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First published online March 12, 2009
Journal of Experimental Biology 212, 961-976 (2009)
Published by The Company of Biologists 2009
doi: 10.1242/jeb.026989

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Mechanical and biological consequences of repetitive loading: crack initiation and fatigue failure in the red macroalga Mazzaella

Katharine J. Mach

Hopkins Marine Station of Stanford University, Pacific Grove, CA 93950, USA

View larger version (11K): [in this window] [in a new window]   Fig. 1. (A) Diagram of specimens used in pull-to-break and fatigue tests. Mazzaella flaccida, tested at HMS, had larger dimensions than M. splendens, tested at FHL. The top and bottom larger portions of specimens were gripped within the testing apparatus. Fracture occurred within the narrow (0.6 cm wide) central portion of specimens. (B) Diagram of a M. flaccida frond indicating orientation of specimen cut from blade. The stem-like stipe is also depicted.

View larger version (12K): [in this window] [in a new window]   Fig. 2. Diagrams used in explanation of crack-simulation procedure. (A) Dimensions quantified for first-observed fatigue cracks. (B) The 0.6 cm by 4 cm region of a female gametophyte specimen with cystocarps, extended during testing; 20 white rectangular simulated cracks have been randomly placed over the test-specimen photograph.

View larger version (20K): [in this window] [in a new window]   Fig. 3. Fatigue data for (A) M. flaccida and (B) M. splendens, shown on logarithmic axes as number of loading cycles to breakage, Nbreakage, versus maximum loading stress per cycle, max (Pa). Additionally, pull-to-break strengths (Pa) are given on the ordinate, also on a logarithmic scale. M. flaccida fatigue data in A include 1 Hz fatigue tests only. For fatigue data in A and B, blue triangles represent male gametophyte test specimens; red circles, tetrasporophyte specimens; and green squares, female gametophyte specimens. Pull-to-break data are given as dashes on the ordinate, blue for male gametophyte specimens, red for tetrasporophyte specimens, and green for female gametophyte specimens. Average pull-to-break strength is shown as a black triangle for male gametophytes, a black circle for tetrasporophytes, and a black square for female gametophytes. Regression lines are shown, and equations for regressions are given in Table 1.

View larger version (13K): [in this window] [in a new window]   Fig. 4. Fatigue data for M. splendens (blue squares) and M. flaccida (red triangles). On logarithmic axes, the plot depicts number of loading cycles to breakage, Nbreakage, versus maximum loading stress per cycle, max (Pa). M. flaccida data include fatigue tests at 0.5, 1 and 2 Hz. For each species, data for only tetrasporophyte and female gametophyte specimens are given; male gametophyte data collected for M. flaccida have been excluded from the plot. Regression lines are shown, with regression equations described in Table 1. Average pull-to-break strengths for each species (male gametophytes excluded) are given on the ordinate, with a black square for M. splendens and a black triangle for M. flaccida.

View larger version (7K): [in this window] [in a new window]   Fig. 5. Fatigue data for M. flaccida tested at 1 Hz, given by season of testing. Data include 1 Hz fatigue tests for all three life history phases. On logarithmic axes, the plot shows number of loading cycles to breakage, Nbreakage, versus maximum loading stress per cycle, max (Pa). Black circles represent fatigue tests from October to December 2007; white circles, from April 2008; and gray circles, from July 2008. Linear regression equations are as follows: for October to December (black line), logmax=–0.075logNbreakage+6.232, R2=0.23; for April (dashed line), logmax=–0.036logNbreakage+6.071, R2=0.07; and for July (gray line), logmax=–0.052logNbreakage+6.196, R2=0.17.

View larger version (9K): [in this window] [in a new window]   Fig. 6. Fatigue data for M. flaccida, shown by loading frequency. The plot includes all data for the three tested life history phases. On logarithmic axes, the plot shows number of loading cycles to breakage, Nbreakage, versus maximum loading stress per cycle, max (Pa). Black circles indicate fatigue tests at 1 Hz; white circles, 0.5 Hz; and gray circles, 2 Hz. Linear regression equations are as follows: for 1 Hz (black line), logmax=–0.068logNbreakage+6.212, R2=0.20; for 0.5 Hz (dashed line), logmax=–0.124logNbreakage+6.376, R2=0.33; and for 2 Hz (gray line), logmax=–0.052logNbreakage+6.226, R2=0.12.

View larger version (4K): [in this window] [in a new window]   Fig. 7. Crack formation index, C, for M. flaccida male gametophytes, tetrasporophytes and female gametophytes, with 0.5, 1 and 2 Hz fatigue tests included in calculations. C is the difference between number of cycles to breakage, Nbreakage, and number of cycles to crack formation, Ncrack formation, with this difference normalized by Nbreakage. Plot depicts mean C ±95% confidence interval for each life history phase.

View larger version (14K): [in this window] [in a new window]   Fig. 8. Fatigue data for M. splendens female gametophytes (A) and tetrasporophytes (B), showing test specimens with (filled symbols) and without (open symbols) reproductive structures. On logarithmic axes, the plots depict number of loading cycles to breakage, Nbreakage, versus maximum loading stress per cycle, max (Pa). Linear regressions with the following equations are shown: for female gametophytes with cystocarps (solid line in A), log(max)=–0.116logNbreakage+6.391, R2=0.65; for female gametophytes without cystocarps (dashed line in A), logmax=–0.115logNbreakage+6.536, R2=0.78; for tetrasporophytes with tetrasporangial sori (solid line in B), logmax=–0.092logNbreakage+6.486, R2=0.49; for tetrasporophytes without tetrasporangial sori (dashed line in B), logmax=–0.118logNbreakage+6.657, R2=0.77.

View larger version (27K): [in this window] [in a new window]   Fig. 9. (A) A representative plot of change in maximum strain during a fatigue test in which an M. flaccida specimen was loaded repeatedly to constant maximum stress. (B) Strain change index S20, indicating change in maximum strain over the first 20 cycles of loading, as a function of maximum stress per cycle, max, applied to specimens. The abscissa is logarithmic. Plot shows data for all M. flaccida tested, with male gametophyte specimens represented by blue circles, tetrasporophyte specimens by red circles and female gametophyte specimens by green circles. Linear regression shown fits data for all three life history phases: S20=0.174logmax–0.930, R2=0.44, P0.001. (C) Strain change index Sentire, indicating change in maximum strain over entire fatigue tests, as a function of maximum stress per cycle, max (log scale). Again, data for all M. flaccida fatigue tests are depicted, with male gametophytes represented by blue squares, tetrasporophytes by red squares and female gametophytes by green squares. Linear regression fits data for female gametophytes: Sentire=–0.291logmax +1.972, R2=0.11, P=0.01. (D) Mean strain change index Sentire ±95% confidence interval for M. flaccida male gametophyes, female gametophytes and tetrasporophytes. Sentire for male gametophytes was significantly greater than Sentire for female gametophytes and tetrasporophytes.

View larger version (16K): [in this window] [in a new window]   Fig. 10. Frond length versus logNbreakage–logNbreakage,predicted for all 1 Hz M. flaccida data (A) and all M. splendens data (B), where Nbreakage is the number of loading cycles to breakage and Nbreakage,predicted is the number of loading cycles predicted from regressions in Table 1. Blue triangles represent data from male gametophytes; red circles, tetrasporophytes; and green squares, female gametophytes. For life history phases tested for both species, only the linear regression for M. splendens female gametophytes, shown in B, was significant.

View larger version (4K): [in this window] [in a new window]   Fig. 11. Drag coefficient, CD, as a function of water velocity, u (m s–1), for M. flaccida. Drag data depicted were from two flumes: at eight velocities below 4 m s–1, 30 data points were collected using a recirculating flume, and at three velocities from 5.4 to 9.5 m s–1, 18 data points were collected using a high velocity, gravity flume. Curve equation is CD=0.0793u–0.7565, R2=0.8721.

View larger version (19K): [in this window] [in a new window]   Fig. 12. Wave-imposed water velocities, u (m s–1), versus number of loading cycles to breakage, Nbreakage, for representative big (A), medium (B) and small (C) M. flaccida fronds. In each plot, the ordinate is logarithmic. Blue lines represent predictions for male gametophytes; red lines, tetrasporophytes; and green lines, female gametophytes.

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