The iridescent cuticle of I. flaccida gives the thallus
some surprising material properties. I performed trouser-tear tests
on a number of blades to investigate differences in their the work
of fracture and the effects of the cuticle and reproductive sori
on crack propagation. The blade's mechanism of fracture serves to
reduce stress concentrations and may be the source of the surprisingly
high strength of the decidedly anisotropic carposporophyte blade.
Variations in thallus strength between seasons, life phases, and
levels of exposure correlate with expected patterns.
Mechanisms of Fracture
Using the trouser-tear machine in the Denny lab here at Hopkins
Marine Station I measured the work of fracture for a variety of specimens
of Iridaea. I cut a rectangle from the center of each thallus
and slit this rectangle either longitudinally along the blade
or laterally across the blade .
I calibrated tensometer by attaching weights to the pulling apparatus.
After I clamped the testing apparatus to the loose flaps of the thallus,
the machine pulled the blade apart at a speed of 16 cm per minute.
Instead of separating the blade cleanly along a plane perpendicular
to the direction of tearing force (as shown above), all tests produced
a diagonal crack surface as shown below.
The diagonal was far more pronounced in the carposporangial blade
than the gametophyte. Under
the microscope it appeared that the diagonal crack surface was due
to the heteromorphic nature of the thallus layers. The iridescent cuticle
ripped at a different rate than the filamentous
This mechanism of fracture forces the production of a greater surface
area and increases the amount of strain energy which much be released
during fracture to pay for separation. The area of the fracture surface
is calculated as the product of the crack width and crack length7:
crack surface area = 2 * crack width * crack length
If the blade had ripped in one clean plane, the crack width would
have equaled the blade thickness, t. In this case:
area = 2 * t * crack length
However, the diagonal nature of the crack forces calculation of
the crack width from the Pythagorean relationship of blade thickness
and crack height , i.e., the height of the diagonal tear:
area = 2 * (t2 + h2)1/2 *
The length of this hypotenuse, the new crack width, will always
be greater than the blade thickness, so the area produced by a diagonal
crack will always exceed that of a simple planar crack.
By forcing the production of greater surface area, this diagonal
tearing would appear to inhibit crack propagation. The production
of surface area requires the input of enough energy to supply the "free
surface energy" associated with any surface. The energy used
for crack propagation must be paid for with the strain energy released
during the relaxation of the slit material. This seems intuitive--
you must pay for the energy you consume (by increasing surface area)
by releasing stored strain energy. The energy required for fracture
is referred to as the work of fracture7:
Work of fracture
= Energy / Area = J / m2
= [ rate of energy expenditure (J/s) ] / [ rate
of surface area production (m/s2) ]
= [ force of extension (J/m) * crack propagation
velocity (m/s) ] / [ 2 * crack width (m) * crack propagation velocity
Work of fracture = F / (2 * crack width)
Work of fracture is a constant property of a homogenous material8.
By increasing the amount of surface area produced (through increasing
the crack width) during fracture, Iridaea apparently raises
the amount of force it can withstand given the blade's fixed work
Yet Denny et al. demonstrated that the release of strain
energy does not control fracture in I. flaccida. 7 Fairly
large cracks grow at stable rates in I. flaccida. If
only strain energy is considered as the criterion for fracture, slits
in the thallus appear to exceed the crack distance at which the onset
of catastrophic failure is predicted. When the crack reaches a length
at which the rate of energy release exceeds the rate of surface area
production (and energy cost), the crack propagates spontaneously.
The thallus fails catastrophically as the split separates at a higher
rate than the constant rate of force application. The energy released
through crack propagation increases as the square of crack length
while the price of propagation varies linearly with this length.
This critical crack length for catastrophic failure can be calculated:
L (critical) = 2 * W *E / (2)
Using a modulus of elasticity (E) of 107 N/m 2 and
a work of fracture (W) of 278 J/m 2 these researchers
calculated the critical crack length under a stress ()
of 4 * 106 N/m 2 . Although the critical crack
length works out as .11 mm, the alga actually survives a crack of
2 mm under this level of stress. If the force the alga can withstand
is not limited by the critical crack length, the release of strain
energy cannot be the determining factor in failure.
But there is another condition which must be met in a material
before failure will occur. The first condition, as discussed above,
involves strain energy: you must release enough strain energy to
pay for increasing crack surface area. Yet the Denny lab determined
that this was not the factor controlling failure. The second condition
for failure concerns the concentration of stress at the crack tip.
The local stress at the crack tip must exceed the breaking stress
of the material. This seems intuitive; in order to break bonds, you
must provide a force greater than that which holds them together.
Apparently this is the limiting factor in the fracture of the thallus.
If stress concentrations control fracture, we would expect a tough
alga to develop mechanisms of reducing the concentration of stress
at the crack tip.
Stress Concentrations in 2-D
The Denny lab identified two mechanisms of avoiding stress concentrations
in 2 dimensions. 7 Like any flexible
material, the tip of a crack in I. flaccida becomes
rounded as the stretching force increases (See A). In contrast, a
rigid material like paper simply splits when force is applied perpendicular
to the axis of a crack (See the high concentration of stress at the
crack tip in B). Recall that stress is simply force divided by the
area on which it acts. Rounding of a crack tip increases the area
on which a force must act to produce a stress. This is merely a passive
mechanism of resisting failure, common to many flexible materials--just
try slitting and ripping a plastic bag to prove this to yourself.
More interesting was the Denny lab's discovery of the growth of a
pit at the tip of a crack within 48-72 hours after being slit by
a razor (See C). In the such a slit would easily result from
the scraping of the thallus on a bed of barnacles. Development of
a pit ensures that forces aiming to further rip the thallus must
act on a larger surface area. Recall that stress equals force divided
by area, so the larger the surface on which the force acts, the less
stress experienced by the blade. A pit in a blade helps distribute
the force around the edges of the pit even better than would a mere
rounding of the crack tip.
Stress Concentrations in 3-D
My research points to a third mechanism of reducing stress concentrations,
this one in 3-dimensions. Recall that the heterogeneity of cuticle
and medullary fibers forced the diagonal propagation
of a crack through the thallus. Instead of acting only on the plane
perpendicular to the direction of crack propagation, the force of
separation had to act on a tilted plane. This 3-D tear process compels
the separation force to act on a larger surface in a less favorably
oriented direction. Imagine trying to rip a sponge lengthwise if
the initial crack is oriented parallel to the direction of force
application. It would be much easier if the crack were oriented perpendicular
to your pulling axis. By ripping diagonally, I. flaccida achieves
a situation half-way between these extremes. A second look at Figure
10 will help to clarify the meaning of diagonal in this context.
Note that "diagonal" does not imply that the length of
the crack is tilted diagonally in the plane of thallus; rather,
the width of the crack extends at a diagonal from this plane across
the thickness of the blade.
Especially notable in my tests was the much greater crack height
(more diagonal crack) which developed
in female gametophyte's blade (remember, the female gametophyte Becomes
the carposporophte) when a crack hit a carpospore. In the carposporangial blade
of I. flaccida the cuticle appeared play an important
role in preventing catastrophic failure of the blade. Each peak on
the graph of applied force corresponded to the stalling of a crack
at cystocarp .
Here a stress concentration developed and when the applied force
finally reached a critical threshold the thallus ripped suddenly,
potentially catastrophically. However, at this point the height of
the crack increased dramatically as the differential ripping of the
cuticle and medulla produced a diagonal crack surface. This apparently
stalled the progress of the crack enough to return to the crack to
a state of equilibrium ripping and at this point the height of the
crack returned to a more typical value.
In contrast, the nonreproductive gametophyte had a uniform tear
A Tetrasporophyte Adapted
to Avoid Stress?
The mechanism of the carposporangial blade fracture has some interesting
implications for Iridaean adaptations to environmental stress.
Although I did not perform tests on the tetrasporangial blade of I. flaccida,
its smooth margins would seem to help avoid fracture after nicking.
This thallus has scattered sori just like the carposporangial blade.
These tetrasporangial sori also create inhomogeneities in the fabric
of the blade which should also concentrate stress when the blade
becomes torn. I would predict a similar variation in the degree of
diagonal tearing for the tetrasporangial blade as I observed in the
The tetrasporangial thallus of intertidal I. flaccida has
an important quality lacking in the tetrasporangial blade of subtidal I. cordata. Recall
that the fully diploid blades of I. flaccida have smooth
margins uninterrupted by sori; this feature provides the most reliable
mechanism for distinguishing it from I. cordata. Without
these sori in the margins of the thallus, I. flaccida avoids
placing nasty stress concentrators in a critical region of the blade.
On the wave-swept shores favored by I. flaccida the
thallus must often get raked across rough barnacles or nicked by
debris. Smaller nicks might penetrate only the smooth margin of the
blade and the lack of stress concentrators here would help to prevent
the propagation of such a nick into the blade. I. cordata lives
further down in the tidal zones, often subtidally, and might be helped
less by such an adaptation. Of course, I have not even had time to
test a tetrasporangial I. flaccida blade, let alone
any type of I. cordata thallus.
am curious why it would be the tetrasporophyte which would show the
stress-avoidance adaptation of smooth margins when its sori are actually
smaller (and probably less of a problem) than those of the carposporangial
blade, which does not have smooth margins. Carposporangial blades
in general appear to be thicker and sturdier than tetrasporangial
blades, so perhaps the advantage of the smooth margins is most pronounced
for the more delicate tetrasporangial blade. Again, however, I need
to measure tetrasporangial work of fracture before I can compare
the blade strength of all three Iridaean life history phases.
Several Comparisons of Works of Fracture
The data which I did obtain does allows some comparison of blade
strength between various life history phases, seasons, locations,
and directions of crack propagation . Unfortunately, I had far too
little time to do statistically accurate experiments so I stress
that my information is generally based on only one test of thallus
strength, not an average of multiple trials.
Blade strength shows a strong seasonality, with the blades almost
twice as strong in the winter. While the Denny lab measured a summertime
work of fracture of 278 J/m2 for the gametophyte stage
growing at Hopkins Marine Station, I measured a winter value of 490
J/m2 for a blade also cut longitudinally. This information
makes sense either selectively or adaptively. Those blades which
survived the harsher wave thrashing in the winter may be better adapted
to survive stress. Alternately, they may simply represent the strongest
fraction of a genetically identical population, and these specimens
alone survived until I went collecting in mid-February.
Degree of Exposure
Work of fracture also correlates with exposure. For the gametophyte
winter stage, cut longitudinally, the work of fracture of 644 J/m2 from
Pt. Pinos far exceeds the figure of 490 J/m2 obtained
for a similar, but fairly sheltered Hopkins blade.
Most surprising to me was the huge difference in strength between
the gametophyte and carposporophyte at Hopkins. The fully reproductive
part of the carposporophyte figured in at 1301 J/m2 ,
tremendously strong when compared with the 490 J/m2 figure
for a similarly cut and located gametophyte. The less developed part
of the carposporangial blade shows a less pronounced but still remarkably
greater work of fracture (700 J/m2) than the gametophyte.
I would speculate that the carposporophyte is stronger because it
is an older blade. Recall that I am referring to the carposporangial
blade of the female gametophyte as the carposporophyte, so the carposporangial
blades I tested were all older gametophytes. Perhaps the gametophyte
would be happier if it were stronger, but it needs time to mature
into a more sturdy blade.
Direction of the Initial Slit
Blades cut horizontally were consistently weaker than blades cut
longitudinally. At first this startled me because when I see a ripped
thallus in the intertidal the tear generally extends horizontally
across the blade, and I would think that the plant would want to
have the highest work of fracture in this direction in order to stay
intact. Yet upon further consideration I realized that it is no surprise
that the blade rips horizontally if it is weakest in this direction.
From Base to Tip
My last test addressed variation in strength along the blade of
the less reproductive carposporangial thallus. From each of two thalli
I cut two rectangles of material from different heights on the blade
and compared their work of fracture. Surprisingly it appears easier
to rip a thallus closer to the stipe than the tip of the blade because
the work of fracture is lower in lower regions.
Yet why would an alga be weaker towards its stem, and risk total
loss of a thallus rather than simple pruning of its tip? At first
I regarded this data as so irrational that it did not deserve examination
without further experimentation. Yet again I changed my mind when
I observed blades in the field. In the carposporophyte, the blade
tends to tatter near the base first, as my strength tests would predict.
This makes sense because the carpospores near the base develop before
the ones towards the tips of the blades and would be ready for release
sooner. Tattering of the blade is a common mechanism for assisting
spore release, so again my data seem to have real meaning. Whatever
biological necessity forces the blade to first become mature towards
its base also requires that thallus fabric be weaker in this region
in order to assist spore release.