The difference in principal stresses estimated using the square and hexagonal cells are
shown in Table 2-10.
For the unidirectional laminate (Sample A), the laminate stresses is zero under free
boundary condition since the laminate undergoes free thermal contraction at cryogenic
temperature in Table 2-8. However, the stresses at micro-scale are generated because of
contraction between fiber and matrix. The micro-stresses in the fiber are very small
compared to the matrix stresses. Therefore, the difference of maximum principal stresses
in the fiber phase shows large in Table 2-10.
The maximum principal stress is relatively consistent for both square and
hexagonal unit cells, but the hexagonal unit cell estimated that the minimum principal
stress in the matrix is reduced by approximately 40%. The results show the hexagonal
unit cell underestimates the micro-stresses.
The results from the finite element simulation can be used to compute the normal
and shear stresses at the fiber/matrix interface in the unit-cell. The normal and tangential
stress components were calculated using the transformation matrix.
C" cos2 0 sin 0 2 sin cos 0 o
s = sin2 0 COS2 0 -2sin0cos (2.6)
Tr -ssinOcosO sin cosos cos2 0- sin2 z
where 0 is the angle measured from the x axis as shown in Figure 2-9.
The normal and shear stresses around the periphery of the fiber are investigated
when the uniaxial laminate is subjected to the cryogenic temperatures AT= -405 K
without external loads. To compare the results for both unit cells, the interfacial stresses
are plotted for 90<0<270. From the results shown in Figure 2-10 and 2-11 one can note