FATIGUE AND FRACTURE AT THE MUSCLE SCAR OF FOUR INTERTIDAL LIMPET SPECIES: C limstule, C. pelte, C digitalis, and d. mitre DANIEL BAGDAD HOPKINS MARINE STATION 1988 ABSTRACT This study examined and compared the forces required to fracture limpet shells. Shells of recently-killed Calliselle pelte, Collisella limatule, Colliselle digitelis, and Acmses mitre were frectured in an apparatus mimicking the crushing behavior of crabs. In addition, shells of C limatule and C. pelte were tested for fatigue fracture by repeatedlg loading the shells. All species save A. mitre showed increased force needed for frecture es shell thickness increased. No significent differences existed in force es a function of shell thickness among the species nor within each species for forces applied at the length and width of the scar and margin. However, shell size at the width of the scar was significantlg smaller than at the other orientations for each species, suggesting that crabs could attack more shells at the scar width than at other places. Also, shells of C limstule had significantlg smaller widths at the scar then the other species, suggesting that perhaps more C limatule shells are found C fractured et the muscle scar because these smaller scar-width shells are within the grasping range of more crabs. Fatigue fracture proved significant (causing fracture below 200 cycles) at force loads above 602 of the predicted breaking force. Above 70-752 of predicted strengths, fracture required less than 50 cycles, indicating that within short time spans crabs could fracture shells without ever exerting a maximum force. Scanning electron microscope observations revealed that the crossed-lamellar lagers along the horseshoe-shaped scar lager form almost continuous sheets that allow cracks to frecture the upper portion of the shell cleanly at the muscle scer. IHTRODUCTION A previous studg on intertidal limpets (Chapin, 1966) focused on the predatorg of the shore creb, Fachygrepsus crassiges. Several limpets, particularly Colliselle limatule, left in an aquarium with a crab were found after several dags to have been crushed neer the muscle scar. This form of attack left the rim of the shell intact, the top was cleanly severed from the rest of the shell. Tests done with needle-nosed pliers showed that for Colliselle limatule substantially less force was required to fracture the shell at the scar than at other points. In this studg l examine the apparent structural weckness of the muscle scar lager both by comparing the forces required to break shells of one species et different locations and by compering the forces necessarg to crush shells of different species at the same point on the shell. To see if high and low-spired limpets differed in fracture strength focused on species that varied in relative height (figure 1). Another reason for focusing in particular on the muscle scar lager was that most limpet shells varg in thickness along the shell (figure 24), with a thickened margin and apez and a relatively thin muscle scar lager. One objective of my studg wes to determine if this thinning-out of the shell neer the scer allowed the shell to fracture more easilg at the scar, especially in comparison to the thickened margin. The horseshoe-sheped muscle scer (figure 28) on the inner surfece of limpet shells results from the attachment of the foot adductor muscles. Although Chapin (1966) found C. limatule shells to break more easilg along the length than width of the scar, was interested to discover if some feature of the actual shell structure along the horeshoe-shaped scar accounted for the frecture characteristics. In particuler, HacClintock (1967) describes the myostracal (muscle scer lager of the shell as differing from the typical crossed-lamellar structure of limpet shells (figure 34). At the scer the muscle attechment interferes with the usuel shell-laging process of the mantle. The resulting structure is usuallg prismatic, and Curreg (1974) describes this structure as stronger than crossed-lamellar (tensile strength »60PN/m- for prisms). The prisms of the myostracum form the inner surface of the shell (figure 3B). Figure 4 shows the effects of a crushing force applied by a crab cheliped, with the result being tension along the inner surece and compression along the C outer surface. The high tensile strength of the prisms would allow this material to resist frecture at higher stresses than the lower strength of the adjacent shell structures. In light of this picture, 1 was interested in investigating which structural festures of the muscle scar lager, if ang, account for the fracture mechanics. Another interesting aspect of limpet shell fracture at the muscle scer involves fatigue fracture. Boulding (1966) and Currey (1984) have examined fatigue fracture in bivalves and shovn that crabs often load a shell repeatedig up to around 200 times (sometimes over several hours or dags). As long as the crab exerts a force/area of at least 60-702 of the predicted breaking strength, the shell is likely to fracture after a number of cycles at this submaximal stress. In this fashion crabs can successfully attack large shells that theg cannot crush in one attempt. As no study thus far has examined fatigue fracture in intertidel limpets, also investigated the effectiveness of the this predatorg technique. MATERIALS AND METHODS A. TEST OF MUSCLE SCAR AND SHELL MARGIN STRENGTH Callisella pelts, Colliselle limstule, Colliselle sigitslis, and Acmses mitre (figure 5) were collected at various locations at the Hopkins Marine Station (Pacific Grove, CA) and placed in an aquerium with running sea water. The limpets were dissected out of the shell and the shells placed in dishes with sea water. Messurements were taken of: length and width of the shell at both the scar and the margin; height from aperture to apex; and the thickness of the shell at the front, back, right side, and left side at the level of both scar and margin. To fracture the shells constructed two nutcrecker-like devices (figure 6). Each crushing device consisted of two blocks of wood connected by a hinge, such that the blocks could close like upper and lower jaws. Two small metal plates (see figure 6) on the same side of each block acted as teeth to contact the shell and transmit the force. When C loaded in the apparatus the apex of the limpet shell pointed toward the blocks. The base of the shell rested on an adjacent block of wood (see figure 6) that served as a substrate to prevent slippage. The force was applied by attaching a spring scale to the hook protruding from the end of the upper block. The force was incressed slowlg until the shell fractured, and this maximum force was recorded. The magnitude of the actual force transmitted to the shell was calculated by accounting for the mass of the wood blocks and the spring scale. By adjusting the orientation and point of contect between shell and crushing device, one could load shells from each species at one of four locations (figure 7): 1) Force applied along the length of the margin, here termed Longitudinal Margin. 2) Force applied along the width of the margin, here termed Lateral Margin. 3) Force applied along the length of the muscle scar, hère termed Longitudinal Scar. C 4) Force applied along the length of the muscle scar, here termed Lateral Scar. The same device was used to test if shells missing the portion of the shell above the scar (such that onlg the rim is left intact) would be easier to break than completelg intact shells. For this test l used Colliselle pelte shells and applied the forces at the front and lateral margin. B. FATIGUE-LOADING EXPERIMENTS Colliselle limatula and Colliselle pelte shells were loaded repeatedlg for five seconds at a time for up to e maximum of 200 cycles. The loads applied were some fraction of the predicted breaking force ranging from around 10-902. Values for the predicted breaking force were determined from the results of part A for the two limpet species in question. The values were teken from the linear regression lines for force vs. thickness (figure 10). The tests were conducted using the same crushing devices previouslg described, with a known mass attached to the spring scale. During each fatigue C sequence examined the shell under a dissecting microscope after every 25-30 cycles to trace the development of fatigue/stress cracks. A scanning electron microscope was used to examine fatigue cracks and fracture surfaces along the muscle scar lager. C. FIMITE ELEMENT ANALVSIS constructed models of four limpet species (Calliselle pelte, Colliselle limatule, Colliselle digitalis, Acmees mitre) on a Macintosh"" computer using e finite element analgsis progrem (HSC/pal"“, MacNeal-Schwendler Corporation). The models consisted of interconnected quadrilateral and triangular plates. The nodal points (XYZ coordinates) for each limpet were determined by first projecting a slide with a grating (see figure 8) onto the shell. The pattern of lines on the shell was then photographed and the resulting picture projected onto a screen. The result was a topographic map of the shell surface, from which ! derived XY coordinetes (2 coordinates were measured on the shell). Also, specified realistic material properties for the shells, including ectuel thicknesses for each plate. used material properties for enother limpet species, Estelle mevicans (Currey, 1980): Voung's Modulus-6.0 x 103 N/m2, Shear Modulus-2.7 x 10° N/m2, Vielding Strength-3.3 x 107 M/m2, Poisson's Ratio-O.1, Calcium Carbonate Mass Densitu-2.93). For each species ! epplied forces equal to 75-602 of the predicted breaking force (ascertained from the force vs. thickness results of part A). RESULTS A. COMPARISON AMONG SPECIES OF FORCE VS. THICKNESS VALUES AT EACH GRASPING ORIENTATION Figure 94 shows the combined force vs. thickness values of the four species tested (C. Felte, C. limstule, C digitelis. 4 mitre) for forces applied along the length of the muscle scar. Figure 98 plots individual linear regressions and reveals that C limatule, C. pelte, end C digitelis eoch showed e significent increase in force required to frecture the shell as thickness et the scor increosed (r.z.65, pc.001, r z.26, pc.05, r =.33, p..02, C respectivelg). A. mitre did not show a significant force vs. thickness relationship. Comparisons of mean force/thickness values between pairs of the three species showing significant positive force/thickness slopes (for longitudinal/scer loading) revealed that C oigitalis shells were easier to crush than those of C. limstule, but only by a factor of 1.3. A similar set of force vs. scer thickness calculations for loading ecross the width of the scar and length/width of the margin produced compareble trends, with only 4. mitra displaging no significant increase in force required for frecture es thickness at the scar increased. For the comparison of forces required to fracture the shell when loaded longitudinallg and laterallg at the margin, plotted force against relative thickness (scar thickness/margin thickness), since the force required to frecture the shell at the margin depends on the margin thickness as well as the thickness at the scar. In all three cases (lateral scer, longitudinal/lateral margin) no significant differences appeared among the species tested. C B. FORCE VS. THICKNESS WITHIN EACH SPECIES Comparisons emong force/thickness means within esch species at the four grasping orientations showed no significant differences, with the sole exception of C limatule shells which break more easily at the margins than the scars (longitudinal margin vs. longitudinal scar, p4.001; lateral margin vs. leteral scer, p«.05). Therefore the grephs of force vs. thickness for each species (figure 10) show the overall trend for all four grasping orientations treated as one set of date. Again, onlg A. mitre produced no overall significant trend in force vs. thickness. Figure 11 shows the results of the forces required to fracture the rims of C pelte shells (missing the top of the shell above the scar) compered to intact shells. Shells missing the apical portion (above the scar) did not fracture at a significentlg lower force than intect shells, and thus onlg the overall trend (with force vs. thickness for all shells grouped together) is plotted. This graph shows again that more force is C O necessary to fracture thicker shells. C. COMPARISONS OF SHELL DIMENSIONS WITHIN AND AMONG SPECIES Measurements at the length and width of the scar and margin revealed (figure 12) that for each species the shell width at the scar was significantlg smaller than the distence which must be spanned by a cheliped in the other three orientations (p«.001 in all three cases). Also, the comparison of sizes emong species (figure 13), using shells with similar lengths (margin length- 18-2 1mm) revealed that C. limatule has the smallest average width at the scar(pe.00 1), with 4 mitre substantially wider at the scar than the others. D. FATIGUE-LOADING EXPERIMENTS The results of repeated force loading along the length of the scar for C limatule and C. pelte show the effectiveness of this type of force loading (Figure 14). As long as the static force exceeded 603 of the predicted breeking force the strength of the shell was reduced. The values for predicted breaking force (obtained from linear regression values of force vs. thickness for C limatule and C pelte respectivelg) appeared fairly accurate, as those shells loaded in excess of 200 cucles at low percentage loads and then tested for breaking strength by fracturing the shell generallg broke near predicted force values. The fatigue plots also illustrate that at eround 70-752 (and ebove) of the predicted breaking force, fracture resulted(almost alwags) after fewer than 50 cycles. Light(dissecting) microscope observations of fatigued shells demonstrated the development end extension of fatigue cracking. Figure 154 shows the typical pattern of 1-2 stress cracks (white lines on the shell) beginning at the front of the shell; over time these cracks spread around the inner surface, generallg traveling along the muscle scar lager (figures 158 &a; 16). Crecks at the margin and scer (seen on the shell's underside) almost always spread out around the shell(in elliptical rings), while closer to the apex the cracks moyed radially (figure 15C). Often, especiallg at the front and back of C the shell, scar-level rings would merge and travel radiallg toward the margin (figure 150). In this manner when the shell ultimately fractured the top would "pop-off" and the margin rim left behind would split in two. E. OBSERVATIONS OF FRACTURE PATTERNS AT THE MUSCLE SCAR 1. Visual-- In longitudinal scar loading most shells would develop a small crack at the very front of the shell at the level of the scer under sub-breaking loads (seen perticulerly in C. limatule during fetigue-loading). Once the force epplied reached the critical level, the entire top would break off cleanly at the scar. In mang cases the fracture at the front of the shell anterior to the actual myostracum was jagged and irregular, while the fracture at the scar itself was smooth. Margin-loaded shells tend to break first at the scar level. In mang instances the entire top would fracture cleanig before the margin shattered. 2. SEM-- Closer inspections of scer fracture surfaces under the scanning electron microscope revealed a smooth C creck surface resulting from cleavage of the crossed-lameller structure between the primarg lamellae (along the grain). As seen in figure 17, the parallel crossed-lamellar sheets ran along the shell at the level of the muscle scar with each sheet parallel normal to the outer surface of the shell (figure 170). Figure 178 illustrates the smooth fracture surface along the side of the scar, showing that the crack passed between lamellae. F. FINITE ELEMENT ANALYSIS STRESS DIAGRAMS The stress diagrems for C. oigitalis in figure 19 show the relative compressive (colored plates) and tensile (white plates with numbers) stresses resulting from forces applied at each grasping orientation. The shells with forces applied along the length and width of the scar show tensile stresses concentrated where the force was applied, with low compressive stresses elsewhere. In contrast, the shells with forces applied at the margin length and width show high tensile stresses ot the point of opplication 9s well os high C compressive stresses at the level of the scar (see color scheme, figure 18). Also of note is that forces applied at the lateral scar and margin produced greater tensile and compressive stresses at the front of the shell and at the scar (compared to forces applied longitudinallg along the scar and margin). also compered stresses between e high profile (4. mitra) end low profile (C. limatula) limpet shell of equel length and found that at each grasping orientation C limatule reached greater stress concentrations then A mitra For instance, application of 802 of the predicted breaking force to C limatule along the length of the scar resulted in a stress equal to 7-103 of gielding strength at the scar and margin, while a comparable load for A. mitre (803 predicted bresking force) produced a stress equal to only 1-32 of gielding strength (figure 20). DISCUSSION C The majority of shells frectured elong the length or width of the muscle scer broke cleanlg, completelg severing the top of the shell from the shell's rim (figure 21). The effectiveness of this form of attack indicates that a crab such as Pechugrepsus crassipes cen preg upon limpets without having to remove the shell from the rock substrate. In mang cases, particulerly those involving Calliselle limetule, forces applied at the level of the muscle scar caused portions of the shell margin just below the point of contact between the simulated claw and the shell to shatter into framents. For an actual crab attacking a limpet such as C limatule, this fragmentation of the shell's margin might enable the crab to reach under the shell directlg and grab the limpet's exposed foot. Crushing attacks by crabs at the muscle scar might also be useful for two other reasons. First, observed mang instences where limpet shells were curved at the base to match the substrate, making an attack at the margin more difficult since the ends were at different heights (see also 18 Morris, Abbott, and Haderlie, 1980). Despite the curve of the margin, the rest of the shell was not changed, such that a crab could still gresp the shell at the level of the scar. Second, also found mang limpets with shell margins either embedded in the rock or wedged against rocks, algae, or even barnacles. In each of the cases a crab might experience difficulty in crushing or prying at the margins, but in all likelihood the crab could still squeeze a shell higher up et the scar level. FORCE TO BREAK VERSUS SHELL THICKNESS AT THE PUSCLE SCAR With the exception of Acmaee mitre shells, found that the force required to fracture limpet shells at the muscle scar increased as the thickness at the scar increased. However, did not discover significant differences in force/thickness means among the three species showing significant trends in force vs. thickness (C limatule, C. pelte, C. digitelis) This result wes true for forces epplied at both the length and width of the shell at the muscle scer and mergin, with the only exception being that Calliselle digitelis shells were about 1.3 times easier to fracture at the length of the scar than Collisella limatule shells. This outcome indicates that the force required to fracture shells of most limpet species depends more on the material properties of the calcium carbonate shell than on the particular shell shape. Thus in general tall, high-spired Acmaes mitre and low, flat Calliselle limetule shells of similar muscle scar thicknesses will fracture at similar crushing forces. Within each species, shells of similer scar thicknesses fractured along both the length and width of the muscle scar and margin did not break at significentlg different force ranges. Taking into account that the thickness of the shell margin might influence the force at which margin-loaded sheil broke by comparing force to relative thickness(scar thickness/margin thickness) similerlg produced no significant differences. Again the only exceptions appeared in Colliselle limatule, where the shell broke more easily along the length of 20 the margin than along the length of the scar by a fector of 1.8. Still, it appears that a crab has no general advantage in crushing a shell at ang one location on the shell. Thus despite the apparent thinning of the shell at the muscle scar region, some other factor is necessarg to make attacks at the scar vulnerable to crabs. In considering the dimensions of a limpet shell at both the muscle scer and the margin, it is cleer that the grasping orientation where a crab would have to open a cheliped least is at the width of the scer. The width of the scar was found to be significantlg less than the other three shell dimensions for each of the four species, suggesting that even relativelg small crabs could still crush large limpets by gresping them at the Width of the scar. For example, a crab that could open a cheliped to a maximum of 7.1 mm at the tip would still be able grasp a 20mm long Calliselle limatule shell along the width of the scar. Moreover, a crab with a 20mm maximum opening that would just barelg fit the cheliped along the margin length could 21 instead obtein a better grasp (apply the force with the teeth of the claw) at the scar width. Furthermore, by gripping the shell at the width of the scar this 2Omm long cheliped would most likely exert a greater total force (similar to a person squeezing an object between the fingers and palm compared to just between two fingers). A possible conclusion is that crabs in general can expand their food resources by crushing limpets along the muscle scar, especiallg along the width. The comparison of scar widths in figure 13 shows that for shells similar in length (18-21mm) from the four species measured Colliselle limatule has the smallest everage width at the scar. This finding suggests that given equal numbers of shells from these species a crab would be able to grasp and crush more C limatule shells than ang other type. This result might help explain why more C. limatule shells are found on the beach having been fractured at the scar (Chapin, 1966). Another reason that C. limatule (the "file limpet") shells might be easier to grosp than, for instence, A. mitre shells is that 22 the ribs on the back of C limatule shells offer a surfece for crab cheliped teeth to grip, while 4. mitre shells are often smooth and slipperg. Finallg, although the force/thickness values were similar for each species, at a given shell length . limatule shells have the smallest average thickness at the scar, implying that not only could more crabs fit their chelae around C limatule shells, but also a smaller force is necesserg to frecture the shells. FATIGUE FRACTURE AT THE SCAR Fatigue fracture of limpet shells mag be important in two manners. First, by repeatedlg loading a shell to a force below that required to immediately fracture the shell a crab avoids using maximum exertion, thus conserving energy in case of a sudden emergency (such as appearance of a predator). Also, through fatigue-loading, a small crab incapable of exerting sufficient force to frecture the shell in one squeeze can eventually crush a lerge limpet. The results of the fatigue experiments show, however, that a crab must exert at least 23 60-653 of the breaking force to frecture the shell within 200 cycles. This result is similar to values given by Boulding (1986) and Curreg (1984) for fatigue in bivalves. Significantig, if a crab can exert at least 70-752 of the predicted breaking force, the number of cycles required for fracture decreases typically to 50 or fewer, as shown in figure 14. As Boulding (1986) demonstrates, mang crabs fatigue shells over periods of hours or even dags. In this manner, a Fechygrepsus crassiges or other crab could eventually fracture a shell (using a few¬ force pulses at a time) without remaining exposed to predators or other adverse conditions for extended periods of time. Although a crab will most likelg not apply the same level of force at the same exact location each time, the total number of cycles required will still be well below 200. The observations of fatigue crack development show that most cracks originate at the front of the shell just below the muscle scer end subsequently travel around the shell along the scor. Regions of high tensile stress were marked by white 24 lines, indicating cracks just beneath the surfece. Eventuslig these cracks would emerge at the inner surface of the shell along the scar, often merging and traveling down to fracture the margin. Fatigue loading thus concentrated the stresses along the scar, ultimatelg producing surface cracks that would join and sever the top of the shell at the muscle scar. SCAMMING ELECTRON MICROSCOPE OBSERVATIONS A possible explenation to the mechanism by which shells loaded at the margin frectured first at the muscle scar lies in the muscle scer microstructure. Anagises of the frectured crossed-lamellar structure at the muscle scar reveal that the lamellee are oriented with the surface of each sheet lying normal to the shell's outer surface. In this manner a crack mag travel along the scer (between the primarg lamellae), leaving behind a smooth fracture surface. This situation is analogous to splitting plywood along the grain(Curreg, 1974,1980), in the direction requiring the leest energg. Although a crock cen spread between crossed-lamellar sheets for a short distance, in most cases the lamellae change direction after a short distence(figure 22), forcing the creck front to fork. Thus in tupical crossed-lamellar structure a crack is halted unless the force applied increases. However, in practicallg all the muscle scar fracture surfaces l observed, the lamellae remained oriented such that the crack could travel completelg around the horseshoe-shaped scar without crossing lamellae. Even where the fracture surface was slightly more ragged, a short distance later the crack surface was once again smooth, having cut across the grein briefly to where it could continue between the sheets. Therefore, it appears that the mechanism for pop-topping' at the muscle scar involves the crossed-lamellar sheets and not the actual prismatic myostracum. This outcome might be anticipated since the myostracum forms only the inner surface of the shell. Although prisms ere stronger than crossed-lemellar sheets (Curreg, 1988), the high tensile stress at the inner surface of the shell is probablg sufficient to frecture the prisms. However, it is not until the crack reaches 26 the crossed-lameller sheets that the actuel muscle scar cleavage occurs. FINITE ELENENT AMALYSIS GRAPHS Comperison of the relative stresses ceused by forces applied along the length and width of the scar and margin for the Colliselle digitelis(figure 19) computer model reveal that forces transmitted along the length and width of the margin produced high compressive stresses at the level of the scar around the front half of the shell. Although the forces applied along the length and width of the scar produce (as expected) higher tensile stresses at the point of application, the shells with equivalent forces applied at the length and width of the margin show high compressive stress at the muscle scar. While the shell will tend to fracture at a lower stress in tension than compression, a high compressive stress mag still lead to fracture, especially at the scar where the shell thickness is much smaller then at the margin. Forces applied at the margin cause both high tensile stress at the margin and 27 C high compressive stress at the scer, resulting in frecture at forces equal to or less than those required for frecture directig at the scar. Further evidence showing the scar lager to be a structurally weak region came in the Calliselle pelte rim fracture tests (figure 11), where shells missing the top portion(above the scar lager) fractured at the same range of forces as intect shells fractured at the margin. Finally, the finite element analysis graphs also demonstrate that equal length C limatule end A mitre shells develop verg different stress concentrations. Comperison of figure 20 A and B (and C and D) show that at each grasping orientation the stresses in C limatule are much greater than those for A. mitra. Again, the most likelg explanation involves the thinner scar lager in Calliselle limatule at equal shell lengths. With less shell material to contain the stress, stress levels cleerly rise in C limatule shells and cause frecture much more quicklg. SUMMARY 1) Shells of Colliselle pelte, Colliselle limatule, Colliselle digitalis, and Acmaes mitre all break cleanly along the muscle scar when crushed in a crab-like manner. 2) Colliselle pelte, C. limatule, and C. digitslis shells require more force to break as scar lager thickness increased. A. mitre shells show no clear trend in force vs. thickness. 3) Aside from C. digitalis being 1.3 times easier to breck along the length of the scar then C. limatule, there were no other significant differences in force/thickness among the species tested. 4) Generallg no significant differences appeared for (force to break)/(scar thickness) within each species among the four grasping orientations. The one exception was E limatule shells which are 1.8 times easier to fracture at the longitudinal margin vs. longitudinal scar. 5) The width of the shell at the scar proved to be significantig less then the other three dimensions for eoch species, suggesting that crabs could grasp morefand larger) shells at 29 C the width of the scar 6) The width of C limstule shells at the scar was significantig less than the other species, suggesting that more crabs are eble to crush this species' shells at the scer since more crabs cen actually grasp these shells et the scar width. 7) Above 602 of the predicted breaking force fatigue loading fractured shells of C pelte and C. limatule in under 200 cycles. Above 70-752 less than 50 cycles were necessarg, suggesting that crabs can crush limpet shells without ever exerting 1002 of the force required to break an unfatigued shell. Also, smaller crabs incapable of exerting 100% breaking force loads for large shells can still crush the limpet shell 8) Fatigue cracks originate at the front of the shell and usuallt travel along the muscle scar, eventuallg severing the top of the shell. 9) SEH observations revealed crossed-lameller sheets at the muscle scar oriented such that cracks mag travel between the sheetstenergetically favorable direction) and eventuallg cause C the 'pop-top' effect at the muscle scar. 10) Finite element analysis computer models indicate that forces applied along the length and width of the margin produce high compressive stresses et the much thinner muscle scer, often ceusing frecture at the scer first. Also, the relativelg flat C limatule shells showed higher overall tensile and compressive stresses than the tall A. mitre shells, probebly due to the thinner scar lager in equal-length C limatule and 4. mitre shells. LITERATURE CITED Boulding, E. G.(1984). Crab-resistant features of shells of burrowing bivalves: decreasing vulnerebilitg by increesing handling time. J. Exp. Mar. Bio. Ecol. 76. pp 201-223 Boulding, E. G., M. Labarbere (1986). Fetigue damege: Repested loading enables crabs to open lerger bivalves. Biol. Bull. pp 538-547 Buikleg, P. Todd( 1968). Shell damage and repair in five members of the Genus Acmaee. The Veliger. Vol. 1 1(Supplement). pp 64-66 Chapin, D.(1968). Some observations of predation on Acmaea species bu the creb Pachggrapsus crassipes. The Veliger. Vol. 11(Supplement). pp 67-68 Curreg, J. D., J. D. Taglor (1974). The mechanical behavior of some molluscen hard tissues. J. Zool. Lond. 173. pp 395-406 Curreg, J. D.(1977). Mechanical properties of mother-of-pearl in tension. Proc. R. Soc. 196B. pp 443-463 Curreg, J. D.(1980). Mechanical properties of mollusc shell. Sump. Soc. Exp. Biol. 34. pp 75-97 Currey, J. D., K. Brear.(1984). Fatigue fracture of mother-of-pearl and its significence for predetorg techniques. J. Zool. Lond. 204. pp 541-543 Curreg, J. D.(1968). Shell form and strength. The Mollusca(wilbur, K. and K. Sinkiss, eds.), Vol. 11. pp 183-208. Academic Press, Inc. Hey York. Gordon, J. E.(1978). "Structures, or Whg Things Don’t Fall Dovin.“ Penquin Books, Middlesex(England) and New Vork. Lowell, R. B.(1986). Crab predation on limpets: predator behavior and defensive features of the shell morphology of the preg. Biol. Bull. 171. pp 577-596 MecClintock, C.(1967). Shell stucture of patelloid and bellerophantoid gastropods(Hollusca). Peabody Mus. Nat. Hist. Yale. Univ. Bull 22. Nachleal-Schwendler (1986). "Stress And Vibration Analusis.“ The Nacheal-Schwendler Corporation. Los Angeles, CA. Watabe, N.(1988). Shell structure. The Mollusca(wilbur, K. and K. Sinkiss, eds.), Vol 11. pp 69-87. Academic Press, Inc. New York. FIGURE LEGENDS Figure 1. Comparison of relative shell heights for the four species tested. The shells are divided into low( C limatule), middle( C. pelte, C. digitelis) and high(A mitra) relative heights. Figure 2. A. Diagram indiceting varieble sheil thickness in limpet shells. The cross-section shows that the margins and apex are thickened relative to the muscle scar. B. Diagram of the underside of a limpet shell. IIlustrating the horseshoe-shape of the muscle scar. Figure 3. A. (From MacClintock, 1967). Diegram showing the orientation of sheil lagers in e limpet shell. The leger labelled "m" is the myostracum(muscle scar lager). B. Cross-section of the shell at the level of the muscle scar, showing that the myostrecum originates on the inner surface of the shell where the "scar“ appears. A crab-like force would produce tension at the inner surface(the myostracum). P-Prisms. CL-Crossed-lameller. Figure 4. Bending caused by crab-like forces at the muscle scer. The calcium carbonate shell would tend to frecture first along the inner surface since the shell is wesker in tension than compression. Figure 5. Photograph of limpets used in studg, showing relative height ditferences. From left to right: C limatule, C. digitelis, A. mitre, C pelte Figure 6. Limpet shell crusher used to frecture shells. A. Side view. showing a loaded shell situated between two metal plates. The plates are sttached to the large wood blocks. B: Front view. The wood block at the left provides a substrete for the shell, preventing the sheil from slipping to the lett. Theright side of the device is wedged against some bject to prevent sliding to the right. C. Side view, showing two aluminum breces attsched to the upper block. The breces prevent the upper block from sliding over the shell(to the left or right). Figure 7. Diegrems showing how forces were applied to shells. Diagrams show external surface of shell from the top. A. "Front scar“ refers to a force epplied longitudinally et the scar. B. Front margin" refers to a force epplied longitudinallg et the mergin. C. "Lateral scar“ refers to a force epplied laterallg et the scar. D. "Leteral mergin" refers to a force applied laterallg et the margin. Figure 8. Technique used to generate XVZ coordinates for the finite element model. A. Greting(perallel bleck lines) used to project lines onto the shells. B. Diegrem of projector set-up. The lines are projected(in e dark room) onto the shell and the contour pattern photographed. C. Top view of B. D. Topogrephic map obtained when contour lines from each side of the shell are pleced next to each other. The coordinate axes pass through the apex(at the origin). E. Final limpet modeltA mitre shown) obteined from topographic map. The dark circles are nodal(XYz) points. Figure 9. Graph showing the force required to fracture a shell versus the shell thickness et the anterior end of the shell(at the level of the muscle scar) for all four species. A. Values for all four species shown together. B. Linear regressions for each species. The mean force/thickness values were not significentlg different among the four species. E gigitalis: U=135,68 434,3, r2-33, p402, n-17. C limatule. y-231 48 433.3, r4-64, 06001,n=22. A. mitre. y-95.98 480.45, r2-.13, p».05, n-11. E. pelte: =153.0, r2=.26, p6.05, n=18. Figure 10. Regression lines for the force required to frecture a shelltin Newtons) plotted against the shell thickness. The force values for esch gresping orientation(for shells frectured longitudinallg and lateralig along the muscle scar and margin) did not differ significentlg from each öther and are combined for each species into one date set. Breaking forces incressed with sheil thickness in all cases except for 4 mitre. A. L. Jimstula u- 211.98 + 14.5. r2-.49, p..001. (n=63) B. C digitelis. U=151.38 + 21.9. r2-.30, p4.001. (n-51) C. A. mitre. g- 45.68 + 75.5. r -.06, p».05 (n=59) D. C. pelta. y-152.98 + 41.7. ré=.28,p..001 (n-451 Figure 11. Lineer regression showing the force necessarg to fracture 2. gelte shells both intect and without the top of the shell(such that onlg the rim remains). Data for forces applied to each tupe of shell longitudinallg and leterelly ere combined since the force required was essentiallg the same in each case. g= 200x + 15. r#=.55, p..005 (n=15) Figure 12. Graphs showing sheil length and width at the scar and margin for A. C digitalis, B. C limatula, C. A. mitra, and D. C. pelta. In each instance the width at the scer is significentlg smaller than the other three orientations(p«.00 1 for all four graphs). Figure 13. Comparison of shell length(A) and shell width(B) at the level of the scar among the four species. Shells from each species were approximatelg equal in length( 18-2 1mm). Both graphs indicate that # limatule hes the smallest dimensions at the scar(among similar length shells), with the difference being greatest at the width of the scar. Figure 14. Fatigue loading in C limatule(A) and C. gelte(B), Shells were odded for 5 seconds for up to a maximum of 200 cycles. When the applied force was greater than 603 of the predicted breaking force(see figure 104 &D), fracture resulted in fewer than 200 cycles. Around 752 fewer than 50 cgcles could result in fracture. Figure 15. Cracking patterns from fatigue-loading(longitudinallu along the scar) in limpet shells. A. Fatigue crecks originating near the front end of the shell, at the level of the muscle scar. B. Typical spreading of cracks along the muscle scar. C. Later stage, showing radial cracks near the apex. D. Stage just prior to fracture, showing crecks merging and moving rädially toward the margin. Crecks are shown on the underside of the shells. Figure 15. Scanning electron micrograph of fatigue cracks. Several cracks are shown running along the muscle scar lager(the outline of the mgostracum is visible near the top left of the picture). Magnification =3508. Figure 17. Fracture along the muscle scar. A. SEM photograph of the shell structure at the muscle scer. Surface shown is the beginning of the muostrecum, viewed(et e slight angle) from the front and towerd the reer of the shell. The cross-lamellar sheets originate just below the upper (ectuelly lower on the shell) lager of prisms. B. SEM photogreph of the fracture surface along the scar. The surface is smooth since the crack treveled between the lamellee. C. Diegrem showing orientation of crossed-lameller sheets at the muscle scer. The primarg lamellee run normel to the external shell surfece, such that a crab-like force can ceuse crecks between the sheets. Once between the lemellee the creck cen spreed eround the shell. Figure 18. Color scheme for the finite element analgsis stress diegrems Velues listed ere for compressive stress in terms of the percentage of maximum gield strength. Tensile stresses appear on the graph as white plates with values included in the legend. Figure 19. Stress diagrams for C digitalis compering forces applied at the margin and scer. Forces applied et the margin produced high compressive stresses along the scar, possibly explaining whg in these cases the shell fractured first along the scar. A. "Front scar“ refers to a force applied longitudinallg along the scar. B. "Front margin" refers to a force epplied longitudinallg along the mergin. In C & D "Lateral" refers to a force applied laterallg along the scar(C) and margin(D). Tensile stresses(Z of gielding strength): A. 1=3.6, 2=3.3, 3=3.1, 4=3.3, 5=3.1 B. =9.3,2=4.7, 3=6.9 C. 1=1.3, 2=6.3 D. 1=14.9, 2=11.5, 3=0.3 Figure 20. Stress diegrams compering stresses in equal length E himetule end 4 mitre computer models. For forces applied longitudinalig along the scar(A B) and the margin(C,D) C Jimatula shows much greater compressive stress along both the scar and mergin. This most likeig occurs because C limetule is much thinner than A. mitre all along the shell. Tensile stresses(Z of gielding strength): A. 1-1.7 B. 1=2.5, 2=2.3 3=2.6,4=2.3, 5=2.2 C. 1=2.0, 2=3.0, 3=8.2 D. 1=1.9, 2=1.8, 3=1.8, 4=2.1 Fiqure 21. Limpets fractured et the muscle scer. A. Examples of shelle crushed with the nutcracker-like device. B. Diegrem of frecture surfece. C Figure et the right is the top of the shell turned over to show thet frecture occured olong the scer. Figure 22. (Used from Curreg, 1988). A. Diegrem indicating that in typical crossed-lemeller structure the lemellee change direction periodicallg, forcing the crack front to divide. B. SEM photo illustrating port 4. O 0 L L E 8 (HLDNHTXHAV)'LH HAILVIHA DAV sele 5 Posr. ANT. LIMPET SHELLTHIC3 ANTERIOR Podst shell sele Sac POSTERIOR —— --...-.- . .... va... m-1 m 58 A Nyostro Coe Suc toce FORCE eOuter Sursace Figure 3 Teosio Conpessio Figure 4 larce — Fure 1 —0 - 5 —10 —15 -2 -25 Ohell Pessed ooinst Lg Pesoed sligin B Figuree io — 0 Bice 4e prevent sidense sligge FRONT Seng LATERAAR FRONT MARGIN LATERAE MARGIN Figure 7 E Grating en a ehetographie slide Side projecht Slide 1 Poeck Figure 9 3n Cmera Sel nee Shell + Sel cator ies p — DMITRAI FORCE VS THICKNESS FRONT SCAR — 500 400 300 + 0 200 f 4 4 1 kos a 40. 100 - 8E + 0 +— 0.1 0.3 0.5 0.7 0.9 1.1 1,3 1,5 1.7 SCAR THICKNESS(mm) + UMATULA MITRA A PETA C DIOTALIS FORCE VS THICKNESS FRONT SCAR 340 - 320 300 280 260 240 220 - 200 1B0 - 150 140 - 120 - 100 - B0 - 50 40 + 1.5 1.7 0.7 0.9 1.1 1.3 0.1 0.3 0.5 SCAR THICKNESS(mm) MITRA A PELTA D DIOTALIS + LIMATULA Figure 2. 320 - 300- 280 - 260 - 240 - 220 200 - 180 - 150 - 140 - 120 100 - 80 - 60 4 40 + 20 + 0.1 400 350 - 300 250 200 - 150 - 100 - 50 0.2 + * FORCE VS THICKNESS COLLSELLA UMATUL 0.5 0.9 0.3 SCAR OR MARGIN THICKNESS(mm) + ALL 4 ONENTATONS FORCE VS THICKNESS COLLISEA DIG LALIS 1 t1 0.6 0.8 0.4 1.2 SCAR OR MAROIN THICKNESS(mm) + ALL 4 ORENTATONS Figure 10 F. FORCE VS THICKNESS ACMAEA MTRA 260 250 - 240 - 230 - 220- 210 200 190 180 - 170 160 150 140 - 130 120 - 110 - 100 - + 90 - + 4 B0 - + 70 - 60 50 40 0.6 0.2 0.4 0.8 SCAR OR MARGIN THICKNESS(mm) + ALL 4 OMENTATIONS FORCE VS THICKNESS COLLISELLA PETA 550 - 500 450 400 350 300 250 - 200 150 - jo pp + + + 4 50 0 + 0.5 0.7 0.9 1.5 1.7 0.3 SCAR OR MARGIN THICKNESS(mm) ALL 4 ORENTATIONS Z Z L O L DD 888188 aaaaa- D —tt- — 8888 (N)yvaa ol soao — 20 - 19 COMPARISON OF GRASPING ORIENTATIONS COLUSEUA GORAES A A SCAR WIOTH MOT SCAR LENOT LENOTH PONNLOE GRASPING N=12 COMPARISON OF GRASPING ORIENTATIONS COLUSELLA UMATULA 22 20 16 14 A A A SCAR WIDTH MDTH SCAR LENGTH LENGTH ORASPINO COMPARISON OF GRASPING ORIENTATIONS AMAAMTR A A SCAR RIOTH LENOTA SCAR LENOT MOT POINTOE, GRASPING J N-16 COMPARISON OF GRASPING ORIENTATIONS COLLISELLA PEIA 26 + 24 22 2 18- 16 14 12 10 - A V oL SCAR LENOT SCAR WIDTH MDT LENOTH POINT GRASPINC N=13 19 15 14 13- 20 19 - 18 17 - 16 15 14- 13- 12 11 - 10 UMATULA LMATUL COMPARISON OF SCAR LENGTHS. ALL 4 SPECIES(18-21m LENOTH) LA L PELIA DIOTAUS SPECIES NPE N=5 COMPARISON OF SCAR WIDTHS ALL 4 SPECIES(1B-21mm LENGTH) PELIA DIOTTALIS SPECIES NPE N=5 MITRA L MITRA Figure 13 FATIGUE LOADING COLSELA UTUL 200 — 190 - 180 - 170 - 160 - 150 140 130 120 - 110 - 100 90 - 80 - 70 - 60 - 50 - 40 30 - 20 10 + — 50 63 55 71 72 75 79 81 B2 85 92 100 LOAD AS X OF PREDICTED BREAKING FORCE FATIGUE LOADING COLLSELLA PELTA 180 170 160 150 - 140 130 120 8. 110 - 100 90 80 - 70 60 - 50 - 40 - 30 - 20 - 10 + 65 50 75 5 LOAD AS X OF PREDICTED BREAKINO FORI 100 Fig Figure 16 - - --. Crossed- anelar sheeks Figure 17 EE FORCE TAESS Colo Veron CRANGE Peo SREEN Buoe Viorer Beown Buck Figure 18 COLoR Snen 6 of Haximom Vteld Streogt O-OS O5 -00 0-200 0-300 381-0 HO -5.00 5O -600 GO-7 O -8.0 80 -0 0500 50 20.00 22000 30 0 5900 o 550 0 ool-8900 85ooo DDIGITALISI DDIGITALISI FRON SCAR FRONT MARGIN Figure 10 DDIGITALISI DDIGITALISI LATERAL SCAR LATERAE MABGIN — — DLIMHI DMITRAI FRONT SCAG RONT S8 - B Figure 20 DLIMRI DMITRAI FRONT MARGIN FBoN MAAGIN D ANT. AN Codecside Post. 057. g. 5. Diagram showing how the front edge of a crack traveling in the easy direction in ed-lamellar structure is broken up when the orientation of the structure changes. 6 5 Tf A d H Rach rig. 6. Fracture in crossed-lamellar structure. The crack traveled first between the sheets. trom right to left, but atter the change in orientation of the sheets it had to break across them Width of field -350 um. 8 (Caped fron Corgey 188) Figore 22