PSI - Issue 41
5
Author name / Structural Integrity Procedia 00 (2019) 000 – 000
Roberta Massabò et al. / Procedia Structural Integrity 41 (2022) 461–469
465
(a)
(b)
Fig. 4. (a) Double Cantilever Beam specimen (DCB)/Asymmetric Double Cantilever Beam specimen (ADCB). (b) End Loaded Split (ELS) specimen
3.1. Application to homogeneous DCB and asymmetric ADCB specimens The first case examined is the Double Cantilever Beam specimen with equal (
0 = = , DCB) and unequal
isotropic layers ( 1 = ) shown in Fig. 4. The applied loads are localized symmetric transverse forces P applied at the ends of the detached layers. In both cases 2 14 1 = + + and (1 ) / (2 2 ) / 2 h = − + = − , which particularize to 16 = , 0 h = and 2 / 3 I = for the homogeneous symmetric DCB, where the neutral axis of the intact layer is at mid-thickness. The applied loads generate crack tip force and moment resultants which are described by the elementary loads for symmetric bending, S M Pa = , and double shear, D P = , while the other elementary loads vanish, 0 0 0, 0 S P S P M = = = = . Root rotations and root displacements for 0 = , using Eq. 6, and the associated coefficients are listed below. 0, 0 = and 0 , ADCB), of the same thickness 1 2 h h h = = (
• Longitudinal root displacements in DCB/ADCB specimens:
1 a a u P a a u P a a h h = + = + 12 13 2 42 ( ), (
(7)
),
43
3 4 3 E −
1
3
1 2
a
= −
a
=
−
+
,
,
with
12
13
2
E
2
2
4 3 −
1
1
( (
) )
1 3
1 +
1 1
+ −
a
=
− +
2
42 a a = −
,
43
1
2
2 2 1
E
−
2
4 3
−
1
• Transverse root displacements in DCB/ADCB specimens:
1 a a v P a a v P a a h h = + = + 32 33 2 62 ( ), (
(8)
),
63
(
)
( 3 1
)
6 3 1
+
+
3
2
1 6
1
4 3 +
p
2 3 9 6 = − + + + +
,
with:
a
−
g
g
a
=
−
(
)
32
33
33
34
5
2
2
E
2
(
4 3 −
)
E
2
2 4 3 E −
2
4 3 −
1
1
1
) (
)
(
(
)
( 3 1
)
2 3 1 4 10 15 20 6 3 1 + + − − + 2
+
−
,
p
2
a
=
+
+
(
)
(
)
62
10 1 E
2 1 E
−
2
4 3 −
E
1
1
1
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