Bimaterial systems in which two dissimilar materials are adhesively joined by a thin adhesive interlayer have been widely used in a variety of modern industries and engineering structures. It is well known that interfacial fracture is the most common failure mode for these bimaterial systems. Particularly, the interface fracture is a mixed mode in nature mode-I (pure peel) and mode-II (pure shear) due to the disrupted symmetry by the bimaterial configuration. Obviously, characterizing individual fracture modes, especially mode-I fracture, is essential in understanding and modeling the complex mixed mode fracture problems. Meanwhile, the J-integral is a highly preferred means to characterize the interfacial fracture behaviors of a bimaterial system because it cannot only capture more accurate toughness value, but also facilitate an experimental characterization of interfacial traction-separation laws (cohesive laws). Motivated by these important issues, a novel idea is proposed in the present work to realize and characterize the pure mode-I nonlinear interface fracture between bonded dissimilar materials. First, a nearly pure mode-I fracture test can be simply realized for a wide range of bimaterial systems by almost eliminating the mode-II component based on a special and simple configuration obtained in this work. Then, the concise forms of the J-integral are derived and used to characterize the interfacial fracture behaviors associated with classical and shear deformation beam theories. The proposed approach may be considered as a promising candidate for the future standard mode-I test method of bimaterial systems due to its obvious accuracy, simplicity, and applicability, as demonstrated by the numerical and experimental results.

1.
Williams
,
M. L.
, 1959, “
The Stress Around a Fault or Crack in Dissimilar Media
,”
Bull. Seismol. Soc. Am.
0037-1106,
49
, pp.
199
204
.
2.
Rice
,
J. R.
, and
Sih
,
G. C.
, 1965, “
Plane Problems of Cracks in Dissimilar Media
,”
ASME J. Appl. Mech.
0021-8936,
32
, pp.
418
423
.
3.
Erdogan
,
F.
, 1965, “
Stress Distribution in Bonded Dissimilar Materials With Cracks
,”
ASME J. Appl. Mech.
0021-8936,
32
, pp.
403
410
.
4.
England
,
A. H.
, 1965, “
A Crack Between Dissimilar Media
,”
ASME J. Appl. Mech.
0021-8936,
32
, pp.
400
402
.
5.
Rice
,
J. R.
, 1988, “
Elastic Fracture Mechanics Concepts for Interfacial Cracks
,”
ASME J. Appl. Mech.
0021-8936,
55
, pp.
98
103
.
6.
Evans
,
A. G.
,
Ruhle
,
M.
,
Dalgleish
,
B. J.
, and
Charalambides
,
P. G.
, 1990, “
The Fracture Energy of Bimaterial Interfaces
,”
Mater. Sci. Eng., A
0921-5093,
126
, pp.
53
64
.
7.
Raju
,
I. S.
,
Crews
,
J. H.
, Jr.
, and
Aminpour
,
M. A.
, 1988, “
Convergence of Strain Energy Release Rate Components for Edge-Delaminated Composite Laminates
,”
Eng. Fract. Mech.
0013-7944,
30
, pp.
383
396
.
8.
Suo
,
Z.
, and
Hutchinson
,
J. W.
, 1990, “
Interface Crack Between Two Layers
,”
Int. J. Fract.
0376-9429,
43
, pp.
1
18
.
9.
Hwu
,
C.
, and
Hu
,
J. S.
, 1992, “
Stress Intensity Factors and Energy Release Rates of Delaminations in Composite Laminates
,”
Eng. Fract. Mech.
0013-7944,
42
(
6
), pp.
977
988
.
10.
Davidson
,
B. D.
,
Hurang
,
H.
, and
Schapery
,
R. A.
, 1995, “
An Analytical Crack-Tip Element for Layered Elastic Structures
,”
ASME J. Appl. Mech.
0021-8936,
62
, pp.
294
305
.
11.
Yang
,
Z.
, and
Sun
,
C. T.
, 2000, “
Fracture Mode Separation for Delamination in Plate-Like Composite Structures
,”
AIAA J.
0001-1452,
38
, pp.
868
874
.
12.
Yang
,
C.
,
Sun
,
W.
,
Tomblin
,
J. S.
, and
Smeltzer
,
S. S.
, 2007, “
A Semi-Analytical Method for Determining the Strain Energy Release Rate of Cracks in Adhesively-Bonded Single-Lap Composite Joints
,”
J. Compos. Mater.
0021-9983,
41
, pp.
1579
1602
.
13.
Bruno
,
D.
,
Greco
,
F.
, and
Lonetti
,
P.
, 2005, “
A 3D Delamination Modelling Technique Based on Plate and Interface Theories for Laminated Structures
,”
Eur. J. Mech. A/Solids
0997-7538,
24
, pp.
127
149
.
14.
Atkinson
,
C.
, 1979, “
Stress Singularities and Fracture Mechanics
,”
Appl. Mech. Rev.
0003-6900,
32
, pp.
123
135
.
15.
Ikeda
,
T.
,
Yamashita
,
A.
,
Lee
,
D.
, and
Miyazaki
,
N.
, 2000, “
Failure of a Ductile Adhesive Layer Constrained by Hard Adherends
,”
ASME J. Eng. Mater. Technol.
0094-4289,
122
, pp.
80
85
.
16.
Madhusudhana
,
K. S.
, and
Narasimhan
,
R.
, 2002, “
Experimental and Numerical Investigations of Mixed Mode Crack Growth Resistance of a Ductile Adhesive Joint
,”
Eng. Fract. Mech.
0013-7944,
69
, pp.
865
883
.
17.
Blackman
,
B. R. K.
,
Hadavinia
,
H.
,
Kinloch
,
A. J.
, and
Williams
,
J. G.
, 2003, “
The Use of a Cohesive Zone Model to Study the Fracture of Fibre Composites and Adhesively-Bonded Joints
,”
Int. J. Fract.
0376-9429,
119
, pp.
25
46
.
18.
Pardoen
,
T.
,
Ferracin
,
T.
,
Landis
,
C. M.
, and
Delannay
,
F.
, 2005, “
Constraint Effects in Adhesive Joint Fracture
,”
J. Mech. Phys. Solids
0022-5096,
53
, pp.
1951
1983
.
19.
Pan
,
J.
, and
Leung
,
C. K. Y.
, 2007, “
Debonding Along the FRP-Concrete Interface Under Combined Pulling/Peeling Effects
,”
Eng. Fract. Mech.
0013-7944,
74
, pp.
132
150
.
20.
Ouyang
,
Z.
, and
Li
,
G.
, 2009, “
Cohesive Zone Model Based Analytical Solutions for Adhesively Bonded Pipe Joints Under Torsional Loading
,”
Int. J. Solids Struct.
0020-7683,
46
, pp.
1205
1217
.
21.
Yang
,
Q. D.
,
Thouless
,
M. D.
, and
Ward
,
S. M.
, 2001, “
Mixed Mode Fracture Analysis of Plastically-Deforming Adhesive Joints
,”
Int. J. Fract.
0376-9429,
110
, pp.
175
187
.
22.
Barenblatt
,
G. I.
, 1959, “
The Formation of Equilibrium Cracks During Brittle Fracture. General Ideas and Hypotheses. Axially-Symmetric Cracks
,”
J. Appl. Math. Mech.
0021-8928,
23
, pp.
622
636
.
23.
Dugdale
,
D. S.
, 1960, “
Yielding of Steel Sheets Containing Slits
,”
J. Mech. Phys. Solids
0022-5096,
8
, pp.
100
104
.
24.
Rice
,
J. R.
, 1968, “
A Path Independent Integral and the Approximate Analysis of Strain Concentration by Notches and Cracks
,”
ASME J. Appl. Mech.
0021-8936,
35
, pp.
379
386
.
25.
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.
0008-8846,
6
, pp.
773
781
.
26.
Needleman
,
A.
, 1987, “
A Continuum Model for Void Nucleation by Inclusion Debonding
,”
ASME J. Appl. Mech.
0021-8936,
54
, pp.
525
531
.
27.
Xu
,
X. P.
, and
Needleman
,
A.
, 1993, “
Void Nucleation by Inclusion Debonding in a Crystal Matrix
,”
Modell. Simul. Mater. Sci. Eng.
0965-0393,
1
, pp.
111
132
.
28.
Tvergaard
,
V.
, and
Hutchinson
,
J. W.
, 1996, “
On the Toughness of Ductile Adhesive Joints
,”
J. Mech. Phys. Solids
0022-5096,
44
, pp.
789
800
.
29.
Camacho
,
G. T.
, and
Ortiz
,
M.
, 1996, “
Computational Modeling of Impact Damage in Brittle Materials
,”
Int. J. Solids Struct.
0020-7683,
33
, pp.
2899
2938
.
30.
Alfano
,
G.
, and
Crisfield
,
M. A.
, 2001, “
Finite Element Interface Models for the Delamination Analysis of Laminated Composites: Mechanical and Computational Issues
,”
Int. J. Numer. Methods Eng.
0029-5981,
50
, pp.
1701
1736
.
31.
Williams
,
J. G.
, and
Hadavinia
,
H.
, 2002, “
Analytical Solutions for Cohesive Zone Models
,”
J. Mech. Phys. Solids
0022-5096,
50
, pp.
809
825
.
32.
Parrinello
,
F.
,
Failla
,
B.
, and
Borino
,
G.
, 2009, “
Cohesive–Frictional Interface Constitutive Model
,”
Int. J. Solids Struct.
0020-7683,
46
, pp.
2680
2692
.
33.
Wei
,
Y.
, and
Hutchinson
,
J. W.
, 1998, “
Interface Strength, Work of Adhesion and Plasticity in the Peel Test
,”
Int. J. Fract.
0376-9429,
93
, pp.
315
333
.
34.
Hutchinson
,
J. W.
, and
Evans
,
A. G.
, 2000, “
Mechanics of Materials: Top-Down Approaches to Fracture
,”
Acta Mater.
1359-6454,
48
, pp.
125
135
.
35.
Ouyang
,
Z.
, and
Li
,
G.
, 2009, “
Local Damage Evolution of DCB Specimens During Crack Initiation Process: A Natural Boundary Condition Based Method
,”
ASME J. Appl. Mech.
0021-8936,
76
, p.
051003
.
36.
Tvergaard
,
V.
, and
Hutchinson
,
J. W.
, 1992, “
The Relation Between Crack Growth Resistance and Fracture Process Parameters in Elastic-Plastic Solids
,”
J. Mech. Phys. Solids
0022-5096,
40
, pp.
1377
1397
.
37.
Kinloch
,
A. J.
, and
Shaw
,
S. J.
, 1981, “
The Fracture Resistance of a Toughened Epoxy Adhesive
,”
J. Adhes.
0021-8464,
12
, pp.
59
77
.
38.
Corigliano
,
A.
, 1993, “
Formulation, Identification and Use of Interface Models in the Numerical Analysis of Composite Delamination
,”
Int. J. Solids Struct.
0020-7683,
30
, pp.
2779
2811
.
39.
Chai
,
H.
, 1995, “
Deformation and Fracture of Particulate Epoxy in Adhesive Bonds
,”
Acta Metall. Mater.
0956-7151,
43
, pp.
163
172
.
40.
Chowdhury
,
S. R.
, and
Narasimhan
,
R.
, 2000, “
A Finite Element Analysis of Stationary Crack Tip Fields in a Pressure Sensitive Constrained Ductile Layer
,”
Int. J. Solids Struct.
0020-7683,
37
, pp.
3079
3100
.
41.
Högberg
,
J. L.
, 2006, “
Mixed Mode Cohesive Law
,”
Int. J. Fract.
0376-9429,
141
, pp.
549
559
.
42.
Sørensen
,
B. F.
, 2002, “
Cohesive Law and Notch Sensitivity of Adhesive Joints
,”
Acta Mater.
1359-6454,
50
, pp.
1053
1061
.
43.
Andersson
,
T.
, and
Stigh
,
U.
, 2004, “
The Stress-Elongation Relation for an Adhesive Layer Loaded in Peel Using Equilibrium and Energetic Forces
,”
Int. J. Solids Struct.
0020-7683,
41
, pp.
413
434
.
44.
Leffler
,
K.
,
Alfredsson
,
K. S.
, and
Stigh
,
U.
, 2007, “
Shear Behaviour of Adhesive Layers
,”
Int. J. Solids Struct.
0020-7683,
44
, pp.
520
545
.
45.
Högberg
,
J. L.
,
Sørensen
,
B. F.
, and
Stigh
,
U.
, 2007, “
Constitutive Behaviour of Mixed Mode Loaded Adhesive Layer
,”
Int. J. Solids Struct.
0020-7683,
44
, pp.
8335
8354
.
46.
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.
0020-7683,
46
(
1
), pp.
31
51
.
47.
Ji
,
G.
,
Ouyang
,
Z.
,
Li
,
G.
,
Ibekwe
,
S.
, and
Pang
,
S. -S.
, 2010, “
Effects of Adhesive Thickness on Global and Local Mode-I Interfacial Fracture of Bonded Joints
,”
Int. J. Solids Struct.
0020-7683,
47
, pp.
2445
2458
.
48.
Williams
,
J. G.
, 1989, “
End Corrections for Orthotropic DCB Specimens
,”
Compos. Sci. Technol.
0266-3538,
35
, pp.
367
376
.
49.
Schapery
,
R. A.
, and
Davidson
,
B. D.
, 1990, “
Prediction of Energy Release Rate for Mixed-Mode Delamination Using Classical Plate Theory
,”
Appl. Mech. Rev.
0003-6900,
43
, pp.
S281
S287
.
50.
Sheinman
,
I.
, and
Kardomateas
,
G. K.
, 1997, “
Energy Release Rate and Stress Intensity Factors for Delaminated Composite Laminates
,”
Int. J. Solids Struct.
0020-7683,
34
, pp.
451
459
.
51.
Bruno
,
D.
, and
Greco
,
F.
, 2001, “
Mixed Mode Delamination in Plates: A Refined Approach
,”
Int. J. Solids Struct.
0020-7683,
38
, pp.
9149
9177
.
52.
Boeman
,
R. G.
,
Erdman
,
D.
,
Klett
,
L.
, and
Lomax
,
R.
, 1999, “
A Practical Test Method for Mode I Fracture Toughness of Adhesive Joints With Dissimilar Substrates
,”
Proceedings of the SAMPE-ACCE-DOE Advanced Composites Conference
, Detroit, MI, Sept. 27–28, pp.
358
366
.
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