PSI - Issue 2_A
M. Nourazar et al. / Procedia Structural Integrity 2 (2016) 3423–3431
3430
Author name / StructuralIntegrity Procedia 00 (2016) 000–000
8
1 h
elastic electro magneto − −
2 R
2 2 h
1 R
2 h
φ φ
1 L
c orthotropi
2 L
Fig. 5. Normalized stress intensity factors for two circular arc cracks.
4. Conclusions In this paper, fracture analysis for bonded medium composed of orthotropic substrate with a magneto-electro-elastic coating is considered. Dislocation solution is obtained to derive integral equations for the orthotropic substrate under anti-plane mechanical and in-plane electric and magnetic loading for impermeable crack surface boundary conditions. The results for stress components exhibit the well-known Cauchy- type singularity at the dislocation location. Numerical result indicates that the stress intensity factors are influenced by the geometry of the layers and cracks, the material properties. Among other findings, we observed that stress intensity factors are enhanced as the bonding imperfection decreases. Appendix The unknown coefficients are:
sg h ξ +
sinh( (
))
χ
i
is
−
η
2
( ) A s b =
( ( ) ) s e πδ −
(A-1)
wz
1
s
sgh
sgh
cosh(
)
sinh(
)
−
χ
2
2
sg h ξ +
sinh( (
))
i
is
−
η
2
( ) A s b =
( ( ) ) s e πδ −
(A-2)
wz
2
s
sgh
sgh
cosh(
)
sinh(
)
χ
−
2
2
i
cosh( ) sg
sinh( ) sg ξ
ξ χ +
is
−
η
( ) B s b =
( ( ) ) s e πδ −
sgh
(A-3)
[
]cosh(
)
wz
1
2
s
sgh
sgh
cosh(
)
sinh(
)
−
χ
2
2
i
cosh( ) sg
sinh( ) sg ξ
ξ χ +
is
−
η
( ) B s b =
( ( ) ) s e πδ −
sgh
(A-4)
[
]sinh(
)
wz
2
2
s
sgh
sgh
cosh(
)
sinh(
)
−
χ
2
2
G G
sg h ξ +
sinh( (
))
i
y x
is
−
η
2
(A-5)
1 C s
b
( ( ) ) s e πδ −
cot ( ) gh sh
( )
= −
wz
1
s
sgh
sgh
cosh(
)
sinh(
)
−
1 α
χ
2
2
G G
sg h ξ +
sinh( (
))
i
y x
is
−
η
2
(A-6)
2 C s
b
( ( ) ) s e πδ −
( )
=
wz
s
sgh
sgh
cosh(
)
sinh(
)
1 α
χ
−
2
2
( ) ( ) ( ) 0 D s D s E s E s = = = = ( )
(A-7)
1
2
1
2
G G
1 44 2 15 3 15 cot ( ) k gh sh e h α α + +
y x
s
where
.
[
]
χ
=
−
k
c
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