Volume 02 Issue 04-2022
64
International Journal of Advance Scientific Research
(ISSN
–
2750-1396)
VOLUME
02
I
SSUE
04
Pages:
64-70
SJIF
I
MPACT
FACTOR
(2021:
5.478
)
(2022:
5.636
)
METADATA
IF
–
7.356
A
BSTRACT
This paper presents the results of research taking into account the stresses and strains of two-layer plates,
which differ in terms of physical and mechanical properties, the shear deformations of the layers under the
influence of temperature and the transverse displacement and inclination of adhesive joints. At the same
time, interlayer displacements and other mechanical characteristics are taken into account in such a way
as to allow a sufficiently accurate assessment of the strength and superiority of engineering problems for
these engineering problems.
K
EYWORDS
Stress-strain state, interlayer shifts, strength, transverse shear, adhesive layer, displacement, shear
function, shear stresses, deflection, shear modulus, temperature effect.
Journal
Website:
http://sciencebring.co
m/index.php/ijasr
Copyright:
Original
content from this work
may be used under the
terms of the creative
commons
attributes
4.0 licence.
Research Article
INTERLAYER SHIFTS OF TWO-LAYER COMBINED PLATES
TAKING INTO ACCOUNT TEMPERATURE LOADS
Submission Date:
April 10, 2022,
Accepted Date:
April 17, 2022,
Published Date:
April 30, 2022
Crossref doi:
https://doi.org/10.37547/ijasr-02-04-12
A.D. Dusmatov
Head teacher, Tashkent State Pedagogical University Independent researcher (PhD), Department of
“Instrumental Performance” Uzbek State Institute of Arts and Culture, Uzbekistan
O.U.Mavlonova
Assistant, Department of Applied Mechanics, Fergana Polytechnic Institute, Fergana, Uzbekistan
Volume 02 Issue 04-2022
65
International Journal of Advance Scientific Research
(ISSN
–
2750-1396)
VOLUME
02
I
SSUE
04
Pages:
64-70
SJIF
I
MPACT
FACTOR
(2021:
5.478
)
(2022:
5.636
)
METADATA
IF
–
7.356
I
NTRODUCTION
The paper presents the results of a study of the
stress-strain state (SSS) of two-layer combined
slabs, taking into account temperature loads.
Interlayer
shifts
and
other
mechanical
characteristics are taken into account, which
makes it possible to estimate strength and stress-
strain states with sufficiently high accuracy for
engineering problems. Adhesive joints between
layers serve to ensure the solidity of structures
and significantly affect the redistribution of forces
between layers [1-3].
When calculating the strength and stability of
combined structures, taking into account the
influence of the adhesive layer is especially
important in cases where the structure is subject
to temperature effects or when there is a risk of
loss of strength and stability of two-layer boards.
Fig 1. Two-layer combined plate.
Let us consider the study of the stress-strain state
of the SSS of a two-layer slab, taking into account
the transverse shear of the composite layers and
the compliance of the adhesive joint (4.5).
Problems of deformability and strength of
laminated two-layer slabs, taking into account
interlayer shifts, built based on metal and
fibreglass. [4-7] The paper considers a combined
slab whose layers are interconnected by pliable
thin adhesive seams under the influence of
temperature and external static loads. The
thermal effect has a significant effect on the
behaviour of the combined two-layer material.
When combined structures are heated, the
stresses in the bonding and fibreglass layers
change significantly. Temperature strongly
influences all mechanical properties of combined
Volume 02 Issue 04-2022
66
International Journal of Advance Scientific Research
(ISSN
–
2750-1396)
VOLUME
02
I
SSUE
04
Pages:
64-70
SJIF
I
MPACT
FACTOR
(2021:
5.478
)
(2022:
5.636
)
METADATA
IF
–
7.356
laminated boards. In this paper, the problem of
thermoelasticity of two-layer plates is solved
using the refined theory of S.A. Ambartsumyan
(1). It is assumed that the second fibreglass
reinforcing layer has a significantly smaller
thickness than the first [8-11].
The construction of the refined theory in this
paper is based on energy considerations. Analysis
of the effect of temperature exposure in layers
and between layers was performed for a
combined slab consisting of metal and fibreglass
(reinforcing) layers. The two-layer slab under
consideration is freely supported along the entire
contour and carries a uniformly distributed load
of 0 [12-16]. It is assumed that the heat flow acts
in the direction of the load [15-18]. From the
solution of the heat conduction problem, the
following temperature distribution in the layers
was obtained:
In the first layer
Т
1
= Т
0
1
+ 𝜃
1
𝛾
In the second layer
Т
2
= Т
0
2
+ 𝜃
2
𝛾
(1)
Wherein -
ℎ
2
≤ 𝛾 ≤ +
ℎ
2
; -
𝛿
𝑛
2
≤ 𝛾
1
≤ +
𝛿
𝑛
2
;
where
𝜃
1
,
𝜃
2
- temperature gradients in layers;
Т
0
1
, Т
0
2
- mid-plane temperatures;
Taking as usual for complete deformations:
𝜀
𝑐𝑜𝑚
=
𝜀
𝑒𝑙𝑎𝑠
+ 𝜀
т
(2)
Где
𝜀
𝑒𝑙𝑎𝑠
- elastic deformation of the system
𝜀
т
- deformation from temperature influences
The physical law for the layers will have the
form:
For the first layer
𝑥
(𝐼)
= С
𝐼𝐼
(𝜀
𝑥
𝐼
+ 𝜇 ∙ 𝜀
𝑦
𝐼
) − 𝐶
𝐼∙
𝑇
𝐼
(𝑥 → 𝑦, 𝐶
11
→ 𝐶
22
, 𝐶
1
→ 𝐶
2
, 𝜇
12
𝐼
→ 𝜇
21
𝐼
); (3)
For the second layer
𝑥
(𝐼𝐼)
= 𝐵
𝐼𝐼
(𝜀
𝑥
𝐼𝐼
+ 𝜇
21
𝐼𝐼
∙ 𝜀
𝑦
𝐼𝐼
) − 𝐷
𝐼∙
𝑇
2
(𝑥 → 𝑦, 𝐵
11
→ 𝐵
22
, 𝐷
1
→ 𝐷
2
, 𝜇
12
𝐼𝐼
→ 𝜇
21
); (4)
Here
𝐶
𝐼𝐼
=
𝐸
1
𝐼
1−𝜇
12
𝐼
∙𝜇
21
𝐼
;
𝐶
22
=
𝐸
21
𝐼
1−𝜇
12
𝐼𝐼
∙𝜇
21
𝐼𝐼
;
𝐵
𝐼𝐼
=
𝐸
1
𝐼𝐼
1−𝜇
12
𝐼𝐼
∙𝜇
21
𝐼𝐼
; 𝐵
22
=
𝐸
2
𝐼𝐼
1−𝜇
12
𝐼𝐼
∙𝜇
21
𝐼𝐼
;
(5)
Where
𝐸
1
𝑖
, 𝐸
2
𝑖
- modulus of elasticity of layers
(i=1,2);
𝜇
12
𝑖
∙ 𝜇
21
𝑖
- Poisson's ratio of layers (i=1,2);
С
𝐼
= С
𝐼𝐼
(𝛼
𝐼𝑥
+ 𝜇
𝐼2
∙ 𝛼
𝐼𝑦
);
С
2
= С
22
(𝛼
𝐼𝑦
+ 𝜇
21
𝐼
∙ 𝛼
𝐼𝑥
);
𝐷
𝐼
= 𝐵
𝐼𝐼
(𝛼
2𝑥
+𝜇
21
∙ 𝛼
2𝑦
);
𝐷
2
= 𝐵
22
(𝛼
2𝑦
+𝜇
21
𝐼𝐼
∙ 𝛼
2𝑥
);
(6)
Where
𝛼
1𝑥
, 𝛼
1𝑦
, 𝛼
2𝑥,
𝛼
2𝑦
-
к
coefficients of thermal
expansion of the first and second layers.
The plate deformation equations are obtained
using the variational principle, and the total
Volume 02 Issue 04-2022
67
International Journal of Advance Scientific Research
(ISSN
–
2750-1396)
VOLUME
02
I
SSUE
04
Pages:
64-70
SJIF
I
MPACT
FACTOR
(2021:
5.478
)
(2022:
5.636
)
METADATA
IF
–
7.356
energy of the system is taken as the functional.
The functionality has the form:
И
(𝑍)
=
1
2
∬
With the help of Euler's variational equation, a
system of fourth-order partial differential
equations concerning unknowns is obtained. As
an example, we take a fibreglass layer with a
metal reinforcing layer.
When determining the stress-strain state of a
two-layer slab, the shear and thickness of the
glueing joint were varied, and the effect of
changing the thicknesses of the bearing layers
was studied.
R
ESULTS AND CONCLUSION
As an example, we consider a fibreglass layer
with a metal reinforcing layer, a calculation is
made of a slab hinged along the contour under
the action of a uniformly distributed load, and
the temperature load is also established.
It is assumed that the outer metal reinforcing
layer is much thinner than the fibreglass one
(Fig. 1), the calculation was made with the
following parameters:
a=b=1,2, =1,5 cm, =0,2 cm
𝐸
1𝑝
(1)
= 3,05 ∙ 10
4
𝑀𝑃𝑎,
𝐸
2𝑝
(2)
= 1,88 ∙ 10
4
𝑀𝑃𝑎 , Е
1
(2)
= 𝐸
2
(2)
= 2,1 ∙ 10
5
𝑀𝑃𝑎,
𝜇
12
(1)
= 𝜇
21
(1)
∙ 0,18,
𝜇
12
(2)
= 026, 𝐺
12
(1)
= 049 ∙
10
4
MPa,
𝐺
13
(1)
= 0,31 ∙ 10
5
MPa,
𝐺
13
(1)
= 0,35 ∙ 10
4
𝑀𝑃𝑎, 𝐺
12
(2)
= 𝐺
13
(2)
= 𝐺
23
(2)
= 0,787 ∙ 10
5
𝑀𝑃𝑎.
Figure 2. Changes in the stress-strain state (SSS) with a varying shear modulus of the weld.
Volume 02 Issue 04-2022
68
International Journal of Advance Scientific Research
(ISSN
–
2750-1396)
VOLUME
02
I
SSUE
04
Pages:
64-70
SJIF
I
MPACT
FACTOR
(2021:
5.478
)
(2022:
5.636
)
METADATA
IF
–
7.356
The calculation results showed (see Fig. 2) that an
increase in G_шik MPA to 5.0 MPa leads to a
decrease in stresses in the fibreglass layer by
4.45%, while the stresses in the metal layer
increase by 10. Changing the thickness of the
adhesive l
ayer by a factor of two (from h_ш=
〖
10
〗
^(-
2) до 0,5
〖
∙
10
〗
^(-
2) см)) cm to 0.5 10 cm)
changes the maximum stresses in fibreglass by
4,1%.
The calculation results under the action of a
temperature difference (Т^(н )=
〖
20
〗
^0
С,Т^(в )=
〖
200
〗
^0 С)) across the p
late
thickness are shown in Figure 3. When the
temperature rises from 110℃ to 200 ℃, the
maximum stress in the first layer of the composite
plate changes by 50%, respectively, in the second
layer it changes by 32%. The analysis showed that
an increase in the thickness of the adhesive layer
made of epoxy adhesive KI47 (5MPA) by 10 times
(from 10 to 10 m) increases the deflection of the
plate by 21% (see Fig. 2.11,) At a large value
(about 5.10 MPa) The thickness of the seam has
little effect on deflections (less than 1%).
Regularity has been established, the greater the
thickness of the bearing fibreglass layer, the less
the effect of the joint shear modulus on stresses
and deformability of two-layer combined slabs.
The deflection of fibreglass slabs with external
metal reinforcement according to the theory
under consideration, taking into account the
interlaminar shift at 1.5, is 64.64% less than the
deflection of the slab.
The results of the calculation show that for two-
layer orthotropic combined glued boards with
low shear stiffness, it is necessary to take into
account transverse shears and compliance of the
adhesive joint. The influence of the adhesive layer
turns out to be significantly higher at its low shear
characteristics.
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International Journal of Advance Scientific Research
(ISSN
–
2750-1396)
VOLUME
02
I
SSUE
04
Pages:
64-70
SJIF
I
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FACTOR
(2021:
5.478
)
(2022:
5.636
)
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IF
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