Page 331 - Engineered Interfaces in Fiber Reinforced Composites

312 Engineered interfaces in fiber reinforced composites

The compressive residual stresses in the fiber direction have been measured
extensively in recent years for many different combinations of fiber and polymer
matrix, e.g. polydiacetylene fiber-epoxy matrix (Galiotis et al., 1984), carbon fiber-
PEEK matrix (Galiotis et al., 1988; Young et al., 1989) and Kevlar fiber-epoxy
matrix (Jahankhani and Galiotis, 1991), using a technique based on the laser Raman
spectroscopy. In the light of the novel observation by Tuinstra and Koenig (1970)
that the peak positions of the Raman-active bands in the fiber are sensitive to the
magnitude of the applied strain, the fiber residual strain can be estimated from the
plots of fiber strain versus composite strain obtained on a model microcomposite
containing a single fiber. Further extension of the micro-Raman technique allows
the measurements of interfacial shear stress distributions along the fiber length at
varying applied strain levels (Jahankhani and Galiotis, 1991), and even during the
single fiber pull-out test (Patrikis et al., 1994; Bannister et al., 1995). More details of
the findings based on the Raman technique is presented in Section 2.3.3.

7.5.1.2. Macro-residuul thermal stresses
Macro-residual stresses, the so-called lamination residual stresses (Doner and
Novak, 1969; Chamis, 1971), are present within the individual ply of a laminate
consisting of multi-plies of different angles. The residual stresses in the laminate
arise from the difference between the ply CTEs in the longitudinal and transverse
directions. These residual stresses are integrated averages through the ply thickness,
and are typically highest at [0°/90"] or [ + 45"/-45"] laminate interfaces because a
tensile stress develops in the 90" plies with a corresponding compressive stress in the
0" plies (Bowles and Griffin, 1991b). Consider the simple [0"/90"]2 symmetric cross-
ply laminate shown in Fig. 7.19. The residual thermal stresses in the plies for a
temperature drop, AT, is derived based on the RoM (Jones, 1994):

(7.1 1)

ET
090"T = --0o"L , (7.12)
EL
(7.13)

(7.14)

09pL and 0ypT are the residual stresses in the longitudinal and transverse directions
of the 90" ply lamina, while C ~ and OPT are the residual stresses in the longitudinal
L
and transverse directions of the 0" ply lamina, respectively. b and d are the 90" and
0" ply thickness, and the CTEs of the laminae in the longitudinal and transverse
directions, ac~ and c(,T, are given in Eqs. (7.8) and (7.9). The tensile stresses that
develop transversely to the fiber direction, OO~T and CTYWL, are counteracted by the
equivalent compressive stresses, co0L and 090q, respectively.