Modeling the interface between two adherents in a co-cured composite joint for a delamination analysis is always a challenge since properties and thickness of the material forming the interface are not clearly defined or well characterized. In a conventional finite element (FE) analysis using virtual crack closure technique (VCCT) based on a linear elastic fracture mechanics (LEFM) theory, adherents are assigned to share the same common nodes along their intact interface. On the other hand, an FE analysis using cohesive elements or analytical methods based on an adhesive joint model for a delamination analysis of a co-cured joint will require modeling of the interface as well as the appropriate selection of its thickness and properties. The purpose of this paper is to establish the applicability and limitation of the adhesive joint model for a delamination analysis of a co-cured composite joint. In particular, it will show that when certain requirements are met, the strain energy release rates (SERR) become independent or nearly independent of the adhesive stiffness and thickness, and thus, SERR of an adhesive joint will be the same as that for a co-cured joint. These requirements are determined from a theoretical consideration, and they can be expressed explicitly in terms of joint characteristic (or load transfer) lengths and joint physical lengths. The established requirements are further validated by numerical results for various cracked joint geometries. Finally, implication of a mode ratio obtained by the proposed adhesive joint model for a corresponding delamination crack is discussed.

References

1.
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
.
2.
Alfredsson
,
K. S.
, and
Hogberg
,
J. L.
,
2007
, “
Energy Release Rate and Mode-Mixity of Adhesive Joint
,”
Int. J. Fract.
,
144
(
4
), pp.
267
283
.
3.
Shahin
,
K.
, and
Taheri
,
F.
,
2008
, “
The Strain Energy Release Rates in Adhesively Bonded Balanced and Unbalanced Specimens and Lap Joints
,”
Int. J. Solids Struct.
,
45
(
25–26
), pp.
6284
6300
.
4.
Duong
,
C. N.
,
2012
, “
A General Approach to Fracture Analysis of Tapered Bonded Joints and Doublers
,”
Eng. Fract. Mech.
,
96
, pp.
335
379
.
5.
Volkensen
,
O.
,
1938
, “
Die niektraftverteiling in zugbeansprunchten mit konstanten laschenquerscritten
,”
Luftfahrforsch
,
15
, pp.
41
47
.
6.
De Bruyne
,
N. A.
,
1944
, “
The Strength of Glued Joints
,”
Aircr. Eng.
,
16
(
4
), pp.
115
118
.
7.
Goland
,
M.
, and
Reissner
,
E.
,
1944
, “
The Stresses in Cemented Joints
,”
ASME J. Appl. Mech.
,
11
(
1
), pp.
A17
A27
.
8.
Hart-Smith
,
L. J.
,
1973
, “
Adhesive-Bonded Single-Lap Joints
,” Technical Report No. NASA CR-112236.
9.
Hart-Smith
,
L. J.
,
1973
, “
Adhesive-Bonded Double-Lap Joints
,” Technical Report No. NASA CR-112235.
10.
Hart-Smith
,
L. J.
,
1973
, “
Adhesive-Bonded Scarf and Stepped-Lap Joints
,” Technical Report No. NASA CR-112237.
11.
Hart-Smith
,
L. J.
,
1999
, “
Nonlinear Closed-Form Analyses of Stresses and Deflections in Bonded One-Sided Splices and Patches
,”
The Proceedings of the 3rd Aging Aircraft Conference
,
Albuquerque, NM
.
12.
Oplinger
,
D. W.
,
1994
, “
Effects of Adherent Deflections in Single-Lap Joints
,”
Int. J. Solids Struct.
,
31
(
18
), pp.
2565
2587
.
13.
Suhir
,
E.
,
1994
, “
Approximate Evaluation of the Interfacial Shearing Stress in Cylindrical Double Lap Shear Joints With Application to Dual-Coated Optical Fibers
,”
Int. J. Solids Struct.
,
31
(
23
), pp.
3261
3283
.
14.
Tsai
,
M. Y.
,
Oplinger
,
D. W.
, and
Morton
,
J.
,
1998
, “
Improved Theoretical Solutions for Adhesive Lap Joints
,”
Int. J. Solids Struct.
,
35
(
12
), pp.
1163
1185
.
15.
Mortensen
,
F.
, and
Thomsen
,
O. T.
,
1997
, “
Simplified Linear and Non-Linear Analysis of Stepped and Scarfed Lap Adhesive Joints Between Composite Laminates
,”
Compos. Struct.
,
38
(
1–4
), pp.
281
294
.
16.
Mortensen
,
F.
, and
Thomsen
,
O. T.
,
2002
, “
Analysis of Adhesive Bonded Joints: A Unified Approach
,”
Compos. Sci. Technol.
,
62
(
7–8
), pp.
1011
1031
.
17.
Tong
,
L.
,
1996
, “
Bond Strength for Adhesive-Bonded Single-Lap Joints
,”
Acta Mech.
,
117
(
1–4
), pp.
101
113
.
18.
Duong
,
C. N.
,
2006
, “
A Unified Approach to Geometrically Nonlinear Analysis of Tapered Bonded Joints and Doublers
,”
Int. J. Solids Struct.
,
43
(
11–12
), pp.
3498
3526
.
19.
Davidson
,
B. D.
,
Hu
,
H.
, and
Schapery
,
R. A.
,
1995
, “
An Analytical Crack Tip Element for Layered Elastic Structures
,”
ASME J. Appl. Mech.
,
62
(
2
), pp.
294
305
.
20.
Yang
,
Z.
,
Sun
,
C. T.
, and
Wang
,
J.
,
2000
, “
Fracture Mode Separation for Delamination in Platelike Composite Structures
,”
AIAA J.
,
38
(
5
), pp.
868
874
.
21.
Wang
,
J.
, and
Qiao
,
P.
,
2004
, “
Interface Crack Between Two Shear Deformable Elastic Layers
,”
J. Mech. Phys. Solids
,
52
(
4
), pp.
891
905
.
22.
Wang
,
J.
, and
Qiao
,
P.
,
2004
, “
On the Energy Release Rate and Mode Mix of Delaminated Shear Deformable Composite Plates
,”
Int. J. Solids Struct.
,
41
(
9–10
), pp.
2757
2779
.
23.
Shahin
,
K.
,
Kember
,
G.
, and
Taheri
,
F.
,
2008
, “
An Asymptotic Solution for Evaluation of Stresses in Balanced and Unbalanced Adhesively Bonded Joints
,”
Mech. Adv. Mater. Struct.
,
15
(
2
), pp.
88
103
.
24.
Cheng
,
S.
,
Chen
,
D.
, and
Shi
,
Y.
,
1991
, “
Analysis of Adhesive-Bonded Joints With Nonidentical Adherends
,”
J. Eng. Mech.
,
117
(
3
), pp.
605
623
.
25.
Song
,
K.
,
Davilla
,
C. G.
, and
Rose
,
C. A.
,
2008
, “
Guidelines and Parameter Selection for the Simulation of Progressive Delamination
,”
2008 ABAQUS User’s Conference
,
Newport, RI
,
May 19–22
.
26.
William
,
M.
,
1959
, “
The Stress Around a Fault or Crack in Dissimilar Media
,”
Bull. Seismol. Soc. Am.
,
49
(
2
), pp.
199
204
.
27.
Rice
,
J.
,
1988
, “
Elastic Fracture Mechanics Concepts for Interfacial Cracks
,”
ASME J. Appl. Mech.
,
55
(
1
), pp.
98
103
.
28.
Tay
,
T.
,
2003
, “
Characterization and Analysis of Delamination Fracture in Composites: An Overview of Development From 1990–2001
,”
ASME Appl. Mech. Rev.
,
56
(
1
), pp.
1
32
.
29.
Tabiei
,
A.
, and
Zhang
,
W.
,
2018
, “
Composite Laminate Delamination Simulation and Experiment: A Review of Recent Development
,”
ASME Appl. Mech. Rev.
,
70
(
3
),
030801
.
30.
Banks-Sills
,
L.
, and
Farkash
,
E.
,
2016
, “
A Note on the Virtual Crack Closure Technique for a Binaterial Interface Crack
,”
Int. J. Fract.
,
201
(
2
), pp.
171
180
.
31.
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
.
32.
Raju
,
I. S.
,
Crews
,
J. H.
, and
Aminpour
,
M. A.
,
1988
, “
Convergence of Strain Energy Release Rate Components for Edge-Delamination Composite Laminates
,”
Eng. Fract. Mech.
,
30
(
3
), pp.
383
396
.
33.
Davidson
,
B. D.
, and
Hu
,
H.
,
1995
, “
Effect of Interlayer Modulus on Fracture Mode Ratio for Interleaved Composite Laminates
,”
Eng. Fract. Mech.
,
52
(
2
), pp.
243
253
.
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