In this investigation, we consider a crack close to and perpendicular to a bimaterial interface. If the crack tip is at the interface then, depending on material properties, the order of the stress singularity will be equal to, less than, or greater than one-half. However, if the crack tip is located any finite distance away from the interface the stress field is square-root singular. Thus, as the crack tip approaches the interface, the stress intensity factor approaches zero (for cases corresponding to a singularity of order less than one-half) or infinity (for a singularity of order greater than one-half). The implication of this behavior is that for a finite applied pressure the crack will either never reach the interface or will reach the interface with vanishing small applied pressure. In this investigation, a cohesive zone model is used in order to model the crack behavior. It is found that the aforementioned anomalous behavior for the crack without a cohesive zone disappears and that the critical value of the applied pressure for the crack to reach the interface is finite and depends on the maximum stress of the cohesive zone model, as well as on the work of adhesion and the Dundurs' parameters.

References

References
1.
Ewalds
,
H. L.
, and
Wanhill
,
R. J. H.
,
1984
,
Fracture Mechanics
,
Edward Arnold Publishing
,
London
.
2.
Erdogan
,
F.
, and
Biricikoglu
,
V.
,
1973
, “
Two Bonded Half Planes With a Crack Going Through the Interface
,”
Int. J. Eng. Sci.
,
11
(
7
), pp.
745
766
.
3.
Atkinson
,
C.
,
1975
, “
On the Stress Intensity Factors Associated With Cracks Interacting With an Interface Between Two Elastic Media
,”
Int. J. Eng. Sci.
,
13
(
5
), pp.
489
504
.
4.
He
,
M.-Y.
, and
Hutchinson
,
J. W.
,
1989
, “
Crack Deflection at an Interface Between Dissimilar Elastic Materials
,”
Int. J. Solids Struct.
,
25
, pp.
1053
1067
.
5.
Romeo
,
A.
, and
Ballarini
,
R.
,
1995
, “
A Crack Very Close to a Bimaterial Interface
,”
ASME J. Appl. Mech.
,
62
(
3
), pp.
614
619
.
6.
Bogy
,
D. B.
,
1971
, “
On the Plane Elastostatic Problem of a Loaded Crack Terminating at a Material Interface
,”
ASME J. Appl. Mech.
,
38
(
4
), pp.
911
918
.
7.
Malyshev
,
B. M.
, and
Salganik
,
R. L.
,
1965
, “
The Strength of Adhesive Joints Using the Theory of Cracks
,”
Int. J. Fract.
,
1
(2), pp.
114
128
.
8.
Chen
,
D.-H.
,
1994
, “
A Crack Normal to and Terminating at a Bimaterial Interface
,”
Eng. Fract. Mech.
,
49
(4), pp.
517
532
.
9.
Adams
,
G. G.
,
2015
, “
Critical Value of the Generalized Stress Intensity Factor for a Crack Perpendicular to an Interface
,”
Proc. R. Soc. A: Math., Phys. Eng. Sci.
,
471
(
2183
), p.
0571
.
10.
Adams
,
G. G.
,
2014
, “
Adhesion and Pull-Off Force of an Elastic Indenter From an Elastic Half-Space
,”
Proc. R. Soc. A: Math., Phys. Eng. Sci.
,
470
(
2169
), p.
0317
.
11.
Gómez
,
F. J.
, and
Elices
,
M.
,
2003
, “
A Fracture Criterion for Sharp V-Notched Samples
,”
Int. J. Fract.
,
123
(
3/4
), pp.
163
175
.
12.
Adams
,
G. G.
, and
Hills
,
D. A.
,
2014
, “
Analytical Representation of the Non-Square-Root Singular Stress Field at a Finite Angle Sharp Notch
,”
Int. J. Solids Struct.
,
51
(
25–26
), pp.
4485
4491
.
13.
Adams
,
G. G.
,
2016
, “
Frictional Slip of a Rigid Punch on an Elastic Half-Plane
,”
Proc. R. Soc. A: Math., Phys. Eng. Sci.
,
472
(
2191
), p.
0352
.
14.
Adams
,
G. G.
,
2018
, “
A Semi-Infinite Strip Pressed Against an Elastic Half-Plane With Frictional Slip
,”
ASME J. Appl. Mech.
,
85
(
6
), p.
061001
.
15.
Dundurs
,
J.
,
1969
, “
Discussion: “Edge-Bonded Dissimilar Orthogonal Elastic Wedges Under Normal and Shear Loading
,”
ASME J. Appl. Mech.
,
36
(
3
), pp.
650
652
.
16.
Erdogan
,
F.
,
Gupta
,
G. D.
, and
Cook
,
T. S.
,
1973
, “
Numerical Solution of Singular Integral Equations
,”
Mechanics of Fracture
,
G. C.
Sih
, ed.,
1
,
Noordhoff International Publishing
, Amsterdam, The Netherlands, pp.
368
425
.
17.
Miller
,
G. R.
, and
Keer
,
L. M.
,
1985
, “
A Numerical Technique for the Solution of Singular Integral Equations of the Second Kind
,”
Q. Appl. Math.
,
42
(
4
), pp.
455
465
.
18.
Barenblatt
,
G. I.
,
1962
, “
Mathematical Theory of Equilibrium Cracks in Brittle Fracture
,”
Advances in Applied Mechanics
, Vol.
7
,
Academic Press
, Cambridge, MA, pp.
55
129
.
19.
Dugdale
,
D.
,
1960
, “
Yielding of Steel Sheets Containing Slits
,”
J. Mech. Phys. Solids
,
8
(
2
), pp.
100
104
.
20.
Debnath
,
L.
, and
Bhatta
,
D.
,
2007
,
Integral Transforms and Their Applications
,
2nd ed.
,
Chapman & Hall/CRC, Boca Raton, FL
.
21.
Williams
,
M. L.
,
1952
, “
Stress Singularities Resulting From Various Boundary Conditions in Angular Corners of Plates in Extension
,”
J. Appl. Mech.
,
19
(4), pp.
526
528
.http://resolver.caltech.edu/CaltechAUTHORS:20140730-111744170
22.
Tranter
,
C. J.
,
1948
, “
The Use of the Mellin Transform in Finding the Stress Distribution in an Infinite Wedge
,”
Q. J. Mech. Appl. Math.
,
1
(
1
), pp.
125
130
.
23.
Timoshenko
,
S. P.
, and
Goodier
,
J. N.
,
1970
,
Theory of Elasticity
,
3rd ed.
,
McGraw-Hill Book Company
,
New York
.
24.
Wolfram, 2017, “Mathematica® 10.0,” Wolfram Inc., Champaign, IL, accessed Dec. 10, 2017, http://wolfram.com/mathematica/?source=wordcloud
You do not currently have access to this content.