Composite laminate has extensive usage in the aerospace and automotive industries. Thus delamination, one of its most prevalent and challenging failure modes, has attracted substantial research efforts, and lead to the rapid development of both simulation and experiment method. Although reviews exist about simulation and experiment methods, there are not many that cover the development in the last five years. This paper is targeted to fill that gap. We covered a broad range of topic in delamination, from the basic delamination onset and propagation theories to complex loading scenarios, like impact and fatigue loading. From a simulation point of view, virtual crack closure technique (VCCT) and cohesive zone model (CZM), the two most famous methods of delamination modeling, are compared and elaborated. Their implementation techniques are described, and their merits and drawbacks are discussed. We also covered the failure mode of combined delamination and matrix cracking, which is prevalent in impact loading scenarios. Simulation techniques, along with the failure mechanisms, are presented. From experiment point of view, the discussed topics range from delamination fracture toughness (DFT) tests under static, dynamic, or cyclic loading conditions, to impact tests that aim to obtain the impact resistance and residual strength after impact. Moreover, a collection of recent experiment data is provided.

References

References
1.
Naebe
,
M.
,
Abolhasani
,
M. M.
,
Khayyam
,
H.
,
Amini
,
A.
, and
Fox
,
B.
,
2016
, “
Crack Damage in Polymers and Composites: A Review
,”
Polym. Rev.
,
56
(
1
), pp.
31
69
.
2.
Zhang
,
H.
,
Bilotti
,
E.
, and
Peijs
,
T.
,
2015
, “
The Use of Carbon Nanotubes for Damage Sensing and Structural Health Monitoring in Laminated Composites: A Review
,”
Nanocomposites
,
1
(
4
), pp.
167
184
.https://www.tandfonline.com/doi/abs/10.1080/20550324.2015.1113639
3.
Liu
,
D.
,
Tang
,
Y.
, and
Cong
,
W.
,
2012
, “
A Review of Mechanical Drilling for Composite Laminates
,”
Compos. Struct.
,
94
(
4
), pp.
1265
1279
.
4.
González
,
E.
,
Maimí
,
P.
,
Camanho
,
P.
,
Turon
,
A.
, and
Mayugo
,
J.
,
2012
, “
Simulation of Drop-Weight Impact and Compression After Impact Tests on Composite Laminates
,”
Compos. Struct.
,
94
(
11
), pp.
3364
3378
.
5.
Carraro
,
P. A.
,
Novello
,
E.
,
Quaresimin
,
M.
, and
Zappalorto
,
M.
,
2017
, “
Delamination Onset in Symmetric Cross-Ply Laminates Under Static Loads: Theory, Numerics and Experiments
,”
Compos. Struct.
,
176
, pp.
420
432
.
6.
Orifici
,
A.
,
Herszberg
,
I.
, and
Thomson
,
R.
,
2008
, “
Review of Methodologies for Composite Material Modelling Incorporating Failure
,”
Compos. Struct.
,
86
(
1–3
), pp.
194
210
.
7.
Liu
,
P. F.
,
Hou
,
S. J.
,
Chu
,
J. K.
,
Hu
,
X. Y.
,
Zhou
,
C. L.
,
Liu
,
Y. L.
,
Zheng
,
J. Y.
,
Zhao
,
A.
, and
Yan
,
L.
,
2011
, “
Finite Element Analysis of Postbuckling and Delamination of Composite Laminates Using Virtual Crack Closure Technique
,”
Compos. Struct.
,
93
(
6
), pp.
1549
1560
.
8.
Turon
,
A.
,
Camanho
,
P.
,
Costa
,
J.
, and
Renart
,
J.
,
2010
, “
Accurate Simulation of Delamination Growth Under Mixed-Mode Loading Using Cohesive Elements: Definition of Interlaminar Strengths and Elastic Stiffness
,”
Compos. Struct.
,
92
(
8
), pp.
1857
1864
.
9.
Feng
,
D.
, and
Aymerich
,
F.
,
2014
, “
Finite Element Modelling of Damage Induced by Low-Velocity Impact on Composite Laminates
,”
Compos. Struct.
,
108
, pp.
161
171
.
10.
Bak
,
B. L.
,
Turon
,
A.
,
Lindgaard
,
E.
, and
Lund
,
E.
,
2016
, “
A Simulation Method for High‐Cycle Fatigue‐Driven Delamination Using a Cohesive Zone Model
,”
Int. J. Numer. Methods Eng.
,
106
(
3
), pp.
163
191
.
11.
Chen
,
B.
,
Tay
,
T.
,
Pinho
,
S.
, and
Tan
,
V.
,
2017
, “
Modelling Delamination Migration in Angle-Ply Laminates
,”
Compos. Sci Technol.
,
142
, pp.
145
155
.
12.
Turon
,
A.
,
Davila
,
C. G.
,
Camanho
,
P. P.
, and
Costa
,
J.
,
2007
, “
An Engineering Solution for Mesh Size Effects in the Simulation of Delamination Using Cohesive Zone Models
,”
Eng. Fract. Mech.
,
74
(
10
), pp.
1665
1682
.
13.
Chen
,
B.
,
Pinho
,
S.
,
De Carvalho
,
N.
,
Baiz
,
P.
, and
Tay
,
T.
,
2014
, “
A Floating Node Method for the Modelling of Discontinuities in Composites
,”
Eng. Fract. Mech.
,
127
, pp.
104
134
.
14.
Simon
,
J.
,
Höwer
,
D.
,
Stier
,
B.
,
Reese
,
S.
, and
Fish
,
J. A.
,
2017
, “
Regularized Orthotropic Continuum Damage Model for Layered Composites: Intralaminar Damage Progression and Delamination
,”
Comput. Mech.
,
60
(
3
), pp.
445
463
.
15.
Harper
,
P. W.
, and
Hallett
,
S. R.
,
2010
, “
A Fatigue Degradation Law for Cohesive Interface Elements–Development and Application to Composite Materials
,”
Int. J. Fatigue
,
32
(
11
), pp.
1774
1787
.
16.
Richardson
,
M.
, and
Wisheart
,
M.
,
1996
, “
Review of Low-Velocity Impact Properties of Composite Materials
,”
Compos. Part A: Appl. Sci. Manuf.
,
27
(
12
), pp.
1123
1131
.
17.
Elder
,
D. J.
,
Thomson
,
R. S.
,
Nguyen
,
M. Q.
, and
Scott
,
M. L.
,
2004
, “
Review of Delamination Predictive Methods for Low Speed Impact of Composite Laminates
,”
Compos. Struct.
,
66
(
1–4
), pp.
677
683
.
18.
Tay
,
T.
,
2003
, “
Characterization and Analysis of Delamination Fracture in Composites: An Overview of Developments From 1990 to 2001
,”
ASME Appl. Mech. Rev.
,
56
(
1
), pp.
1
32
.
19.
Reeder
,
J. R.
,
2006
, “
3D Mixed-Mode Delamination Fracture Criteria–an Experimentalist's Perspective
,”
21st Annual Technical Conference
, Dearborn, MI, Sept. 17–20, pp.
1
18
.https://ntrs.nasa.gov/search.jsp?R=20060048260
20.
Shi
,
Y.
,
Pinna
,
C.
, and
Soutis
,
C.
,
2014
, “
Modelling Impact Damage in Composite Laminates: A Simulation of Intra-and Inter-Laminar Cracking
,”
Compos. Struct.
,
114
, pp.
10
19
.
21.
Chen
,
J.
,
Morozov
,
E. V.
, and
Shankar
,
K.
,
2014
, “
Simulating Progressive Failure of Composite Laminates Including In-Ply and Delamination Damage Effects
,”
Compos. Part A: Appl. Sci. Manuf.
,
61
, pp.
185
200
.
22.
Främby
,
J.
,
Fagerström
,
M.
, and
Brouzoulis
,
J.
,
2016
, “
Adaptive Modelling of Delamination Initiation and Propagation Using an Equivalent Single‐Layer Shell Approach
,”
Int. J. Numer. Methods Eng.
,
112
(
8
), pp.
882
908
.
23.
Tong
,
L.
,
1997
, “
An Assessment of Failure Criteria to Predict the Strength of Adhesively Bonded Composite Double Lap Joints
,”
J. Reinf. Plast. Compos.
,
16
(
8
), pp.
698
713
.
24.
Diaz
,
A. D.
, and
Caron
,
J.
,
2006
, “
Interface Plasticity and Delamination Onset Prediction
,”
Mech. Mater.
,
38
(
7
), pp.
648
663
.
25.
Brewer
,
J. C.
, and
Lagace
,
P. A.
,
1988
, “
Quadratic Stress Criterion for Initiation of Delamination
,”
J. Compos. Mater.
,
22
(
12
), pp.
1141
1155
.
26.
Ye
,
L.
,
1988
, “
Role of Matrix Resin in Delamination Onset and Growth in Composite Laminates
,”
Compos. Sci. Technol.
,
33
, pp.
257
277
.
27.
Camanho
,
P. P.
, and
Dávila
,
C. G.
,
2002
, “
Mixed-Mode Decohesion Finite Elements for the Simulation of Delamination in Composite Materials
,” National Aeronautics and Space Administration Langley Research Center, Hampton, VA, Report No.
NASA/TM-2002-211737
.https://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/20020053651.pdf
28.
Camanho
,
P. P.
,
Davila
,
C.
, and
De Moura
,
M.
,
2003
, “
Numerical Simulation of Mixed-Mode Progressive Delamination in Composite Materials
,”
J. Compos. Mater.
,
37
(
16
), pp.
1415
1438
.
29.
Camanho
,
P.
, and
Matthews
,
F.
,
1999
, “
Delamination Onset Prediction in Mechanically Fastened Joints in Composite Laminates
,”
J. Compos. Mater.
,
33
(
10
), pp.
906
927
.
30.
Luo
,
R.
,
Green
,
E.
, and
Morrison
,
C.
,
1999
, “
Impact Damage Analysis of Composite Plates
,”
Int. J. Impact Eng.
,
22
(
4
), pp.
435
447
.
31.
Fish
,
J. C.
, and
Lee
,
S. W.
,
1989
, “
Delamination of Tapered Composite Structures
,”
Eng. Fract. Mech.
,
34
(
1
), pp.
43
54
.
32.
Zhang
,
J.
, and
Zhang
,
X.
,
2015
, “
Simulating Low-Velocity Impact Induced Delamination in Composites by a Quasi-Static Load Model With Surface-Based Cohesive Contact
,”
Compos. Struct.
,
125
, pp.
51
57
.
33.
Christensen
,
R. M.
, and
DeTeresa
,
S. J.
,
2004
, “
Delamination Failure Investigation for out-of-Plane Loading in Laminates
,”
J. Compos. Mater.
,
38
(
24
), pp.
2231
2238
.
34.
Daniel
,
I. M.
,
Luo
,
J.
,
Schubel
,
P. M.
, and
Werner
,
B. T.
,
2009
, “
Interfiber/Interlaminar Failure of Composites Under Multi-Axial States of Stress
,”
Compos. Sci. Technol.
,
69
(
6
), pp.
764
771
.
35.
Daniel
,
I.
,
Werner
,
B.
, and
Fenner
,
J.
,
2011
, “
Strain-Rate-Dependent Failure Criteria for Composites
,”
Compos. Sci. Technol.
,
71
(
3
), pp.
357
364
.
36.
ASTM
,
2013
, “
Standard Test Method for Mode I Interlaminar Fracture Toughness of Unidirectional Fiber-Reinforced Polymer Matrix Composites
,”
ASTM International
,
West Conshohocken, PA
, Standard No.
ASTM D5528-13
.https://infostore.saiglobal.com/en-au/standards/astm-d5528-13-1694007/
37.
ASTM
,
2014
, “
Standard Test Method for Determination of the Mode II Interlaminar Fracture Toughness of Unidirectional Fiber-Reinforced Polymer Matrix Composites
,”
ASTM International
,
West Conshohocken, PA
, Standard No.
ASTM D7905/D7905M-14
.https://www.astm.org/Standards/D7905.htm
38.
Reeder
,
J.
,
1992
, “
An Evaluation of Mixed-Mode Delamination Failure Criteria
,” National Aeronautics and Space Administration, Langley Research Center, Hampton,VA, Report No.
NASA TM 104210
.https://ntrs.nasa.gov/search.jsp?R=19920009705
39.
Camanho
,
P. P.
,
Davila
,
C.
, and
Pinho
,
S.
,
2004
, “
Fracture Analysis of Composite Co‐Cured Structural Joints Using Decohesion Elements
,”
Fatigue Fract. Eng. Mater. Struct.
,
27
(
9
), pp.
745
757
.
40.
Whitcomb
,
J. D.
,
1984
, “
Analysis of Instability-Related Growth of a Through-Width Delamination
,” National Aeronautics and Space Administration, Langley Research Center, Hampton,VA, Report No.
NASA TM-86301
.https://ntrs.nasa.gov/search.jsp?R=19840025453
41.
De Morais
,
A.
,
Pereira
,
A.
,
De Moura
,
M.
,
Silva
,
F.
, and
Dourado
,
N.
,
2015
, “
Bilinear Approximations to the Mixed-Mode I–II Delamination Cohesive Law Using an Inverse Method
,”
Compos. Struct.
,
122
, pp.
361
366
.
42.
Reeder
,
J. R.
,
1993
, “
A Bilinear Failure Criterion for Mixed-Mode Delamination
,”
ASTM International
, West Conshohocken, PA, Standard No.
STP1206
.https://www.astm.org/DIGITAL_LIBRARY/STP/PAGES/STP12636S.htm
43.
Donaldson
,
S.
,
1985
, “
Fracture Toughness Testing of Graphite/Epoxy and Graphite/PEEK Composites
,”
Composites
,
16
(
2
), pp.
103
112
.
44.
Benzeggagh
,
M.
, and
Kenane
,
M.
,
1996
, “
Measurement of Mixed-Mode Delamination Fracture Toughness of Unidirectional Glass/Epoxy Composites With Mixed-Mode Bending Apparatus
,”
Compos. Sci. Technol.
,
56
(
4
), pp.
439
449
.
45.
Liu
,
Y.
,
Zhang
,
C.
, and
Xiang
,
Y.
,
2015
, “
A Critical Plane-Based Fracture Criterion for Mixed-Mode Delamination in Composite Materials
,”
Compos. Part B: Eng.
,
82
, pp.
212
220
.
46.
Brunner
,
A.
,
Blackman
,
B.
, and
Davies
,
P.
,
2008
, “
A Status Report on Delamination Resistance Testing of Polymer–Matrix Composites
,”
Eng. Fract. Mech.
,
75
(
9
), pp.
2779
2794
.
47.
ASTM
,
2013
, “
Standard Test Method for Mode I Interlaminar Fracture Toughness of Unidirectional Fiber-Reinforced Polymer Matrix Composites
,”
ASTM International
,
West Conshohocken, PA
, Report No.
ASTM D5528-13
.https://www.astm.org/Standards/D5528
48.
Mathews
,
M. J.
, and
Swanson
,
S. R.
,
2007
, “
Characterization of the Interlaminar Fracture Toughness of a Laminated Carbon/Epoxy Composite
,”
Compos. Sci. Technol.
,
67
(
7–8
), pp.
1489
1498
.
49.
Zhao
,
L.
,
Gong
,
Y.
,
Zhang
,
J.
,
Chen
,
Y.
, and
Fei
,
B.
,
2014
, “
Simulation of Delamination Growth in Multidirectional Laminates Under Mode I and Mixed Mode I/II Loadings Using Cohesive Elements
,”
Compos. Struct.
,
116
, pp.
509
522
.
50.
Solaimurugan
,
S.
, and
Velmurugan
,
R.
,
2008
, “
Influence of in-Plane Fibre Orientation on Mode I Interlaminar Fracture Toughness of Stitched Glass/Polyester Composites
,”
Compos. Sci. Technol.
,
68
(
7–8
), pp.
1742
52
.
51.
Andersons
,
J.
,
Hojo
,
M.
, and
Ochiai
,
S.
,
2004
, “
Empirical Model for Stress Ratio Effect on Fatigue Delamination Growth Rate in Composite Laminates
,”
Int. J. Fatigue
,
26
(
6
), pp.
597
604
.
52.
Shiino
,
M. Y.
,
Alderliesten
,
R. C.
,
Donadon
,
M. V.
,
Voorwald
,
H. J. C.
, and
Cioffi
,
M. O. H.
,
2015
, “
Applicability of Standard Delamination Tests (Double Cantilever Beam and End Notch Flexure) for 5HS Fabric-Reinforced Composites in Weft-Dominated Surface
,”
J. Compos. Mater.
,
49
(
21
), pp.
2557
2565
.
53.
Nikbakht
,
M.
,
Yousefi
,
J.
,
Hosseini-Toudeshky
,
H.
, and
Minak
,
G.
,
2017
, “
Delamination Evaluation of Composite Laminates With Different Interface Fiber Orientations Using Acoustic Emission Features and Micro Visualization
,”
Compos. Part B: Eng.
,
113
, pp.
185
196
.
54.
Alfred Franklin
,
V.
, and
Christopher
,
T.
,
2013
, “
Fracture Energy Estimation of DCB Specimens Made of Glass/Epoxy: An Experimental Study
,”
Adv. Mater. Sci. Eng.
,
2013
, p. 412601.
55.
Pereira
,
A.
, and
De Morais
,
A.
,
2004
, “
Mode I Interlaminar Fracture of Carbon/Epoxy Multidirectional Laminates
,”
Compos. Sci. Technol.
,
64
(
13–14
), pp.
2261
2270
.
56.
De Morais
,
A.
, and
Pereira
,
A.
,
2007
, “
Application of the Effective Crack Method to Mode I and Mode II Interlaminar Fracture of Carbon/Epoxy Unidirectional Laminates
,”
Compos. Part A: Appl. Sci. Manuf.
,
38
(
3
), pp.
785
794
.
57.
Arai
,
M.
,
Noro
,
Y.
,
Sugimoto
,
K.
, and
Endo
,
M.
,
2008
, “
Mode I and Mode II Interlaminar Fracture Toughness of CFRP Laminates Toughened by Carbon Nanofiber Interlayer
,”
Compos. Sci. Technol.
,
68
(
2
), pp.
516
525
.
58.
Velmurugan
,
R.
, and
Solaimurugan
,
S.
,
2007
, “
Improvements in Mode I Interlaminar Fracture Toughness and in-Plane Mechanical Properties of Stitched Glass/Polyester Composites
,”
Compos. Sci. Technol.
,
67
(
1
), pp.
61
69
.
59.
Shokrieh
,
M.
,
Zeinedini
,
A.
, and
Ghoreishi
,
S.
,
2017
, “
On the Mixed Mode I/II Delamination R-Curve of E-Glass/Epoxy Laminated Composites
,”
Compos. Struct.
,
171
, pp.
19
31
.
60.
Murri
,
G. B.
,
2014
, “
Effect of Data Reduction and Fiber-Bridging on Mode I Delamination Characterization of Unidirectional Composites
,”
J. Compos. Mater.
,
48
(
19
), pp.
2413
2424
.
61.
Gogotsi
,
G. A.
,
2003
, “
Fracture Toughness of Ceramics and Ceramic Composites
,”
Ceram. Int.
,
29
(
7
), pp.
777
784
.
62.
Göktaş
,
D.
,
Kennon
,
W.
, and
Potluri
,
P.
,
2017
, “
Improvement of Mode I Interlaminar Fracture Toughness of Stitched Glass/Epoxy Composites
,”
Appl. Compos. Mater.
,
24
(
2
), pp.
351
375
.
63.
Pinto
,
M. A.
,
Chalivendra
,
V. B.
,
Kim
,
Y. K.
, and
Lewis
,
A. F.
,
2013
, “
Effect of Surface Treatment and Z-Axis Reinforcement on the Interlaminar Fracture of Jute/Epoxy Laminated Composites
,”
Eng. Fract. Mech.
,
114
, pp.
104
114
.
64.
Ravandi
,
M.
,
Teo
,
W.
,
Tran
,
L.
,
Yong
,
M.
, and
Tay
,
T.
,
2016
, “
The Effects of Through-the-Thickness Stitching on the Mode I Interlaminar Fracture Toughness of Flax/Epoxy Composite Laminates
,”
Mater. Des.
,
109
, pp.
659
669
.
65.
Wang
,
J.
, and
Qiao
,
P.
,
2004
, “
Novel Beam Analysis of End Notched Flexure Specimen for Mode-II Fracture
,”
Eng. Fract. Mech.
,
71
(
2
), pp.
219
231
.
66.
Blackman
,
B.
,
Brunner
,
A.
, and
Williams
,
J.
,
2006
, “
Mode II Fracture Testing of Composites: A New Look at an Old Problem
,”
Eng. Fract. Mech.
,
73
(
16
), pp.
2443
2455
.
67.
Schuecker
,
C.
, and
Davidson
,
B. D.
,
2000
, “
Evaluation of the Accuracy of the Four-Point Bend End-Notched Flexure Test for Mode II Delamination Toughness Determination
,”
Compos. Sci. Technol.
,
60
(
11
), pp.
2137
2146
.
68.
Davidson
,
B. D.
, and
Sun
,
X.
,
2005
, “
Effects of Friction, Geometry, and Fixture Compliance on the Perceived Toughness From Three-and Four-Point Bend End-Notched Flexure Tests
,”
J. Reinf. Plast. Compos.
,
24
(
15
), pp.
1611
1628
.
69.
Machado
,
J.
,
Marques
,
E.
,
Campilho
,
R.
, and
da Silva
,
L. F.
,
2017
, “
Mode II Fracture Toughness of CFRP as a Function of Temperature and Strain Rate
,”
Compos. Part B: Eng.
,
114
, pp.
311
318
.
70.
De Moura
,
M.
, and
De Morais
,
A.
,
2008
, “
Equivalent Crack Based Analyses of ENF and ELS Tests
,”
Eng. Fract. Mech.
,
75
(
9
), pp.
2584
2596
.
71.
Zabala
,
H.
,
Aretxabaleta
,
L.
,
Castillo
,
G.
, and
Aurrekoetxea
,
J.
,
2016
, “
Dynamic 4 ENF Test for a Strain Rate Dependent Mode II Interlaminar Fracture Toughness Characterization of Unidirectional Carbon Fibre Epoxy Composites
,”
Polym. Test.
,
55
, pp.
212
218
.
72.
Davidson
,
B. D.
,
2015
, “
Standardization of the End-Notched Flexure Test for Mode II Interlaminar Fracture Toughness Determination of Unidirectional Laminated Composites
,”
J. Test. Eval.
,
43
(
6
), pp.
1540
1553
.
73.
Tanaka
,
K.
,
Kageyama
,
K.
, and
Hojo
,
M.
,
1995
, “
Prestandardization Study on Mode II Interlaminar Fracture Toughness Test for CFRP in Japan
,”
Composites
,
26
(
4
), pp.
257
267
.
74.
Wang
,
W.
,
Nakata
,
M.
,
Takao
,
Y.
, and
Matsubara
,
T.
,
2009
, “
Experimental Investigation on Test Methods for Mode II Interlaminar Fracture Testing of Carbon Fiber Reinforced Composites
,”
Compos. Part A: Appl. Sci. Manuf.
,
40
(
9
), pp.
1447
1455
.
75.
Pereira
,
A.
,
De Morais
,
A.
,
Marques
,
A.
, and
De Castro
,
P.
,
2004
, “
Mode II Interlaminar Fracture of Carbon/Epoxy Multidirectional Laminates
,”
Compos. Sci. Technol.
,
64
(
10–11
), pp.
1653
1659
.
76.
Pereira
,
A.
, and
De Morais
,
A.
,
2004
, “
Mode II Interlaminar Fracture of Glass/Epoxy Multidirectional Laminates
,”
Compos. Part A: Appl. Sci. Manuf.
,
35
(
2
), pp.
265
272
.
77.
Samborski
,
S.
,
2017
, “
Analysis of the End-Notched Flexure Test Configuration Applicability for Mechanically Coupled Fiber Reinforced Composite Laminates
,”
Compos. Struct.
,
163
, pp.
342
349
.
78.
Davies
,
P.
,
Casari
,
P.
, and
Carlsson
,
L.
,
2005
, “
Influence of Fibre Volume Fraction on Mode II Interlaminar Fracture Toughness of Glass/Epoxy Using the 4ENF Specimen
,”
Compos. Sci. Technol.
,
65
(
2
), pp.
295
300
.
79.
Marannano
,
G.
,
Parrinello
,
F.
, and
Pasta
,
A.
,
2015
, “
Numerical and Experimental Analysis of the Frictional Effects on 4ENF Delamination Tests Performed on Unidirectional CFRP
,”
Procedia Eng.
,
109
, pp.
372
380
.
80.
Crews
,
J. H.
, Jr.
, and
Reeder
,
J. R.
,
1988
, “
A Mixed-Mode Bending Apparatus for Delamination Testing
,” National Aeronautics and Space Administration Langley Research Center, Hampton, VA, Report No.
NSAS/TM-100662
.https://ntrs.nasa.gov/search.jsp?R=19890001574
81.
ASTM
,
2013
, “
Standard Test Method for Mixed Mode I-Mode II Interlaminar Fracture Toughness of Unidirectional Fiber Reinforced Polymer Matrix Composites
,”
ASTM International
,
West Conshohocken, PA
, Standard No.
ASTM D6671/D6671M-13e1
.https://www.astm.org/Standards/D6671.htm
82.
Bennati
,
S.
,
Colleluori
,
M.
,
Corigliano
,
D.
, and
Valvo
,
P. S.
,
2009
, “
An Enhanced Beam-Theory Model of the Asymmetric Double Cantilever Beam (ADCB) Test for Composite Laminates
,”
Compos. Sci. Technol.
,
69
(
11–12
), pp.
1735
1745
.
83.
Mollón
,
V.
,
Bonhomme
,
J.
,
Viña
,
J.
, and
Argüelles
,
A.
,
2010
, “
Theoretical and Experimental Analysis of Carbon Epoxy Asymmetric Dcb Specimens to Characterize Mixed Mode Fracture Toughness
,”
Polym. Test
,
29
(
6
), pp.
766
770
.
84.
Bennati
,
S.
,
Fisicaro
,
P.
, and
Valvo
,
P. S.
,
2013
, “
An Enhanced Beam-Theory Model of the Mixed-Mode Bending (MMB) Test—Part II: Applications and Results
,”
Meccanica
,
48
(
2
), pp.
465
484
.
85.
Banks-Sills
,
L.
,
2015
, “
Interface Fracture Mechanics: Theory and Experiment
,”
Int. J. Fract.
,
191
(
1–2
), pp.
131
146
.
86.
Rubiera
,
S.
,
Argüelles
,
A.
,
Viña
,
J.
,
Rocandio
,
C.
, and
Bonhomme
,
J.
,
2016
, “
Fracture Behavior Under Mixed Mode I/II Static and Dynamic Loading of ADCB Specimens
,”
J. Reinf. Plast. Compos.
,
35
(
20
), pp.
1513
1523
.
87.
Banks‐Sills
,
L.
,
2014
, “
50th Anniversary Article: Review on Interface Fracture and Delamination of Composites
,”
Strain
,
50
(
2
), pp.
98
110
.
88.
Banks-Sills
,
L.
,
Freed
,
Y.
,
Eliasi
,
R.
, and
Fourman
,
V.
,
2006
, “
Fracture Toughness of the 45°/–45° Interface of a Laminate Composite
,”
Int. J. Fract.
,
141
(
1–2
), pp.
195
210
.
89.
Mollón
,
V.
,
Viña
,
J.
,
Argüelles
,
A.
,
Bonhomme
,
J.
, and
Viña
,
I.
,
2011
, “
Influence of the Mode Mixity Ratio and Test Procedures on the Total Energy Release Rate in Carbon-Epoxy Laminates
,”
Procedia Eng.
,
10
, pp.
953
958
.
90.
Chaves
,
F. J.
,
Da Silva
,
L.
,
De Moura
,
M.
,
Dillard
,
D.
, and
Esteves
,
V.
,
2014
, “
Fracture Mechanics Tests in Adhesively Bonded Joints: A Literature Review
,”
J. Adhes.
,
90
(
12
), pp.
955
992
.
91.
Da Silva
,
L.
,
Esteves
,
V.
, and
Chaves
,
F.
,
2011
, “
Fracture Toughness of a Structural Adhesive Under Mixed Mode Loadings
,”
Materialwiss. Werkstofftech.
,
42
(
5
), pp.
460
470
.
92.
Kim
,
B. W.
, and
Mayer
,
A. H.
,
2003
, “
Influence of Fiber Direction and Mixed-Mode Ratio on Delamination Fracture Toughness of Carbon/Epoxy Laminates
,”
Compos. Sci. Technol.
,
63
(
5
), pp.
695
713
.
93.
Choupani
,
N.
,
2008
, “
Experimental and Numerical Investigation of the Mixed-Mode Delamination in Arcan Laminated Specimens
,”
Mater. Sci. Eng.: A
,
478
(
1–2
), pp.
229
242
.
94.
Dharmawan
,
F.
,
Simpson
,
G.
,
Herszberg
,
I.
, and
John
,
S.
,
2006
, “
Mixed Mode Fracture Toughness of GFRP Composites
,”
Compos. Struct.
,
75
(
1–4
), pp.
328
338
.
95.
Marat-Mendes
,
R. M.
, and
Freitas
,
M. M.
,
2010
, “
Failure Criteria for Mixed Mode Delamination in Glass Fibre Epoxy Composites
,”
Compos. Struct.
,
92
(
9
), pp.
2292
2298
.
96.
Rybicki
,
E. F.
, and
Kanninen
,
M.
,
1977
, “
A Finite Element Calculation of Stress Intensity Factors by a Modified Crack Closure Integral
,”
Eng. Fract. Mech.
,
9
(
4
), pp.
931
938
.
97.
Watwood
,
V.
,
1970
, “
The Finite Element Method for Prediction of Crack Behavior
,”
Nucl. Eng. Des.
,
11
(
2
), pp.
323
332
.
98.
Krueger
,
R.
,
2004
, “
Virtual Crack Closure Technique: History, Approach, and Applications
,”
ASME Appl. Mech. Rev.
,
57
(
2
), pp.
109
143
.
99.
Oneida
,
E.
,
van der Meulen
,
M.
, and
Ingraffea
,
A.
,
2015
, “
Method for Calculating G, GI, and GII to Simulate Crack Growth in 2D, Multiple-Material Structures
,”
Eng. Fract. Mech.
,
140
, pp.
106
126
.
100.
Farkash
,
E.
, and
Banks-Sills
,
L.
,
2017
, “
Virtual Crack Closure Technique for an Interface Crack Between Two Transversely Isotropic Materials
,”
Int. J. Fract.
,
205
(
2
), pp.
189
202
.
101.
Sun
,
C.
, and
Manoharan
,
M.
,
1989
, “
Strain Energy Release Rates of an Interfacial Crack Between Two Orthotropic Solids
,”
J. Compos. Mater.
,
23
(
5
), pp.
460
478
.
102.
Shahverdi
,
M.
,
Vassilopoulos
,
A. P.
, and
Keller
,
T.
,
2015
, “
12 - Simulating the Effect of Fiber Bridging and Asymmetry on the Fracture Behavior of Adhesively-Bonded Composite Joints
,”
Fatigue and Fracture of Adhesively-Bonded Composite Joints
,
A. P.
Vassilopoulos
, ed.,
Woodhead Publishing
, Cambridge, UK, pp.
345
367
.
103.
Banks-Sills
,
L.
, and
Farkash
,
E.
,
2016
, “
A Note on the Virtual Crack Closure Technique for a Bimaterial Interface Crack
,”
Int. J. Fract.
,
201
(
2
), pp.
171
180
.
104.
De Carvalho
,
N.
,
Chen
,
B.
,
Pinho
,
S.
,
Ratcliffe
,
J.
,
Baiz
,
P.
, and
Tay
,
T.
,
2015
, “
Modeling Delamination Migration in Cross-Ply Tape Laminates
,”
Compos. Part A: Appl. Sci. Manuf.
,
71
, pp.
192
203
.
105.
Cox
,
B.
, and
Yang
,
Q.
,
2006
, “
In Quest of Virtual Tests for Structural Composites
,”
Science
,
314
(
5802
), pp.
1102
1107
.
106.
Liu
,
P.
,
Gu
,
Z.
,
Peng
,
X.
, and
Zheng
,
J.
,
2015
, “
Finite Element Analysis of the Influence of Cohesive Law Parameters on the Multiple Delamination Behaviors of Composites Under Compression
,”
Compos. Struct.
,
131
, pp.
975
986
.
107.
Marjanović
,
M.
,
Meschke
,
G.
, and
Vuksanović
,
D.
,
2016
, “
A Finite Element Model for Propagating Delamination in Laminated Composite Plates Based on the Virtual Crack Closure Method
,”
Compos. Struct.
,
150
, pp.
8
19
.
108.
McElroy
,
M.
,
2017
, “
Use of an Enriched Shell Finite Element to Simulate Delamination-Migration in a Composite Laminate
,”
Compos. Struct.
,
167
, pp.
88
95
.
109.
Pietropaoli
,
E.
, and
Riccio
,
A.
,
2011
, “
Formulation and Assessment of an Enhanced Finite Element Procedure for the Analysis of Delamination Growth Phenomena in Composite Structures
,”
Compos. Sci. Technol.
,
71
(
6
), pp.
836
846
.
110.
Riccio
,
A.
,
Raimondo
,
A.
, and
Scaramuzzino
,
F.
,
2013
, “
A Study on Skin Delaminations Growth in Stiffened Composite Panels by a Novel Numerical Approach
,”
Appl. Compos. Mater.
,
20
(
4
), pp.
465
488
.
111.
Riccio
,
A.
,
Raimondo
,
A.
, and
Scaramuzzino
,
F.
,
2015
, “
A Robust Numerical Approach for the Simulation of Skin–Stringer Debonding Growth in Stiffened Composite Panels Under Compression
,”
Compos. Part B: Eng.
,
71
, pp.
131
142
.
112.
Orifici
,
A. C.
, and
Krueger
,
R.
,
2010
, “
Assessment of Static Delamination Propagation Capabilities in Commercial Finite Element Codes Using Benchmark Analysis
,” National Aeronautics and Space Administration, Hampton, VA, Report No.
NASA/CR-2010-216709
.https://ntrs.nasa.gov/search.jsp?R=20100023298
113.
Davies
,
G.
, and
Guiamatsia
,
I.
,
2012
, “
The Problem of the Cohesive Zone in Numerically Simulating Delamination/Debonding Failure Modes
,”
Appl. Compos. Mater.
,
19
(
5
), pp.
831
838
.
114.
Krueger
,
R.
,
2008
, “
An Approach to Assess Delamination Propagation Simulation Capabilities in Commercial Finite Element Codes
,” National Aeronautics and Space Administration, Hampton, VA, Report No.
NASA TM/2008-215123
.https://ntrs.nasa.gov/search.jsp?R=20080015439
115.
Gasco
,
F.
, and
Feraboli
,
P.
,
2014
, “
A Crack Length Control Scheme for Solving Nonlinear Finite Element Equations in Stable and Unstable Delamination Propagation Analysis
,”
Compos. Struct.
,
117
, pp.
267
273
.
116.
Skvortsov
,
Y. V.
,
Chernyakin
,
S.
,
Glushkov
,
S.
, and
Perov
,
S.
,
2015
, “
Finite Element Modeling of Delamination Propagation in Composite Laminates
,”
Appl. Mech. Mater.
,
756
, pp. 347–352.
117.
Ahn
,
J. S.
, and
Woo
,
K. S.
,
2015
, “
Delamination of Laminated Composite Plates by p-Convergent Partial Discrete-Layer Elements With VCCT
,”
Mech. Res. Commun.
,
66
, pp.
60
69
.
118.
Bisagni
,
C.
,
Brambilla
,
P.
, and
Bavila
,
C. G.
,
2013
, “
Modeling Delamination in Postbuckled Composite Structures Under Static and Fatigue Loads
,”
SAMPE 2013
, Long Beach, CA, May 6–9.
119.
Barbero
,
E.
, and
Reddy
,
J.
,
1991
, “
Modeling of Delamination in Composite Laminates Using a Layer-Wise Plate Theory
,”
Int. J. Solids Struct.
,
28
(
3
), pp.
373
388
.
120.
Reddy
,
J.
,
1993
, “
An Evaluation of Equivalent-Single-Layer and Layerwise Theories of Composite Laminates
,”
Compos. Struct.
,
25
(
1–4
), pp.
21
35
.
121.
Turon
,
A.
,
Costa
,
J.
,
Camanho
,
P.
, and
Dávila
,
C.
,
2007
, “
Simulation of Delamination in Composites Under High-Cycle Fatigue
,”
Compos. Part A: Appl. Sci. Manuf.
,
38
(
11
), pp.
2270
2282
.
122.
Pietropaoli
,
E.
, and
Riccio
,
A.
,
2010
, “
On the Robustness of Finite Element Procedures Based on Virtual Crack Closure Technique and Fail Release Approach for Delamination Growth Phenomena. Definition and Assessment of a Novel Methodology
,”
Compos. Sci. Technol.
,
70
(
8
), pp.
1288
1300
.
123.
Samborski
,
S.
,
2016
, “
Numerical Analysis of the DCB Test Configuration Applicability to Mechanically Coupled Fiber Reinforced Laminated Composite Beams
,”
Compos. Struct.
,
152
, pp.
477
487
.
124.
DeCarvalho
,
N. V.
,
Chen
,
B.
,
Pinho
,
S. T.
,
Baiz
,
P.
,
Ratcliffe
,
J. G.
, and
Tay
,
T.
,
2013
, “
Floating Node Method and Virtual Crack Closure Technique for Modeling Matrix Cracking-Delamination Migration
,” 19th International Conference on Composite Materials (
ICCM19
), Montreal, QC, Canada, July 28–Aug. 2.https://ntrs.nasa.gov/search.jsp?R=20140000837
125.
Li
,
D.
,
Liu
,
Y.
, and
Zhang
,
X.
,
2015
, “
An Extended Layerwise Method for Composite Laminated Beams With Multiple Delaminations and Matrix Cracks
,”
Int. J. Numer. Methods Eng.
,
101
(
6
), pp.
407
434
.
126.
Li
,
D.
,
2016
, “
Delamination and Transverse Crack Growth Prediction for Laminated Composite Plates and Shells
,”
Comput. Struct.
,
177
, pp.
39
55
.
127.
Chen
,
B.
,
Tay
,
T.
,
Pinho
,
S.
, and
Tan
,
V.
,
2016
, “
Modelling the Tensile Failure of Composites With the Floating Node Method
,”
Comput. Methods Appl. Mech. Eng.
,
308
, pp.
414
442
.
128.
Krueger
,
R.
, and
Carvalho
,
N.
, In
2016
, “
Search of a Time Efficient Approach to Crack and Delamination Growth Predictions in Composites
,” 31st
American Society for Composites Technical Conference
, Williamsburg, VA, Sept. 19–22, p.17.https://ntrs.nasa.gov/search.jsp?R=20160012031
129.
Song
,
J.
,
Areias
,
P.
, and
Belytschko
,
T.
,
2006
, “
A Method for Dynamic Crack and Shear Band Propagation With Phantom Nodes
,”
Int. J. Numer. Methods Eng.
,
67
(
6
), pp.
868
893
.
130.
McElroy
,
M.
,
2015
, “
An Enriched Shell Element for Delamination Simulation in Composite Laminates
,” National Aeronautics and Space Administration, Hampton, VA, Report No.
NF1676 L-20621
.https://ntrs.nasa.gov/search.jsp?R=20160006284
131.
Dugdale
,
D.
,
1960
, “
Yielding of Steel Sheets Containing Slits
,”
J. Mech. Phys. Solids
,
8
(
2
), pp.
100
104
.
132.
Barenblatt
,
G. I.
,
1962
, “
The Mathematical Theory of Equilibrium Cracks in Brittle Fracture
,”
Adv. Appl. Mech.
,
7
, pp.
55
129
.
133.
Sosa
,
J. C.
, and
Karapurath
,
N.
,
2012
, “
Delamination Modelling of GLARE Using the Extended Finite Element Method
,”
Compos. Sci. Technol.
,
72
(
7
), pp.
788
791
.
134.
Camacho
,
G. T.
, and
Ortiz
,
M.
,
1996
, “
Computational Modelling of Impact Damage in Brittle Materials
,”
Int. J. Solids Struct.
,
33
(
20–22
), pp.
2899
2938
.
135.
Ortiz
,
M.
, and
Pandolfi
,
A.
,
1999
, “
Finite-Deformation Irreversible Cohesive Elements for Three-Dimensional Crack-Propagation Analysis
,”
Int. J. Numer. Methods Eng.
,
44
(
9
), pp.
1267
1282
.
136.
Zhang
,
Z.
, and
Chen
,
Y.
,
2015
, “
A Constrained Intrinsic Cohesive Finite Element Method With Little Stiffness Reduction for Fracture Simulation
,”
Eng. Fract. Mech.
,
136
, pp.
213
225
.
137.
Blal
,
N.
,
Daridon
,
L.
,
Monerie
,
Y.
, and
Pagano
,
S.
,
2011
, “
Criteria on the Artificial Compliance Inherent to the Intrinsic Cohesive Zone
,”
C. R. Méc.
,
339
, pp.
789
795
.
138.
Blal
,
N.
,
Daridon
,
L.
,
Monerie
,
Y.
, and
Pagano
,
S.
,
2012
, “
Artificial Compliance Inherent to the Intrinsic Cohesive Zone Models: Criteria and Application to Planar Meshes
,”
Int. J. Fract.
,
178
(
1–2
), pp.
71
83
.
139.
Wu
,
L.
,
Becker
,
G.
, and
Noels
,
L.
,
2014
, “
Elastic Damage to Crack Transition in a Coupled Non-Local Implicit Discontinuous Galerkin/Extrinsic Cohesive Law Framework
,”
Comput. Methods Appl. Mech. Eng.
,
279
, pp.
379
409
.
140.
Becker
,
G.
, and
Noels
,
L.
,
2013
, “
A Full‐Discontinuous Galerkin Formulation of Nonlinear Kirchhoff–Love Shells: Elasto‐Plastic Finite Deformations, Parallel Computation, and Fracture Applications
,”
Int. J. Numer. Methods Eng.
,
93
(
1
), pp.
80
117
.
141.
Dooley
,
I.
,
Mangala
,
S.
,
Kale
,
L.
, and
Geubelle
,
P.
,
2009
, “
Parallel Simulations of Dynamic Fracture Using Extrinsic Cohesive Elements
,”
J. Sci. Comput.
,
39
(
1
), pp.
144
165
.
142.
Abrate
,
S.
,
Ferrero
,
J.
, and
Navarro
,
P.
,
2015
, “
Cohesive Zone Models and Impact Damage Predictions for Composite Structures
,”
Meccanica
,
50
(
10
), pp.
2587
2620
.
143.
Xu
,
X.
, and
Needleman
,
A.
,
1994
, “
Numerical Simulations of Fast Crack Growth in Brittle Solids
,”
J. Mech. Phys. Solids
,
42
(
9
), pp.
1397
1434
.
144.
Van den Bosch
,
M.
,
Schreurs
,
P.
, and
Geers
,
M.
,
2006
, “
An Improved Description of the Exponential Xu and Needleman Cohesive Zone Law for Mixed-Mode Decohesion
,”
Eng. Fract. Mech.
,
73
(
9
), pp.
1220
1234
.
145.
Zhang
,
W.
, and
Tabiei
,
A.
, “
Improvement of an Exponential Cohesive Zone Model for Fatigue Analysis
,”
J. Fail. Anal. Prev.
,
18
(3), pp.
1
12
.
146.
Tvergaard
,
V.
, and
Hutchinson
,
J. W.
,
1993
, “
The Influence of Plasticity on Mixed Mode Interface Toughness
,”
J. Mech. Phys. Solids
,
41
(
6
), pp.
1119
1135
.
147.
Tabiei
,
A.
, and
Zhang
,
W.
,
2017
, “
Cohesive Element Approach for Dynamic Crack Propagation: Artificial Compliance and Mesh Dependency
,”
Eng. Fract. Mech.
,
180
, pp.
23
42
.
148.
Manual
,
L. D. K. U. S.
,
2013
, “LS-DYNA,” Vol. II, Livermore Software Technology Corporation, Livermore, CA.
149.
Chandra
,
N.
,
Li
,
H.
,
Shet
,
C.
, and
Ghonem
,
H.
,
2002
, “
Some Issues in the Application of Cohesive Zone Models for Metal–Ceramic Interfaces
,”
Int. J. Solids Struct.
,
39
(
10
), pp.
2827
2855
.
150.
Alfano
,
G.
,
2006
, “
On the Influence of the Shape of the Interface Law on the Application of Cohesive-Zone Models
,”
Compos. Sci. Technol.
,
66
(
6
), pp.
723
730
.
151.
Campilho
,
R.
,
Banea
,
M. D.
,
Neto
,
J.
, and
da Silva
,
L. F.
,
2013
, “
Modelling Adhesive Joints With Cohesive Zone Models: Effect of the Cohesive Law Shape of the Adhesive Layer
,”
Int. J. Adhes. Adhes.
,
44
, pp.
48
56
.
152.
Volokh
,
K. Y.
,
2004
, “
Comparison Between Cohesive Zone Models
,”
Commun. Numer. Methods Eng.
,
20
(
11
), pp.
845
856
.
153.
Balzani
,
C.
, and
Wagner
,
W.
,
2008
, “
An Interface Element for the Simulation of Delamination in Unidirectional Fiber-Reinforced Composite Laminates
,”
Eng. Fract. Mech.
,
75
(
9
), pp.
2597
2615
.
154.
Jousset
,
P.
, and
Rachik
,
M.
,
2014
, “
Comparison and Evaluation of Two Types of Cohesive Zone Models for the Finite Element Analysis of Fracture Propagation in Industrial Bonded Structures
,”
Eng. Fract. Mech.
,
132
, pp.
48
69
.
155.
Joki
,
R.
,
Grytten
,
F.
,
Hayman
,
B.
, and
Sørensen
,
B. F.
,
2016
, “
Determination of a Cohesive Law for Delamination Modelling–Accounting for Variation in Crack Opening and Stress State Across the Test Specimen Width
,”
Compos. Sci. Technol.
,
128
, pp.
49
57
.
156.
Dourado
,
N.
,
de Moura
,
M.
,
de Morais
,
A.
, and
Pereira
,
A.
,
2012
, “
Bilinear Approximations to the Mode II Delamination Cohesive Law Using an Inverse Method
,”
Mech. Mater.
,
49
, pp.
42
50
.
157.
Nguyen
,
N.
, and
Waas
,
A. M.
,
2016
, “
A Novel Mixed-Mode Cohesive Formulation for Crack Growth Analysis
,”
Compos. Struct.
,
156
, pp.
253
262
.
158.
Xie
,
J.
,
Waas
,
A. M.
, and
Rassaian
,
M.
,
2017
, “
Analytical Predictions of Delamination Threshold Load of Laminated Composite Plates Subject to Flexural Loading
,”
Compos. Struct.
,
179
, pp.
181
194
.
159.
Xie
,
J.
,
Waas
,
A. M.
, and
Rassaian
,
M.
,
2016
, “
Closed-Form Solutions for Cohesive Zone Modeling of Delamination Toughness Tests
,”
Int. J. Solids Struct.
,
88
, pp.
379
400
.
160.
Long
,
S.
,
Yao
,
X.
, and
Zhang
,
X.
,
2015
, “
Delamination Prediction in Composite Laminates Under Low-Velocity Impact
,”
Compos. Struct.
,
132
, pp.
290
298
.
161.
Dávila
,
C. G.
,
2007
, “
Cohesive Elements for Shells
,” Camanho, Pedro Manuel Ponces Rodrigues De Castro, Turon Travesa A, National Aeronautics and Space Administration Langley Research Center, Hampton, VA, Report No.
NASA/TP-2007-214869
.https://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/20070018344.pdf
162.
Li
,
B.
,
Li
,
Y.
, and
Su
,
J.
,
2014
, “
A Combined Interface Element to Simulate Interfacial Fracture of Laminated Shell Structures
,”
Compos. Part B: Eng.
,
58
, pp.
217
227
.
163.
Dávila
,
C. G.
,
Camanho
,
P. P.
, and
Turon
,
A.
,
2008
, “
Effective Simulation of Delamination in Aeronautical Structures Using Shells and Cohesive Elements
,”
J Aircr.
,
45
(
2
), pp.
663
672
.
164.
Cirak
,
F.
,
Ortiz
,
M.
, and
Pandolfi
,
A.
,
2005
, “
A Cohesive Approach to Thin-Shell Fracture and Fragmentation
,”
Comput. Methods Appl. Mech. Eng.
,
194
(
21–24
), pp.
2604
2618
.
165.
Borg
,
R.
,
Nilsson
,
L.
, and
Simonsson
,
K.
,
2004
, “
Simulating DCB, ENF and MMB Experiments Using Shell Elements and a Cohesive Zone Model
,”
Compos. Sci. Technol.
,
64
(
2
), pp.
269
278
.
166.
Allix
,
O.
, and
Corigliano
,
A.
,
1999
, “
Geometrical and Interfacial Non-Linearities in the Analysis of Delamination in Composites
,”
Int. J. Solids Struct.
,
36
(
15
), pp.
2189
2216
.
167.
Hallquist
,
J. O.
,
2006
, “
LS-DYNA Theory Manual
,” Vol.
3
,
Livermore Software Technology Corporation
, Livermore, CA, pp.
25
31
.
168.
Schellekens
,
J.
, and
De Borst
,
R.
,
1993
, “
On the Numerical Integration of Interface Elements
,”
Int. J. Numer. Methods Eng.
,
36
(
1
), pp.
43
66
.
169.
Yang
,
Q.
,
Fang
,
X.
,
Shi
,
J.
, and
Lua
,
J.
,
2010
, “
An Improved Cohesive Element for Shell Delamination Analyses
,”
Int. J. Numer. Methods Eng.
,
83
, pp.
611
641
.
170.
Bak
,
B. L.
,
Sarrado
,
C.
,
Turon
,
A.
, and
Costa
,
J.
,
2014
, “
Delamination Under Fatigue Loads in Composite Laminates: A Review on the Observed Phenomenology and Computational Methods
,”
ASME Appl. Mech. Rev.
,
66
(
6
), p.
060803
.
171.
Vignollet
,
J.
,
May
,
S.
, and
Borst
,
R.
,
2015
, “
On the Numerical Integration of Isogeometric Interface Elements
,”
Int. J. Numer. Methods Eng.
,
102
(
11
), pp.
1733
1749
.
172.
Do
,
B.
,
Liu
,
W.
,
Yang
,
Q.
, and
Su
,
X.
,
2013
, “
Improved Cohesive Stress Integration Schemes for Cohesive Zone Elements
,”
Eng. Fract. Mech.
,
107
, pp.
14
28
.
173.
Hosseini
,
S.
,
Remmers
,
J. J. C.
,
Verhoosel
,
C. V.
, and
de Borst
,
R.
,
2014
, “
An Isogeometric Continuum Shell Element for Non-Linear Analysis
,”
Comput. Methods Appl. Mech. Eng.
,
271
, pp.
1
22
.
174.
Hosseini
,
S.
,
Remmers
,
J. J.
,
Verhoosel
,
C. V.
, and
Borst
,
R.
,
2015
, “
Propagation of Delamination in Composite Materials With Isogeometric Continuum Shell Elements
,”
Int. J. Numer. Methods Eng.
,
102
(
3–4
), pp.
159
179
.
175.
Tomar
,
V.
,
Zhai
,
J.
, and
Zhou
,
M.
,
2004
, “
Bounds for Element Size in a Variable Stiffness Cohesive Finite Element Model
,”
Int. J. Numer. Methods Eng.
,
61
(
11
), pp.
1894
1920
.
176.
Irwin
,
G.
,
1957
, “
Relation of Stresses Near a Crack to the Crack Extension Force
,”
Ninth International Congress of Applied Mechanics
, Brussels, Belgium, Sept. 5–13.
177.
Rice
,
J. R.
, and
Tracey
,
D. M.
,
1969
, “
On the Ductile Enlargement of Voids in Triaxial Stress Fields
,”
J. Mech. Phys. Solids.
,
17
(
3
), pp.
201
217
.
178.
Hillerborg
,
A.
,
Modéer
,
M.
, and
Petersson
,
P.
,
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
.
179.
Falk
,
M. L.
,
Needleman
,
A.
, and
Rice
,
J. R.
,
2001
, “
A Critical Evaluation of Cohesive Zone Models of Dynamic Fracture
,”
Le J. De Phys. IV
,
11
(
Pr5
), pp. Pr-5-43–Pr-5-50.
180.
Harper
,
P. W.
, and
Hallett
,
S. R.
,
2008
, “
Cohesive Zone Length in Numerical Simulations of Composite Delamination
,”
Eng. Fract. Mech.
,
75
(
16
), pp.
4774
4792
.
181.
Song
,
K.
,
Dávila
,
C. G.
, and
Rose
,
C. A.
,
2008
, “
Guidelines and Parameter Selection for the Simulation of Progressive Delamination
,”
ABAQUS User's Conference
, Newport, RI, May 19–22, pp.
43
44
.https://ntrs.nasa.gov/search.jsp?R=20080020385
182.
Xie
,
D.
, and
Biggers
,
S. B.
,
2006
, “
Strain Energy Release Rate Calculation for a Moving Delamination Front of Arbitrary Shape Based on the Virtual Crack Closure Technique—Part I: Formulation and Validation
,”
Eng. Fract. Mech.
,
73
(
6
), pp.
771
785
.
183.
Hermes
,
F. H.
,
2010
, “
Process Zone and Cohesive Element Size in Numerical Simulations of Delamination in Bi-Layers
,”
Master's thesis
, Eindhoven University of Technology, Eindhoven, The Netherlands.http://www.mate.tue.nl/mate/pdfs/12147.pdf
184.
Xie
,
D.
, and
Waas
,
A. M.
,
2006
, “
Discrete Cohesive Zone Model for Mixed-Mode Fracture Using Finite Element Analysis
,”
Eng. Fract. Mech.
,
73
(
13
), pp.
1783
1796
.
185.
Sarrado
,
C.
,
Leone
,
F. A.
, and
Turon
,
A.
,
2016
, “
Finite-Thickness Cohesive Elements for Modeling Thick Adhesives
,”
Eng. Fract. Mech.
,
168
, pp.
105
113
.
186.
Zubillaga
,
L.
,
Turon
,
A.
,
Maimí
,
P.
,
Costa
,
J.
,
Mahdi
,
S.
, and
Linde
,
P.
,
2014
, “
An Energy Based Failure Criterion for Matrix Crack Induced Delamination in Laminated Composite Structures
,”
Compos. Struct.
,
112
, pp.
339
344
.
187.
Reiner
,
J.
,
Veidt
,
M.
,
Dargusch
,
M.
, and
Gross
,
L. A.
,
2016
, “
Progressive Analysis of Matrix Cracking-Induced Delamination in Composite Laminates Using an Advanced Phantom Node Method
,”
J. Compos. Mater.
,
51
(
20
), p. 15.
188.
Jalalvand
,
M.
,
Wisnom
,
M. R.
,
Hosseini-Toudeshky
,
H.
, and
Mohammadi
,
B.
,
2014
, “
Experimental and Numerical Study of Oblique Transverse Cracking in Cross-Ply Laminates Under Tension
,”
Compos. Part A: Appl. Sci. Manuf.
,
67
, pp.
140
148
.
189.
Pernice
,
M. F.
,
De Carvalho
,
N. V.
,
Ratcliffe
,
J. G.
, and
Hallett
,
S. R.
,
2015
, “
Experimental Study on Delamination Migration in Composite Laminates
,”
Compos. Part A: Appl. Sci. Manuf.
,
73
, pp.
20
34
.
190.
Ratcliffe
,
J. G.
,
Czabaj
,
M. W.
, and
O'Brien
,
T. K.
,
2013
, “
A Test for Characterizing Delamination Migration in Carbon/Epoxy Tape Laminates
,” National Aeronautics and Space Administration Langley Research Center, Hampton, VA, Report No.
NASA/TM–2013-218028
.https://ntrs.nasa.gov/search.jsp?R=20140000686&hterms=Test+Charac-+terizing+Delamination+Migration+Carbon%2fEpoxy+Tape+Laminates&qs=N%3D0%26Ntk%3DAll%26Ntt%3DA%2520Test%2520for%2520Charac-%2520terizing%2520Delamination%2520Migration%2520in%2520Carbon%252FEpoxy%2520Tape%2520Laminates%26Ntx%3Dmode%2520matchallpartial
191.
Iarve
,
E. V.
,
Gurvich
,
M. R.
,
Mollenhauer
,
D. H.
,
Rose
,
C. A.
, and
Dávila
,
C. G.
,
2011
, “
Mesh‐Independent Matrix Cracking and Delamination Modeling in Laminated Composites
,”
Int. J. Numer. Methods Eng.
,
88
(
8
), pp.
749
773
.
192.
Tay
,
T.
,
Sun
,
X.
, and
Tan
,
V.
,
2014
, “
Recent Efforts Toward Modeling Interactions of Matrix Cracks and Delaminations: An Integrated XFEM-CE Approach
,”
Adv. Compos. Mater.
,
23
(
5–6
), pp.
391
408
.
193.
Su
,
Z.
,
Tay
,
T.
,
Ridha
,
M.
, and
Chen
,
B.
,
2015
, “
Progressive Damage Modeling of Open-Hole Composite Laminates Under Compression
,”
Compos. Struct.
,
122
, pp.
507
517
.
194.
Hinton
,
M.
,
Kaddour
,
A.
, and
Soden
,
P.
,
2002
, “
A Comparison of the Predictive Capabilities of Current Failure Theories for Composite Laminates, Judged against Experimental Evidence
,”
Compos. Sci. Technol.
,
62
(
12–13
), pp.
1725
1797
.
195.
Kaddour
,
A.
,
Hinton
,
M.
,
Smith
,
P.
, and
Li
,
S.
,
2013
, “
A Comparison Between the Predictive Capability of Matrix Cracking, Damage and Failure Criteria for Fibre Reinforced Composite Laminates: Part a of the Third World-Wide Failure Exercise
,”
J. Compos. Mater.
,
47
(
20–21
), pp.
2749
2779
.
196.
Puck
,
A.
, and
Schürmann
,
H.
,
2002
, “
Failure Analysis of FRP Laminates by Means of Physically Based Phenomenological Models
,”
Compos. Sci. Technol.
,
62
(
12–13
), pp.
1633
1662
.
197.
Liu
,
K.
, and
Tsai
,
S. W.
,
1998
, “
A Progressive Quadratic Failure Criterion for a Laminate
,”
Compos. Sci. Technol.
,
58
(
7
), pp.
1023
1032
.
198.
Wolfe
,
W. E.
, and
Butalia
,
T. S.
,
1998
, “
A Strain-Energy Based Failure Criterion for Non-Linear Analysis of Composite Laminates Subjected to Biaxial Loading
,”
Compos. Sci. Technol.
,
58
(
7
), pp.
1107
1124
.
199.
Edge
,
E.
,
2002
, “
A Comparison of Theory and Experiment for the Stress-Based Grant–Sanders Method
,”
Compos. Sci. Technol.
,
62
(
12–13
), pp.
1571
1589
.
200.
Maimı
,
P.
,
Camanho
,
P.
,
Mayugo
,
J.
, and
Turon
,
A.
,
2011
, “
Matrix Cracking and Delamination in Laminated Composites—Part I: Ply Constitutive Law, First Ply Failure and Onset of Delamination
,”
Mech. Mater.
,
43
(
4
), pp.
169
185
.
201.
Kumar
,
D.
,
Roy
,
R.
,
Kweon
,
J.
, and
Choi
,
J.
,
2016
, “
Numerical Modeling of Combined Matrix Cracking and Delamination in Composite Laminates Using Cohesive Elements
,”
Appl. Compos. Mater.
,
23
(
3
), pp.
397
419
.
202.
Li
,
X.
, and
Chen
,
J.
,
2017
, “
A Highly Efficient Prediction of Delamination Migration in Laminated Composites Using the Extended Cohesive Damage Model
,”
Compos. Struct.
,
160
, pp.
712
721
.
203.
Li
,
X.
, and
Chen
,
J.
,
2016
, “
An Extended Cohesive Damage Model for Simulating Multicrack Propagation in Fibre Composites
,”
Compos. Struct.
,
143
, pp.
1
8
.
204.
Jäger
,
S.
,
Pickett
,
A.
, and
Middendorf
,
P.
,
2016
, “
A Discrete Model for Simulation of Composites Plate Impact Including Coupled Intra-and Inter-Ply Failure
,”
Appl. Compos. Mater.
,
23
(
2
), pp.
179
195
.
205.
Shojaei
,
A.
,
Li
,
G.
,
Tan
,
P. J.
, and
Fish
,
J.
,
2015
, “
Dynamic Delamination in Laminated Fiber Reinforced Composites: A Continuum Damage Mechanics Approach
,”
Int. J. Solids Struct.
,
71
, pp.
262
276
.
206.
Mohammadi
,
B.
,
Olia
,
H.
, and
Hosseini-Toudeshky
,
H.
,
2015
, “
Intra and Damage Analysis of Laminated Composites Using Coupled Continuum Damage Mechanics With Cohesive Interface Layer
,”
Compos. Struct.
,
120
, pp.
519
530
.
207.
Topac
,
O. T.
,
Gozluklu
,
B.
,
Gurses
,
E.
, and
Coker
,
D.
,
2017
, “
Experimental and Computational Study of the Damage Process in CFRP Composite Beams Under Low-Velocity Impact
,”
Compos. Part A: Appl. Sci. Manuf.
,
92
, pp.
167
182
.
208.
Panettieri
,
E.
,
Fanteria
,
D.
,
Montemurro
,
M.
, and
Froustey
,
C.
,
2016
, “
Low-Velocity Impact Tests on Carbon/Epoxy Composite Laminates: A Benchmark Study
,”
Compos. Part B: Eng.
,
107
, pp.
9
21
.
209.
Liang
,
S.
,
Guillaumat
,
L.
, and
Gning
,
P.
,
2015
, “
Impact Behaviour of Flax/Epoxy Composite Plates
,”
Int. J. Impact Eng.
,
80
, pp.
56
64
.
210.
Wiegand
,
J.
,
Hornig
,
A.
,
Gerlach
,
R.
,
Neale
,
C.
,
Petrinic
,
N.
, and
Hufenbach
,
W.
,
2015
, “
An Experimental Method for Dynamic Delamination Analysis of Composite Materials by Impact Bending
,”
Mech. Adv. Mater. Struct.
,
22
(
5
), pp.
413
421
.
211.
Liu
,
Y.
, and
Liaw
,
B.
,
2010
, “
Effects of Constituents and Lay-Up Configuration on Drop-Weight Tests of Fiber-Metal Laminates
,”
Appl. Compos. Mater.
,
17
(
1
), pp.
43
62
.
212.
Maio
,
L.
,
Monaco
,
E.
,
Ricci
,
F.
, and
Lecce
,
L.
,
2013
, “
Simulation of Low Velocity Impact on Composite Laminates With Progressive Failure Analysis
,”
Compos. Struct.
,
103
, pp.
75
85
.
213.
Zhang
,
X.
,
Bianchi
,
F.
, and
Liu
,
H.
,
2012
, “
Predicting Low-Velocity Impact Damage in Composites by a Quasi-Static Load Model With Cohesive Interface Elements
,”
Aeronaut. J.
,
116
(
1186
), pp.
1367
1381
.
214.
Bouvet
,
C.
,
Castanié
,
B.
,
Bizeul
,
M.
, and
Barrau
,
J.
,
2009
, “
Low Velocity Impact Modelling in Laminate Composite Panels With Discrete Interface Elements
,”
Int. J. Solids Struct.
,
46
(
14–15
), pp.
2809
2821
.
215.
Li
,
X.
,
Hallett
,
S. R.
, and
Wisnom
,
M. R.
,
2008
, “
Predicting the Effect of Through-Thickness Compressive Stress on Delamination Using Interface Elements
,”
Compos. Part A: Appl. Sci. Manuf.
,
39
(
2
), pp.
218
230
.
216.
Sitnikova
,
E.
,
Li
,
S.
,
Li
,
D.
, and
Yi
,
X.
,
2017
, “
Subtle Features of Delamination in Cross-Ply Laminates Due to Low Speed Impact
,”
Compos. Sci. Technol.
,
149
, pp.
149
158
.
217.
Kim
,
E.
,
Rim
,
M.
,
Lee
,
I.
, and
Hwang
,
T.
,
2013
, “
Composite Damage Model Based on Continuum Damage Mechanics and Low Velocity Impact Analysis of Composite Plates
,”
Compos. Struct.
,
95
, pp.
123
134
.
218.
Liu
,
P.
,
Liao
,
B.
,
Jia
,
L.
, and
Peng
,
X.
,
2016
, “
Finite Element Analysis of Dynamic Progressive Failure of Carbon Fiber Composite Laminates Under Low Velocity Impact
,”
Compos. Struct.
,
149
, pp.
408
422
.
219.
Tan
,
W.
,
Falzon
,
B. G.
,
Chiu
,
L. N.
, and
Price
,
M.
,
2015
, “
Predicting Low Velocity Impact Damage and Compression-After-Impact (CAI) Behaviour of Composite Laminates
,”
Compos. Part A: Appl. Sci. Manuf.
,
71
, pp.
212
226
.
220.
Rivallant
,
S.
,
Bouvet
,
C.
, and
Hongkarnjanakul
,
N.
,
2013
, “
Failure Analysis of CFRP Laminates Subjected to Compression After Impact: FE Simulation Using Discrete Interface Elements
,”
Compos. Part A: Appl. Sci. Manuf.
,
55
, pp.
83
93
.
221.
Ruiz
,
G.
,
Pandolfi
,
A.
, and
Ortiz
,
M.
,
2001
, “
Three‐Dimensional Cohesive Modeling of Dynamic Mixed‐Mode Fracture
,”
Int. J. Numer. Methods Eng.
,
52
(
12
), pp.
97
120
.
222.
Ostré
,
B.
,
Bouvet
,
C.
,
Minot
,
C.
, and
Aboissière
,
J.
,
2016
, “
Experimental Analysis of CFRP Laminates Subjected to Compression After Edge Impact
,”
Compos. Struct.
,
152
, pp.
767
778
.
223.
Yu
,
H.
,
Olsen
,
J. S.
,
Olden
,
V.
,
Alvaro
,
A.
,
He
,
J.
, and
Zhang
,
Z.
,
2016
, “
Viscous Regularization for Cohesive Zone Modeling Under Constant Displacement: An Application to Hydrogen Embrittlement Simulation
,”
Eng. Fract. Mech.
,
166
, pp.
23
42
.
224.
Rivallant
,
S.
,
Bouvet
,
C.
,
Abdallah
,
E. A.
,
Broll
,
B.
, and
Barrau
,
J.
,
2014
, “
Experimental Analysis of CFRP Laminates Subjected to Compression After Impact: The Role of Impact-Induced Cracks in Failure
,”
Compos. Struct.
,
111
, pp.
147
157
.
225.
ASTM
,
2015
, “Standard Test Method for Measuring the Damage Resistance of a Fiber-Reinforced Polymer Matrix Composite to a Drop-Weight Impact Event,”
ASTM International
,
West Conshohocken, PA
, Standard No. ASTM D7136/D7136M-15.
226.
Evci
,
C.
, and
Gülgeç
,
M.
,
2012
, “
An Experimental Investigation on the Impact Response of Composite Materials
,”
Int. J. Impact Eng.
,
43
, pp.
40
51
.
227.
Zhang
,
D.
,
Sun
,
Y.
,
Chen
,
L.
, and
Pan
,
N.
,
2013
, “
A Comparative Study on Low-Velocity Impact Response of Fabric Composite Laminates
,”
Mater. Des.
,
50
, pp.
750
756
.
228.
Mouritz
,
A.
,
2013
, “
Delamination Properties of z-Pinned Composites in Hot–Wet Environment
,”
Compos. Part A: Appl. Sci. Manuf.
,
52
, pp.
134
142
.
229.
Shyr
,
T.
, and
Pan
,
Y.
,
2003
, “
Impact Resistance and Damage Characteristics of Composite Laminates
,”
Compos. Struct.
,
62
(
2
), pp.
193
203
.
230.
Sutherland
,
L.
, and
Soares
,
C. G.
,
2012
, “
The Use of Quasi-Static Testing to Obtain the Low-Velocity Impact Damage Resistance of Marine GRP Laminates
,”
Compos. Part B: Eng.
,
43
(
3
), pp.
1459
1467
.
231.
Guan
,
Z.
,
He
,
W.
,
Chen
,
J.
, and
Liu
,
L.
,
2014
, “
Permanent Indentation and Damage Creation of Laminates With Different Composite Systems: An Experimental Investigation
,”
Polym. Compos.
,
35
(
5
), pp.
872
883
.
232.
Wagih
,
A.
,
Maimí
,
P.
,
Blanco
,
N.
, and
Costa
,
J.
,
2016
, “
A Quasi-Static Indentation Test to Elucidate the Sequence of Damage Events in Low Velocity Impacts on Composite Laminates
,”
Compos. Part A: Appl. Sci. Manuf.
,
82
, pp.
180
189
.
233.
May
,
M.
,
2016
, “
Measuring the Rate-Dependent Mode I Fracture Toughness of Composites–a Review
,”
Compos. Part A: Appl. Sci. Manuf.
,
81
, pp.
1
12
.
234.
Jacob
,
G. C.
,
Starbuck
,
J. M.
,
Fellers
,
J. F.
,
Simunovic
,
S.
, and
Boeman
,
R. G.
,
2005
, “
The Effect of Loading Rate on the Fracture Toughness of Fiber Reinforced Polymer Composites
,”
J. Appl. Polym. Sci.
,
96
(
3
), pp.
899
904
.
235.
Zabala
,
H.
,
Aretxabaleta
,
L.
,
Castillo
,
G.
, and
Aurrekoetxea
,
J.
,
2015
, “
Loading Rate Dependency on Mode I Interlaminar Fracture Toughness of Unidirectional and Woven Carbon Fibre Epoxy Composites
,”
Compos. Struct.
,
121
, pp.
75
82
.
236.
Navarro
,
P.
,
Aubry
,
J.
,
Pascal
,
F.
,
Marguet
,
S.
,
Ferrero
,
J.
, and
Dorival
,
O.
,
2014
, “
Influence of the Stacking Sequence and Crack Velocity on Fracture Toughness of Woven Composite Laminates in Mode I
,”
Eng. Fract. Mech.
,
131
, pp.
340
348
.
237.
Cui
,
H.
,
Yasaee
,
M.
,
Kalwak
,
G.
,
Pellegrino
,
A.
,
Partridge
,
I. K.
,
Hallett
,
S. R.
, et al. .,
2017
, “
Bridging Mechanisms of Through-Thickness Reinforcement in Dynamic Mode I&II Delamination
,”
Compos. Part A: Appl. Sci. Manuf.
,
99
, pp.
198
207
.
238.
Kusaka
,
T.
,
Hojo
,
M.
,
Mai
,
Y.
,
Kurokawa
,
T.
,
Nojima
,
T.
, and
Ochiai
,
S.
,
1998
, “
Rate Dependence of Mode I Fracture Behaviour in Carbon-Fibre/Epoxy Composite Laminates
,”
Compos. Sci. Technol.
,
58
(
3–4
), pp.
591
602
.
239.
Hug
,
G.
,
Thevenet
,
P.
,
Fitoussi
,
J.
, and
Baptiste
,
D.
,
2006
, “
Effect of the Loading Rate on Mode I Interlaminar Fracture Toughness of Laminated Composites
,”
Eng. Fract. Mech.
,
73
(
16
), pp.
2456
2462
.
240.
de Verdiere
,
M. C.
,
Skordos
,
A.
,
Walton
,
A.
, and
May
,
M.
,
2012
, “
Influence of Loading Rate on the Delamination Response of Untufted and Tufted Carbon Epoxy Non-Crimp Fabric Composites/Mode II
,”
Eng. Fract. Mech.
,
96
, pp.
1
10
.
241.
Zhang
,
X.
,
Hounslow
,
L.
, and
Grassi
,
M.
,
2006
, “
Improvement of Low-Velocity Impact and Compression-After-Impact Performance by z-Fibre Pinning
,”
Compos. Sci. Technol.
,
66
(
15
), pp.
2785
2794
.
242.
ASTM
,
2012
, “
Standard Test Method for Compressive Residual Strength Properties of Damaged Polymer Matrix Composite Plates
,”
ASTM International
,
West Conshohocken, PA
, Standard no.
ASTM D7137/D7137M-17
.https://www.astm.org/Standards/D7137.htm
243.
Hart
,
K. R.
,
Chia
,
P. X.
,
Sheridan
,
L. E.
,
Wetzel
,
E. D.
,
Sottos
,
N. R.
, and
White
,
S. R.
,
2017
, “
Comparison of Compression-After-Impact and Flexure-After-Impact Protocols for 2D and 3D Woven Fiber-Reinforced Composites
,”
Compos. Part A: Appl. Sci. Manuf.
,
101
, pp. 471–479.
244.
Sánchez-Sáez
,
S.
,
Barbero
,
E.
,
Zaera
,
R.
, and
Navarro
,
C.
,
2005
, “
Compression After Impact of Thin Composite Laminates
,”
Compos. Sci. Technol.
,
65
(
13
), pp.
1911
1919
.
245.
Aktaş
,
A.
,
Aktaş
,
M.
, and
Turan
,
F.
,
2014
, “
Impact and Post Impact (CAI) Behavior of Stitched Woven–Knit Hybrid Composites
,”
Compos. Struct.
,
116
, pp.
243
253
.
246.
Erdogan
,
G.
, and
Bilisik
,
K.
,
2017
, “
Compression After Low Velocity Impact (CAI) Properties of Multi-Stitched Composites
,”
Mech. Adv. Mater. Struct.
,
25
(8), pp. 623–636.
247.
Remacha
,
M.
,
Sánchez-Sáez
,
S.
,
López-Romano
,
B.
, and
Barbero
,
E.
,
2015
, “
A New Device for Determining the Compression After Impact Strength in Thin Laminates
,”
Compos. Struct.
,
127
, pp.
99
107
.
248.
Cromer
,
K.
,
Gillespie
,
J. W.
, Jr.
, and
Keefe
,
M.
,
2012
, “
Effect of Multiple Non-Coincident Impacts on Residual Properties of Glass/Epoxy Laminates
,”
J. Reinf. Plast. Compos.
,
31
(
12
), pp.
815
827
.
249.
Zhang
,
Z.
,
Shankar
,
K.
,
Morozov
,
E. V.
, and
Tahtali
,
M.
,
2016
, “
Vibration-Based Delamination Detection in Composite Beams Through Frequency Changes
,”
J. Vib. Control
,
22
(
2
), pp.
496
512
.
250.
Sohn
,
H.
,
Dutta
,
D.
,
Yang
,
J.
,
Park
,
H.
,
DeSimio
,
M.
,
Olson
,
S.
, et al. .,
2011
, “
Delamination Detection in Composites Through Guided Wave Field Image Processing
,”
Compos. Sci. Technol.
,
71
(
9
), pp.
1250
1256
.
251.
Tian
,
Z.
,
Yu
,
L.
, and
Leckey
,
C.
,
2015
, “
Delamination Detection and Quantification on Laminated Composite Structures With Lamb Waves and Wavenumber Analysis
,”
J. Intell. Mater. Syst. Struct.
,
26
(
13
), pp.
1723
1738
.
252.
Pasquali
,
M.
, and
Lacarbonara
,
W.
,
2015
, “
Delamination Detection in Composite Laminates Using High-Frequency P-and S-Waves—Part I: Theory and Analysis
,”
Compos. Struct.
,
134
, pp.
1095
1108
.
253.
Rogge
,
M. D.
, and
Leckey
,
C. A.
,
2013
, “
Characterization of Impact Damage in Composite Laminates Using Guided Wavefield Imaging and Local Wavenumber Domain Analysis
,”
Ultrasonics
,
53
(
7
), pp.
1217
1226
.
254.
Saeedi
,
N.
,
Sab
,
K.
, and
Caron
,
J.
,
2012
, “
Delaminated Multilayered Plates Under Uniaxial Extension—Part I: Analytical Analysis Using a Layerwise Stress Approach
,”
Int. J. Solids Struct.
,
49
(
26
), p.
3711
.
255.
Ghadermazi
,
K.
,
Khozeimeh
,
M.
,
Taheri-Behrooz
,
F.
, and
Safizadeh
,
M.
,
2015
, “
Delamination Detection in Glass–Epoxy Composites Using Step-Phase Thermography (SPT)
,”
Infrared Phys. Technol.
,
72
, pp.
204
209
.
256.
Takeda
,
S.
,
Minakuchi
,
S.
,
Okabe
,
Y.
, and
Takeda
,
N.
,
2005
, “
Delamination Monitoring of Laminated Composites Subjected to Low-Velocity Impact Using Small-Diameter FBG Sensors
,”
Compos. Part A: Appl. Sci. Manuf.
,
36
(
7
), pp.
903
908
.
257.
Frieden
,
J.
,
Cugnoni
,
J.
,
Botsis
,
J.
, and
Gmür
,
T.
,
2012
, “
Low Energy Impact Damage Monitoring of Composites Using Dynamic Strain Signals From FBG Sensors–Part I: Impact Detection and Localization
,”
Compos. Struct.
,
94
(
2
), pp.
438
445
.
258.
Hu
,
H.
,
Li
,
S.
,
Wang
,
J.
,
Wang
,
Y.
, and
Zu
,
L.
,
2016
, “
FBG-Based Real-Time Evaluation of Transverse Cracking in Cross-Ply Laminates
,”
Compos. Struct.
,
138
, pp.
151
160
.
259.
Zhu
,
Q.
,
Xu
,
C.
, and
Yang
,
G.
,
2017
, “
Experimental Research on Damage Detecting in Composite Materials With FBG Sensors Under Low Frequency Cycling
,”
Int. J. Fatigue
,
101
, pp.
61
66
.
260.
Amenabar
,
I.
,
Mendikute
,
A.
,
López-Arraiza
,
A.
,
Lizaranzu
,
M.
, and
Aurrekoetxea
,
J.
,
2011
, “
Comparison and Analysis of Non-Destructive Testing Techniques Suitable for Delamination Inspection in Wind Turbine Blades
,”
Compos. Part B: Eng.
,
42
(
5
), pp.
1298
1305
.
261.
Post
,
W.
,
Kersemans
,
M.
,
Solodov
,
I.
,
Van Den Abeele
,
K.
,
García
,
S.
, and
van der Zwaag
,
S.
,
2017
, “
Non-Destructive Monitoring of Delamination Healing of a CFRP Composite With a Thermoplastic Ionomer Interlayer
,”
Compos. Part A: Appl. Sci. Manuf.
,
101
, pp.
243
253
.
262.
Abot
,
J. L.
,
Song
,
Y.
,
Vatsavaya
,
M. S.
,
Medikonda
,
S.
,
Kier
,
Z.
,
Jayasinghe
,
C.
, et al. .,
2010
, “
Delamination Detection With Carbon Nanotube Thread in Self-Sensing Composite Materials
,”
Compos. Sci. Technol.
,
70
(
7
), pp.
1113
1119
.
263.
Wen
,
J.
,
Xia
,
Z.
, and
Choy
,
F.
,
2011
, “
Damage Detection of Carbon Fiber Reinforced Polymer Composites Via Electrical Resistance Measurement
,”
Compos. Part B: Eng.
,
42
(
1
), pp.
77
86
.
264.
Roe
,
K.
, and
Siegmund
,
T.
,
2003
, “
An Irreversible Cohesive Zone Model for Interface Fatigue Crack Growth Simulation
,”
Eng. Fract. Mech.
,
70
(
2
), pp.
209
232
.
265.
Lemaitre
,
J.
,
2012
,
A Course on Damage Mechanics
,
Springer Science & Business Media
, Heidelberg, Germany.
266.
Jiang
,
H.
,
Gao
,
X.
, and
Srivatsan
,
T. S.
,
2009
, “
Predicting the Influence of Overload and Loading Mode on Fatigue Crack Growth: A Numerical Approach Using Irreversible Cohesive Elements
,”
Finite Elem. Anal Des
,
45
(
10
), pp.
675
685
.
267.
Beaurepaire
,
P.
, and
Schuëller
,
G.
,
2011
, “
Modeling of the Variability of Fatigue Crack Growth Using Cohesive Zone Elements
,”
Eng. Fract. Mech.
,
78
(
12
), pp.
2399
2413
.
268.
Siegmund
,
T.
,
2004
, “
A Numerical Study of Transient Fatigue Crack Growth by Use of an Irreversible Cohesive Zone Model
,”
Int. J. Fatigue
,
26
(
9
), pp.
929
939
.
269.
Bouvard
,
J.
,
Chaboche
,
J.
,
Feyel
,
F.
, and
Gallerneau
,
F.
,
2009
, “
A Cohesive Zone Model for Fatigue and Creep–Fatigue Crack Growth in Single Crystal Superalloys
,”
Int. J. Fatigue
,
31
(
5
), pp.
868
879
.
270.
Maiti
,
S.
, and
Geubelle
,
P. H.
,
2005
, “
A Cohesive Model for Fatigue Failure of Polymers
,”
Eng. Fract. Mech.
,
72
(
5
), pp.
691
708
.
271.
Wang
,
B.
, and
Siegmund
,
T.
,
2006
, “
Simulation of Fatigue Crack Growth at Plastically Mismatched Bi-Material Interfaces
,”
Int. J. Plast.
,
22
(
9
), pp.
1586
1609
.
272.
Yao
,
L.
,
Alderliesten
,
R.
,
Zhao
,
M.
, and
Benedictus
,
R.
,
2014
, “
Discussion on the Use of the Strain Energy Release Rate for Fatigue Delamination Characterization
,”
Compos. Part A: Appl. Sci. Manuf.
,
66
, pp.
65
72
.
273.
Allegri
,
G.
,
Wisnom
,
M.
, and
Hallett
,
S.
,
2013
, “
A New Semi-Empirical Law for Variable Stress-Ratio and Mixed-Mode Fatigue Delamination Growth
,”
Compos. Part A: Appl. Sci. Manuf.
,
48
, pp.
192
200
.
274.
Al-Khudairi
,
O.
,
Hadavinia
,
H.
,
Waggott
,
A.
,
Lewis
,
E.
, and
Little
,
C.
,
2015
, “
Characterising Mode I/Mode II Fatigue Delamination Growth in Unidirectional Fibre Reinforced Polymer Laminates
,”
Mater. Des.
,
66
, pp.
93
102
.
275.
Kenane
,
M.
,
2009
, “
Delamination Growth in Unidirectional Glass/Epoxy Composite Under Static and Fatigue Loads
,”
Phys. Procedia
,
2
(
3
), pp.
1195
1203
.
276.
Paris
,
P. C.
,
Gomez
,
M. P.
, and
Anderson
,
W. E.
,
1961
, “
A Rational Analytic Theory of Fatigue
,”
Trend Eng.
,
13
, pp.
9
14
.https://ci.nii.ac.jp/naid/10018490580/en/
277.
Alderliesten
,
R.
,
Schijve
,
J.
, and
Van der Zwaag
,
S.
,
2006
, “
Application of the Energy Release Rate Approach for Delamination Growth in Glare
,”
Eng. Fract. Mech.
,
73
(
6
), pp.
697
709
.
278.
Jones
,
R.
,
Pitt
,
S.
,
Bunner
,
A.
, and
Hui
,
D.
,
2012
, “
Application of the Hartman–Schijve Equation to Represent Mode I and Mode II Fatigue Delamination Growth in Composites
,”
Compos. Struct.
,
94
(
4
), pp.
1343
1351
.
279.
Landry
,
B.
, and
LaPlante
,
G.
,
2012
, “
Modeling Delamination Growth in Composites Under Fatigue Loadings of Varying Amplitudes
,”
Compos. Part B: Eng.
,
43
(
2
), pp.
533
541
.
280.
Kenane
,
M.
, and
Benzeggagh
,
M.
,
1997
, “
Mixed-Mode Delamination Fracture Toughness of Unidirectional Glass/Epoxy Composites Under Fatigue Loading
,”
Compos. Sci. Technol.
,
57
(
5
), pp.
597
605
.
281.
May
,
M.
, and
Hallett
,
S. R.
,
2010
, “
A Combined Model for Initiation and Propagation of Damage Under Fatigue Loading for Cohesive Interface Elements
,”
Compos. Part A: Appl. Sci. Manuf.
,
41
(
12
), pp.
1787
1796
.
282.
Moroni
,
F.
, and
Pirondi
,
A.
,
2011
, “
A Procedure for the Simulation of Fatigue Crack Growth in Adhesively Bonded Joints Based on the Cohesive Zone Model and Different Mixed-Mode Propagation Criteria
,”
Eng. Fract. Mech.
,
78
(
8
), pp.
1808
1816
.
283.
Kawashita
,
L. F.
, and
Hallett
,
S. R.
,
2012
, “
A Crack Tip Tracking Algorithm for Cohesive Interface Element Analysis of Fatigue Delamination Propagation in Composite Materials
,”
Int. J. Solids Struct.
,
49
(
21
), pp.
2898
2913
.
284.
Naghipour
,
P.
,
Bartsch
,
M.
, and
Voggenreiter
,
H.
,
2011
, “
Simulation and Experimental Validation of Mixed Mode Delamination in Multidirectional CF/PEEK Laminates Under Fatigue Loading
,”
Int. J. Solids Struct.
,
48
(
6
), pp.
1070
1081
.
285.
Wang
,
C.
, and
Xu
,
X.
,
2015
, “
Cohesive Element Analysis of Fatigue Delamination Propagation in Composite Materials With Improved Crack Tip Tracking Algorism
,”
Compos. Struct.
,
134
, pp.
176
184
.
286.
Bak
,
B.
,
Turon
,
A.
,
Lindgaard
,
E.
, and
Lund
,
E.
,
2017
, “
A Benchmark Study of Simulation Methods for High-Cycle Fatigue-Driven Delamination Based on Cohesive Zone Models
,”
Compos. Struct.
,
164
, pp.
198
206
.
287.
Zhang
,
W.
, and
Tabiei
,
A.
,
2017
, “
Fatigue Life Prediction of Composite Material's Adhesive Joints in Automotive Applications
,”
Int. J. Autom. Compos.
,
3
(
1
), pp.
61
79
.
288.
ASTM
,
2011
, “Standard Test Method for Mode I Fatigue Delamination Growth Onset of Unidirectional Fiber-Reinforced Polymer Matrix Composites,”
ASTM International
,
West Conshohocken, PA
, Standard No.
ASTM D6115-97(2011)
.https://www.astm.org/Standards/D6115.htm
289.
Sjögren
,
A.
, and
Asp
,
L. E.
,
2002
, “
Effects of Temperature on Delamination Growth in a Carbon/Epoxy Composite Under Fatigue Loading
,”
Int. J. Fatigue
,
24
(
2–4
), pp.
179
184
.
290.
Blanco
,
N.
,
Gamstedt
,
E. K.
,
Asp
,
L.
, and
Costa
,
J.
,
2004
, “
Mixed-Mode Delamination Growth in Carbon–Fibre Composite Laminates Under Cyclic Loading
,”
Int. J. Solids Struct.
,
41
(
15
), pp.
4219
4235
.
291.
Shivakumar
,
K.
,
Chen
,
H.
,
Abali
,
F.
,
Le
,
D.
, and
Davis
,
C.
,
2006
, “
A Total Fatigue Life Model for Mode I Delaminated Composite Laminates
,”
Int. J. Fatigue
,
28
(
1
), pp.
33
42
.
292.
Hojo
,
M.
,
Ando
,
T.
,
Tanaka
,
M.
,
Adachi
,
T.
,
Ochiai
,
S.
, and
Endo
,
Y.
,
2006
, “
Modes I and II Interlaminar Fracture Toughness and Fatigue Delamination of CF/Epoxy Laminates With Self-Same Epoxy Interleaf
,”
Int. J. Fatigue
,
28
(
10
), pp.
1154
1165
.
293.
Brunner
,
A.
,
Stelzer
,
S.
,
Pinter
,
G.
, and
Terrasi
,
G.
,
2013
, “
Mode II Fatigue Delamination Resistance of Advanced Fiber-Reinforced Polymer–Matrix Laminates: Towards the Development of a Standardized Test Procedure
,”
Int. J. Fatigue
,
50
, pp.
57
62
.
294.
Peng
,
L.
,
Xu
,
J.
,
Zhang
,
J.
, and
Zhao
,
L.
,
2012
, “
Mixed Mode Delamination Growth of Multidirectional Composite Laminates Under Fatigue Loading
,”
Eng. Fract. Mech.
,
96
, pp.
676
686
.
295.
Fernández
,
M.
,
De Moura
,
M.
,
Da Silva
,
L.
, and
Marques
,
A.
,
2013
, “
Mixed-Mode I II Fatigue/Fracture Characterization of Composite Bonded Joints Using the Single-Leg Bending Test
,”
Compos. Part A: Appl. Sci. Manuf.
,
44
, pp.
63
69
.
296.
Khan
,
R.
,
Alderliesten
,
R.
,
Badshah
,
S.
, and
Benedictus
,
R.
,
2015
, “
Effect of Stress Ratio or Mean Stress on Fatigue Delamination Growth in Composites: Critical Review
,”
Compos. Struct.
,
124
, pp.
214
227
.
297.
Pegorin
,
F.
,
Pingkarawat
,
K.
, and
Mouritz
,
A.
,
2015
, “
Comparative Study of the Mode I and Mode II Delamination Fatigue Properties of z-Pinned Aircraft Composites
,”
Mater. Des.
,
65
, pp.
139
146
.
298.
Matsubara
,
G.
,
Ono
,
H.
, and
Tanaka
,
K.
,
2006
, “
Mode II Fatigue Crack Growth From Delamination in Unidirectional Tape and Satin-Woven Fabric Laminates of High Strength GFRP
,”
Int. J. Fatigue
,
28
(
10
), pp.
1177
1186
.
299.
Coronado
,
P.
,
Argüelles
,
A.
,
Viña
,
J.
, and
Viña
,
I.
,
2014
, “
Influence of Low Temperatures on the Phenomenon of Delamination of Mode I Fracture in Carbon-Fibre/Epoxy Composites Under Fatigue Loading
,”
Compos. Struct.
,
112
, pp.
188
193
.
300.
Charalambous
,
G.
,
Allegri
,
G.
, and
Hallett
,
S. R.
,
2015
, “
Temperature Effects on Mixed Mode I/II Delamination Under Quasi-Static and Fatigue Loading of a Carbon/Epoxy Composite
,”
Compos. Part A: Appl. Sci. Manuf.
,
77
, pp.
75
86
.
301.
Nakai
,
Y.
, and
Hiwa
,
C.
,
2002
, “
Effects of Loading Frequency and Environment on Delamination Fatigue Crack Growth of CFRP
,”
Int. J. Fatigue
,
24
(
2–4
), pp.
161
170
.
302.
Stelzer
,
S.
,
Brunner
,
A.
,
Argüelles
,
A.
,
Murphy
,
N.
, and
Pinter
,
G.
,
2012
, “
Mode I Delamination Fatigue Crack Growth in Unidirectional Fiber Reinforced Composites: Development of a Standardized Test Procedure
,”
Compos. Sci. Technol.
,
72
(
10
), pp.
1102
1107
.
303.
Carreras
,
L.
,
Renart
,
J.
,
Turon
,
A.
,
Costa
,
J.
,
Essa
,
Y.
, and
de la Escalera
,
F. M.
,
2017
, “
An Efficient Methodology for the Experimental Characterization of Mode II Delamination Growth Under Fatigue Loading
,”
Int. J. Fatigue
,
95
, pp.
185
193
.
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