Page 337 - Mechanics Analysis Composite Materials

322 Mechanics and analysis of composite materiab
The inverse form of Eq. (7.31) is
1
R(t - r)&(r)dr . (7.32)

Here, R(t - z) is the relaxation modulus or the relaxation kernel that can be
expressed, as shown below, in terms of C(t - z).
The creep compliance is determined using experimental creep diagrams. Passing
to a new variable 0 = t - z we can write Eq. (7.31) in the following form:

(7.33)

For the creep test, stress is constant, so (T = go, and Eq. (7.32) yields

(7.34)

where EO = oo/E = ~(t= 0) is the instant elastic strain (see Fig. 7.1 1). Differenti-
ating this equation with respect to t we get

1 dE(t)
C(t)= -- .
EO dt
This expression allows us lo determine the creep compliance differentiating the
given experimental creep diagram or its analytical approximation. However, for
practical analysis, C(0) is usually determined directly from Eq. (7.34) introducing
some approximation for C(0) and matching thus obtained function ~(t)with the
experimental creep diagram. For this purpose, Eq. (7.34) is written in the form

(7.35)

Experimental creep diagrams for unidirectional glass-epoxy composite are presented
in this form in Fig. 7.15 (solid lines).
The simplest is the exponential approximation of the type

(7.36)

Substituting Eq. (7.36) into Eq. (7.35) we obtain