• Tidak ada hasil yang ditemukan

ハ タニサ ョフソZーサ

N/A
N/A
Protected

Academic year: 2024

Membagikan "ハ タニサ ョフソZーサ"

Copied!
11
0
0

Teks penuh

(1)

mme.modares.ac.ir

1

*

2

1 -

2 -

* 13114 - 16846

[email protected]

27 :

1394

: 05 1394 16 : 1394

.

/

.

) .

( UMAT

.

- -

.

. .

.

Tensile characteristic length determination of notched woven composite laminates by means of progressive damage analysis

Fathollah Taheri-Behrooz

*

Hadi Bakhshan

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 17 May 2015 Accepted 26 May 2015 Available Online 07 July 2015

The analysis of notched composite parts in structure due to the existence of high stress concentration and undetermined behavior is an exigent issue. In this research, the progressive damage analysis has been applied to predict the failure of notched woven glass-epoxy composite laminates under tensile loading. Stress analysis and investigation of the effect of the hole size on it have been performed by the analytical and numerical methods. Developing UMAT in the ABAQUS finite element package has made th utilization of the 3D progressive damage analysis feasible. Max. Stress, Yamada-Sun and Tsai-Wu failure criterions have been implemented to predict the damage initiation due to the absence of significant failure criteria for woven composites. Instantaneous and recursive property degradation methods have been used to simulate the damage propagation. The tensile characteristic distance has been computed without any experiments. The comparison of stress and failure analysis with experimental results shows good agreement. Finally, using tensile characteristic length obtained by progressive damage method, the possibility of safety factor determination in the composite joints for optimum design has been provided.

Keywords:

Woven Composites Progressive Damage Failure Criteria

Tensile Characteristic Length

1 -

.

. .

] 1 .[

.

[ Downloaded from mme.modares.ac.ir on 2023-12-06 ]

(2)

. .

.

] 3 .[

)

) (

w/d

(

e/d

] 4 - 6 .[

] 7 [ .

] 8 [

] 9 [ -

] 10 [

. ]

11 - 13

] .[

14 [

)

(

.

] 15 - 20 .[

. ] 21 [ - -

] 22 [ .

. ] 23

. [

] 24 [ -

. -

.

] .

25 [

.

LaRC04

] 26 [ ] 27

. [

.

.

-

. -

- .

.

.

2 - 1

- .

3 - .

] 7 [

.

r

1 -

. .

y

y x

) 1 ( ]

28 :[

) 1 (

2 4 8

2 3 3 5 7

y T

2

r r r r

x x K x x

K

T

) 2 (

) 2

2

(

11 22 12 11 22 12

11 66

1 2

T

A A 2 A

K A A A

A A

A

ij

x

) .

r

1 (

) 3 (

) 3 (

2

( ,0)

y T

K r K

[ Downloaded from mme.modares.ac.ir on 2023-12-06 ]

(3)

1

( (

] 7 [

) 3 ( .

.( )

) 3

] (

7 [

. ( , 0)

d0

1 - .

) 4

0 0

(

y

( )| x

x r d

) 4

) (

1 (

) 5 (

) 5 (

2 4 6 8

1 1 1 1

2

( ) 1

2 3 ( 3) 5 7

2

PSC y

T

K x K

) 6

1

(

0

r r d

) 5 ( .

.

.

4 -

.

.

( )

( )

. ) .(

. .

. .

- . .

.

] 29 .[

4 - 1 -

. -

) 7 (

0 0 0

11 11 12 13 11

0 0 0

22 21 22 23 22

0 0 0

33 31 32 33 33

0

12 44 12

0

13 55 13

0

23 66 23

0 1 0

0 0 0

0 0 0

0 0 0

0 0 0 0 0

0 0 0 0 0

0 0 0 0 0

C C C

C C C

C C C

C C

C

S C

0

C

ij

) 7 (

) 8 (

23 32 11 110

13 31 22 0

22

12 21 33 330

1 ;

1 ;

1 ;

C E C E

C E

[ Downloaded from mme.modares.ac.ir on 2023-12-06 ]

(4)

) 8 (

12 13 32 22 21 31 23 11

0 0

12 21

13 12 32 33 31 21 23 11

0 0

13 31

23 13 21 33 32 31 12 22

0 0

23 32

0 0 0

44 12 55 13 66 23

12 21 23 32 13 31 21 32 13

;

;

;

; ;

1 2

E E

C C

E E

C C

E E

C C

C G C G C G

.

4 - 2 - )

. .

] 30 .[

) (

4 - 3 -

.

] 31 .[

. .

- -

.

- .

-

.

) 10 9 (

)

9 (

11 11

0 0

T C

X X X X

) 10 (

22 22

0 0

T C

Y Y Y Y

) 11 (

) 11 (

11 22 12

max , ,| | 1

I

f

X Y S

X

T

X

C

Y

T

Y

C

S

I

f

.

. -

) 12 (

) 12 (

2 2

11 12 2

c

X S e

1 e 1

e

1

X

12

S

c

-

] 32 [

) 13 - 17 (

)

11

0

:(

) 13 (

2 2

11 12

1

T c

X S

)

11

0

:(

) 14 (

2 2

11 12

1

C c

X S

)

22 33

0

:(

) 15 (

2 2

22 12

1

T c

Y S

)

22 33

0

:(

) 16 (

2 2 2

22

1

22 12

1

2

C

c C C C

Y

S S Y S

-

) 17 (

2 2

11 12

1

T c

X S

- ] 22 [

[ Downloaded from mme.modares.ac.ir on 2023-12-06 ]

(5)

.

) 18 (

) 18 (

1 11 2 22 3 33 11 11 2

2 2

22 22 33 33 12 11 22

23 22 33 13 22 33

2 2 2

44 13 55 23 66 12

( )

( ) ( ) 2

2 2

( ) ( ) ( )

F F F F

F F F

F F

F F F

) 18 (

i

) ( F

ij

) ( F .

) 19 (

) 19 (

1 2 3

11 22 33

44 2 55 2 66 2

12

13 23

12 13

23

1 1 1 1 1 1

; ;

1 1 1

; ;

1 1 1

; ;

1 1 1 1

2 ; 2

1 1

2

T C T C T C

T C T C T C

T C T C T C T C

T C T C

F F F

X X Y Y Z Z

F F F

X X Y Y Z Z

F F F

S

S S

F F

X X Y Y X X Z Z

F Y Y Z Z

) 20 (

) 20 (

2

0

ii jj ij

F F F

- )

( 1

.

) 21 (

) 21 (

1 2 3 4 5 6

6

1

1

i

1

i

.

i

) 22 ( .

e

i i

.

e

i

.

-

) 22 (

1 1 11 11 11 2 12 11 22 13 22 33 2 2 22 22 22 2 12 11 22 23 22 33 3 3 33 33 33 2 13 22 33 23 22 33 4 66 12 2

5 44 13 2 6 55 23 2

( )

( )

( )

( )

( )

( )

F F F F

F F F F

F F F F

F F F

4 - 4 -

. .

1

:

2

.

)

I

(

i

th

.

C0 I

.

.

3

.

. 10

-6

8/

0

4

.

( ) .

( )

) ( 0.5

.

5

5/

0

. .

. 1

-

-

5 -

12

E

2/

0

200

ML506

.

250 25

2/

2

.

2

1- Ply- discounting approach 2- Internal state variable 3- Instantaneous 4- Recursive 5- Singularity

[ Downloaded from mme.modares.ac.ir on 2023-12-06 ]

(6)

mm

1

50

. 8

2/ GPa

20 4/ MPa

364 .

kg/m

3

2560

kg/m

3

1100 1/

43

4 7 10

3 .

5

3 .

( )

F wt

1

-

-

0

( )11 T C

11 0 0 44

( ) ( )

T S

C C

0

( )11 T C

0

( )11 C C

0

( )11 C C

0

( )11 C C

0

( )22 T C

22 0 0 44

( ) ( )

T S

C C

0

( )22 T C

0

( )22 C C

0 22 44 0

( ) ( )

C S

C C

0

( )22 C C

0

( )33 T C

0

-

( )33 T C

0

( )33 C C

0

-

( )33 C C

0

( )44 S C

0

( )44 S C

0

( )44 S C

0

( )55 S C

0

-

( )55 S C

0

( )66 S C

0

-

( )66 S C

2 /

E3(GPa) E2(GPa)

*

E1(GPa)*

2 2/

20 2/

20

G23(GPa) G13(GPa)

G12(GPa)*

3 3

6/

4

23 12* 13

28 /0 28

/0 046

/0

YT(MPa)* XC(MPa)*

XT(MPa)*

3/

364 3/

364 3/

364

ZC(MPa) ZT(MPa)

YC(MPa)*

40 40

3/

364

S23(MPa) S13(MPa)

S12(MPa)*

20 20

46

* 1- Extensometer

w F

d

t

. 2 - 4

. 2

-

10 .

. 3

6 -

- 5/

0

4 5 -

4 7

10 .

.

3

(MPa)

(MPa)

F(N)

4 48

/ 262 8/

220 68

/ 13431

7 32

/ 249 85

/ 179 62

/ 10847

10 85

/ 248 88

/ 148 52

/ 8957

2

( (

10

[ Downloaded from mme.modares.ac.ir on 2023-12-06 ]

(7)

. .

-

.

-

6 .

3

4 -

4

4 SDV1

y

z

10

4 7 .

.

y

7 -

-

. 7

- .

.

. ( )

5 -

( 10 ( 7

0.4 0.6 0.8 1 1.2

0 3 6 9 12

) (

0 2000 4000 6000 8000 10000 12000 14000 16000

0 1 2 3 4 5 6

) (

) (

-

[ Downloaded from mme.modares.ac.ir on 2023-12-06 ]

(8)

d=10 mm d=7 mm

d=4 mm

6

8 -

. .

. -

) .

(

.

9 .

. .

. 9

. 4

.

- .

[ Downloaded from mme.modares.ac.ir on 2023-12-06 ]

(9)

)

)

)

-

7 (

4 ( 7 ( 10

8

-

- )

( -

8 -

9

0.8 1 1.2 1.4 1.6

3 4 5 6 7 8 9 10 11

) (

) (

-

0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6

1 3 5 7 9

) (

) (

w/d

[ Downloaded from mme.modares.ac.ir on 2023-12-06 ]

(10)

4 4 7

10

) 64

/ 13 5/

11 87

/8

64 /8 78

/6 51

/5

- 55

/ 13 79

/ 11 72

/9

35 / 12 39

/ 11 25

/9

) -

31 /1 398

/1 49

/1

015 /1 121

/1 24

/1

72 /0 684

/0 677

/0

285 /0 285

/0 285

/0

67 /0 585

/0 525

/0

. .

- -

. .

-

-

- 5/

0 -

- -

- .

- 10

10

9 - )

A

GPa.m (

C

(mm)

d

0

) ( mm

) ( GPa

(N) )

( GPa

I K

) ( MPa

1 SDV1

2 SDV2

3 SDV3

2 SDV4

- 1

3 SDV5

- 1

(mm) )

( MPa ) ( MPa ) ( MPa

) ( mm

, x

) ( MPa

[ Downloaded from mme.modares.ac.ir on 2023-12-06 ]

(11)

0 11

22

T C

1

i,

2 3

f

10 -

[1] M. C. Niu, Composite airframe structures: practical design information and dat, Adaso Adastra Engineering Center, 1992.

[2] P. P .Camanho and F. Matthews, Stress analysis and strength prediction of mechanically fastened joints in FRP: review, Composites Part A:

Applied Science and Manufacturing Vol. 28, pp. 529-547, 1997.

[3] S. D. Thoppul, J. Finegan, R. F. Gibson, Mechanics of mechanically fastened joints in polymer–matrix composite structures–a review, Composites Science and Technology, Vol. 69.3, pp. 301-329, 2009.

[4] B. Okutan, Z. Aslan, and R. Karakuzu, study of the effects of various geometric parameters on the failure strength of pin-loaded woven-glass- fiber reinforced epoxy laminate, Composites science and technology Vol.

61, pp. 1491-1497, 2001.

[5] B. Okutan and R. Karakuzu, The strength of pinned joints in laminated composites, Composites science and technology Vol. 63, pp. 893-905, 2003.

[6] R. Karakuzu, T. Gülem, and B. M. çten, Failure analysis of woven laminated glass–vinylester composites with pin-loaded hole, Composite structures Vol. 72, pp. 27-32, 2006.

[7] J. Whitney and R. Nuismer, Stress fracture criteria for laminated composites containing stress concentrations, Journal of Composite Materials Vol. 8, pp. 253-265, 1974.

[8] F.Taheri-Behrooz, R. Nouhi Hefzabad, A. Shamaei Kashani, Determining nonlinear behavior effects of material on load distribution in single- column multi-bolt composite joints, Modares Mechanical Engineering, Vol. 15, No. 1, pp. 67-74, 2015. (In Persian)

[9] F. K. Chang, R. A. Scott, Strength of mechanically fastened composite joints, Journal of Composite materials, 16.6, 470-494, 1982.

[10] S. Yamada and C. Sun, Analysis of laminate strength and its distribution, Journal of Composite Materials Vol. 12, pp. 275-284, 1978.

[11] J.-H. Choiand Y.-J. Chun, Failure load prediction of mechanically fastened composite joints, Journal of Composite materials Vol. 37, pp. 2163-2177, 2003.

[12] A. Aktas and M. Husnu Dirikolu, An experimental and numerical investigation of strength characteristics of carbon-epoxy pinned-joint

plates, Composites science and technology Vol. 64, pp. 1605-1611, 2004.

[13] A. Akta H. mrek, and Y. Cunedio lu, Experimental and numerical failure analysis of pinned-joints in composite materials, Composite structures Vol. 89, pp. 459-466, 2009.

[14] J. Zhang, F. Liu, L. Zhao, Y. Chen, and B. Fei, progressive damage analysis based characteristic length method for multi-bolt composite joints, Composite Structures Vol. 108, pp. 915-923, 2014.

[15] F. K. Chang, K. Y. Chang, progressive damage model for laminated composites containing stress concentrations, Journal of Composite Materials, 21.9, pp. 834-855, 1987.

[16] F. K. Chang, K. Y. Chang, Post-failure analysis of bolted composite joints in tension or shear-out mode failure, Journal of Composite Materials, 21.9, pp. 809-833, 1987.

[17] S. C. Tan, progressive failure model for composite laminates containing openings, Journal of Composite Materials Vol. 25, pp. 556-577 1991.

[18] M. M. Shokrieh and L. B. Lessard, Effects of material nonlinearity on the three-dimensional stress state of pin-loaded composite laminates, Journal of Composite Materials Vol. 30, pp. 839-861, 1996.

[19] K. I. Tserpes, G. Labeas, P. Papanikos, T. Kermanidis, Strength prediction of bolted joints in graphite/epoxy composite laminates, Composites Part B: Engineering, 33.7, pp. 521-529, 2002.

[20] P. Camanho and F. Matthews, progressive damage model for mechanically fastened joints in composite laminates, Journal of Composite Materials Vol. 33, pp. 2248-2280, 1999.

[21] Z. Hashin, Failure criteria for unidirectional fiber composites, Journal of applied mechanics Vol. 47, pp. 329-334, 1980.

[22] S. W. Tsai and E. M. Wu, general theory of strength for anisotropic materials, Journal of composite materials Vol. 5, pp. 58-80, 1971.

[23] M. R. Garnich, V. M. Akula, Review of degradation models for progressive failure analysis of fiber reinforced polymer composites, Applied Mechanics Reviews, 62.1, pp. 010801, 2009.

[24] M.-L. Dano, G. Gendron, and A. Picard, Stress and failure analysis of mechanically fastened joints in composite laminates, Composite Structures Vol. 50, pp. 287-296, 2000.

[25] Y. Xiao and T. Ishikawa, Bearing strength and failure behavior of bolted composite joints (part II: modeling and simulatio), Composites science and technology Vol. 65, pp. 1032-1043, 2005.

[26] C. G. Davila, P. P. Camanho, C. A. Rose, Failure criteria for FRP laminates, Journal of Composite materials, 39.4, 323-345, 2005.

[27] P.P. Camanho, and M. Lambert, design methodology for mechanically fastened joints in laminated composite materials, Composites Science and Technology 66.15, 3004-3020, 2006.

[28] S. G. Leknitskii, Theory of elasticity of an anisotropic body Mir Publishers, 1981.

[29] F. L. Matthews, Davies, G.A.O., Hitchings, D. and Soutis, Finite Element Analysis of Composite Materials and Structures Abington: Woodhead Publishing Ltd, 2000.

[30] A. Documentation, ABAQUS Analysis User’s Manual Materials. Other plasticity models. Concrete, 2010.

[31] M. J. Hinton, A. Kaddour, P. D. Soden, Failure criteria in fibre reinforced polymer composites: the world-wide failure exercise Elsevier, 2004.

[32] F. K. Chang, K. Y. Chang, Post-failure analysis of bolted composite joints in tension or shear-out mode failure, Journal of Composite Materials 21(9), pp. 809-833, 1987.

[ Downloaded from mme.modares.ac.ir on 2023-12-06 ]

Referensi

Dokumen terkait