Page 375 - Mechanics Analysis Composite Materials
P. 375
360 Mechanics and analysis of composite materials
&T_-e2T--aoAT, (7.79)
I
where a0 is the CTE of the mandrel material and A T = TO- T,. On the other hand,
if the layer is cooled being preliminary removed from the mandrel, its strains can be
calculated as
The first terms in the right-hand sides of these equations are free temperature strains
along and across the fibers (see Fig. 7.51), while E(: and E! correspond to the possible
layer shrinkage in these directions.
Using Eqs. (7.79) and (7.80) we can determine the strains that appear in the layer
when it is removed from the mandrel, i.e.
(7.81)
These strains can be readily found if we measure the layer diameter and length
before and after it is removed from the mandrel. Then, the shrinkage strains can be
determined as
For a glass-epoxy composite with the following thermo-mechanical properties:
EI = 37.24 GPa, E2 = 2.37 GPa, Gl2 = 1.2 GPa,
ltl2 =0.26, = 3.1 x lo-‘ 1/”C, ~12= 25 x I/OC ,
Morozov and Popkova (1987) found 8: = -93.6 x = -64. IO? Further
experiments performed for different winding tensions and materials of the mandrel
have shown that, while strain E(: strongly depends on these parameters, strain e! -
practically does not change. This supports the assumption that strain 6; is caused by
the chemical shrinkage of the resin and depends only on its properties.
For a cylinder in which fibers make angle 4 with the x-axis in Fig. 7.51, the
strains induced by the removal of the mandrel can be found from Eqs. (4.70),i.e.
EX = 11 cos24 + ~2 sin26,
E,, = 11 sin24 + cos24, (7.82)
jJxy = (El - E2) sin 24 ,
where El and E2 are specified by Eqs. (7.81). Dependencies of E,, E.”, and +,, on 4
plotted with the aid of Eqs. (7.82) are shown in Fig. 7.52 together with expenmental