The present article is concerned with the application of the finite element method to the analysis of the onset of delamination growth in composites by means of the virtual crack closure technique (VCCT). The article reviews first the application of linear elastic fracture mechanics (LEFM) to the analysis of delamination, as well as the reasons why the VCC technique is the standard method of combining LEFM and the finite element method to predict onset of delamination growth. The article also reviews the different solutions proposed in the literature to deal with the oscillatory singularity associated with a crack between two dissimilar materials (as is the case for a delamination) and the practical details of the VCCT application in a general 3D analysis. Finally, the results of a numerical study of the mixed mode bending (MMB) interlaminar fracture test are shown. The study applies the concepts reviewed along the rest of this article and presents some practical recommendations for the analysis of a delamination front using finite elements. This review article includes 77 references.
Issue Section:
Review Articles
1.
Miller
AG
, Lowell
DT
, and Seferis
JC
(1994
), The evolution of an aerospace material: Influence of design, manufacturing and in-service performance
, Compos. Struct.
, 27
, 193
–206
.2.
Chamis CC and Ginty CA (1989), Fibre composite structural durability and damage tolerance: Simplified predictive methods, Composite Materials: Fatigue and Fracture 2, ASTM STP 1012, 338–355.
3.
Wolf K (1993), Strength prediction of impact damaged composites-an engineering model, Proc of ICCM-9, 6, Madrid, 343–350.
4.
Ferrigno A, La Barbera A, and Perugini P (1995), An engineering assessment of the static residual strength of composite laminates with impact-induced damages: integrated procedure based on 3D FEM and 2D theoretical analyses and experimental investigations, Proc of ICCM-10, 5, Whistler, BC, Canada, 679–686.
5.
Ishikawa T, Sugimoto S, Matsushuima M, and Hayashi Y (1995), Mechanical behaviour in compression after impact (CAI) test of CF/PEEK (APC-2) and conventional CF/epoxy flat laminates, Proc of ICCM-10, 5, Whistler, BC, Canada, 687–694.
6.
Kimpara I, Kageyama K, Ohsawa I, Suzuki T, and Yamashita A (1995), A proposal of prediction method of compressive residual strength of impact-damaged CFRP laminates, Proc of ICCM-10, 5, Whistler, BC, Canada, 655–662.
7.
Schellekens
JC
and De Borst
R
(1993
), Free edge delamination in carbon epoxy laminates: a novel numerical/experimental approach
, Compos. Struct.
, 28
, 467
–474
.8.
Cui
W
and Wisnom
MR
(1993
), A combined stress-based and fracture-mechanics-based model for predicting delamination in composites
, Composites
, 6
, 467
–474
.9.
Crisfield MA, Mi Y, Davies GAO, and Hellweg HB (1997), Finite element method and the progressive failure modelling of composite structures, CIMNE Proceedings, Computational plasticity: Fundamental and applications, Barcelona, 239–254.
10.
Chen
J
, Crisfield
M
, Kinloch
AJ
, Busso
EP
, Matthews
FL
, and Qiu
Y
(1999
), Predicting progressive delamination of composite material specimens via interface elements
, Mech. Compos. Mater.
, 6
, 301
–317
.11.
Ireman
T
, Thesken
JC
, Greenhalgh
E
, Sharp
R
, Ga¨dke
M
, Maison
S
, Ousset
Y
, Roudolff
F
, and La Barbera
A
(1996
), Damage propagation in composite structural elements-Coupon experiments and analyses
, Compos. Struct.
, 36
, 209
–220
.12.
Olsson
R
, Thesken
JC
, Brandt
F
, Jo¨nsson
N
, and Nilsson
S
(1996
), Investigations of delamination criticality and the transferability of growth criteria
, Compos. Struct.
, 36
, 221
–247
.13.
Ko¨nig M, Albinger J, and Ha¨nsel C (1993), Delamination buckling: numerical simulation of experiments, Proc of ICCM-9, 6, Madrid, 535–542.
14.
Ko¨nig M, Kru¨ger R, and Rinderknecht S (1995), Numerical simulation of delamination bucking and growth, Proc of ICCM-10, 1, Whistler, BC, Canada, 269–276.
15.
Krueger R, Ko¨nig M, and Ga¨dke M (1995), Predicting delamination growth under cyclic loading: an approach using computational structural analysis and testing, Proc of ICCM-10, 1, Whistler, BC, Canada, 561–568.
16.
Kutlu
Z
and Chang
FK
(1995
), Composite panels containing multiple through-the-width delaminations and subjected to compression. Part I: analysis
, Compos. Struct.
, 31
, 273
–296
.17.
Kutlu
Z
and Chang
FK
(1995
), Composite panels containing multiple through-the-width delaminations and subjected to compression. Part II: Experiments and verification
, Compos. Struct.
, 31
, 297
–314
.18.
Pradhan
SC
and Tay
TE
(1998
), Three-dimensional finite element modelling of delamination growth in notched composite laminate under compression loading
, Eng. Fract. Mech.
, 60
(2
), 157
–171
.19.
Martin RH (1998), Incorporating interlaminar fracture mechanics into design, Int Conf on Designing Cost-Effective Composites, London, 83–92.
20.
Awerbuch
J
and Madhukar
M
(1985
), Notched strength of composite laminates: predictions and experiments: A review
, J. Reinf. Plast. Compos.
, 4
, 3
–159
.21.
Friedrich K (1989), Fractographic analysis of polymer composites, Application of Fracture Mechanics to Composite Materials, Elsevier.
22.
O’Brien TK (1982), Characterisation of delamination onset and growth in a composite laminate, Damage in Composite Materials, ASTM STP 775.
23.
Griffith AA (1924), The Theory of Rupture, Proc 1st Int Congress of Applied Mechanics, J Waltman Sr (ed) Delft, 55–63.
24.
Irwin GR (1958), Fracture, Handbuck der Physik 6, Springer, Berlin, 551–590.
25.
Kinloch
AJ
, Wang
Y
, Williams
JG
, and Yaila
P
(1993
), The mixed-mode delamination of fibre composite materials
, Compos. Sci. Technol.
, 47
, 225
–237
.26.
Hashemi S, Kinloch AJ, and Williams JG (1991), Mixed-mode fracture in fiber-polymer composite laminates, Composite Materials: Fatigue and Fracture, ASTM STP 1110, 143–168.
27.
Charalambrides
M
, Williams
JG
, Kinloch
AJ
, and Wang
Y
(1992
), On the analysis of mixed mode fracture
, Int. J. Fract.
, 54
, 269
–291
.28.
Davidson BD, Fariello PL, Hudson RC, and Sundaraman V (1997), Accuracy assessment of the singular-field-based mode-mix decomposition procedure for the prediction of delamination, Composite Materials: Testing and Design, 13, ASTM STP 1242, 109–128.
29.
Russell AJ and Street KN (1985), Moisture and temperature effects on the mixed mode delamination of unidirectional graphite/epoxy, Delamination and Debonding of Materials, ASTM-STP-876.
30.
Ramkumar RL and Whitcomb JD (1985), Characterization of mode I and mixed mode delamination growth in T300/5208 graphite/epoxy, Delamination and Debonding of Materials, ASTM-STP-876.
31.
Reeder JR and Crews JH (1991), Redesign of the mixed-mode bending test for delamination toughness. ICCM-8, Hawaii, Paper 36-B3.
32.
Sriram P, Khourchid Y, Hooper SJ, and Martin RH (1995), Experimental delamination of a mixed-mode fatigue delamination criterion, Composite Materials: Fatigue and Fracture 5, ASTM STP 1230.
33.
Hashemi
S
, Kinloch
AJ
, and Williams
JG
(1990
), Mechanics and mechanism of delamination in a polyether sulphone fibre composite
, Compos. Sci. Technol.
, 37
, 429
–462
.34.
Bradley WL (1989), Relationship of matrix toughness to interlaminar fracture toughness, Application of Fracture Mechanics to Composite Materials, Elsevier Publ 159–188.
35.
Gong X and Benzeggagh M (1995), Mixed mode interlaminar fracture toughness of unidirectional glass/epoxy composite, Composite Materials: Fatigue and Fracture, 5, ASTM STP 1230, Philadelphia, 100–123.
36.
Whitney JM (1989), Experimental characterisation of delamination fracture, Interlaminar Response of Composite Materials, Elsevier Publ 161–250.
37.
Svenson
N
and Gilchrist
MD
(1998
), Mixed mode delamination of multidirectional carbon fiber/epoxy laminates
, Mech. Compos. Mater.
, 5
, 291
–307
.38.
Purslow D (1986), Matrix fractography of fibre-expoxy composites, Royal Aircraft Establishment, Tech Report 86046.
39.
Cvitkovich MK, Krueger R, O’Brien TK, and Minguet P (1998), De-bonding in composite skin/stringer configurations under multi-axial loading, Proc of 13th Annual Tech Conf on Composite Materials, Baltimore, 1014–1048.
40.
Broek D (1986), Elementary Engineering Fracture Mechanics, Kluwer Academic Publ, Dordrecht, The Netherlands.
41.
Wang
Y
and Williams
JG
(1992
), Corrections for mode II fracture toughness specimens of composite materials
, Compos. Sci. Technol.
, 43
, 251
–256
.42.
Parks
DM
(1974
), A stiffness derivative finite element technique for determination of crack tip stress intensity factors
, Int. J. Fract.
, 10
, 487
–502
.43.
Hellen
TK
(1975
), On the method of virtual crack extension
, Int. J. Numer. Methods Eng.
, 9
, 187
–207
.44.
Delorenzi
HG
(1985
), On the energy release rate calculations by the finite element method
, Eng. Fract. Mech.
, 21
, 129
–143
.45.
Krueger R, Koenig M, and Schneider T (1993), Computation of local energy release rates along straight and curved delamination fronts of unidirectionally laminated DCB and ENF specimens, 34th SDM Conf, La Jolla, AIAA 93-1457.
46.
Ishikawa
H
(1980
), A finite element analysis of stress intensity factors for combined tensile and shear loading by only a virtual crack extension method
, Int. J. Fract.
, 38
, 217
–235
.47.
Sha
GT
(1984
), On the virtual crack extension technique for stress intensity factors and energy release rate calculations for mixed fracture mode
, Int. J. Fract.
, 25
, 33
–42
.48.
Rybicki
EF
and Kanninen
MF
(1987
), A finite element calculation of stress-intensity factors by a modified crack closure integral
, Eng. Fract. Mech.
, 9
, 931
–938
.49.
Williams
ML
(1959
), The stresses around a fault or crack in dissimilar media
, Bull. Seismol. Soc. Am.
, 49
, 199
–204
.50.
Quian
W
and Sun
CT
(1997
), Calculation of stress intensity factors for interlaminar cracks in composite laminates
, Compos. Sci. Technol.
, 57
, 637
–650
.51.
Conminou
M
(1978
), The interface crack in a shear field
, ASME J. Appl. Mech.
, 45
, 287
–290
.52.
Conminou
M
(1979
), The interface crack in a combined tension-compression and shear field
, ASME J. Appl. Mech.
, 46
, 345
–348
.53.
Rice
JR
(1988
), Elastic fracture mechanics concepts for interfacial cracks
, ASME J. Appl. Mech.
, 55
, 98
–103
.54.
Raju
IS
, Crews
Jr JH
, and Aminpour
MA
(1988
), Convergence of strain energy release rate components for edge-delaminated composite laminates
, Eng. Fract. Mech.
, 30
(3
), 383
–396
.55.
Liu S, Kutlu Z, and Chang FK (1993), Matrix cracking-induced delamination propagation in graphite/epoxy laminated composites due to a transverse concentrated load, Composite Materials: Fatigue and Fracture, 4, ASTM STP 1156, 86–101.
56.
Davidson BD (1995), Prediction of energy release rate for edge delamination using a crack tip element approach, Composite Materials: Fatigue and Fracture, 5, ASTM STP 1230, 155–175.
57.
Raju
IS
, Sistla
R
, and Frishnamurthy
T
(1996
), Fracture mechanics analyses for skin-stiffener debonding
, Eng. Fract. Mech.
, 54
(3
), 371
–385
.58.
Glaessgen EH, Riddell WT, and Raju IS (1998), Effect of shear deformation and continuity on delamination modelling with plate elements, AIAA Paper No. AIAA-98-2023.
59.
Krueger R (1999), A shell/3D modelling technique for delamination in composite laminates, Proc of 14th Tech Conf of the American Society for Composites, 843–852.
60.
Raju
IS
(1987
), Calculation of strain-energy release rates with higher order and singular finite elements
, Eng. Fract. Mech.
, 28
(3
), 251
–274
.61.
De Roeck
G
and Abdel-Wahab
MM
(1995
), Strain energy release rate formulae for 3D finite element
, Eng. Fract. Mech.
, 50
(4
), 569
–580
.62.
Atluri
SN
, Kobayashi
AS
, and Nakagaki
M
, (1975
), An assumed displacement hybrid finite element model for linear fracture mechanics
, Int. J. Fract.
, 11
, 257
–261
.63.
Atluri SN and Nakagaki M (1986), Computational methods for plane problems of fracture, Computational Methods in the Mechanics of Fracture, Elsevier Sci Publ, 169–222.
64.
Atluri SN and Nishioka T (1986), Computational methods for three-dimensional problems of fracture, Computational Methods in the Mechanics of Fracture, Elsevier Sci Pub, 229–283.
65.
Barsoum
RS
(1977
), A triangular quarter point elements as elastic and perfectly-plastic crack tip elements
, Int. J. Numer. Methods Eng.
, 11
, 85
–98
.66.
Abaqus/Standard Manuals, Release 5.8, Hibbitt, Karlsson, and Sorenssen, Inc.
67.
Raju IS (1986), Simple formulae for strain strain-energy release rates with higher order and singular finite elements. National Aeronautics and Space Administration, NASA CR 178186.
68.
Jime´nez MA, Revuelta D, Cuartero J, Clemente R, and Calvo J (1999), Simulacion mediante el me´todo de los elementos finitos del ensayo de fractura interlaminar en modo mixto MMB, Proc of Materiales Compuestos 99 AEMAC Conf, Malaga.
69.
Wilkins DJ, Eisenmann JR, Camin RA, Margolis WS, and Benson RA (1982), Characterising delamination growth in graphite-epoxy, Damage in Composite Materials, ASTM STP 775, 168–183.
70.
Sundaraman V and Davidson BD (1995), New test methods for determining fracture toughness as a function of mode mix for bimaterial interfaces, Application of Fracture Mechanics in Electronic Packaging and Materials, 11, 141–154.
71.
Davidson BD (1998), A predictive methodology for delamination growth in laminated composites, Part I: theoretical development and preliminary experimental results, Report AR-97/87 Department of Transportation, FAA.
72.
Reeder
JR
and Crews
JH
(1990
), The mixed mode bending method for delamination testing
, AIAA J.
, 28
(7
), 1270
–1276
.73.
Shivakumar
KN
, Crews
JH
, and Avva
VS
(1998
), Modified mixed-mode bending test apparatus for measuring delamination fracture toughness of laminated composites
, J. Compos. Mater.
, 32
(9
), 814
–828
.74.
Bhashyam S and Davidson B (1996), An evaluation of data reduction methods for the mixed mode bending test, 37 AIAA Structures, Structural Dynamics, and Materials Conf, 886–896.
75.
Asp
LE
(1998
), The effects of moisture and temperature on the interlaminar delamination toughness of a carbon/epoxy composite
, Compos. Sci. Technol.
, 58
, 967
–977
.76.
Juntti
M
, Asp
LE
, and Olsson
R
(1999
), Assessment of evaluation methods for the mixed-mode bending test
, J. Compos. Technol. Res.
, 21
(1
), 37
–48
.77.
Krueger R, Minguet PJ, and O’Brien TK (1999), A method for calculating strain energy release rates in preliminary design of composite skin/stringer debonding under multiaxial loading, NASA TM-1999-209365, ARL-TR-2012.
Copyright © 2002
by ASME
You do not currently have access to this content.
