Numerical Simulation of Moisture Diffusion in Pultruded GFRP

Composite Profile

Haohui Xin

1,2 a

, Ayman Mosallam

3b

, Yuqing Liu

2,* c

1

School of Human Settlements and Civil Engineering, Xi’an Jiaotong University, Xi’an,China;

2

Department of Bridge Engineering,Tongji University,Shanghai,China

3

Department of Civil and Environment Engineering,University of California, Irvine,CA, USA

Keywords: Pultruded fiber-reinforced polymer (FRP) materials; Non-Fick Moisture Diffusion; Numerical Simulation.

Abstract: Long-term exposure of fiber-reinforced polymer (FRP) profile to harsh in-service environment will lead to

irreversible degradation of mechanical properties. Understanding the exposure “aging” effects on pultruded

FRP composites is important for their application in bridge structures. The moisture diffusion process plays

a very important role to understand material degradation of GFRP laminations exposed to hydrothermal

environment. In this paper, the moisture diffusion process with focusing on pultruded GFRP composites used

in bridge applications is numerically simulated. The parameters of moisture diffusion are calibrated by

gravimetric tests of thin plates.

1 INTRODUCTION

Pultruded glass fiber-reinforced polymer (GFRP) is

favorable by civil engineers because its economic

elegant performance(Bank, 2006; Mosallam,

Bayraktar, Elmikawi, Pul, & Adanur, 2014). Several

GFRP profiles have been exploited in bridge

structures(Bank, 2006; Mosallam et al., 2014; Xin,

Liu, & Du, 2015; Xin, Liu, He, Fan, & Zhang, 2015;

Xin, Liu, Mosallam, He, & Du, 2017; Xin et al., 2020;

Xin, Mosallam, Liu, Veljkovic, & He, 2019; Xin,

Mosallam, Liu, Wang, & Zhang, 2017a; Xin,

Mosallam, Liu, Wang, & He, 2018; Xin, Mosallam,

Liu, Xiao, et al., 2017; Xiong, Liu, Zuo, & Xin, 2019;

Zhang et al., 2019; Zuo, Mosallam, Xin, Liu, & He,

2018). Bridge structures are generally exposed to

harsh in-service environment. The temperature and

humidity varied a lot (Xin, Liu, Mosallam, & Zhang,

2016; Xin, Liu, Mosallam, Zhang, & Wang, 2016;

Xin, Mosallam, Liu, & Wang, 2018; Xin, Mosallam,

Liu, Wang, & Zhang, 2017b; Xin, Mosallam, Liu,

Yang, & Zhang, 2017). Long-term exposure of fiber-

reinforced polymer (FRP) profile to harsh in-service

environment will lead to irreversible degradation of

mechanical properties. The performance degradation

a

https://orcid.org/0000-0002-6205-5248

b

https://orcid.org/0000-0002-1897-1775

c

https://orcid.org/0000-0002-1211-0018

due to aging may lead to catastrophic failure of bridge

structural component. While the moisture diffusion

process plays a very important role to understand

material degradation of GFRP laminations exposed to

hydrothermal environment.

Hence, it is essential to understand the moisture

diffusion process with focusing on pultruded GFRP

composites used in bridge applications. The authors’

previous publication(Xin, Liu, Mosallam, & Zhang,

2016) showed that the moisture uptakes of pultruded

GFRP plate could be divided into three stages:

diffusion-dominated uptake, a polymer relaxation-

dominated uptake and a composite damage-dominated

uptake. The non-Fick moisture diffusion is quite

important to understand material degradation of GFRP

laminations exposed to hydrothermal environment.

Investigation of non-Fick moisture diffusion process

with time will benefit to reveal the aging degradation

mechanism of GFRP profiles serviced as components

of bridge structures. Numerical simulation is an

efficient tool to model the moisture diffusion of bridge

profile with complicated geometry.

The moisture progression with focusing on

pultruded GFRP profiles serviced as components of

bridge structures is numerically simulated in this

paper. The parameters of moisture diffusion are

calibrated by gravimetric tests of thin plates

(100.0mm×6.0mm×2.3mm) at different temperature

and different environment.

2 GRAVIMETRIC TESTS

Pultruded GFRP laminations for the tests are cut form

GFRP profiles serviced as a component of bridge

structures(ASTM D5229/D5229M-14 Standard,

2014). The laminates include three types of lamina,

namely Roving, axial compound fabric and biaxial

compound fabric, see Fig. 1. The experiment is

conducted in four hygrothermal environment, namely

T_W(water) and T _SW(artificial seawater), T=40°C

and 60°C, based on the ASTM D5229/D5229M

procedures(ASTM D5229/D5229M-14 Standard,

2014). The details of gravimetric experiment can be

referred to (Xin, Liu, Mosallam, & Zhang, 2016).

Figure 1: Configurations of GFRP laminate (Xin, Liu,

Mosallam, & Zhang, 2016)

The gravimetric tests of thin plates with a

dimension of 100.0mm×6.0mm×2.3mm were used

for the one dimensional moisture diffusion of

pultruded GFRP laminates in the authors’ previous

publication(Xin, Liu, Mosallam, & Zhang, 2016).

D11 denoted the specimens along the roving direction

while D22 denoted the specimens vertical to the

roving direction. The parameters of time-varying

boundary conditions are calibrated by gravimetric

tests of this thin plates at different temperature and

environment.

3 MASS DIFFUSION

SIMULATION OF GFRP

LAMINATIONS

Mass diffusion analysis is performed using three-

dimensional solid elements DC3D8 with a 1mm mesh

size based on commercial finite element software

ABAQUS(Abaqus, 2019). Eq. (1) is used to obtain

the mass concentration through a Python script to

read the ABAQUS simulation data.



1

n

ii

i

n

i

CtV

Ct

V





(1)

Where: C

i

is the mass concentration of the i

th

integration point, and V

i

is the volume of the i

th

integration point.

The experimental results were given as weight

gain M(t) in percentage against time (Xin, Liu,

Mosallam, & Zhang, 2016). The average

concentration could be converted to the weight-gain

data by equations (2).

 

=

water

GFRP

M

tCt



(2)

Where: ρ

GFRP

=2000 kg/m

3

is the density of the

pultruded GFRP laminations, ρ

water

=1000kg/m

3

is the

density of the water.

The moisture diffusion coefficients of pultruded

GFRP laminates can be referred to the reference (Xin,

Liu, Mosallam, & Zhang, 2016). For the one-

dimensional diffusion, the time-varying boundary is

applied to the largest cross section, see Fig. 2. Based

on the experimental results(Xin, Liu, Mosallam, &

Zhang, 2016), the moisture uptake along the roving

direction is larger than it vertical to roving direction.

The magnitude of mass concentration is assumed to

be 1.0. The non-Fick behavior of moisture diffusion

is mainly controlled by the amplitude of multi-stage

points of amplitude function.

Figure 2: Illustration of time-varying boundary conditions

of one-dimensional diffusion

4 EXPOSED TO ENVIRONMENT

WITH A TEMPERATURE OF

40°C

The values of multi-stage points of the amplitude

function were determined by conducting the fit on the

moisture uptake at the temperature of 40°C. The

comparisons between FE simulation and

experimental moisture uptake of specimens at the

temperature of 40°C are shown in Fig.3 and Fig.4,

respectively. A good agreement is observed. The

fitted time-varying boundary conditions could

effectively describe the one-dimensional moisture

migration of GFRP specimens exposed to 40°C

hygrothermal environment.

(a)

(b)

Figure 3: Comparisons between FE simulation and

experimental moisture uptake of specimens exposed to

water environment at 40°C

(a)

(b)

Figure 4: Comparisons between FE simulation and

experimental moisture uptake of specimens exposed to

artificial seawater environment at 40°C

The moisture diffusion process of D11 and D22

specimens at the temperature of 40°C is shown in

Fig.5 and Fig.6. The minimum CONC at the inner

side reached to 97.3% and 99.2% times of CONC at

the out surface for D11 specimen at 1.70×106 s and

1.70×107 s respectively, and increased to 88.0% and

99.2% times of CONC at the out surface for D22

specimen at 1.73×106 s and 1.70×107 s respectively.

(a) t = 9.0 s

(b) t = 4.1×10

5

s

(c) t=1.7×10

6

s

(d) t=1.70×10

7

s

Figure 5:One dimensional diffusion of D11 specimen

exposed to water environment at 40°C

(a) t = 9.0 s

(b) t=7.31×10

5

s

(c) t=1.7×10

6

s

(d) t=1.7×10

7

s

Figure 6: One dimensional diffusion of D22 specimen

exposed to water environment at 40°C

5 EXPOSED TO ENVIRONMENT

WITH A TEMPERATURE OF

60°C

The values of multi-stage points of the amplitude

function were determined by conducting the fit on the

moisture uptake at the temperature of 60°C. The

comparisons between FE simulation and experimental

moisture uptake at 60°C are shown in Fig. 7 and Fig.

8, respectively. A good agreement is observed,

indicating that the fitted time-varying boundary

conditions could effectively describe the one-

dimensional moisture migration of GFRP specimens

exposed to 60°C hygrothermal environment.

(a)

(b)

Figure 7: Comparisons between FE simulation and

experimental moisture uptake of specimens exposed to

water environment at 60°C

(a)

(b)

Figure 8. Comparisons between FE simulation and

experimental moisture uptake of specimens exposed to

artificial seawater environment at 60°C

The moisture diffusion process of D11 and D22

specimens exposed to artificial seawater environment

is shown in Fig.9 and Fig.10. With the diffusion time

increasing, the CONC of inner side gradually

increased. The mass concentration presented gradient

distribution along the thickness direction. The

minimum CONC at the inner side reached 96.3% and

100.0% times of CONC at the out surface for D11

specimen at 1.7×10

6

s and 1.7×10

7

s, respectively, and

increased to 98.7% and 99.6% times of CONC at the

out surface for D22 specimen at 1.7×10

6

s and

1.7×10

7

s, respectively. The mass concentration

distribution gradually tended to be uniform along the

thickness direction when the diffusion time is larger

than 1 million seconds.

(a) t=9.0s

(b) t=7.3×10

5

s

(c) t=1.7×10

6

s

(d) t=1.7×10

7

s

Figure 9. One dimensional diffusion of D11 specimen

exposed to artificial seawater environment at 60°C

(a) t=9.0s

(b) t=7.3×10

5

s

(c) t=1.7×10

6

s

(d) t=1.7×10

7

s

Figure 10. One dimensional diffusion of D22 specimen

exposed to artificial seawater environment at 60°C

6 CONCLUSIONS

Long-term exposure of fiber-reinforced polymer

(FRP) profile to harsh in-service environment will

lead to irreversible degradation of mechanical

properties. Understanding the exposure “aging”

effects on pultruded FRP composites is important for

their application in bridge structures. The moisture

diffusion process plays a very important role to

understand material degradation of GFRP

laminations exposed to hydrothermal environment.

The parameters of moisture diffusion are

calibrated by gravimetric tests of thin plates (one-

dimensional diffusion). The calibrated mass diffusion

parameters are validated by comparing the average

time-dependent moisture concentration obtained

from non-Fick FE simulation with experimental

observation.

For one-dimensional moisture diffusion of thin

plates, with the diffusion time increasing, the CONC

of inner side gradually increased. With the diffusion

time increasing, the CONC of inner side gradually

increased. The mass concentration presented gradient

distribution along the thickness direction gradually.

The mass concentration distribution gradually tended

to be uniform along the thickness direction when the

diffusion time is larger than 1 million seconds.

ACKNOWLEDGEMENTS

The authors gratefully acknowledge the financial

support provided by the National Natural Science

Foundation (Grants #51808398 and 52078362) of the

People’s Republic of China.

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