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mme.modares.ac.ir

1

*

2

1 -

2 -

* 13114

- 16846 [email protected]

22 :

1393 1393 10 :

: 11 1393

.

.

SBT 9244

AL2024-T3

.

30 60 90 100

. %

.

. .

-

Numerical study of the effect of moisture–induced swelling stresses on damage behavior of adhesive joints under static loading

Hadi Khoramishad

*

Zahra Abbasi

Department of Mechanical Engineering, Iran University of Science and Technology, Tehran, Iran

*P.O.B. 16846-13114 Tehran, Iran,[email protected]

A RTICLE I NFORMATION A BSTRACT

Original Research Paper Received 13 November 2014 Accepted 31 December 2014 Available Online 31 January 2015

The main limitation of the use of adhesive joints is susceptibility of the adhesive layer to damaging environmental factors such as humidity. Use of numerical methods for predicting the strength of adhesive joints exposed to moist environment can save significant amount of time and cost. In this study, first, experimental investigation and numerical modeling of the complete process of moisture diffusion into the adhesive layer and its damaging effect on the adhesive joint strength were determined. Then this process was applied for single lap joint of SBT 9244 pressure sensitive adhesive and AL2024-T3 aluminum alloy substrate with two 12.5 and 50 mm overlap of lengths. In the irst step, moisture distribution for 30, 60 and 90 days exposure time in environmental condition of 100% relative humidity was obtained. Then single lap joint tensile test was simulated using cohesive zone model for different exposure times. In this simulation cohesive zone model parameters were determined in such way that numerical failure load and the existing experimental failure load were in good agreement. The cohesive zone model parameters were determined depending on the moisture content. The first simulation was done without considering swelling and in the second, swelling was considered. Swelling stress was obtained separately at different exposure time periods. It was found that swelling effect was more considerable in the joints with longer overlap length and shortened exposure time.

Keywords:

Adhesivejoints Moisture Swelling

cohesive zone model environmental degradation

1 - .

[ Downloaded from mme.modares.ac.ir on 2023-12-10 ]

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= 8

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AL2024-T3

]

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) 1

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%

. ) 2 ( .

)

tsat

(

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SBT

] % 14 [

2

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) (

g

) (

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600 10

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2- Yield tensile strength 3- Ultimate tensile strength 4- Hot press

0 0.5 1 1.5 2 2.5 3

0 200 400 600 800

Mt%

t(h)

AL2024-T3 SBT

)

kg/m3

( 2780

880

1

120

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MPa

)

2

)3 (MPa

485

20

18

% 96

%

) ) (E (MPa

72400

6/

61

)

(

33 /0 35

/0

25

25 62 /1

[ Downloaded from mme.modares.ac.ir on 2023-12-10 ]

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AL2024-T3

.

3 .

30 60

90 100

%

2 - 2 -

. . .

. )

b

4 (

) .

(

F

]

1

15 [ )

3 (

) 3 (

=

c

D

x Fx

x

)

) (

c

(

t

)

2

4 (

) 4 (

=

2 - 2 - 1 -

) 5

6 (

) 5 (

=

) 6 (

=

)

5 ) ( 6 ( .

3

AL2024-T3

)

SBT

] ( 14 [

1- Fick's first law 2- Fick's second law

4

) .(

.

3 .

.

)

) (

(

D

.

2 - 2 - 2 -

- .

) ( )

7 (

) 7 (

=

3 S 4

.

] 16 [

.

)

csat

( .

5

/ ) 8 (

) 8 (

=

Pvp

) (

RH%

)

Pvp,sat

( )

9 (

) 9 (

= % ×

,

.

] 17 [ 3

.

2 - 2 - 3 -

SBT

3- Solubility 4- Activity 5- Henry's law

b

y x

25 /0

L

25

5/

87

L

62 5/ 25

[ Downloaded from mme.modares.ac.ir on 2023-12-10 ]

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3 16

[

) ( )

(

c

) (

1

1

D S

cP

1

DS

9244 AL2024-T3

100 %

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.

3 .

1

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(

) (

= 1

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)

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10 (

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= ( / ) × ×

) (

( )

) 2

(

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( )

11 (

] 2 [

.

) 11 (

=

) 11 (

2.27 × 10

4

5

M%

SBT 9244

4

SBT 9244

5/

12 100

%

)

( / ) ( )

M%

30 994898

/0 00176439 /0 566385 /2

60 999965

/0 00177338 /0

579455 /2

90 1

00177344 /0

579545 /2

1- Transient heat transfer 2- Heat transfer

5/

12 50

100 % . 5

5

SBT 9244

50 100

%

)

( / ) ( )

M%

30 982574

/0 0069701 /0 534594 /2

60 999551

/0 0070906 /0 578387 /2

90 1

0070938 /0 579545 /2

)

)

)

)

)

)

5 5/

12

( ) 30 ( ) 60 ( ) 90 50

( ) 30 ( ) 60 ( ) 90

[ Downloaded from mme.modares.ac.ir on 2023-12-10 ]

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3 -

9244 SBT AL2024-T3

5/

12 50 .

mm/min

5

] 14 .[

3 - 1 -

.

. . ]

18 [.

.

] 19 .[

. .

-

3 - 1 - 1 - -

-

( )

( )

. . .

) (

. 19

.[

-

1 3 2

3 - 2 -

SBT 9244 AL2024-T3

- .

)

4

12 (

1- Initial elastic stiffness 2- Damage initiation criterion 3- Damage propagation criterion 4- Quadratic nominal stress criterion 5

)

(

6

. . 12

- .

7

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- )

. (

BK

BK

20 .[

13

BK

. 13

G

n s t

.

BK

) 13

(

) 13 (

+ ( ) +

+ + = + +

2

BK

. - .

6

.

)

a

6 ( -

.

B B

a

.

B x

. 6

b

.

B

. .

)

COH3D8

( (

C3D8R

)

9

5- Cohesive strength 6-Macaulay bracket 7- Power law fracture 8- Benzeggagh- Kenane 9- 3D stress

) 12 ( + + = 1

[ Downloaded from mme.modares.ac.ir on 2023-12-10 ]

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50

.

5/

12 1872

50 3991

4 -

4 - 1 - 2

- 1

9244 SBT

AL2024-T3

5/

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100 %

90 30

mm/min

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7

. 7

90

5/

12 35

% 50

7 % .

] 14 .[

4 - 2 -

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AL2024-T3

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1

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.

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8

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6 . 7

5 -

2

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22 .[

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8

6

1- Predefined field 2- Free water 3- Bonded water

0 3 6 9 12 15 18

0 20 40 60 80 100

) (

) (

12/5 50

0.7 0.8 0.9 1 1.1

0 0.2 0.4 0.6 0.8 1

Gs Gt

) kj/m2 (

Gn

) kj/m2 (

Ts Tt

) (MPa

Tn

) (MPa

Ks Kt

) MPa/mm (

Kn

) MPa/mm (

10 5 /9 85 22 22 8/ 61 6/ 0

09

/9 /4 54 /8 95 20 20 / 72 56 1

[ Downloaded from mme.modares.ac.ir on 2023-12-10 ]

(8)

7

AL2024-T3

SBT

) (

mm

) )

(

kN

)

(

kN

(%)

5/

12 0 26

/3 9/

2 04

/ 11 -

5/

12 30 09

/3 61

/2 53 / 15 -

5/

12 60 25

/2 61

/2 16

5/

12 90 25

/2 61

/2 16

50 0

7/

11 7/

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11 7/

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.

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- .

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= ×

1 CME 2

. -

. 9 -

. 9

0063

/wt%

/0

] 9 .[

5 - 2 -

) .

.

8 .

8

1- coefficient of moisture expansion 2- Swelling coefficient

5 - 2 - 1 -

. .

. 90

. 10 11

. 12

9

] 9 [

8

AL2024-T3

SBT

) (

mm

) )

(

kN

)

(

kN

(%)

5/

12 0 26

/3

5/

12 30 09

/3 72

/2 97 / 11 -

5/

12 60 25

/2 72

/2 89 / 20

5/

12 90 25

/2 72

/2 89 / 20

50 0

7/

11

50 30 7/

11 3/

9 51 / 20 -

50 60 7/

11 3/

9 51 / 20 -

50 90 7/

10 3/

9 08 / 13 -

12 5/ 10

-3.00E-07 -1.00E-07 1.00E-07 3.00E-07 5.00E-07

0 5 10 15

) (

) (

[ Downloaded from mme.modares.ac.ir on 2023-12-10 ]

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50 11

12

12

. .

.

.

. .

. 5

- 2 - 1

. .

6 - .

] 14 [ .

SBT 9244 AL2024-T3

5/

12 50

100

. %

90

30 .

- .

.

. -

. .

.

BK

)

(

.

.

7 - )

b

(

m

c

)

kg/m3

(

cp

)

kj/kgK

(

D

)

m2/s

(

)

E

(

Pa

)

F kg/m2s

(

)

G kj/m2

(

)

K

(

Pa/m

L

) (

m

)

M

(

kg

P

) (

Pa

-2.70E-06 -1.20E-06 3.00E-07 1.80E-06 3.30E-06

0 20 40 60

) (

) (

[ Downloaded from mme.modares.ac.ir on 2023-12-10 ]

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RH

)

S Kg m-3Pa-1

(

)

t

(

s

)

T

(

Pa

)

V m3

(

)

W

(

N

BK

) (

C

)

(

W/Km

)

kg/m3

(

)

(

Pa

) (

Pa

C

adh

avg

Dry

H2o

n

s

sat

t

vp

8 -

[1] M. R. Bowditch, The durability of adhesive joints in the presence of water, International Journal of Adhesion and Adhesives Vol. 16, p.p. 73- 79, 1996

[2] A. Mubashar, Modelling degradation in adhesive joints subjected to fluctuating service conditions Doctoral dissertation in Mechanical Engineering, Loughborough University, 2010.

[3] W. K. Loh, A. D. Crocombe, M. M. Abdel Wahab, I. A. Ashcroft, Modelling anomalous moisture uptake, swelling and thermal characteristics of rubber toughened epoxy adhesive, International Journal of Adhesion and Adhesives vol. 25, pp. 1-12, 2005.

[4] C. D. M. Liljedahl, A. D. Crocombe, M. A. Wahab, I. A. Ashcroft, Modelling the environmental degradation of the interface in adhesively bonded joints using cohesive zone approach, The Journal of Adhesion vol. 82, pp. 1061-1089, 2006.

[5] C. D. M. Liljedahl, A. D. Crocombe, M. A. Wahab, I. A. Ashcroft, Modelling the environmental degradation of adhesively bonded aluminium composite joints using CZM approach, International Journal of Adhesion and Adhesives vol. 27, pp. 505-518, 2007.

[6] A. Mubashar, I. A. Ashcroft, G. W. Critchlow, A. D. Crocombe, Modelling cyclic moisture uptake in an epoxy adhesive, The Journal of Adhesion vol.

85, pp. 711-735, 2009.

[7] A. Mubashar, I. A. Ashcroft, G. W. Critchlow, A. D. Crocombe, Moisture absorption–desorption effects in adhesive joints, International Journal of Adhesion and Adhesives vol. 29, pp. 751-760, 2009.

[8] K. B. Katnam, J. P. Sargent, A. D. Crocombe, H. Khoramishad, I. Ashcroft, Characterisation of moisture-dependent cohesive zone properties for adhesively bonded joints, Engineering Fracture Mechanics vol. 77, pp.

3105-3119, 2010

[9] S. Sugiman, Combined environmental and fatigue degradation of adhesively bonded metal structures,Doctoral dissertation inMechanical Engineering University of Surrey, United Kingdom 2012.

[10] S. Sugiman, A. D. Crocombe, K. B. Katnam, Investigating the static response of hybrid fibre–metal laminate doublers loaded in tension, Composites Part B: Engineering vol. 42, pp. 1867-1884, 2011.

[11] S. Sugiman, A. D. Crocombe, I. A. Aschroft, Experimental and numerical investigation of the static response of environmentally aged adhesively bonded joints, International Journal of Adhesion and Adhesives vol. 40, pp. 224-237, 2013.

[12] L. D. Jofre, E. O. Julian, Durability of adhesively-bonded CFRP/steel joints Master’s Thesis in the Master’s Programme Structural Engineering and Building, Chalmers University of Technology, 2013.

[13] X. Han, A. D. Crocombe, S. N. R. Anwar, P. Hu, The strength prediction of adhesive single lap joints exposed to long term loading in hostile environment, International Journal of Adhesion and Adhesives vol. 90, pp.

420-436, 2014.

[14] S. Temiz, A. Özel, M. D. Aydin, study on durability of joints bonded with pressure-sensitive adhesives, Journal of Adhesion Science and Technology vol. 18, pp. 1187-1198, 2004.

[15] J. Crank, The Mathematic of diffusion Oxford University Press, London 1975 .

[16] S. Yoon, B. Han, Z. Wang, On moisture diffusion modeling using thermal- moisture analogy, Journal of Electronic Packaging vol. 129 ,pp. 421-426, 2007.

[17] W. R. Vieth, Diffusion in and through polymers: principles and applications, Hanser Publishers 1991.

[18] M. M. Shokrieh, M. Salamat-Talab, M. Heidari-Rarani, Numerical analysis of mode delamination growth in laminated DCB specimens using cohesive zone models, Modares Mechanical Engineering Vol. 13, No 1, p.p. 38-48. 2013. (In Persian)

[19] B. Mohammadi, D. Salimi-Majd, M. H. Ali-Bakhshi, Analysis of composite skin/stringer debonding and failure under static loading using cohesive zone model, Modares Mechanical Engineering Vol. 14, No 10, p.p. 17-25.

2014. (In Persian)

[20] ABAQUS 6.4, Analysis users manual, section 6.8.1

[21] M. J. Adamson, Thermal-expansion and swelling of cured epoxy-resin used in graphite-epoxy composite materials, Journal of Materials Science vol. 15, pp. 1736-1745, 1980.

[22] M. R. Vanlandingham, E. F. Eduljee, J. W. Gillespie, Moisture diffusion in epoxy system, Journal of Applied Polymer Science vol. 71, pp. 787-798, 1999.

[23] G. Z. Xiao, M. E. R. Shanahan, Swelling of DGEBA/DDA epoxy resin during hygrothermal ageing, Polymer vol. 39, pp. 3253-3260, 1998.

[ Downloaded from mme.modares.ac.ir on 2023-12-10 ]

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