Ultimate strain to failure for [0] and [90]

Question:

Under tensile stress why do you see matrix cracking in the
90 plies of a 0/90 laminate before failure of the 0 ply such
as seen in Slide 42? Isn't the strain allowable of the 90 ply
much higher than the strain allowable of the 0 ply?”

Comments:

Generally for most fiber reinforced polymer systems the
transverse strain alowable is lower than the longitudinal
strain allowable. Therefore, it is expected that 90 degrees
plys fail before 0 degrees plys in a cross-ply laminate for
in-plane traction N={1,0,0}. The presence of fibers stiffen
the resin and introduce strain concentrations that make
the failure strain to dramatically decrease. It gets to about
half of the 0 degree failure strain.

Attached is a figure from Prof. Herakovich's book "Mechanics
of Fibrous Composites" showing stress-strain relation of
unidirectional T300/5208 for tensile loading. It can be seen
that the failure strain for the 90 degree unidirectional laminate
is around 0.42% while the failure strain for the 0 degree
unidirectional laminate is almost double (around 0.8%).
Considering linear stres-strain relation the 0 to 90 failure strain
ratio for this material would be:

e0/e90 = (s0/E1)/(s90/E2) = (s0/s90)(E2/E1) =
= (1551MPa/52MPa)(9.8GPa/136.5GPa) = 2.14

Of course the linear stress-strain relation does not hold up
to failure for some unidirectional composites, especially in
the transverse direction. But assuming stress-strain linearity
could be a good prediction for first approximation since
reinforced unidirectional composites tend not to present
large non-linearities for stress-strain plot up to failure.

Also attached is a figure of the FE simulated sqare unit cell
stress concentration field in the matrix around the fiber. This
was presented by Prof. Tsai in the first session of the tutorial.
Same kind of pattern would be found for strain concentrations
on the presence of the stiff fibers making the strain allowable
of the neat resin to decrease.