未來展望

第四章結論與未來展望

4.2 未來展望

本研究以實驗與模擬探討含脫層三明治結構的挫屈行為，並對含脫層三明治結構的破壞強度預估已有一套初步的方法，接下來可再進一步討論的議題如下:

1. 本研究目前只探討不同表層厚度以及改變脫層長度對三明治結構試片在軸向壓縮實驗時的影響，對於芯材厚度的改變尚未有深入探討。因此，往後可延續本研究提出之實驗與分析方法，討論不同厚度的芯材對含脫層三明治結構的挫屈行為、破壞強度與破壞初始發生位置的影響。

2. 藉由觀察因局部挫屈所導致破壞的試片裂紋發現，在靠近脫層尖端的裂紋會繞過剛性較強之片膠，以某個特定角度朝芯材方向延伸。

在未來可嘗試利用破壞力學之觀點，預估脫層尖端的裂紋延伸角度。

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交通大學機械工程研究所論文, 2012.

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附表

表 2.1 單軸向碳纖維複合材料之材料性質

Young’s modulus Poisson’s ratio Shear modulus E₁₁

表 2.3 含脫層之三明治結構實驗試片規格

Face-sheet laminate Face-sheet thickness (t_f, mm)

Debond length (L_d, mm)

Specimen Buckling load (kN)

Failure load

(kN) Failure mode Specimen - 1 17.8 18.1

“Global buckling”

induce foam core failure Specimen - 2 18.1 18.5

Specimen - 3 18.1 18.4 Specimen - 4 17.8 18.1

Average 18.0 ± 0.2 18.3 ± 0.2

表 2.5 含 60 mm 脫層之[(0/90)₂]S三明治試片實驗結果

Specimen Buckling load (kN)

Failure load

(kN) Failure mode Specimen - 1 3.4 8.0

“Local buckling” induce face-sheet and core

separation

Specimen Buckling load (kN)

Failure load

(kN) Failure mode Specimen - 1 3.4 7.7

“Local buckling” induce face-sheet and core

separation

表 2.7 [(0/90)₂]S三明治試片之實驗結果 Debond

length(mm)

Buckling load (kN)

Failure load

(kN) Buckling mode Failure mode 0 18.0 ± 0.2 18.3 ± 0.2 Global Foam core

failure 10* 17.7  1.9 18.3 ± 1.6 Global

30* 10.8  0.4 12.7 ± 0.7 Local

Face-sheet and core separation 50* 4.6  0.8 8.0 ± 1.7 Local

60 3.6 ± 0.2 8.0 ± 0.6 Local 70 2.9 ± 0.6 7.7 ± 0.9 Local

*[20] 賴彥錕, "以實驗與模擬探討含脫層之複合材料三明治結構破壞行為," 交通大學機械工程研究所論文, 2012.

表 2.8 無脫層之[(0/90)₃]S三明治試片實驗結果

Specimen Buckling load (kN)

Failure load

(kN) Failure mode Specimen - 1 21.8 22.5

“Global buckling” induce foam core failure Specimen - 2 21.4 22.2

Specimen - 3 21.7 22.6 Average 21.6 ± 0.2 22.4 ± 0.2

表 2.9 含 10 mm 脫層之[(0/90)₃]S三明治試片實驗結果

Specimen Buckling load (kN)

Failure load

(kN) Failure mode Specimen - 1 20.9 22.3

“Global buckling” induce foam core failure Specimen - 2 21.0 21.8

Specimen - 3 21.4 22.4 Specimen - 4 22.1 22.7

Average 21.4 ± 0.7 22.3 ± 0.5

表 2.10 含 60 mm 脫層之[(0/90)₃]S三明治試片實驗結果

Specimen Buckling load (kN)

Failure load

(kN) Failure mode Specimen - 1 8.8 13.4

“Local buckling” induce face-sheet and core

separation Specimen - 2 9.6 13.6

Specimen - 3 9.7 14.0 Specimen - 4 10.4 14.2

Average 9.6 ± 0.8 13.8 ± 0.4

表 2.11 含 70 mm 脫層之[(0/90)₃]S三明治試片實驗結果

Specimen Buckling load (kN)

Failure load

(kN) Failure mode Specimen - 1 8.7 12.1

“Local buckling” induce face-sheet and core

separation

Buckling load (kN)

Failure load

(kN) Buckling mode Failure mode 0 21.6 ± 0.2 22.4 ± 0.2 Global

Face-sheet and core separation 60 9.6 ± 0.8 13.8 ± 0.4 Local

70 8.0 ± 0.7 11.7 ± 0.5 Local

*[20] 賴彥錕, "以實驗與模擬探討含脫層之複合材料三明治結構破壞行為," 交通大學機械工程研究所論文, 2012.

表 2.13 不同脫層長度之[(0/90)₂]S與[(0/90)₃]S三明治試片實驗結果 Face-sheet

laminate

Debond length(mm)

Buckling load (kN)

Failure load

(kN) Buckling mode Failure mode

[(0/90)2]S

Critical buckling load (kN)

Buckling load (Exp.) (kN)

表 3.2 挫屈分析與實驗結果之比較 Face-sheet

laminate

Debond

length(mm) Imperfection

Buckling load (kN) Element size

(mm)

Critical buckling load (kN)

Failure area (mm²)

0.4 7.28 2.65

0.2 7.27 2.45

0.1 7.26 2.47

0.05 7.26 2.47

表 3.4 分析步數收斂性

Step number Buckling load (kN)

70 5.09

100 5.06

200 5.06

表 3.5 含 50 mm 脫層之[(0/90)₂]S三明治試片破壞區域臨界值 Face-sheet

laminate

Debond length (mm)

Failure load (Exp.) (kN)

Critical damage zone size Element amount Area (mm²) [(0/90)2]S 50 8.0 ± 1.7 242 2.47

表 3.6 [(0/90)₂]S三明治試片破壞強度預估結果

Debond

length (mm) Imperfection

Failure load

(kN) Buckling

mode

Initial failure position Analysis Exp.

0 0.01 % 17.6(39˚) 18.3 ± 0.2(43.2˚) Global Intermediate of upper and lower half

core 10 0.1 % 17.6(-) 18.3  1.6(47.5˚) Global

10 -0.1 % 17.6(40˚) 18.3  1.6(47.5˚) Global

30 3 % 13.0 12.7  0.7 Local

Core failure near the

length (mm) Imperfection

Failure load

(kN) Buckling

mode

Initial failure position Analysis Exp.

0 0.3 % 23.7(40˚) 22.4 ± 0.2(43.8˚) Global Intermediate of upper and lower half

core 10 0.3 % 23.6(-) 22.3 ± 0.5(47˚) Global

10 -0.3 % 23.7(40˚) 22.3 ± 0.5(47˚) Global

30 0.5 % 21.6 21.7 ± 0.2 Global

Core failure near the

附圖

圖 2.1 試片基本尺寸示意圖

Clamped region 10

Foam core Face-sheet

Clamped region Gauge length

120 10

L_d

Unit:mm t_f

Gauge-A

Gauge-B Gauge-A Debond region

10 mm

圖 2.3 無脫層之[(0/90)₂]S三明治試片負載與應變響應圖

-0.004 -0.002 0 0.002

Strain gauge - A Strain gauge - B

Failure load

圖 2.5 無脫層之[(0/90)2]S三明治試片破壞行為

Crack

Clamped range

Crack path

圖 2.7 無脫層之[(0/90)2]S三明治試片破壞情形 Core

Glue

Failure load

Local buckling

o a

b c

Strain

L o a d (k N )

-0.0040 -0.002 0 0.002 0.004

2 4 6 8 10 12 14

Strain gauge - A(debond) Strain gauge - B

圖 2.9 含 60 mm 脫層之[(0/90)2]S三明治試片破壞行為((a)局部挫屈 (b)試片一端先行破壞 (c)試片完全破壞)

(a) (b) (c)

Displacement (mm)

Load(kN)

0 0.1 0.2 0.3 0.4 0.5

0 2 4 6 8 10 12

Failure load

圖 2.11 含 60 mm 脫層之[(0/90)₂]S三明治試片破壞裂紋路徑((a)整體裂紋路徑 (b)脫層尖端裂紋路徑)

圖 2.12 含 60 mm 脫層之[(0/90) ] 三明治試片破壞情形

Clamped region

X=30 Debond

region

Clamped region X

Face-sheet Core

(a)

(b) L_d=60 mm

Core

Glue Debond region

圖 2.13 含 70 mm 脫層之[(0/90)₂]S三明治試片負載與應變響應圖

圖 2.14 含 70 mm 脫層之[(0/90)₂]_S三明治試片破壞裂紋路徑((a)整體裂紋路徑 (b)脫層尖端裂紋路徑)

Strain

L o a d (k N )

-0.002 0 0.002 0.004

Strain gauge - A(debond) Strain gauge - B

Failure load

圖 2.15 無脫層之[(0/90)₃]S三明治試片負載與應變響應圖

圖 2.16 無脫層之[(0/90) ] 三明治試片破壞行為

Failure load Global buckling

o c

Strain

L o a d (k N )

-0.004 -0.002 0 0.002

0 5 10 15 20 25 30 35

Strain gauge - A Strain gauge - B

Crack

-0.0060 -0.004 -0.002 0 0.002 0.004 5

Strain gauge - A (debond) Strain gauge - B

圖 2.19 含 10 mm 脫層之[(0/90)₃]S三明治試片破壞行為

圖 2.20 含 10 mm 脫層之[(0/90) ] 三明治試片破壞裂紋路徑 Crack

Clamped range

Clamped range Crack path

L

=10 mm

圖 2.21 含 60 mm 脫層之[(0/90)₃]S三明治試片負載與應變響應圖

圖 2.22 含 60 mm 脫層之[(0/90)₃]_S三明治試片破壞行為((a)局部挫屈 (b)表層與芯材分離)

Strain

L o a d (k N )

-0.0040 -0.002 0 0.002 0.004

5 10 15 20 25

Strain gauge - A(debond) Strain gauge - B

Failure load

Local buckling

(a) (b)

圖 2.23 含 60 mm 脫層之[(0/90)₃]S三明治試片破壞裂紋路徑((a)整體裂紋路徑 (b)脫層尖端裂紋路徑)

圖 2.24 含 60 mm 脫層之[(0/90) ] 三明治試片破壞情形

Clamped region

Clamped region Debond region

L_d=60 mm

Core

X=30

X Y

Face-sheet

(a)

(b)

Core

Glue

Debond

region

圖 2.25 含 70 mm 脫層之[(0/90)₃]S三明治試片負載與應變響應圖

圖 2.26 含 70 mm 脫層之[(0/90) ] 三明治試片破壞行為((a)局部挫屈 (b)表

Strain

L o a d (k N )

-0.002 0 0.002

0 5 10 15 20

Strain gauge - A (debond) Strain gauge - B

Failure load

Local buckling

(b) (a)

圖 2.27 含 70 mm 脫層之[(0/90)₃]S三明治試片破壞裂紋路徑((a)整體裂紋路

Debond length (mm)

L o a d (k N )

圖 3.1 挫屈之負載與位移關係圖

P

_cr Bifurcation point

Load

Limit point

Displacement

Nonlinear analysis

Linear buckling analysis

Linear buckling analysis - get the 1

^st

buckling mode shape

Use the mode shape to give the imperfection into the original shape

Nonlinear analysis - large geometry deflection

Get the buckling solution

Use damage zone method and maximum

principal strain criterion to predict the failure load

圖 3.3 缺陷定義示意圖

圖 3.4 有限元素模型網格示意圖((a)模型整體網格示意圖 (b)脫層尖端網格局部放大圖)

Face-sheet

Foam core

e

_max

t

(a)

10 mm

3 mm Face-sheet

Foam core

Debonded region

(b)

圖 3.5 邊界條件示意圖

圖 3.6 無脫層之[(0/90)₂]_S三明治結構第一挫屈模態變形圖

Face-sheet

Foam core

Displacement controlled (U_Y=0)

Debond region

X Clamped boundary condition:

U_X= U_Y= 0

Face-sheet

Foam core

圖 3.7 含 60 mm 脫層之[(0/90)₂]S三明治結構第一挫屈模態變形圖

圖 3.8 不同缺陷之負載與應變響應圖(無脫層之[(0/90) ] 三明治試片)

Face-sheet

Foam

core L

=60 mm

Strain of X direction

L o a d (k N )

-0.0030 -0.002 -0.001 0 0.001 0.002 0.003

5 10 15 20 25

FEM (r = 0.01%) FEM (r = 0.1%) FEM (r = 0.5%) Exp.

圖 3.9 無脫層之[(0/90)₂]S三明治試片變形圖

圖 3.10 不同缺陷之負載與應變響應圖(含 60 mm 脫層之[(0/90)₂]_S三明治試片)

Face-sheet

Foam core

Strain of X direction

L o a d (k N )

-0.0020 -0.001 0 0.001 0.002 0.003 0.004 2

4 6 8 10 12

FEM (r = 0.5%) FEM (r = 1%) FEM (r = 5%) FEM (r = 9%) Exp.

圖 3.11 含 60 mm 脫層之[(0/90)₂]S三明治試片變形圖

圖 3.12 不同缺陷之負載與應變響應圖(含 70 mm 脫層之[(0/90)₂]_S三明治試片)

Face-sheet

Foam

core L

=60 mm

Strain of X direction

L o a d (k N )

-0.0020 -0.001 0 0.001 0.002 0.003 0.004 2

4 6 8 10 12

FEM ( r = 0.5%) FEM (r = 1%) FEM (r = 5%) FEm (r = 12%) Exp.

圖 3.13 含 70 mm 脫層之[(0/90)₂]S三明治試片變形圖

圖 3.14 不同缺陷之負載與應變響應圖(無脫層之[(0/90) ] 三明治試片)

Face-sheet

Foam

core L

=70 mm

Strain of X direction

L o a d (k N )

-0.0030 -0.002 -0.001 0 0.001 0.002 0.003 5

10 15 20 25 30 35

FEM (r = 0.3%) FEM (r = 1%) FEM (r = 5%) Exp.

圖 3.15 無脫層之[(0/90)₃]S三明治試片變形圖

圖 3.16 不同缺陷之負載與應變響應圖(含 10 mm 脫層之[(0/90)₃]_S三明治試片，缺陷值為正值)

Face-sheet

Foam core

Strain of X direction

L o a d (k N )

-0.0030 -0.002 -0.001 0 0.001 0.002 0.003 5

10 15 20 25 30 35

FEM (r = 0.3%) FEM (r = 1%) FEM (r = 5%) Exp.

圖 3.17 含 10 mm 脫層之[(0/90)₃]S三明治試片變形圖(缺陷值為 0.3%)

圖 3.18 不同缺陷之負載與應變響應圖(含 10 mm 脫層之[(0/90)₃]_S三明治試片，缺陷值為負值)

Face-sheet

Foam core

L_d=10 mm

Strain of X direction

L o a d (k N )

-0.0030 -0.002 -0.001 0 0.001 0.002 0.003 5

10 15 20 25 30 35

FEM (r = -0.3%) FEM (r = -1%) FEM (r = -5%) Exp.

圖 3.19 含 10 mm 脫層之[(0/90)₃]S三明治試片變形圖(缺陷值為-0.3%)

圖 3.20 不同缺陷之負載與應變響應圖(含 60 mm 脫層之[(0/90)₃]_S三明治試片)

L_d=10 mm Face-sheet

Foam core

Strain of X direction

L o a d (k N )

-0.0020 -0.001 0 0.001 0.002 0.003 0.004 5

10 15 20 25

FEM (r = 1%) FEM (r = 3%) FEM (r = 5%) FEM (r = 10%) Exp.

Strain of X direction

L o a d (k N )

-0.002 -0.001 0 0.001 0.002 0.003

Debond length (mm)

Imperfection(%)

圖 3.25 破壞強度預估流程圖

圖 3.26 含 50 mm 脫層之[(0/90)₂]_S三明治試片主應變分布圖((a)整體試片 (b) 脫層尖端區域)

Analyze the model under experiment failure load

Use max. principal strain criterion to decide the critical damage zone

Use the critical damage zone to predict the failure load Chose one of the experiment data

[(0/90)₂]_sface-sheet , L_d= 50 mm

Exp. failure load = 8.0 kN

The break strain of foam core is 0.03

Failure

(a)

(b) L_d=50 mm

圖 3.27 含 50 mm 脫層之[(0/90)₂]S三明治試片破壞情形[20]

圖 3.28 無脫層之[(0/90) ] 三明治試片預估結果((a)主應變分布圖 (b)主應變

Failure

Failure Face-sheet

Foam core

Core Face-sheet

Principal strain direction

Crack direction

(a)

(b)

圖 3.29 含 10 mm 脫層之[(0/90)₂]S三明治試片破壞情形[20]

圖 3.30 含 10 mm 脫層之[(0/90) ] 三明治試片主應變分布圖(模型朝含脫層

Crack

Debond region

(a)

(b)

L

=10 mm

Failure Failure

Failure area > critical damage zone

圖 3.31 含 10 mm 脫層之[(0/90)₂]S三明治試片預估結果(朝無脫層方向翹屈) ((a)試片主應變分布圖 (b)脫層尖端主應變分布圖 (c)主應變方向分布圖)

Failure area < critical damage zone

Failure

(a)

(b) Failure

Principal strain direction

Core

Crack direction

(c)

圖 3.32 含 60 mm 脫層之[(0/90)₂]S三明治試片預估結果((a)試片主應變分布圖 (b)脫層尖端主應變分布圖)

圖 3.33 無脫層之[(0/90)₃]S三明治試片預估結果((a)主應變分布圖 (b)主應變

Failure area > critical damage zone

L_d=60 mm

Failure Failure

(a)

(b)

Failure

Failure Foam core Face-sheet

Core Face-sheet

Principal strain direction

Crack direction

(b)

(a)

圖 3.34 含 10 mm 脫層之[(0/90)₃]S三明治試片主應變分布圖(模型朝含脫層側表層翹屈)

Failure area > critical damage zone

Failure

圖 3.35 含 10 mm 脫層之[(0/90)3]S三明治試片預估結果(朝無脫層方向翹屈) ((a)試片主應變分布圖 (b)脫層尖端主應變分布圖 (c)主應變方向分布圖)

Failure

(a)

Failure area < critical damage zone

(b)

Principal strain direction

Core

Crack direction

(c)

圖 3.36 含 30 mm 脫層之[(0/90)₃]S三明治試片破壞裂紋路徑[20]

圖 3.37 含 30 mm 脫層之[(0/90)₃]_S三明治試片預估結果((a)試片主應變分布圖 (b)脫層尖端主應變分布圖)

Clamped range

Clamped range Crack path

L_d=30 mm

X Y

L

=30 mm

Failure Failure

(a)

(b)

Failure area > critical damage zone

圖 3.38 含 60 mm 脫層之[(0/90)₃]S三明治試片預估結果((a)試片主應變分布圖 (b)脫層尖端主應變分布圖)

L

=60 mm

Failure Failure

(a)

(b)

Failure area > critical damage zone

在文檔中模擬含脫層複合材料三明治結構之破壞強度 (頁 60-108)

第四章 結論與未來展望

4.2 未來展望

參考文獻

Structures, vol. 44, pp. 263-278, 1999.

Composites Part B: Engineering, vol. 35, pp. 583-590, 2004.

Materials, vol. 8, pp. 7-31, 2006.

Congress on Applied Mechanics, pp. 375-380, 2007.

Structures and Materials, vol. 3, pp. 197-219, 2001.

composite materials, vol. 46, pp. 193-202, 2012.

mechanics, vol. 74, pp. 794-806, 2007.

Engineering fracture mechanics, vol. 44, pp. 581-590, 1993.

international conference on composite materials, 2007.

Sandwich Structures and Materials, vol. 4, pp. 31-47, 2002.

and adhesives, vol. 18, pp. 385-400, 1998.

附表

附圖

Failure load

Crack

Clamped range

Clamped range

Crack path

Failure load

Local buckling

Strain

L o a d (k N )

Failure load

Strain

L o a d (k N )

Failure load

Failure load Global buckling

Strain

L o a d (k N )

Crack

Clamped range

Clamped range Crack path

L

=10 mm

Strain

L o a d (k N )

Failure load

Local buckling

Glue

Debond

region

Strain

L o a d (k N )

Failure load

Local buckling

Debond length (mm)

L o a d (k N )

P

Load

Displacement

Linear buckling analysis - get the 1

buckling mode shape

Use the mode shape to give the imperfection into the original shape

Nonlinear analysis - large geometry deflection

Get the buckling solution

Use damage zone method and maximum

principal strain criterion to predict the failure load

e

t

Face-sheet

Foam

core L

=60 mm

Strain of X direction

L o a d (k N )

Strain of X direction

L o a d (k N )

Face-sheet

Foam

core L

=60 mm

Strain of X direction

L o a d (k N )

Face-sheet

Foam

core L

第四章結論與未來展望