Time-dependent out-of-plane deformation of UD-CFRP in humid environment
, Jun Koyanagi
, Shin Utsunomiya
, Hiroyuki Kawada
Graduate School of Waseda University, 3-4-1 Okubo, Shinjuku-ku, Tokyo 169-8555, Japan
Japan Aerospace Exploration Agency, 3-1-1 Yoshinodai, Sagamihara, Kanagawa 229-8510, Japan
Department of Mechanical Engineering, Waseda University, 3-4-1 Okubo, Shinjuku-ku, Tokyo 169-8555, Japan
Received 18 December 2007
Received in revised form 29 August 2008
Accepted 31 August 2008
Available online 11 September 2008
A. Polymer-matrix composites (PMCs)
B. Hygrothermal effect
C. Finite element analysis (FEA)
Time-dependent out-of-plane deformation of UD-CFRP (unidirectional CFRP laminate) caused by subjec-
tion to a humid environment was examined and analyzed. The UD-CFRP plate showed unpredictable geo-
metrical variation with time in a humid environment, like asymmetric materials. The unpredictability
was caused by non-uniform ﬁber distribution in the thickness direction of the specimen. A three-dimen-
sional diffusion-stress coupling analysis considering the non-uniform ﬁber distribution was conducted
based on ﬁnite element analysis. The analytical results showed very good agreement with the experimen-
tal results. Furthermore, the relationship between the non-uniform ﬁber distribution and the out-
of-plane deformation with time was obtained quantitatively.
Ó 2008 Elsevier Ltd. All rights reserved.
CFRP composites are currently used in a variety of applications
due to their high mechanical performance. CFRP composites have
negative thermal expansion in the ﬁber axial direction, so it is
possible to design dimensionally stable structures against thermal
cycling. Many attempts have been conducted to produce light-
weight precision structures made by CFRP [1–5]. Examples of these
structures are antenna reﬂectors and optical mirrors. Still, compos-
ites are not yet considered an obvious choice for high-accuracy
space components such as micron-accuracy reﬂectors and tele-
scopes. Limited understanding of their dimensional and geometri-
cal stability remains a serious deterrent against the expanded
application of CFRP composites. Quantitative assessments of their
distortions in shape are greatly needed.
Dimensional instability in CFRP composites is caused by defor-
mations derived from moisture absorption , residual stress
relaxation , weight creep , and shrinkage caused by post-cur-
ing or by physical aging . Moisture absorption is the most com-
mon agent of environmentally induced strains. The diffusion of
moisture into the FRP is described by Fick’s law . The moisture
concentration in the material can be predicted if the diffusivity D is
available. The diffusivity D is strongly temperature-dependent, and
governed by the Arrhenius relation . CME (Coefﬁcient of Mois-
ture Expansion) is an important parameter for designing precision
machinery and has been measured for various materials .
Jacquemin et al. suggested a hygroelastic self-consistent model in
order to predict CME of FRPs . Also, Collings et al. measured
CME experimentally using a beam with an asymmetric lay-up
. These articles regarding deformation caused by moisture
absorption mainly selected asymmetric laminates as specimens
to enhance the deformation ; this is one reason that no-one
has yet discussed dimensional stability on the microscopic level.
In order to determine the micro-dimensional deformation of vari-
ous CFRP structures, it is essential to understand the micro-defor-
mation of unidirectional CFRP.
In the present study, the deformation caused by moisture
absorption in unidirectional composites was examined. The exper-
iment revealed an unexpected out-of-plane deformation that
needed to be explained. The non-uniform ﬁber distribution in the
thickness direction was expected to be a factor. We measured
the non-uniform ﬁber distribution and conducted a diffusion-
stress coupling analysis considering the non-uniform ﬁber distri-
bution, in which CMEs and diffusivities were determined by the
rule of mixture. The analytical results showed good agreement
with the experimental results. The relationship between the non-
uniform ﬁber distribution in the thickness direction and mois-
ture-absorption deformation with time is discussed.
2.1. Materials and specimens
Specimens were fabricated from a single batch of the pre-
preg tape made of high- elasticity carbon ﬁber (K13170) and
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* Corresponding author. Tel.: +81 3 5286 3261; fax: +81 3 5273 2667.
E-mail address: firstname.lastname@example.org (Y. Arao).
Composites Science and Technology 69 (2009) 1720–1725
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