glass fiber reinforced hybrid composite

Accepted Manuscript Sandwich diffusion model for moisture absorption of flax/glass fiber reinforced hybrid composite Hang Yu, Chuwei Zhou PII: DOI: Reference:

S0263-8223(17)33179-3 https://doi.org/10.1016/j.compstruct.2017.12.061 COST 9218

To appear in:

Composite Structures

Received Date: Revised Date: Accepted Date:

26 September 2017 4 December 2017 21 December 2017

Please cite this article as: Yu, H., Zhou, C., Sandwich diffusion model for moisture absorption of flax/glass fiber reinforced hybrid composite, Composite Structures (2017), doi: https://doi.org/10.1016/j.compstruct.2017.12.061

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Sandwich diffusion model for moisture absorption of flax/glass fiber reinforced hybrid composite Hang Yu, Chuwei Zhou* State Key Laboratory of Mechanics and Control of Mechanical Structures，Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China

Abstract Flax/glass fiber reinforced hybrid composites take up a high amount of moisture from humid environment due to hydrophilic nature of flax fibers. Some experimental works have been carried out to investigate the diffusion kinetic of these hybrid composites with different stacking sequences. However, few analytical efforts have been made to effectively describe their moisture diffusion behaviors thus far. In this paper, a sandwich diffusion model is established to predict the moisture absorption behavior of flax/glass hybrid composites with different stacking sequences. To deal with interface concentration problem across flax fiber layers and glass fiber layers, the continuous normalized concentration and mass-conserving condition are employed. Both finite element analysis and moisture absorption experiments are performed to validate the proposed model, and the results shows that good agreements are achieved. Keywords Flax fiber; Hybrid composite; Sandwich diffusion model; Moisture absorption; Interface condition;

*

Corresponding author. Tel.:+8613851556829. E-mail address:[email protected](Hang Yu),[email protected] (ChuweiZhou).

Introduction In recent years, the use of cellulosic fibers as a potential alternative to glass fibers in polymer composite materials has gained interest among researchers [1-4]. Compared to glass fibers, cellulosic fibers such as flax, hemp and sisal present low relative density, low cost, good specific mechanical properties and easy recyclability at the end of the life cycle [5, 6]. Despite of these advantages, the main drawback of cellulosic fibers is their inherent susceptibility to the moisture absorption when they are exposed to humid environment [7]. The hollow parts called lumen in the middle of cellulosic fibers give them tubular structures which contribute to a high amount of moisture absorption [8]. The moisture uptake of hydrophilic cellulosic fibers could develop mismatch stress at the fiber/matrix interface which causes damage in interface or matrix and finally degrades the mechanical performance of cellulosic fiber reinforced composites. This environmental susceptibility will restrain their applications in many fields, e.g. automotive industries and building constructions [9]. Different approaches have been developed to improve the moisture resistance behavior and mechanical properties of cellulosic fiber reinforced composites, such as physical or chemical treatment of cellulosic fiber, matrix or both of them [10-12]. Besides, some studies suggest that hybridizing the cellulosic fibers with stronger glass fibers in the same matrix might produce a material with expected properties, and the new hybrid composite materials can reach a balanced properties of environment friendly and environment impact resistance [13-15]. Some experimental studies have been done on moisture absorption behavior of

cellulosic/glass fiber hybrid composites [8, 16]. For example, Saidane et al. [8] studied the effect of stacking sequences on moisture diffusion of flax/glass fibers reinforced epoxy composites, and the results show that the water uptake and diffusivities are clearly reduced by the addition of glass fiber layers in laminates, the diffusion behavior of all laminates almost follows Fick’s law after an immersion time of 38 days. Ghasemzadeh-Barvarz et al. [16] investigated the aging properties of flax/glass fiber reinforced hybrid composites, and they found that glass fibers suppresses water absorption of the composites and the specimens which having glass fibers showed higher water resistance than those of flax fiber even at the lowest concentration studied (10%). Although some experimental works have been reported on the moisture diffusion mechanism of cellulosic/glass fibers reinforced composites, few analytical efforts have been made to characterize the moisture diffusion behavior of these new hybrid composites. The moisture concentration and equilibrium moisture content of cellulosic fibers layers are different from those of glass fiber layers, thus, the moisture diffusion parameters of hybrid composites laminates are not homogeneous inside. Therefore, an diffusion model should developed to represent this inhomogeneity. Nurge et al. [17] presented a finite-difference method to describe the moisture absorption of multi-layer composites and sandwich structures, and it was proved that the predictions became more accurate after applying a mass-conserving condition at the interfaces of different layers for a fixed relative humidity and temperature. Joshi and Muliana [18] developed an analytical solution on moisture absorption of

sandwich structures, in their approach “continuous moisture concentrations” condition was used at the interface. They pointed out that the concentration condition at the interface may be given in different forms, and “continuous concentrations” is the simplest one. Hybrid composite laminates are inhomogeneous for materials as well as for moisture parameters, some researchers [19, 20] indicated that the concentration continuity condition in homogeneous material is not real across the interface between different materials, but the “normalized concentration” could be considered continuous across the interface instead. In this paper, a sandwich diffusion model was built to describe the moisture absorption of cellulosic/glass fiber reinforced hybrid composites. An analytical solution of this issue was solved using two interface conditions, i.e. conditions of normalized concentration continuity and mass-conserving. Flax and glass fibers hybrid composites were manufactured in this study and their moisture absorptions were investigated experimentally and theoretically. Conclusions were drawn finally based on the results reported herein. 2 Experimental 2.1 Materials The unidirectional glass fabric of 200g/m2 was supplied by Nanjing Fiber glass Research & Design Institute and its density is of 2.6g/cm3. The unidirectional flax fabric of 200g/m2 was supplied by Nanjing Hitech Composite Company and its density is 1.4g/cm3. The matrix material used for manufacturing the composite materials is a E51 epoxy resin with a density of 1.18g/cm3. The glass fabric and flax

fabric are shown in Figure 1.

Glass fabric

Flax fabric

Figure 1. Glass fabric and flax fabric 2.2 Fabrication of composite laminates The composite laminates were manufactured by compression molding. The epoxy impregnated flax and glass fabrics were placed in the same orientation. The assembly was placed between two steel platens to cure in room temperature for 36 hours. Five types of non-hybrid and hybrid laminates with 8 plies were made and their stacking sequences and thicknesses are given in Table 1, the laminate plates were cut and shaped in rectangular form by using a diamond saw blade. Table 1 Plies number, layer configuration and thickness of hybrid laminates Laminate

Plies number

Layer configuration Thickness (mm)

designation

(Flax/Glass)

F8

8/0

FFFFFFFF

3.68/0

[F3/G]s

6/2

FFFGGFFF

2.76/0.44

[F2/G2]s

4/4

FFGGGGFF

1.84/0.88

[F/G3]s

2/6

FGGGGGGF

0.92/1.32

G8

0/8

GGGGGGGG

0/1.76

(Flax/Glass)

F: Flax fabric, G: Glass fabric, s: symmetric stacking sequences.

2.3 Water absorption testing Water absorption tests were carried out after being dried in an oven at 60oC during 24 h. The specimens were put into an environmental test chamber with a relative humidity (RH) of 100% at 60oC. The lateral surfaces of specimens were clogged by waterproof coating to ensure the moisture diffusion through thickness direction. During the ageing time, the specimens were periodically taken out of the chamber at certain periods of time. To assess the weight change, the specimens were wiped dry with tissue paper and weighed using an electronic balance (Mettler Toledo AL-104). The weighing of the specimens was repeated up to saturation, which meant that the specimens do not show significant variation in the mass. The water absorption characteristics of the composites were assessed by the relative uptake of weight according to: Mt 

Wt  W0 100% W0

(1)

where W0 is the weight of the dry specimen and Wt is the weight of the wet specimen at time t . Generally, the moisture uptake of flax fiber and glass fiber laminated composites follows a Fickian behavior [8]. In the case of one dimensional approach, the expression of Fick’s solution is given as follows:     2n  1  2   8   M t  M m 1   2 exp   D    t  2     n 0  (2n  1)    h 

(2)

where h is the specimen thickness, D is the diffusivity and M m is its maximum moisture uptake at equilibrium state. Fick’s laws show that the water uptake increases linearly with the square root of time, and then gradually slows until saturated moisture

uptake is reached. The diffusivity D in Fick’s law is given by [21]，

 hk  D     4M m 

2

(3)

where k is the slope of the linear part of M t versus

t curve.

3 Theory A typical flax/glass fiber hybrid composite is illustrated in Figure 2(a). The orange layers and green layers represent unidirectional flax fiber layer and glass fiber layer, respectively. The configuration of this flax/glass fiber hybrid composite is a symmetric sandwich structure. If moisture is applied at the surface, the schematic of moisture diffusion through thickness direction in this composite can be illustrated in Figure 2(b). The moisture concentration at the surface is constant Cs for flax fiber layer and the internal saturated moisture concentration is constant Ci for glass fiber layer. The diffusivities of phase 1 and phase 3 are D1 , the diffusivity of phase 2 is

D2 . The thicknesses of phase 1 and phase 2 are l  a and 2a respectively. Moisture

xl

Flax fiber

Phase1, D1 , Cs

xa

Phase2, D2 , Ci

Glass fiber

x  -a Phase3, D1 , Cs

Flax fiber

x  l

Moisture

(a)

(b)

Figure 2. The moisture diffusion model in flax/glass fiber hybrid laminate The moisture concentration in different phases are derived by Fick’s second law as

below

C1 ( x, t )  2C1 ( x, t )  D1 , a  x  l, t  0 t x 2

(4)

C2 ( x, t )  2C2 ( x, t )  D2 ,  a  x  a, t  0 t x 2

(5)

C3 ( x, t )  2C3 ( x, t )  D1 ,  l  x   a, t  0 t x 2

(6)

The boundary condition is

C1 (l , t )  Cs , t  0

(7)

C3 (l , t )  Cs , t  0

(8)

C1 ( x,0)  0, a  x  l

(9)

C2 ( x,0)  0,  a  x  a

(10)

C3 ( x,0)  0, - l  x  a

(11)

The initial condition is

The interface conditions were discussed by some studies. One condition states that the normalized concentration is equal across the interface of the joined surfaces [19, 20]. The normalized concentration  is defined as

=

C C

(12)

where C represents saturated moisture concentration. Using continuous normalized concentration condition for two interfaces of a sandwich structure leads to

C1 (a, t ) C2 (a, t )  , t0 Cs Ci C3 (a, t ) C2 (a, t )  , t0 Cs Ci

(13)

Another condition called mass-conserving condition [17] states that the masses of moisture across the surfaces of two adjacent layers per unit area and unit time are equal. This condition leads to, C1 (a, t ) C (a, t )  D2 2 , t0 x x C (a, t ) C (a, t ) D1 3  D2 2 , t0 x x D1

The application of Laplace transform

 

(14)

to Eq.(4)-(6) leads to

 2C1 ( x, p)  q12C1 ( x, p)  0 , a  x  l 2 x

(15)

 2C2 ( x, p)  q22C2 ( x, p)  0 ,  a  x  a x 2

(16)

 2C3 ( x, p)  q12C3 ( x, p)  0 ,  l  x  a 2 x

(17)

where q1   p / D1  ， q2   p / D2  . 1/2

1/2

With Laplace transform, the boundary conditions described in Eq.(7) and (8) turn to be

C1 (l , p) 

Cs , t0 p

(18)

C3 (-l , p) 

Cs , t0 p

(19)

Similarly, Laplace transform for interface conditions (Eq.(13) and (14)) are

C1 (a, p ) C2 (a, p )  , t0 Cs Ci C1 (a, p ) C (a, p )  D2 2 , t0 x x C3 ( a, p ) C2 (a, p )  , t0 Cs Ci

D1

D1

(20)

C3 ( a, p ) C (a, p )  D2 2 , t0 x x

The solutions of Eq.(15)-(17) are C1 ( x, p )  A1e  q1x  B1e q1x C2 ( x, p )  A2e  q2 x  B2e q2 x

(21)

C3 ( x, p )  A3e  q1x  B3e q1x

Substituting Eq.(18)-(20) into Eq.(21) leads to the solutions of Eq.(21) as below

C1 ( x, p) 

Cs p

1   r  cosh   ka  a  x   1   r  cosh   ka  a  x   1   r  cosh  (a  l  ka)  1   r  cosh  (a  l  ka ) 

C 2 cosh  kx C2 ( x, p)  i p 1   r  cosh  (a  l  ka)  1   r  cosh  (a  l  ka ) 

(22)

where k   D1 / D2  ,    kD2 / D1  , Ci / Cs  r ,    / D1 . 1/2

Applying inverse Laplace transform to Eq.(22) leads to

1   r  cosh   ka  a  x   1   r  cosh   ka  a  x   d  (23) 1   r  cosh  (a  l  ka)  1   r  cosh  (a  l  ka) 

C1 ( x, t ) 

Cs  i et 2 i  -i 

C2 ( x, t ) 

Ci  i et 2cosh  kx d  (24)  2 i  -i  1   r  cosh  (a  l  ka)  1   r  cosh  (a  l  ka) 

Define   i m ( m  1, 2,3,... ) is the roots of equation below

1   r  cosh  (a  l  ka)  1   r  cosh  (a  l  ka)  0

(25)

For Eq.(23), the residue at   0 is 1, the residue at the poles    D1m2 is

2e D1mt  1   r  cos  m  ka  a  x   1   r  cos  m  ka  a  x    m d  2

For Eq.(24), the residue at   0 is 1, the residue at the poles    D1m2 is

(26)

4e D1mt  cos  m kx  m d 2

(27)

where,

d  1   r  a  l  ka  sin m (a  l  ka)  1   r  a  l  ka  sin m (a  l  ka) (28) Thus, the solutions of C1 ( x, t ) and C2 ( x, t ) are   1   r  cos m  ka  a  x   1   r  cos m  ka  a  x  e D1m2t  (29) C1 ( x, t )  Cs 1  2   m d m 1     cos  m kx  D1m2 t  C2 ( x, t )  Ci 1  4 e  m 1  m d  

(30)

Finally, the moisture uptake of phase 1 and phase 2 can be obtained,  l 2   d M1 (t )   C1 ( x, t )dx =Cs l  a  2 2 1 e  D1mt  a m 1  m d    a  sin  m ka  D1m2 t  M 2 (t )   C2 ( x, t )dx  Ci 2a  8 e  2 a m 1 k  m d  

(31)

(32)

where,

d1  1   r  sin  m  ka  a  l   1    sin  m  ka  a  l    1   r  sin  m  ka   1   r  sin  m  ka  

(33)

Thus, the total moisture uptake of a sandwich structure is

M total  t   2M1  t   M 2  t 

(34)

4 Results and Discussion 4.1 Finite element analysis validation The sandwich diffusion model is derived to deal with the moisture diffusion problem of hybrid composites through the thickness direction, to verify the theoretical model, a two-dimensional sandwich structure is established in the commercial software Abaqus 6.11, the same boundary condition (normalized concentration is 1) is applied at the

upper and bottom surfaces of the sandwich structure to ensure the diffusion through the thickness direction, the moisture uptake of a sandwich structure is obtained by a mass diffusion analysis. The diffusivities and equilibrium moisture contents of different phases in sandwich structures for two cases are given to validate the analytical solution, and nondimensional parameters are shown in Table 2. With the various thicknesses of different phases in sandwich models, the moisture absorptions of the whole structure for two cases by finite element analysis are compared with the results obtained from analytical solution in Figure 3 and Figure 4. It is observed that good agreements are achieved for both two cases. Table 2 Parameters used in sandwich diffusion model for two cases Parameters

D1

D2

Cs

Ci

l

Case 1

0.001

0.0005

1

0.5

0.5

Case 2

0.0005

0.001

0.5

1

0.5

1.0

Moisture uptake

a=0.1 0.8

a=0.2

0.6

a=0.4

0.4

Theoretical FEA

a=0.3

0.2

0.0

0

5

10

15

20

25

30

t0.5

Figure 3. Theoretical and FEA results of sandwich diffusion model for case 1

1.0 a=0.4 0.8

a=0.3

Moisture uptake

a=0.2 0.6

a=0.1

0.4

Theoretical FEA

0.2

0.0

0

5

10

15

20

25

30

35

40

45

t0.5

Figure 4. Theoretical and FEA results of sandwich diffusion model for case 2 4.2 Effect of interface condition The objective of this section is to investigate the effect of interface condition on moisture diffusion of sandwich structures. The solution of a sandwich diffusion problem is given by Eq.(34) in Section 3. If the interface condition in Eq.(13) is replaced by a continuous concentration condition, which is

C1 (a, t )  C2 (a, t ), t  0 C3 (a, t )  C2 (a, t ), t  0

(35)

The solution of moisture uptake of a sandwich structure can be obtained bellow:

M total  t   2M 1  t   M 2  t   2   d M 1 (t )=Cs  l  a  2 2 3 e  D1mt  m 1  m d 2     sin  m ka  D1m2 t  M 2 (t )  Cs  2a  8 e  2 m 1 k  m d 2  

(36)

where, d 2  1    a  l  ka  sin  m (a  l  ka )  1    a  l  ka  sin  m (a  l  ka ) d3  1    sin  m  ka  a  l   1    sin  m  ka  a  l    1    sin  m  ka   1    sin  m  ka  

(37)

The moisture uptake of sandwich structures using continuous concentration condition,

continuous normalized concentration condition, and finite element analysis are compared in Figure 5 and Figure 6 for two cases (Table2). The results show that the solution using continuous concentration condition deviates the finite element solution. It is seem that the interface condition may give sensible response in describing moisture diffusion in sandwich structure, and the solution using continuous normalized concentration condition is more accurate. This is because if the different materials are in contact with each other, their temperatures at the interface are equal, in the analogy between the moisture diffusion and thermal conduction, Kondo and Taki [19] pointed out that the moisture concentration corresponds to the temperature is incorrect, since the moisture concentrations at the interface are not the same in general. In correct analogy, the normalized concentration rather than absolute concentration corresponds to the temperature. The normalized concentration condition can be used to form the basis for finite element formulation [20] and this condition is also used in the mass diffusion approach to deal with interface concentration problem in Abaqus 6.11. 1.2

Moisture uptake

1.0 0.8 0.6

Condition 1 Condition 2 FEA

0.4 0.2 0.0

0

5

10

15

20

25

30

0.5

t

Figure 5. Theoretical and FEA results of sandwich diffusion model for case 1 ( a  0.3 ). Condition 1: continuous normalized concentration condition. Condition 2:

continuous concentration condition. 1.0

Moisture uptake

0.8 0.6 0.4

Condition 1 Condition 2 FEA

0.2 0.0

0

5

10

15

20

25

30

35

40

0.5

t

Figure 6. Theoretical and FEA results of sandwich diffusion model for case 2 ( a  0.3 ). Condition 1: continuous normalized concentration condition. Condition 2: continuous concentration condition. 4.3 Sandwich diffusion model for water absorptions of composites Figure 7 shows the experimental and theoretical percentage moisture content according to the square root of ageing time ( t ) for hybrid and non-hybrid composites, it is seen that the predicted moisture absorptions of hybrid composites with different stacking sequences by sandwich diffusion model have good agreements with the experimental results. The experimental values are obtained by an average value of three measurements. The diffusivities and saturated moisture contents of glass fiber layers and flax fiber layers used in proposed model are derived from experimental data of non-hybrid composites in Table 3.

10 Theoretical Experimental

Moisture content (%)

8

[FFFF]S [FFFG]S

6

[FFGG]S

4

[FGGG]S

2 [GGGG]S 0

0

1

2

3

4

5

6

7

t0.5/h (hour0.5/mm)

Figure 7. The experimental and theoretical moisture uptake of hybrid and non-hybrid composites Table 3 Moisture diffusion parameters of non-hybrid composite Parameters

Flax fiber laminate

Glass fiber laminate

D (mm2/h)

0.0165

0.0031

M  (%)

8.60%

1.05%

It is found that the moisture diffusion behavior of all composites is almost a Fickian behavior during an aging time of 30 days. The weight saturations of composites are clearly different, the weight saturation of flax fiber laminate is 8 times higher than that of glass fiber laminate (around 8.60% for the flax fiber laminate and 1.05% for the glass fiber laminate). The diffusivities are about 0.0165 mm2/h for flax fiber and 0.0031 mm2/h for glass fiber laminate in a ratio 5. The saturated moisture contents decrease significantly when increasing of glass fiber content, this is attributed to the replacement of hydrophilic flax fiber with the addition of glass fiber in the composite. Compared to flax fiber laminates, the flax/glass fiber composites improve the moisture resistance by reducing the water absorption.

5 Conclusion This paper presents a sandwich diffusion model to describe the moisture diffusion behavior of flax/glass fiber reinforced hybrid composites. Comparisons to experimental data and finite element analysis reveal that the proposed model works effectively. It is shown that the saturated moisture contents of hybrid composites significantly decrease with the increase of glass fiber layers, this is attributed to the removal of hydrophilic flax fiber with the addition of glass fiber in the composite. It is worth noticed that the results of sandwich diffusion model are sensitive to the interface condition. For comparison, continuous concentration condition and continuous normalized concentration are used for proposed model respectively. The outcomes show that the calculations using continuous normalized concentration condition are in good agreement with the finite element analysis results, however, a deviation is observed when the moisture uptake is obtained by continuous concentration condition. This is because adjacent layers in sandwich structures may be made of different materials, the mass concentration is not continuous across the interface between these layers. In addition, although the sandwich diffusion model is established for the moisture diffusion of flax/glass fiber reinforced hybrid composites in this paper, this model may have potential applications in other diffusion problems. If the interface condition is not complicated, normalized concentration condition and mass-conserving condition can be employed to deal with moisture diffusion across interface, this model may be extended to the moisture diffusion of other sandwich structures, such as

viscoelastic sandwich composites. Acknowledgments This paper is partially supported by Fund of Jiangsu Innovation Program for Graduate Education (CXZZ13_0149) and the Fundamental Research Funds for the Central Universities, National Natural Science Foundation of China (11272147,10772078), Aviation Science Foundation (2013ZF52074), Fund of State Key Laboratory of Mechanical Structural Mechanics and Control (0214G02), and Project Funded by the Priority Academic Program Development of Jiangsu Higher Education Institutions (PAPD).

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