10.1016/S0997-7538(01)01184-6
88.
Andrzej
,
S.
,
1994
, “
Brittle Fracture Criterion for Structures With Sharp Notches
,”
Eng. Fract. Mech.
,
47
(
5
), pp.
673
681
.10.1016/0013-7944(94)90158-9
89.
Kannan
,
V. K.
,
Murali
,
V.
,
Rajadurai
,
A.
, and
Rao
,
B. N.
,
2010
, “
Tension and Compression Strength Evaluation of Composite Plates With Circular Holes
,”
J. Reinf. Plast. Compos.
,
29
(
10
), pp.
1500
1514
.10.1177/0731684409337904
90.
Ritchie
,
R. O.
,
Knott
,
J. F.
, and
Rice
,
J. R.
,
1973
, “
On the Relationship Between Critical Tensile Stress and Fracture Toughness in Mild Steel
,”
J. Mech. Phys. Solids
,
21
(
6
), pp.
395
410
.10.1016/0022-5096(73)90008-2
91.
Eriksson
,
I.
, and
Aronsson
,
C. G.
,
1990
, “
Strength of Tensile Loaded Graphite/Epoxy Laminates Containing Cracks, Open and Filled Holes
,”
J. Compos. Mater.
,
24
, pp.
456
482
.10.1177/002199839002400501
92.
Srivastava
,
V. K.
,
2002
, “
Notched Strength Prediction of Laminated Composite Under Tensile Loading
,”
Mater. Sci. Eng. A
,
328
(
1–2
), pp.
302
309
.10.1016/S0921-5093(01)01759-2
93.
Potti
,
P. K. G.
,
Rao
,
B. N.
, and
Srivastava
,
V. K.
,
2001
, “
Tensile Fracture Strength of Boron/Aluminum Laminates With Holes and Slits
,”
Mater. Sci. Eng. A
,
301
(
2
), pp.
244
252
.10.1016/S0921-5093(00)01409-X
94.
Potti
,
P. K. G.
,
Rao
,
B. N.
, and
Srivastava
,
V. K.
,
2000
, “
Notched Tensile Strength of Randomly Oriented E-Glass Composite Laminates
,”
Mater. Sci. Eng. A
,
282
(
1–2
), pp.
59
66
.10.1016/S0921-5093(99)00775-3
95.
Tada
,
H.
,
Paris
,
P. C.
, and
Irwin
,
G. R.
,
2000
,
The Stress Analysis of Cracks Handbook
,
3rd ed.
,
American Society of Mechanical Engineers
,
New York
.
96.
El Haddad
,
M. H.
,
Smith
,
K. N.
, and
Topper
,
T. H.
,
1979
, “
Fatigue Crack Propagation of Short Cracks
,”
ASME J. Eng. Mater. Technol.
,
101
(
1
), pp.
42
46
.10.1115/1.3443647
97.
El Haddad
,
M. H.
,
Topper
,
T. H.
, and
Smith
,
K. N.
,
1979
, “
Prediction of Non Propagating Cracks
,”
Eng. Fract. Mech.
,
11
(
3
), pp.
573
584
.10.1016/0013-7944(79)90081-X
98.
Taylor
,
D.
,
Cornetti
,
P.
, and
Pugno
,
N.
,
2005
, “
The Fracture Mechanics of Finite Crack Extension
,”
Eng. Fract. Mech.
,
72
(
7
), pp.
1021
1038
.10.1016/j.engfracmech.2004.07.001
99.
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
.10.1016/j.engfracmech.2006.03.010
100.
Williams
,
T. N.
,
Newman
,
J. C.
, Jr.
, and
Gullett
,
P. M.
,
2011
, “
Crack-Surface Displacements for Cracks Emanating From a Circular Hole Under Various Loading Conditions
,”
Fatigue Fract. Eng. Mater. Struct.
,
34
(
4
), pp.
250
259
.10.1111/j.1460-2695.2010.01512.x
101.
Camanho
,
P. P.
, and
Lambert
,
M.
,
2006
, “
A Design Methodology for Mechanically Fastened Joints in Laminated Composite Materials
,”
Compos. Sci. Technol.
,
66
(
15
), pp.
3004
3020
.10.1016/j.compscitech.2006.02.017
102.
Whitworth
,
H. A.
,
Aluko
,
O.
, and
Tomlinson
,
N. A.
,
2008
, “
Application of the Point Stress Criterion to the Failure of Composite Pinned Joints
,”
Eng. Fract. Mech.
,
75
(
7
), pp.
1829
1839
.10.1016/j.engfracmech.2006.12.003
103.
Carpinteri
,
A.
,
Spagnoli
,
A.
,
Vantadori
,
S.
, and
Viappiani
,
D.
,
2008
, “
A Multiaxial Criterion for Notch High-Cycle Fatigue Using a Critical-Point Method
,”
Eng. Fract. Mech.
,
75
(
7
), pp.
1864
1874
.10.1016/j.engfracmech.2006.11.002
104.
Reifsnider
,
K.
,
Case
,
S.
, and
Duthoit
,
J.
,
2000
, “
The Mechanics of Composite Strength Evolution
,”
Compos. Sci. Technol.
,
60
(
12–13
), pp.
2539
2546
.10.1016/S0266-3538(00)00047-6
105.
Bellett
,
D.
,
Taylor
,
D.
,
Marco
,
S.
,
Mazzeo
,
E.
,
Guillois
,
J.
, and
Pircher
,
T.
,
2005
, “
The Fatigue Behaviour of Three-Dimensional Stress Concentrations
,”
Int. J. Fatigue
,
27
(
3
), pp.
207
221
.10.1016/j.ijfatigue.2004.07.006
106.
Iarve
,
E. V.
,
Kim
,
R.
, and
Mollenhauer
,
D.
,
2007
, “
Three Dimensional Stress Analysis and Weibull Statistics Based Strength Prediction in Open Hole Composites
,”
Composites Part A
,
38
(
1
), pp.
174
185
.10.1016/j.compositesa.2006.01.004
107.
Hunt
,
R. A.
, and
McCartney
,
L. N.
,
1979
, “
A New Approach to Weibull's Statistical Theory of Brittle Fracture
,”
Int. J. Fract.
,
15
(
4
), pp.
365
375
.
108.
Suo
,
Z.
,
Ho
,
S.
, and
Gong
,
X.
,
1993
, “
Notch Ductile-to-Brittle Transition Due to Localized Inelastic Band
,”
J. Eng. Mater. Technol.
,
115
(
3
), pp.
319
326
.10.1115/1.2904225
109.
Maiti
,
S. K.
,
Ashby
,
M. F.
, and
Gibson
,
L. J.
,
1984
, “
Fracture Toughness of Brittle Cellular Solids
,”
Scr. Metall.
,
18
(
3
), pp.
213
217
.10.1016/0036-9748(84)90510-6
110.
Maimí
,
P.
,
Turon
,
A.
, and
Trias
,
D.
,
2011
, “
Crack Propagation in Quasi-Brittle Two-Dimensional Isotropic Lattices
,”
Eng. Fract. Mech.
,
78
(
1
), pp.
60
70
.10.1016/j.engfracmech.2010.09.014
111.
Leguillon
,
D.
, and
Piat
,
R.
,
2008
, “
Fracture of Porous Materials Influence of the Pore Size
,”
Eng. Fract. Mech.
,
75
(
7
), pp.
1840
1853
.10.1016/j.engfracmech.2006.12.002
112.
Leguillon
,
D.
,
Quesada
,
D.
,
Putot
,
C.
, and
Martin
,
E.
,
2007
, “
Prediction of Crack Initiation at Blunt Notches and Cavities—Size Effects
,”
Eng. Fract. Mech.
,
74
(
15
), pp.
2420
2436
.10.1016/j.engfracmech.2006.11.008
113.
Hitchen
,
S. A.
,
Ogin
,
S. L.
,
Smith
,
P. A.
, and
Soutis
,
C.
,
1994
, “
The Effect of Fibre Length on Fracture Toughness and Notched Strength of Short Carbon Fibre/Epoxy Composites
,”
Composites
,
25
(
6
), pp.
407
413
.10.1016/0010-4361(94)90096-5
114.
Belmonte
,
H. M. S.
,
Manger
,
C. I. C.
,
Ogin
,
S. L.
,
Smith
,
P. A.
, and
Lewin
,
R.
,
2001
, “
Characterisation and Modelling of the Notched Tensile Fracture of Woven Quasi-Isotropic GFRP Laminates
,”
Compos. Sci. Technol.
,
61
(
4
), pp.
585
597
.10.1016/S0266-3538(00)00238-4
115.
Belmonte
,
H. M. S.
,
Ogin
,
S. L.
,
Smith
,
P. A.
, and
Lewin
,
R.
,
2004
, “
A Physically Based Model for the Notched Strength of Woven Quasi-Isotropic CFRP Laminates
,”
Composites
, Part A,
35
(
7–8
), pp.
763
778
.10.1016/j.compositesa.2004.01.006
116.
Camanho
,
P. P.
,
Ercin
,
G. H.
,
Catalanotti
,
G.
,
Mahdi
,
S.
, and
Linde
,
P.
,
2012
, “
A Finite Fracture Mechanics Model for the Prediction of the Open-Hole Strength of Composite Laminates
,”
Composites
, Part A,
43
(
8
), pp.
1219
1225
.10.1016/j.compositesa.2012.03.004
117.
Li
,
J.
, and
Zhang
,
X. B.
,
2005
, “
A Criterion Study for Non-Singular Stress Concentrations With Size Effect
,”
Strength, Fract. Complexity
,
3
(
2–4
), pp.
205
215
.
118.
Li
,
J.
, and
Zhang
,
X. B.
,
2006
, “
A Criterion Study for Non-Singular Stress Concentrations in Brittle or Quasi-Brittle Materials
,”
Eng. Fract. Mech.
,
73
(
4
), pp.
505
523
.10.1016/j.engfracmech.2005.09.001
119.
Zhang
,
X. B.
, and
Li
,
J.
,
2008
, “
A Failure Criterion for Brittle and Quasi-Brittle Materials Under Any Level of Stress Concentration
,”
Eng. Fract. Mech.
,
75
(
17
), pp.
4925
4932
.10.1016/j.engfracmech.2008.06.020
120.
Newman
,
J. C.
, Jr.
,
James
,
M. A.
, and
Zerbst
,
U.
,
2003
, “
A Review of the CTOA/CTOD Fracture Criterion
,”
Eng. Fract. Mech.
,
70
(
3–4
), pp.
371
385
.10.1016/S0013-7944(02)00125-X
121.
Scheider
,
I.
,
Schödel
,
M.
,
Brocks
,
W.
, and
Schönfeld
,
W.
,
2006
, “
Crack Propagation Analyses With CTOA and Cohesive Model: Comparison and Experimental Validation
,”
Eng. Fract. Mech.
,
73
(
2
), pp.
252
263
.10.1016/j.engfracmech.2005.04.005
122.
Zhu
,
X.-K.
, and
Joyce
,
J. A.
,
2012
, “
Review of Fracture Toughness (G, K, J, CTOD, CTOA) Testing and Standardization
,”
Eng. Fract. Mech.
,
85
, pp.
1
46
.10.1016/j.engfracmech.2012.02.001
123.
Jenq
,
Y. S.
, and
Shah
,
S. P.
,
1985
, “
Two Parameter Fracture Model for Concrete
,”
J. Eng. Mech.
,
111
(
10
), pp.
1227
1241
.10.1061/(ASCE)0733-9399(1985)111:10(1227)
124.
Jenq
,
Y. S.
, and
Shah
,
S. P.
,
1985
, “
A Fracture Toughness Criterion for Concrete
,”
Eng. Fract. Mech.
,
21
(
5
), pp.
1055
1069
.10.1016/0013-7944(85)90009-8
125.
Jenq
,
Y. S.
, and
Shah
,
S. P.
,
1988
, “
Mixed-Mode Fracture of Concrete
,”
Int. J. Fract.
,
38
(
2
), pp.
123
142
.
126.
Gettu
,
R.
,
Saldívar
,
H.
, and
Kazemi
,
M. T.
,
1998
, “
Implications of the Size Effect Method for Analyzing the Fracture of Concrete
,”
Int. J. Solids Struct.
,
35
(
31–32
), pp.
4121
4132
.10.1016/S0020-7683(97)00305-3
127.
Bilby
,
B. A.
,
Cottrell
,
A. H.
, and
Swinden
,
K. H.
,
1963
, “
The Spread of Plastic Yield From a Notch
,”
Proc. R. Soc. London, Ser. A
,
272
(
1350
), pp.
304
314
.10.1098/rspa.1963.0055
128.
Bilby
,
B. A.
,
Cottrell
,
A. H.
,
Smith
,
E.
, and
Swinden
,
K. H.
,
1964
, “
Plastic Yielding From Sharp Notches
,”
Proc. R. Soc. London, Ser. A
,
279
(
1376
), pp.
1
9
.10.1098/rspa.1964.0085
129.
Soutis
,
C.
,
Fleck
,
N. A.
, and
Smith
,
P. A.
,
1991
, “
Failure Prediction Technique for Compression Loaded Carbon Fibre-Epoxy Laminate With Open Holes
,”
J. Compos. Mater.
,
25
(
11
), pp.
1476
1498
.
130.
Backlund
,
J.
, and
Aronsson
,
C.-G.
,
1986
, “
Tensile Fracture of Laminates With Holes
,”
J. Compos. Mater.
,
20
(
3
), pp.
259
286
.10.1177/002199838602000304
131.
Aronsson
,
C.-G.
, and
Backlund
,
J.
,
1986
, “
Tensile Fracture of Laminates With Cracks
,”
J. Compos. Mater.
,
20
(
3
), pp.
287
307
.10.1177/002199838602000305
132.
Carpinteri
,
A.
,
1990
, “
A Catastrophe Theory Approach to Fracture Mechanics
,”
Int. J. Fract.
,
44
(
1
), pp.
57
69
.10.1007/BF00012552
133.
He
,
M. Y.
,
Wu
,
B.
, and
Suo
,
Z.
,
1994
, “
Notch-Sensitivity and Shear Bands in Brittle Matrix Composites
,”
Acta Metall. Mater.
,
42
(
9
), pp.
3065
3070
.10.1016/0956-7151(94)90403-0
134.
Connell
,
S. J.
,
Zok
,
F. W.
,
Du
,
Z. Z.
, and
Suo
,
Z.
,
1994
, “
On the Tensile Properties of a Fiber Reinforced Titanium Matrix Composite—II. Influence of Notches and Holes
,”
Acta Metall. Mater.
,
42
(
10
), pp.
3451
3461
.10.1016/0956-7151(94)90478-2
135.
Shin
,
C. S.
, and
Wang
,
C. M.
,
2004
, “
An Improved Cohesive Zone Model for Residual Notched Strength Prediction of Composite Laminates With Different Orthotropic Layups
,”
J. Compos. Mater.
,
38
(
9
), pp.
713
736
.10.1177/0021998304031635
136.
Afaghi-Khatibi
,
A.
,
Ye
,
L.
, and
Mai
,
Y.-W.
,
1996
, “
Evaluations of Effective Crack Growth and Residual Strength of Fibre Reinforced Metal Laminates With a Sharp Notch
,”
Compos. Sci. Technol.
,
56
(
9
), pp.
1079
1088
.10.1016/0266-3538(96)00070-X
137.
Newman
,
J. C.
, Jr.
,
1983
, “
A Nonlinear Fracture Mechanics Approach to the Growth of Small Cracks
,”
AGARD Conf. Proc.
,
328
(
6
), pp.
1
26
.
138.
Cox
,
B. N.
, and
Marshall
,
D. B.
,
1994
, “
Concepts for Bridged Cracks in Fracture and Fatigue
,”
Acta Metall. Mater.
,
42
(
2
), pp.
341
363
.10.1016/0956-7151(94)90492-8
139.
Guinea
,
G. V.
,
Elices
,
M.
, and
Planas
,
J.
,
2000
, “
Assessment of the Tensile Strength Through Size Effect Curves
,”
Eng. Fract. Mech.
,
65
(
2–3
), pp.
189
207
.10.1016/S0013-7944(99)00115-0
140.
Yu
,
M. H.
,
2002
, “
Advances in Strength Theories for Materials Under Complex Stress State in the 20th Century
,”
ASME Appl. Mech. Rev.
,
55
(
3
), pp.
169
218
.10.1115/1.1472455
141.
Bažant
,
Z. P.
, and
Becq-Giraudon
,
E.
,
2002
, “
Statistical Prediction of Fracture Parameters of Concrete and Implications for Choice of Testing Standard
,”
Cem. Concr. Res.
,
32
(
4
), pp.
529
556
.10.1016/S0008-8846(01)00723-2
142.
Planas
,
J.
, and
Elices
,
M.
,
1990
, “
Fracture Criteria for Concrete: Mathematical Approximations and Experimental Validation
,”
Eng. Fract. Mech.
,
35
(
13
), pp.
87
94
.10.1016/0013-7944(90)90186-K
143.
Ceb-90
,
1991
,
Final Draft CEB-FIP Mode Code 1990. Bulletin Information 203
,
Committee Euro-International du Beton
, London.
144.
Camanho
,
P. P.
,
Maimí
,
P.
, and
Dávila
,
C. G.
,
2007
, “
Prediction of Size Effects in Notched Laminates Using Continuum Damage Mechanics
,”
Compos. Sci. Technol.
,
67
(
13
), pp.
2715
2727
.10.1016/j.compscitech.2007.02.005
145.
Evans
,
R. H.
, and
Marathe
,
M. S.
,
1968
, “
Microcracking and Stress-Strain Curves for Concrete in Tension
,”
Mater. Construct.
,
1
(
1
), pp.
61
64
.10.1007/BF02479001
146.
Markeset
,
G.
, and
Hillerborg
,
A.
,
1995
, “
Softening of Concrete in Compression Localization and Size Effects
,”
Cem. Concr. Res.
,
25
(
4
), pp.
702
708
.10.1016/0008-8846(95)00059-L
147.
Sangha
,
C. M.
, and
Dhir
,
R. K.
,
1972
, “
Strength and Complete Stress-Strain Relationships for Concrete Tested in Uniaxial Compression Under Different Test Conditions
,”
Mater. Construct.
,
5
(
6
), pp.
361
370
.10.1007/BF02476284
148.
van Mier
,
J. G. M.
, and
van Vliet
,
M. R. A.
,
2002
, “
Uniaxial Tension Test for the Determination of Fracture Parameters of Concrete: State of the Art
,”
Eng. Fract. Mech.
,
69
(
2
), pp.
235
247
.10.1016/S0013-7944(01)00087-X
149.
Guinea
,
G. V.
,
Planas
,
J.
, and
Elices
,
M.
,
1992
, “
Measurement of the Fracture Energy Using Three-Point Bend Tests: Part 1—Influence of Experimental Procedures
,”
Mater. Struct.
,
25
(
4
), pp.
212
218
.10.1007/BF02473065
150.
Planas
,
J.
,
Elices
,
M.
, and
Guinea
,
G. V.
,
1992
, “
Measurement of the Fracture Energy Using Three-Point Bend Tests: Part 2—Influence of Bulk Energy Dissipation
,”
Mater. Struct.
,
25
(
5
), pp.
305
312
.10.1007/BF02472671
151.
Elices
,
M.
,
Guinea
,
G. V.
, and
Planas
,
J.
,
1992
, “
Measurement of the Fracture Energy Using Three-Point Bend Tests: Part 3—Influence of Cutting the P-Tail
,”
Mater. Struct.
,
25
(
6
), pp.
327
334
.10.1007/BF02472591
152.
Tang
,
T.
,
Ouyang
,
C.
, and
Shah
,
S.
,
1996
, “
A Simple Method for Determining Material Fracture Parameters From Peak Loads
,”
ACI Mater. J.
,
93
(
2
), pp.
147
157
.
153.
Kurihara
,
N.
,
Kunieda
,
M.
,
Kamada
,
T.
,
Uchida
,
Y.
, and
Rokugo
,
K.
,
2000
, “
Tension Softening Diagrams and Evaluation of Properties of Steel Fiber Reinforced Concrete
,”
Eng. Fract. Mech.
,
65
(
2–3
), pp.
235
245
.10.1016/S0013-7944(99)00116-2
154.
Kunieda
,
M.
,
Kurihara
,
N.
,
Uchida
,
Y.
, and
Rokugo
,
K.
,
2000
, “
Application of Tension Softening Diagrams to Evaluation of Bond Properties at Concrete Interfaces
,”
Eng. Fract. Mech.
,
65
(
2–3
), pp.
299
315
.10.1016/S0013-7944(99)00125-3
155.
Gregory
,
J. R.
, and
Spearing
,
S. M.
,
2004
, “
A Fiber Bridging Model for Fatigue Delamination in Composite Materials
,”
Acta Mater.
,
52
(
19
), pp.
5493
5502
.10.1016/j.actamat.2004.08.009
156.
Zhu
,
Y.
,
Liechti
,
K. M.
, and
Ravi-Chandar
,
K.
,
2009
, “
Direct Extraction of Rate-Dependent Traction Separation Laws for Polyurea/Steel Interfaces
,”
Int. J. Solids Struct.
,
46
(
1
), pp.
31
51
.10.1016/j.ijsolstr.2008.08.019
157.
Jacobsen
,
T. K.
, and
Sorensen
,
B. F.
,
2001
, “
Mode I Intra-Laminar Crack Growth in Composites—Modelling of R-Curves From Measured Bridging Laws
,”
Composites, Part A
,
32
(
1
), pp.
1
11
.10.1016/S1359-835X(00)00139-1
158.
Mihashi
,
H.
, and
Nomura
,
N.
,
1996
, “
Correlation Between Characteristics of Fracture Process Zone and Tension-Softening Properties of Concrete
,”
Nucl. Eng. Des.
,
165
(
3
), pp.
359
376
.10.1016/0029-5493(96)01205-8
159.
Hanson
,
J. H.
,
Bittencourt
,
T. N.
, and
Ingraffea
,
A. R.
,
2004
, “
Three-Dimensional Influence Coefficient Method for Cohesive Crack Simulations
,”
Eng. Fract. Mech.
,
71
(
15
), pp.
2109
2124
.10.1016/j.engfracmech.2003.12.008
160.
Planas
,
J.
,
Guinea
,
G. V.
, and
Elices
,
M.
,
1999
, “
Size Effect and Inverse Analysis in Concrete Fracture
,”
Int. J. Fract.
,
95
(
1–4
), pp.
367
378
.10.1023/A:1018681124551
161.
Guo
,
X. H.
,
Tin-Loi
,
F.
, and
Li
,
H.
,
1999
, “
Determination of Quasibrittle Fracture Law for Cohesive Crack Models
,”
Cem. Concr. Res.
,
29
(
7
), pp.
1055
1059
.10.1016/S0008-8846(99)00089-7
162.
Tin-Loi
,
F.
, and
Que
,
N. S.
,
2002
, “
Identification of Cohesive Crack Fracture Parameters by Evolutionary Search
,”
Comput. Methods Appl. Mech. Eng.
,
191
(
49–50
), pp.
5741
5760
.10.1016/S0045-7825(02)00483-8
163.
Que
,
N. S.
, and
Tin-Loi
,
F.
,
2002
, “
Numerical Evaluation of Cohesive Fracture Parameters From a Wedge Splitting Test
,”
Eng. Fract. Mech.
,
69
(
11
), pp.
1269
1286
.10.1016/S0013-7944(01)00131-X
164.
Que
,
N. S.
, and
Tin-Loi
,
F.
,
2002
, “
An Optimization Approach for Indirect Identification of Cohesive Crack Properties
,”
Comput. Struct.
,
80
(
16–17
), pp.
1383
1392
.10.1016/S0045-7949(02)00096-2
165.
Park
,
K.
,
Paulino
,
G. H.
, and
Roesler
,
J. R.
,
2008
, “
Determination of the Kink Point in the Bilinear Softening Model for Concrete
,”
Eng. Fract. Mech.
,
75
(
13
), pp.
3806
3818
.10.1016/j.engfracmech.2008.02.002
166.
Cusatis
,
G.
, and
Schauffert
,
E. A.
,
2009
, “
Cohesive Crack Analysis of Size Effect
,”
Eng. Fract. Mech.
,
76
(
14
), pp.
2163
2173
.10.1016/j.engfracmech.2009.06.008
167.
Cedolin
,
L.
, and
Cusatis
,
G.
,
2008
, “
Identification of Concrete Fracture Parameters Through Size Effect Experiments
,”
Cem. Concr. Compos.
,
30
(
9
), pp.
788
797
.10.1016/j.cemconcomp.2008.05.007
168.
Sorensen
,
B. F.
,
Gamstedt
,
E. K.
,
Ostergaard
,
R. C.
, and
Goutianos
,
S.
,
2008
, “
Micromechanical Model of Cross-Over Fibre Bridging Prediction of Mixed Mode Bridging Laws
,”
Mech. Mater.
,
40
(
4–5
), pp.
220
234
.10.1016/j.mechmat.2007.07.007
169.
Cusatis
,
G.
,
Pelessone
,
D.
, and
Mencarelli
,
A.
,
2011
, “
Lattice Discrete Particle Model (LDPM) for Failure Behavior of Concrete. I: Theory
,”
Cem. Concr. Compos.
,
33
(
9
), pp.
881
890
.10.1016/j.cemconcomp.2011.02.011
170.
Cusatis
,
G.
, and
Cedolin
,
L.
,
2007
, “
Two-Scale Study of Concrete Fracturing Behavior
,”
Eng. Fract. Mech.
,
74
(
12
), pp.
3
17
.10.1016/j.engfracmech.2006.01.021
171.
Bažant
,
Z. P.
,
Ožbolt
,
J.
, and
Eligehausen
,
R.
,
1994
, “
Fracture Size Effect: Review of Evidence for Concrete Structures
,”
J. Struct. Eng.
,
120
(
8
), pp.
2377
2398
.10.1061/(ASCE)0733-9445(1994)120:8(2377)
172.
Bažant
,
Z. P.
,
Daniel
,
I. M.
, and
Li
,
Z.
,
1996
, “
Size Effect and Fracture Characteristics of Composite Laminates
,”
ASME J. Eng. Mater. Technol.
,
118
(
3
), pp.
317
324
.10.1115/1.2806812
173.
Bažant
,
Z. P.
, and
Yu
,
Q.
,
2006
, “
Size Effect on Strength of Quasibrittle Structures With Reentrant Corners Symmetrically Loaded in Tension
,”
J. Eng. Mech.
,
132
(
11
), pp.
1168
1176
.10.1061/(ASCE)0733-9399(2006)132:11(1168)
174.
Bažant
,
Z. P.
, and
Pfeiffer
,
P. A.
,
1987
, “
Determination of Fracture Energy From Size Effect and Brittleness Number
,”
ACI Mater. J.
,
84
(
6
), pp.
463
480
.
175.
de Azevedo Soriano
,
E.
, and
de Almeida
,
S. F. M.
,
1999
, “
Notch Sensitivity of Carbon/Epoxy Fabric Laminates
,”
Compos. Sci. Technol.
,
59
(
8
), pp.
1143
1151
.10.1016/S0266-3538(98)00154-7
176.
Taylor
,
D.
,
2007
, “
Chapter 9-Fatigue: Predicting Fatigue Limit and Fatigue Life
,”
The Theory of Critical Distances
,
Elsevier
,
Oxford
, pp.
163–II
.
177.
Taylor
,
D.
,
2007
, “
Chapter 6-Polymers: Brittle Fracture in Polymeric Materials
,”
The Theory of Critical Distances
,
Elsevier
,
Oxford
, pp.
93–I
.
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