Issue 71
E. Kormanikova et alii, Fracture and Structural Integrity, 71 (2025) 182-192; DOI: 10.3221/IGF-ESIS.71.13
( ) = x ζ 0
(2)
signifies that the adhesive is completely damaged at a specific point. i.e. complete delamination. ( ) = x ζ 1
(3)
indicates an undamaged interface. The total ERR in DCB sample can be formulated as
dU b da 1
=−
G
(4)
where dU is stress increment, da is length increment (or crack increment) and b is width of sample. With respect to the examination of the DCB sample using Mode I, the value of the ERR can be expressed using the Euler-Bernoulli theory as
2 2
F a
(5)
= I
G
bEI
where EI is bending stiffness. According to ASTM standards [21], there are several ways to determine the value of ERR, one of the methods is the so called Modified Beam Theory (MBT). The I G value according to this theory is determined as
δ
F
3
= I
G
(6)
ba
2
Due to the fact that the experiment is partially imperfect due to theoretical studies, a correction is introduced, which assumes that the delamination value is increased by the value | Δ |. Thus, the total crack length is (a + | Δ |) and so the adjusted I G calculation looks as follows
δ
F
( b a 3
=
(7)
G
)
I
+ ∆
2
where Δ is calculated in accordance with the ASTM standards.
M ATERIAL CHARACTERISTICS OF COMBINED LAMINATE COMPOSED OF SUBLAMINATES f the laminate consists of S sublaminates, each containing n q plies, where q = 1,…, S , then components of in-plane stiffness matrix A can be expressed as the sum of S terms [22]
I
( ) ij A
( ) A E h 1 = ∑ n ij ij kn =
∑
∑
∑
n
n
S q
+
+ + ...
=
( ) E h ij kn
( ij kn E h )
(8)
S
2
kn
kn
kn
=
=
=
k
k
k
1
1
1
1
q
S
1
2
S
1
2
1
E is component of transformed reduced stiffness matrix of the k th layer of the q th
q kn h
where
is thickness and
( )
q ij kn
sublaminate, and ( ) ij q A is the component of the in-plane stiffness matrix of the q For the two sublaminates M and N the combined in-plane stiffness matrix A is ( ) ( ) ( ) = + ij ij ij MN M N A A A .
th sublaminate.
(9)
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