The effect of surface treatment on the creep behavior of flax fiber reinforced composites under hygrothermal aging conditions

Construction and Building Materials 208 (2019) 220–227

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Construction and Building Materials journal homepage: www.elsevier.com/locate/conbuildmat

The effect of surface treatment on the creep behavior of flax fiber reinforced composites under hygrothermal aging conditions Xiaomeng Wang a, Michal Petru˚ a,⇑, Hang Yu b a b

Institute for Nanomaterials, Advanced Technologies and Innovation, Technical University of Liberec, Studentska 2, Liberec 461 17, Czech Republic School of Transportation and Civil Engineering, Nantong University, Nantong 226019, China

h i g h l i g h t s
The creep behavior of FFRP under hygrothermal aging conditions is studied.
Surface treatment can effectively improve the creep performance of FFRP.
The proposed model can be applied in creep analysis of other natural FRPs.

a r t i c l e

i n f o

Article history: Received 7 November 2018 Received in revised form 28 February 2019 Accepted 1 March 2019

Keywords: Flax fiber Composite Creep Surface treatment Hygrothermal Fractional calculus

a b s t r a c t The application of natural FRP (Fiber Reinforced Polymer) is being targeted in various fields due to both environmental and economic benefits. FFRP (Flax Fiber Reinforced Polymer) is one of the major natural FRPs. The durability and long-term performance of FFRP have been proven a key to its practical engineering application. Some experimental works have been conducted to investigate the creep properties of FFRP. However, fewer efforts have been made to improve its creep performance thus far. In this paper, the effect of surface treatment on the creep behavior of FFRP under hygrothermal aging conditions is studied, and a fractional-order creep model is established to predict its creep behavior. Ó 2019 Elsevier Ltd. All rights reserved.

1. Introduction In the last three decades, FRPs have been adopted as alternatives to traditional structural materials such as steel, due to their high tensile strength, high stiffness to weight ratio and superior fatigue resistance. The recent developments of FRPs are towards the growth and usage of natural FRP in the field of engineering. FFRP is one of the most commonly used natural FRP. FFRP has the advantages of lightweight, low cost and easy recyclability [1– 3]. However, due to a short history of FFRP in the engineering field, the durability and long-term performance of FFRP remains an open question. Some recent researches [4,5] show that flax fiber with porous structure is susceptible to the humid environment. For example, Scida et al. [6] and Thuault et al. [7] found that the hygrothermal aging causes disorganization of flax microfibrils network and the

⇑ Corresponding author. E-mail address: [email protected] (M. Petru˚). https://doi.org/10.1016/j.conbuildmat.2019.03.001 0950-0618/Ó 2019 Elsevier Ltd. All rights reserved.

plasticization of matrix, which leads to mechanical property degradation of FFRP. Scida et al. [6] reported that after 38 days of hygrothermal aging with a relative humidity of 90% at 40 , the elastic modulus and tensile strength of FFRP decrease by 58% and 52%, respectively. Thuault et al. [7] found that tensile strength of FFRP deceases when RH is above 68%. For example, the tensile strength decreases more than 60% after 2 months of aging with a relative humidity of 100% at temperature above 85 . Du et al. [8] reported that humidity produces a significant acceleration of the creep strain of natural fiber reinforced composite sandwich panels. Compared with specimens in ambient relative humidity, specimens at higher relative humidity (65%) exhibit larger creep deformation and enter the tertiary creep stage relatively earlier. Some recent researches show that the mechanical properties and water resistance of FFRP can be improved by chemical treatments such as alkalization [9,10], acetylation [11,12], silanization [13,14]. For example, Lin et al. [9] and Amiri et al. [10] found that the tensile strength and flexural strength of FFRP increase significantly after alkali-treatment. Compared with the SEM pictures of

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X. Wang et al. / Construction and Building Materials 208 (2019) 220–227

untreated flax fiber, the surface of alkali-treated fiber is cleaner and rougher because of the hemicelluloses, lignin and surface impurities (such as waxes and oils) are taken away [9,10]. The treated fiber surface facilitates both mechanical interlocking and bonding reaction. Therefore, the performance of fiber/matrix bond interface is improved. The reaction of sodium hydroxide with fiber cell is [15] (Scheme 1). Besides, alkali-treatment reduces the hydrophilic hydroxyl groups in the fiber and improves the moisture resistance [16]. Bledzki et al. [11] reported that the tensile strength of FFRP increases by 20–35% after acetylation treatment, and the water uptake of the specimen is significantly reduced. And they found the surface morphology of the treated fiber is smother because the wax and cuticle are taken away. Acetyl group (CH3CO) reacts with the hydrophilic hydroxyl groups (OH) of the fiber (as shown in Scheme 2 [18]). The hydrophilic of the modified fiber is reduced and the dimensional stability is improved [17]. Georgiopoulos et al. [14] investigated the effect of silane treatment on the mechanical properties of FFRP. They found that the specimen treated with 1 wt% silane solution shows an optimum increment of 11% in flexural modulus, and the specimen treated with 2 wt% silane solution shows an optimum increment of 18% in flexural strength. Compared with the SEM pictures of the untreated specimens, there are more matrix attached to the treated fiber, which indicates the adhesion between the flax fibers and the matrix can be improved by silane treatment. They also noted that silane treatment of flax fiber slows the process of creep in FFRP. Firstly, the silane coupling agent creates a chemical bond between the fiber and matrix. Secondly, silane coupling agent forms a hydrophobic organic silicate protective layer on the fiber surface, which can effectively reduce water abortion [19]. The reaction between fiber cell and the silane coupling agent is shown in Scheme 3 [20].

Fiber-cell-O-Na+ + H2O + impurities

Fiber-cell-OH + NaOH

Scheme 1. Reaction between sodium hydroxide and fiber cell.

Acetylation with acid catalyst O

(a) Fiber-cell-OH + CH3COOH

(CH3CO)2O

Fiber-cell-O-C-CH3 + H2O

Conc. H2SO4

In the presence of moisture, silane is hydrolyzed to form silanol (Scheme 3(a)). The silanol then reacts with the hydroxyl group of fiber cell to form a strong covalent bond between fiber and silane (Scheme 3(b)). The other end of silanol forms a bond with matrix functional group [21]. This co-reactivity provides molecular continuity across the interface of the composite. Therefore, the performance of fiber/matrix interface is improved. Although some experimental works have been reported on the creep of FFRP, fewer analytical efforts have been made to model and predict its creep behavior. Creep of FFRP is influenced by the mechanical properties of flax fiber, matrix and the interface between them. To get accurate fitting results, Marklund et al. [22] and Varna et al. [4] introduced Schapery’s model [23], which contains three stress-dependent functions to characterize the viscoelastic behavior of FFRP. Wong and Shanks [24] compared Maxwell model, Kelvin-Voigt model and Burgers model, and Burgers model is found to produce a better creep description of modified FFRP with different additives. Gemant et al. [25] found some limitations of traditional integer order calculus-based viscoelastic models and introduced fractional differential into the basic differential equation to model the viscoelastic behavior of materials. Some researches [26,27] show that, compared with traditional viscoelastic models, the fractional calculus-based ones have proved to be powerful tools to characterize the creep behaviors of polymers and other materials with less parameters. However, the fractional calculus approach to creep of FFRP is rarely reported up to now. In this work, the effect of surface treatment on the creep behavior of flax fiber reinforced composites under hygrothermal aging condition is studied, and a fractional derivative creep model is adopted to describe the creep response of the FFRP.

2. Test methods The unidirectional flax fabric (Fig. 1) was supplied by Nanjing Hitech Composite Co., Ltd. Three kinds of chemical treatments of flax fiber were adopted: alkalization, silanization and acetylation. The alkali-treated group was soaked in 5 wt% NaOH solution for 0.5 h at 25 °C. The silanization group was soaked in 0.1 wt% silane solution (triethoxy silane) for 1 h at 25 °C. The acetylated group was initially soaked in glacial acetic acid for 2 h at 30 °C, and consequently treated with acetic anhydride (with FeCl3 as catalyzer) for 1 h at 50 °C. After the treatment, the flax fabric was washed by distilled water and dried in an oven. The treated flax fabric was used to manufacture FFRP. Epoxy resin (E 44) and curing agent (C 650) from Nantong Xingchen

Acetylation without acid catalyst O

O

(b) Fiber-cell-OH + CH3-C-O-C-CH3

O

O

Fiber-cell-O-C-CH3 + CH3C-OH

Scheme 2. Acetylation reaction with and without acid catalyst.

O

(a)

OCH3

O

H2C-CH-R-Si-OCH3 + 3H2O

H2C-CH-R-Si-OH + 3CH3OH

OCH3

OCH3

O

(b)

OCH3

OCH3

H2C-CH-R-Si-OH + Fiber-cell-OH OCH3

O

OCH3

H2C-CH-R-Si-O-Fiber-cell + H2O OCH3

Scheme 3. Reaction between silane coupling agent and fiber cell.

Fig. 1. Flax fabric.

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X. Wang et al. / Construction and Building Materials 208 (2019) 220–227

Synthetic Material Co. were used as the matrix. The FFRP specimen was made of approximately 30% fiber in volume. The dimension of FFRP specimen in rectangular form is 50 mm  10 mm  1.35 mm. After curing (25 °C for 2 weeks), the specimens were first dried in an oven at 60 °C for 24 h, and then soaked in distilled water at 60 °C in an environmental test chamber. Both the water uptake and creep properties of the specimens were measured. (1) Water uptake tests. Dry specimens were weighed after oven drying. The soaked specimens in test chamber were periodically taken out and dried by blotting paper and weighed to assess the water uptake. (2) Creep tests. The creep tests scheme is shown in Table 1. Creep tests were carried out with DMS (Dynamic Mechanical Spectrometer) 6100 (Fig. 2), at a three-point bending mode, with a constant stress level of 20 MPa for 30 min. All experimental values were obtained by an average value of three specimens. After the creep test was finished, a fractionalorder creep model was adopted, and the test data were used to determine the parameters of the model.

DMS

Specimen

Fig. 2. Creep test of FFRP.

3. Fractional derivative rheological modeling

Da f ðt Þ ¼

1 d Cð1  aÞ dt

Z 0

t

f ðsÞ ds; ðt  sÞa

ε1

E1

The definition for Riemann-Liouville fractional calculus [28] is

ð1Þ

where Da is the a order differential operator, 0  a < 1. In the classical viscoelastic theory, the mechanical response of the Hook spring is defined as rðt Þ ¼ Eeðt Þ, and the mechanical response of the Newton dashpot is: rðt Þ ¼ ge_ ðt Þ. The mechanical response of a fractional derivative spring-pot can be regarded as an extension of 1a

ε2

τ

rðtÞ ¼ Esa Da eðtÞ:

ð2Þ

where elastic modulus E, relaxation time s and fractional derivative order a are material parameters. The fractional derivative springpot can be used to simulate the viscoelastic behavior of material between ideal solid (when a ¼ 0) and ideal fluid (when a ¼ 1). When subjected to creep stress, the strain of fractional derivative spring-pot does not increase linearly as ideal fluid or complete instantaneously as linear elastic solids but exhibits a nonlinear growth. Fig. 3 shows creep models with different combinations of springs and fractional derivative spring-pot. Traditional combination such as Maxwell model is unable to simulate a decreasing creep strain rate under constant stress. Kelvin model fails in capturing the instantaneous deformation. Therefore, FPT (Fractional derivative Poynting-Thomson) model is adopted. The constitutive relation of FPT model can be described as

r þ Asa Da r ¼ Be þ C sa Da e;

ð3Þ

E1

ε

E3 τ

a

E2

a

ε2

a (a)

ga Da eðtÞ.

the classical creep model components as: rðt Þ ¼ E The relaxation time is defined as s ¼ g=E, and the constitutive relation of the fractional derivative spring-pot is

E2 τ

E2

ε1

E1

(b)

(c)

Fig. 3. Creep models: (a) Maxwell model, (b) Kelvin model, (c) FPT model.

where A ¼ E3 =ðE1 þ E2 Þ, B ¼ E1 E2 =ðE1 þ E2 Þ, C ¼ E1 E3 =ðE1 þ E2 Þ. By using Laplace transform technique, the creep compliance J ðtÞ of FPT model is obtained

J ðt Þ ¼

  a  1 AB  C B t ; þ Ea;1  B BC C s

where P1

Mittag-Leffler

zk k¼0 CðakþbÞ ; ð

ð4Þ

function

is

defined

as:

Ea;b ðzÞ ¼

a; b > 0Þ. For simplification of the parameters of the

parallel parts in the FPT model, E2 and E3 are postulated as the same:E3 ¼ E2 ¼ E . The simplified expression of creep compliance is

J ðt Þ ¼

   a  1 1 t ; þ  1  Ea;1  E1 E s

ð5Þ

The material parameters E1 , E , s, a can be obtained by fitting the experimental data as

minf ðxÞ ¼

m X

½J ðx; ti Þ  r i 2 ;

ð6Þ

i¼1

Table 1 Creep test scheme. Surface treatment

Untreated Alkalization Silanization Acetylation

Hygrothermal aging time/days 0

1

4

9

16

U-0 Al-0 S-0 Ac-0

U-1 Al-1 S-1 Ac-1

U-4 Al-4 S-4 Ac-4

U-9 Al-9 S-9 Ac-9

U-16 Al-16 S-16 Ac-16

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X. Wang et al. / Construction and Building Materials 208 (2019) 220–227

10

(2) space

a counter. The one-dimensional search on dynamic changes of xðn;i1Þ , e.g.  ðn;i1Þ  ðk;1Þ ðn;i1Þ xi 2 d1 x ; d2 x , i ¼ 1; 2; c. Let xðn;0Þ ¼ xðn1Þ , for i ¼ 1; 2; c, the one-dimensional search starts from the initial point xðn;i1Þ , along the direction of lðn;iÞ , to find wi that makes

Untreated Untreated-Fick's model

8

M t (%)

Alkalization 6

Alkalization-Fick's model Silanization

4

Silanization-Fick's model Acetylation

2

f ðxðn;i1Þ þ wi lðn;iÞ Þ ¼ minf ðxðn;i1Þ þ wi lðn;iÞ Þ;

Acetylation-Fick's model 0

Set n as is based

0

5

10

15

20

t0.5 (hour 0.5) Fig. 4. Relative water uptake of FFRP.

 xi  0; i ¼ 1; c  1 s:t: 0  xc  1 where Jðx; ti Þ is the creep compliance calculated by Eq. (5) at time t i , r i is the creep compliance obtained from the test. x ¼ ðx1 ; xc ÞT is the column vector of material parameters. c is the number of parameters. The parameter represents the order of fractional calculus is set as xc . m is the number of test points, and m > c is required. As the derivative of the Mittag-Leffler function is not obtainable. The optimization problem in Eq. (6) can be solved by replacing the Mittag-Leffler function by an approximate differentiable function, or using other optimization methods without calculating derivatives. The second approach is adopted. A direct search strategy Powell method [29] is applied. The search process is executed by round, and each round is carried out following a group of feasible orthogonal directions in turn as follows. (1) Set the initial value of xð0Þ , the linearly dependent search 0 1 0 ð0Þ 1 0 x1 B xð20Þ C B 0 C B C B C directions are defined as lð1Þ ¼ B . C lð2Þ ¼ B . C lðcÞ ¼ @ .. A @ .. A 0

0

1 0 B 0 C B . C. @ .. A

0

ð7Þ

Then update x ¼x þ wi l ; i ¼ 1; 2; c: Where 0 1 0 ðn;0Þ 1 0 1 0 0 x1 B xð2n;0Þ C B 0 C B 0 C B C C C wi lðn;1Þ ¼ B is B .. C lðn;2Þ ¼ B .. C lðn;cÞ ¼ B @ ... A, @ . A @ . A ðn;0Þ xc 0 0 restricted as wi 2 ½d1 ; d2 . To ensure that the fractional derivative order parameter 0  xc  1, wc should satisfy

ðn;i1Þ wc  min d2 ; 1=xc 1 . ðn;iÞ

ðn;i1Þ

ðn;iÞ

(3) Let xðnÞ ¼ xðn1;cÞ , set a permissible error e > 0, if the convergent condition (as shown in Eq. (8)) is met, end the computation, or n ¼ n þ 1, go to (1).

  xðnÞ  xðn1Þ    i i  < e i ¼ 1; 2; c:   xðn1Þ 

ð8Þ

i

The search speed of this algorithm is related to its initial value, search range and termination criteria. In order to obtain better fitting results and minimize the amount of computation, xð0Þ should assigned appropriately. The initial values of FPT model parameters can be determined according to the characteristics of Mittag-Leffler function. When t ¼ 0, Ea;1 ð0Þ ¼ 1, the initial creep compliance is h i a ¼ 0\* J ð0Þ ¼ E11 \* MERGEFORMAT. When t ! þ1, lim Ea;1  st t!þ1

MERGEFORMAT, the long term creep compliance (or equilibrium creep compliance) is lim J ðtÞ ¼ E11 þ E1 . The creep compliances at t!þ1

the beginning and the end of the test are denoted as J t0 and J tmax . J t0 and J tmax can be approximately equal to the initial and

ð0Þ

xc

Table 2 Maximum relative water uptake M m and diffusion coefficient D of FFRP. Surface treatment

Untreated

Alkalization

Silanization

Acetylation

M m (%) D(10-6 mm2/s)

7.75 4.19

6.40 2.93

5.60 2.36

4.48 2.21

Aging time

Untreated

Alkali-treated

Silane treated

1 day

4 days

9 days

16 days

Fig. 5. The effect of hygrothermal aging on FFRP specimens.

Acetylated treated

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X. Wang et al. / Construction and Building Materials 208 (2019) 220–227

Creep compliance J/GPa -1

Creep compliance J/GPa -1

0.5

0.125 0.12 0.115 0.11 0.105 0.1 0.095 0.09 0.085 0.08 0.075

U-0 Al-0 S-0 Ac-0 U-0-F Al-0-F S-0-F Ac-0-F 0

10

20

30

U-1 Al-1

0.45

S-1 0.4

Ac-1 U-1-F

0.35

Al-1-F 0.3

S-1-F Ac-1-F

0.25

40

0

Time/min

10

20

(a) 0 day

Creep compliance J/GPa -1

Creep compliance J/GPa -1

0.6

U-4

0.55

Al-4

0.5

S-4 Ac-4

0.45

U-4-F 0.4

Al-4-F

0.35

S-4-F Ac-4-F 20 Time/min

30

U-9

0.55

Al-9

0.5

S-9 Ac-9

0.45

U-9-F

0.4

Al-9-F S-9-F

0.35

Ac-9-F 0.3

0.3 10

40

0

10

20

30

40

Time/min

(c) 4 days

(d) 9 days

0.75

Creep compliance J/GPa -1

40

(b) 1 days

0.6

0

30

Time/min

U-16

0.7 0.65

Al-16

0.6

S-16

0.55

Ac-16

0.5

U-16-F

0.45

Al-16-F

0.4

S-16-F

0.35

Ac-16-F

0.3 0

10

20

30

40

Time/min

(e) 16 days Fig. 6. Creep curves of FFRP from experiment and FPT model (Note: F stands for the fitting curve of FPT model).

long-term

creep

compliances

as

J t0 ¼ E11 \*

MERGEFORMAT,

J tmax ¼ E11 þ E1 \* MERGEFORMAT, then the initial values of E1 and E can be approximately considered as: ð0Þ

E1 ¼

1 ; J t0

Eð0Þ ¼

1 : J tmax  J t0

ð9Þ



að0Þ ¼ logm ln

 J tmax  J m : J tmax  Jt0

ð12Þ

ð10Þ

when b ¼ 1, 0  a  1, t=s ¼ 0:7, the value of Mittag-Leffler func

tion is within the range of Ea 0:7a 2 ð0:474; 0:5. In this paper,

an approximate is made as: Ea 0:7a ¼ 0:5. The corresponding time when Jt0:5 ¼ 0:5ðJt0 þ J tmax Þ is denoted as t0:5 . Then the initial value of s is

sð0Þ ¼ t0:5 =0:7:

a

an approximation is adopted as Ea ðza Þ ’ ez . It is assumed that

there is one point t m ; Jtm on the creep compliance test curve, which satisfies t m ¼ ms, 0 < m 1. Combining the approximation with Eq. (5), Eq. (9), and Eq. (10) leads to the initial value of a as

ð11Þ

when 0 < z 1, the Mittag-Leffler function is approximated by a [30]: Ea ðza Þ ’ eðz =Cð1þaÞÞ . When 0  a  1, Cð1 þ aÞ 2 ð0:885; 1,

4. Results and discussion 4.1. Water uptake results The relative water uptake of FFRP is assessed according to:

Mt ¼

Wt  W0  100% W0

ð13Þ

where W 0 and W t is the weight of the dry specimen and the wet specimen, respectively. Generally, the moisture uptake of FFRP

225

X. Wang et al. / Construction and Building Materials 208 (2019) 220–227 Table 3 Parameters of FPT model. Surface treatment

Parameters

Untreated

E1 E

Hygrothermal aging time/days

s a Alkalization

E1 E

s a Silanization

E1 E

s a Acetylation

E1 E

s a

follows a Fickian behavior [6,31]. When

0

1

4

9

16

9.133 109.189 17.571 0.820

2.571 8.412 17.824 0.892

2.336 6.953 18.129 0.920

2.225 6.168 17.555 0.959

1.936 4.916 15.034 0.977

11.464 110.882 17.048 0.786

3.009 8.292 16.748 0.875

2.786 7.981 16.953 0.915

2.569 8.184 17.713 0.927

2.547 5.178 16.783 0.940

10.053 103.302 16.206 0.804

3.282 9.706 16.640 0.816

2.883 9.048 19.801 0.876

2.680 9.027 18.462 0.881

2.601 6.047 17.526 0.902

12.154 106.902 17.142 0.780

3.270 7.916 16.778 0.801

3.088 8.375 16.147 0.805

2.925 8.150 15.585 0.845

2.810 6.417 19.473 0.861

< 0:6, the diffusivity

Mt Mm

coefficient D in Fick’s law is determined by [32]:



D¼

p hMt t

2 ð14Þ

4Mm

where h is the thickness of the specimen, M m is the maximum relative water uptake. To predict the water uptake of FFRP, Scida et al. [6] proposed the following approximation:

8 qffiffiffiffiffiffi > 4 Dt >
Mt  ¼

 > 1  exp 7:3 Di t 0:75 ; Mm > : w s2

Mt Mm

< 0:6

Mt Mm

 0:6

ð15Þ

3.5

 13

As shown in Fig. 4, M t increases with the hygrothermal aging time rapidly first, and then followed by a slow plateau segment, revealing a typical Fickian behavior as described by Eq. (15). The relative water uptake of treated specimen is significantly lower than untreated specimen, and the acetylated group exhibit the lowest water uptake. Table 2 shows diffusion coefficient D calculated by Eq. (14). Compared with the untreated group, the diffusion coefficient of specimen decreases by 30.09%, 43.57%, 47.32%, after alkalization, silanization, acetylation treatment, respectively. In general, strong fiber-matrix interfacial adhesion reduces the water absorption of FRP [33,34]. Lower water uptake of the treated specimen reveals a better fiber-matrix adhesion for treated flax fibers. As shown in Fig. 5, the color of the specimens has changed obviously after hygrothermal aging. And with the increase of aging time, the boundary between matrix and fiber is more and more obvious.

U-test

11

25

2.5

U-test

Al-test

22

1.5

7

2

4

6

8

S-test

5 3

Ac-test

1 0

2

4

6

τ (s)

E 1 (MPa)

9

19

Al-test

16

S-test

13

8

Ac-test

M t (%)

10

0

2

4

6

8

Mt (%)

Fig. 7. Evolution of E1.

Fig. 9. Evolution of s.

120

10 U-test

E * (MPa)

100

8

1.00

80

6

0.95

60

4

Al-test

U-test

Al-test

0.90 2

4

6

8

S-test

40

0.85 S-test

0.80 20 Ac-test 0

0

2

4

M t (%) Fig. 8. Evolution of E*.

6

8

0.75 0.70

Ac-test 0

2

4

6

M t (%) Fig. 10. Evolution of a.

8

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X. Wang et al. / Construction and Building Materials 208 (2019) 220–227

4.2. Creep test results After the creep test data was obtained, the algorithm in Section 3 and software Mathematica were used to calculate the parameters of FPT model by fitting the test results with Eq. (5). The curve-fitting results in Fig. 6 show good agreement with test data for both untreated and treated specimens. The parameters of the FPT model are presented in Table 3. The influence of moisture content on FPT model parameters is depicted in Figs. 7–10. The creep compliance increases with the hygrothermal aging time, as shown in Fig. 6. For example, the creep compliance of the untreated group at the end of the test increases by 316.03%, 366.28%, 398.61%, 494.80%, after 1 day, 4 days, 9 days and 16 days of aging, respectively. Compared with the untreated specimens under the same aging time, the creep compliances of the treated specimens are significantly reduced. For example, after 16 days of aging, compared with the untreated group, the creep compliance at the end of the test decreases by 31.54%, 20.78%, 25.73% after alkalization, silanization and acetylation treatment, respectively. The elastic modulus of the Hook spring in series part E1 determines the initial strain of FPT model: e0 ¼ r=E1 . As illustrated in Table 3 and Fig. 7, the value of E1 decreases with hygrothermal aging time and moisture content, resulting in the increase of e0 . For example, e0 of the untreated group increases by 255.24%, 291.01%, 310.55%, 371.66% after 1 day, 4 days, 9 days and 16 days of aging, respectively. Compared with the untreated specimens under the same aging time, e0 of the treated group is smaller. For example, after hygrothermal aging of 16 days, e0 decreases by 23.96%, 25.54%, 31.08% after alkalization, silanization, acetylation treatment, respectively. When t ! þ1, the final strain of FPT model is e1 ¼ r=E1 þ r=E . The elastic modulus of Hook spring in the parallel part E determines the final creep strain ec1 ¼ r=E . It can be observed from Table 3 and Fig. 8 that the value of E decreases with the hygrothermal aging time and relative water uptake, leading to the increase of ec1 and e1 . Compared with the untreated specimens under the same aging time, ec1 and e1 of the treated group are smaller. For example, after hygrothermal aging of 16 days, e1 decreases by 18.62%, 34.72% and 42.06%, and ec1 decreases by 5.07%, 58.02% and 69.92%, after alkalization, silanization, acetylation treatment, respectively. As shown in Table 3 and Fig. 9, hygrothermal aging does not have a noticeable effect on s. As illustrated in Table 3 and Fig. 10, a increases with hygrothermal aging time and moisture content. For example, after 1 day, 4 days, 9 days and 16 days of aging, a of the untreated group increases by 8.81%, 12.20%, 16.91%, 19.15%, respectively. Compared with the untreated specimens, after 16 days of aging, a decreases by 3.79%, 7.68%, 11.86% after alkalization, silanization and acetylation treatment, respectively. According to the definition of the fractional derivative, the close of a to 1, the nearer the material to the ideal fluid. The trend of a indicates that more viscous character after the hygrothermal aging.

5. Conclusions The experimental study carried out in this paper aimed at developing a better understanding of the creep behavior of flax fiber reinforced composite. The results show that the performance of FFRP is improved by alkalization, silanization and acetylation treatment. The water uptake and diffusion coefficients of the treated specimens are lower than untreated group. The effect of the chemical treatment is further confirmed by the lower creep deformation of the treated specimens.

A four-parameter FPT model is proposed to describe the creep behavior of FFRP, and the results show that the fractional-order creep model agrees well with test data. Although this model is established for the FFRP in this paper, it may have potential applications in creep analysis of other natural fiber reinforced composite materials, and influencing factors such as creep stress, temperature, et al. can be introduced by parameter modification.

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