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Copyright copy 2010 American Scientific PublishersAll rights reservedPrinted in the United States of America

Journal ofNanoscience and Nanotechnology

Vol 10 6453ndash6460 2010

Nanoindentations on Conch Shells of Gastropoda andBivalvia Molluscs Reveal AnisotropicEvolution Against External Attacks

Cristina Bignardi1lowast Michele Petraroli1 and Nicola M Pugno231Department of Mechanics Politecnico di Torino Corso Duca degli Abruzzi 24 10129 Torino Italy

2Department of Structural Mechanics Politecnico di Torino Corso Duca degli Abruzzi 24 10129 Torino Italy3National Institute of Nuclear PhysicsmdashNational Laboratories of Frascati via E Fermi 40 00044 Frascati Italy

Nanoindentation method has been used to explore at the nanoscale the mechanical properties offour different representative types of conch shells belonging to the two biggest classes of molluscsGastropoda and Bivalvia in order to compare nanohardness and Youngrsquos modulus with respect tothe microstructural anisotropic architectures For the experimental tests a Nano Indenter XP (MTSNano Instruments Oak Ridge TN) has been used The mechanical tests have been carried out onthe inner and outer surfaces of the shells as well as on their cross-section near to the inneroutersurfaces and in the middle layer The results confirm the three layered anisotropic architecture ofthe investigated conchs On each of these 5 surfaces 2times5 indentations have been performed atdifferent maximum depth from 250 nm to 4 m with a step of 250 nm for a total of 3200 testsThe numerous observations have been analysed applying an ad hoc modification of the WeibullStatistics suggesting a natural evolution of the shells against external attacks

Keywords Nanoindentation Conch Shell Nanohardness Youngrsquos Modulus Weibull

1 INTRODUCTION

Growth and self-strengthening of natural materials is veryattractive According to Darwin (the year 2009 is the150th anniversary of the publication of On the Origin ofSpecies (November 24th 1859) and the 200th anniversaryof Darwinrsquos birth (February 12th 1809)) the reason forthe survival of living organisms is that they could evolveand improve themselves in such a way to be always com-patible with the environment (even if humans seem to beradically different modifying the environment rather thanthemselves) Therefore in such a sense it is no doubt thatnatural materials are the most optimized materials in theworld Their hard structures are highly integrated in softtissues as in natural organisms as for bone tooth molluscshell bark etc The laminated organization of these struc-tures is inherent at different spatial scales (nano micromeso macro) They all exhibit special properties and func-tions From the view-point of the material scientist it isbeneficial to learn from these natural materials and struc-tures and learning from Nature has become now one ofthe most fascinating subjects in material research

lowastAuthor to whom correspondence should be addressed

The majority of shell-forming marine molluscs belongto two main classes Gastropoda (univalves or snails)and Bivalvia (bivalves including clams oysters and scal-lops) Sea shells are composed of calcium carbonate crys-tals interleaved with layers of viscoelastic proteins havingdense tailored structures that yield excellent mechanicalproperties12 Shells have architectures that differ depend-ing on growth requirements and shell formation of theparticular molluscConch shells have a cross-lamellar structure that con-

sists of lath-like aragonite crystals (999 wt) and a ten-uous organic layer (01 wt)3 The architecture of conchshell is organized in three macro-layers4 Each macro-layer consists of many crossed first-order lamellae eachof them composed by second-order lamellae Furthermorethe second-order lamella is made up of third-order lamel-lae which are considered single-crystals and multicrystalsFurther analysis indicates that each lamella is connectedto its neighbour lamellae by a proteinaceous adhesive Thefirst-order lamellae have thickness of 5ndash30 m and areseveral micrometers wide while the second-order ones areabout 5 m thick and 5ndash30 m wide the third orderlamellae are nanosized Thus the thickness of the lamel-lae varies to some extents In some zones lamellae become

J Nanosci Nanotechnol 2010 Vol 10 No 10 1533-48802010106453008 doi101166jnn20102626 6453

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Nanoindentations on Conch Shells Bignardi et al

Fig 1 Schematic diagram of crossed-lamellar three layered anisotropicarchitecture of conch shell

rather thinner or eventually disappear Each lamella con-sists of lath-like crystals The hierarchical lamellae havedifferent orientations Moreover the lamellae are rotated inthe ldquolamellar planerdquo of an angle about 70ndash90 with respectto their neighbour layerlayers The complete microscopicplywood sketch map of conch shell is shown in Figure 1In this paper we have investigated the nanomechanical

anisotropic properties of the shells with a nanoindentermaking 3200 tests then treated with an ah hoc modifica-tion of the Weibull Statistics

2 NANOINDENTATION EXPERIMENTS

Nanoindentation method has been used to explore atthe nanoscale the mechanical properties of four differ-ent representative types of conch shells belonging to thetwo biggest classes of molluscs Gastropoda and Bivalviain order to compare nanohardness and Youngrsquos moduluswith respect to the microstructural anisotropic architectureThe conch shells chosen are Pecten jacobeus (Linnaeus1758)5 Pinna nobilis (Linnaeus 1758) Venus verru-cosa (Linnaeus 1758) and Conus mediterraneus (Hwass1792)6 Figure 2

For the experimental tests a Nano Indenter XP (MTSNano Instruments Oak Ridge TN) has been used Themechanical tests have been carried out on the inneroutersurfaces of each shell and on three zones along their crosssection (inner middle and outer) in order to determinethe nanohardness and Youngrsquos modulus by varying posi-tion and orientation Figure 3 Specimens were incorpo-rated inside a resin support Figure 4 and those of the

(a) (b) (c) (d)

Fig 2 (a) Conus mediterraneus conch (b) Pecten jacobeus conch(c) Venus verrucosa conch and (d) Pinna nobilis conch

Inner or outer (back)surfaces

Cross sectionrsquos outer zone

Cross sectionrsquos middle zone

Cross sectionrsquos inner zone

Fig 3 Example of indentation zones on Conus mediterraneus conch

(a) (b) (c)

Fig 4 Some of the specimens used (a) outer surface of the Conusmediterraneus conch shell (b) cross section zones of the Venus verrucosaconch shell (c) inner surface of the Pinna nobilis conch shell

cross-section have been lapped in order to obtain a flatsurface On each of these surfaces the indentation has beenperformed at different maximum depth from 250 nm to4 m with a step of 250 nm Both on the innerouter sur-faces and on each cross-sectional zone every test consistedof an indentation matrix 2times 5 thus globally 3200 inden-tations have been performed 800 for each conch shell Inthe choice of the area to indent it has been taken careto avoid the nanoindentation-boundary interaction and foreach matrix the distance between the indentation pointshas been increased by increasing the indentation depth inorder to avoid their self-interactions tooThe Oliver-Pharr model was used for data extraction7

According to this method a loadingndashunloading cycle isapplied and the maximum force measured averaged on thecorresponding indentation area gives the nanohardness ofthe specimen while from the slope of the unloading curveits Youngrsquos modulus can be derived Each indentation wasmade using a diamond Berkovich tip

3 STATISTICAL DATA TREATMENT

Results obtained for nanohardness are reported in Table Iand Figure 5 or for Youngrsquos modulus in Table II andFigure 6 Each table or Figure is related to one of the fivesurfaces tested and shows nanohardness or Youngrsquos modu-lus at 16 different depths Each data reported in Tables I II

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RESEARCH

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Bignardi et al Nanoindentations on Conch Shells

Table I(a)ndash(e) (a) Nanohardness measurements on the inner surface (b) Nanohardness measurements on the cross section inner zone (c) Nanohard-ness measurements on the cross section middle zone (d) Nanohardness measurements on the cross section outer zone (e) Nanohardness measurementson the outer surface

Depth [nm] CM PJ VV PN

(a) Inner surface-Nanohardness [GPa]250 2960plusmn1938 6648plusmn6060 2983plusmn3530 1612 plusmn1608500 2355plusmn1828 1470plusmn1754 3901plusmn3226 2258plusmn1894750 2715plusmn1110 2167plusmn2548 2878plusmn2214 2657plusmn30101000 2466plusmn0612 1806plusmn1654 2449plusmn1748 2383plusmn15661250 2813plusmn0762 1238plusmn1908 2215plusmn1396 2491plusmn11261500 1549plusmn1678 2759plusmn0888 2556plusmn2140 2010plusmn16181750 1456plusmn2204 2587plusmn2040 2669plusmn2056 2119plusmn10742000 2631plusmn0406 2938plusmn0624 3289plusmn1542 2482plusmn10302250 2067plusmn2530 2795plusmn0792 3352plusmn1616 2384plusmn07862500 2766plusmn0760 2655plusmn0514 3299plusmn1510 2144plusmn07102750 2443plusmn1028 1333plusmn1806 2691plusmn2656 2415plusmn12623000 2208plusmn1360 0719plusmn1458 3363plusmn1764 2488plusmn08863250 2642plusmn1278 1647plusmn1678 3355plusmn1432 2411plusmn07343500 2366plusmn1838 1722plusmn1874 3097plusmn1852 2256plusmn08243750 2431plusmn1280 2421plusmn0568 2789plusmn2566 2615plusmn06424000 3064plusmn1292 2321plusmn0926 3335plusmn0862 2858plusmn0788

(b) Cross section inner zone-Nanohardness [GPa]250 0225plusmn0044 0736plusmn1050 0302plusmn0440 0080 plusmn0242500 0140plusmn0096 1073plusmn1468 0253plusmn0152 0440plusmn1132750 0105plusmn0066 1086plusmn1602 0216plusmn0110 0419plusmn05481000 0118plusmn0106 0785plusmn0478 0203plusmn0106 0580plusmn05821250 0097plusmn0034 1030plusmn0612 0217plusmn0110 0629plusmn06661500 0061plusmn0032 0977plusmn0672 0218plusmn0100 0602plusmn08761750 0096plusmn0036 1132plusmn0360 0230plusmn0074 0601plusmn06102000 0080plusmn0044 0825plusmn0468 0240plusmn0076 0570plusmn06142250 0074plusmn0036 0737plusmn0266 0189plusmn0054 0722plusmn05602500 0085plusmn0048 0804plusmn0310 0215plusmn0064 1016plusmn06142750 0082plusmn0038 0759plusmn0302 0221plusmn0062 1220plusmn04563000 0068plusmn0030 0632plusmn0190 0220plusmn0066 1499plusmn06943250 0071plusmn0034 0674plusmn0330 0325plusmn0256 1334plusmn08883500 0073plusmn0020 0655plusmn0544 0205plusmn0036 0877plusmn10703750 0071plusmn0022 0584plusmn0440 0223plusmn0044 1111plusmn08644000 0060plusmn0024 0652plusmn0246 0201plusmn0064 1086plusmn0722

(c) Cross section middle zone-Nanohardness [GPa]250 2308plusmn2458 2413plusmn2222 2023plusmn3482 1301plusmn2022500 2045plusmn1236 2580plusmn1970 3600plusmn1594 1029plusmn1914750 3178plusmn1376 3889plusmn3012 4001plusmn1938 1275plusmn18161000 3786plusmn2900 3936plusmn1872 3940plusmn2350 2794plusmn16641250 3520plusmn1878 3879plusmn1636 2842plusmn1892 2503plusmn17701500 3090plusmn2320 3892plusmn1112 2851plusmn1056 2702plusmn18281750 3587plusmn0996 4008plusmn1096 1817plusmn1734 2739plusmn09482000 3610plusmn2276 3964plusmn1060 2984plusmn1752 2975plusmn08462250 3664plusmn1538 3799plusmn0716 1673plusmn1742 2702plusmn05342500 3253plusmn0554 4142plusmn1072 2281plusmn1912 1802plusmn13662750 3691plusmn1594 3683plusmn0720 2794plusmn1122 2002plusmn07023000 3590plusmn0860 3921plusmn0708 2621plusmn0814 1799plusmn04083250 3823plusmn0482 3872plusmn0894 1370plusmn1548 1935plusmn11723500 3676plusmn0718 3438plusmn0588 1931plusmn1230 1881plusmn05403750 3675plusmn0664 3850plusmn0766 2646plusmn1230 1620plusmn07324000 3551plusmn0986 3839plusmn1262 2747plusmn1024 1789plusmn0598

(d) Cross section outer zone-Nanohardness [GPa]

250 1891plusmn1664 0308plusmn0136 3623plusmn2564 1020plusmn1192500 2005plusmn1944 1028plusmn1392 3212plusmn2672 1118plusmn1504750 2461plusmn1862 1599plusmn0898 3205plusmn1490 0347plusmn02921000 2922plusmn1382 2149plusmn1470 3199plusmn1576 0303plusmn06761250 1863plusmn1978 1893plusmn1338 3543plusmn0504 1015plusmn13881500 2947plusmn0784 2289plusmn0956 3341plusmn0558 1021plusmn14781750 2924plusmn2816 1269plusmn1282 2976plusmn1188 0590plusmn0680

Continued

J Nanosci Nanotechnol 10 6453ndash6460 2010 6455

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Nanoindentations on Conch Shells Bignardi et al

Table I(a)ndash(e) Continued

Depth [nm] CM PJ VV PN

2000 3344plusmn0830 1065plusmn1508 2872plusmn1386 0834plusmn07862250 4000plusmn0822 1011plusmn0900 3292plusmn1098 0905plusmn09302500 4257plusmn1084 0612plusmn0772 2945plusmn1072 1079plusmn08122750 3422plusmn1126 1114plusmn0620 3095plusmn1096 0476plusmn03003000 2837plusmn0838 1026plusmn0516 2998plusmn0856 0821plusmn10863250 3846plusmn1288 0818plusmn1266 2224plusmn2254 0015plusmn00263500 3332plusmn1212 0781plusmn1056 1295plusmn1794 0371plusmn05983750 3395plusmn0940 0903plusmn0926 0490plusmn0490 0221plusmn01884000 2893plusmn0442 0366plusmn0402 0497plusmn0448 0200plusmn0152

(e) Outer surface-Nanohardness [GPa]250 4585plusmn3238 1586plusmn3270 1492plusmn2174 3880plusmn0540500 4198plusmn3616 0877plusmn1236 0894plusmn0534 3398plusmn1240750 4471plusmn2134 0362plusmn0560 0783plusmn0612 3669plusmn14781000 4473plusmn2740 0567plusmn0676 0575plusmn0286 2576plusmn14661250 3043plusmn3058 0898plusmn0710 0498plusmn0188 2666plusmn14221500 4485plusmn1770 0707plusmn0972 0492plusmn0228 2938plusmn16241750 4635plusmn0742 0578plusmn1018 0374plusmn0212 2156plusmn11522000 4043plusmn3270 0420plusmn0656 0504plusmn0106 0777plusmn09122250 3926plusmn2394 0745plusmn1170 0472plusmn0204 2334plusmn12222500 3940plusmn3792 0857plusmn0968 0433plusmn0126 2119plusmn06382750 3992plusmn1368 0518plusmn1002 0442plusmn0336 2085plusmn14183000 3652plusmn1678 1592plusmn1590 0646plusmn0674 1671plusmn16203250 4296plusmn2304 0665plusmn0908 1121plusmn0844 1241plusmn14703500 3418plusmn1926 0869plusmn1102 1229plusmn1246 0427plusmn04263750 3334plusmn2788 0592plusmn0812 0658plusmn0646 0533plusmn12544000 3557plusmn2474 1178plusmn1404 0627plusmn0668 0346plusmn0336

Matrix mean values and standard deviations (CM) Conus Mediterraneus (PJ) Pecten Jacobeus (VV) Venus Verrucosa (PN) Pinna Nobilis

01234567

(a)

0 500 1000 1500 2000 2500 3000 3500 4000

Indentation depth [nm]

Nan

ohar

dnes

s [G

Pa] CM PJ VV PN

CM PJ VV PN

(c)

Nan

ohar

dnes

s [G

Pa]

005

115

225

335

445

0 500 1000 1500 2000 2500 3000 3500 4000

Indentation depth [nm]

CM PJ VV PN CM PJ VV PN

(b)

002040608

1121416

0 500 1000 1500 2000 2500 3000 3500 4000

Indentation depth [nm]

CM PJ VV PN CM PJ VV PN

Nan

ohar

dnes

s [G

Pa]

Fig 5 Continued

(d) CM PJ VV PN CM PJ VV PN

005

115

225

335

445

0 500 1000 1500 2000 2500 3000 3500 4000

Indentation depth [nm]

(e)CM PJ VV PN CM PJ VV PN

005

115

225

335

445

5

0 500 1000 1500 2000 2500 3000 3500 4000

Indentation depth [nm]

Nan

ohar

dnes

s [G

Pa]

Nan

ohar

dnes

s [G

Pa]

Fig 5 (a) Results obtained for nanohardness regarding tests performedon the inner surface of the four shells (b) Results obtained for nanohard-ness regarding tests performed on the cross section inner zone of the fourshells (c) Results obtained for nanohardness regarding tests performedon the cross section middle zone of the four shells (d) Results obtainedfor nanohardness regarding tests performed on the cross section outerzone of the four shells (e) Results obtained for nanohardness regard-ing tests performed on the outer surface of the four shells (CM) ConusMediterraneus (PJ) Pecten Jacobeus (VV) Venus Verrucosa (PN) PinnaNobilis

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Bignardi et al Nanoindentations on Conch Shells

Table II(a)ndash(e) (a) Youngrsquos modulus measurements on the inner surface (b) Youngrsquos modulus measurements on the cross section inner zone(c) Youngrsquos modulus measurements on the cross section middle zone (d) Youngrsquos modulus measurements on the cross section outer zone (e) Youngrsquosmodulus measurements on the outer surface

Depth [nm] CM PJ VV PN

(a) Inner surfacendashYoungrsquos modulus [GPa]250 81279plusmn17816 158140plusmn41988 76077plusmn46928 43722plusmn25560500 74370plusmn18576 63099plusmn32914 102189plusmn47702 51170plusmn22662750 72426plusmn10712 70070plusmn29798 83247plusmn38488 49904plusmn272481000 68667plusmn7910 68301plusmn24380 74024plusmn18026 44490plusmn130961250 70714plusmn6768 54039plusmn43578 74393plusmn21308 42212plusmn81141500 52981plusmn32346 75782plusmn8228 76652plusmn23400 37870plusmn110721750 49288plusmn29130 70110plusmn36068 76038plusmn21730 37314plusmn78242000 63450plusmn2448 73509plusmn6724 88814plusmn19330 38703plusmn53522250 52015plusmn34358 71831plusmn9854 85201plusmn20594 37627plusmn44862500 59701plusmn5894 69745plusmn6844 84908plusmn19012 36027plusmn48142750 56869plusmn13532 51203plusmn34800 73265plusmn34562 36980plusmn82943000 55101plusmn12122 45240plusmn29758 79923plusmn18584 38371plusmn48003250 60612plusmn12366 54518plusmn25204 76997plusmn10844 37617plusmn45123500 54667plusmn13148 57345plusmn27006 76154plusmn17686 38309plusmn35143750 55266plusmn12908 63713plusmn6658 73751plusmn39782 39307plusmn39224000 60041plusmn8536 62636plusmn11576 73211plusmn11726 41351plusmn4806

(b) Cross section inner zonendashYoungrsquos modulus [GPa]250 1148plusmn0370 36575plusmn40406 4984plusmn3260 1130plusmn2282500 0811plusmn0168 42990plusmn38016 4741plusmn1862 26457plusmn38744750 0616plusmn0136 40620plusmn39684 4608plusmn1456 19404plusmn256561000 0553plusmn0208 34607plusmn19128 4315plusmn1474 26832plusmn177261250 0461plusmn0070 39035plusmn11178 4717plusmn1464 27574plusmn83401500 0352plusmn0084 39460plusmn14116 4629plusmn0946 23686plusmn228841750 0377plusmn0054 41777plusmn13302 4816plusmn0982 24590plusmn174362000 0325plusmn0086 36470plusmn12830 5445plusmn3578 23728plusmn160822250 0309plusmn0050 32501plusmn3210 4231plusmn0766 30475plusmn104982500 0288plusmn0092 34194plusmn4866 4440plusmn0956 40052plusmn128742750 0260plusmn0076 33637plusmn4934 4649plusmn0972 42492plusmn114903000 0240plusmn0060 32064plusmn8040 4519plusmn0748 47624plusmn104223250 0235plusmn0066 30021plusmn9272 11864plusmn20064 44846plusmn105203500 0235plusmn0052 33249plusmn19940 4266plusmn0426 36853plusmn220023750 0222plusmn0058 30588plusmn12498 4424plusmn0612 41776plusmn152504000 0212plusmn0042 29249plusmn8166 4118plusmn0662 39905plusmn10018

(c) Cross section middle zonendashYoungrsquos modulus [GPa]250 71655plusmn48894 81889plusmn40584 54291plusmn58910 40942plusmn42484500 71315plusmn27448 78443plusmn28356 76019plusmn22378 36495plusmn45432750 74650plusmn14360 88513plusmn31648 71383plusmn11840 47723plusmn358101000 78856plusmn28222 85835plusmn21426 65405plusmn15322 74669plusmn239281250 73304plusmn20580 83654plusmn16882 53780plusmn11834 70897plusmn282321500 61911plusmn25920 80019plusmn12346 49263plusmn5284 71225plusmn255021750 71338plusmn9928 81225plusmn13060 42051plusmn9480 71729plusmn149442000 71174plusmn22840 77939plusmn11126 46813plusmn7454 75633plusmn151522250 71822plusmn14384 75745plusmn8120 34226plusmn16398 69159plusmn80162500 65045plusmn6768 77914plusmn15054 41678plusmn10780 60981plusmn274922750 69830plusmn13836 73380plusmn6586 42704plusmn6046 61925plusmn97323000 67038plusmn10758 74489plusmn7376 41666plusmn4306 56636plusmn119943250 66316plusmn2820 72934plusmn9862 32498plusmn11618 61709plusmn160063500 63516plusmn6200 67930plusmn5954 35910plusmn7720 57928plusmn106703750 62770plusmn6102 72175plusmn10096 38138plusmn5982 52967plusmn151384000 62323plusmn8710 70002plusmn8232 36956plusmn5812 53883plusmn10218

(d) Cross section outer zonendashYoungrsquos modulus [GPa]250 67321plusmn32026 5135plusmn1982 71345plusmn26300 29613plusmn33994500 64372plusmn40712 28634plusmn35434 67633plusmn16862 45177plusmn30642750 66923plusmn27956 45858plusmn7546 61235plusmn15370 19371plusmn128221000 72572plusmn18380 47969plusmn19354 56635plusmn9426 20492plusmn377941250 56387plusmn27206 36296plusmn20492 53308plusmn4172 46354plusmn339141500 69231plusmn15104 38056plusmn11456 48775plusmn1900 43150plusmn358961750 68175plusmn28194 25664plusmn16456 43905plusmn6624 33701plusmn248022000 70863plusmn10676 23729plusmn15744 60831plusmn7902 41386plusmn20218

Continued

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Nanoindentations on Conch Shells Bignardi et al

Table II(a)ndash(e) Continued

Depth [nm] CM PJ VV PN

2250 67929plusmn6502 25842plusmn14930 40776plusmn5028 46703plusmn220282500 69148plusmn8270 21603plusmn21340 38759plusmn3532 50566plusmn188562750 60788plusmn6416 38125plusmn12594 36877plusmn3832 34328plusmn177243000 62926plusmn9312 37966plusmn12296 34495plusmn2750 42746plusmn360603250 58085plusmn8288 27762plusmn31224 28957plusmn11436 0634plusmn12283500 54617plusmn9722 22801plusmn24670 24200plusmn9742 28779plusmn200263750 52964plusmn7564 27527plusmn22962 17267plusmn5692 15918plusmn285864000 62467plusmn4316 16159plusmn24342 16020plusmn7052 15395plusmn15930

(e) Outer surfacendashYoungrsquos modulus [GPa]250 83946plusmn36172 34904plusmn33518 26146plusmn12810 58133plusmn8366500 75668plusmn28860 29083plusmn32668 30066plusmn21320 50565plusmn15452750 80058plusmn15162 21090plusmn32514 53334plusmn37128 53672plusmn102601000 79559plusmn20274 29378plusmn42356 50011plusmn25766 45708plusmn116021250 74599plusmn46044 41159plusmn12902 37239plusmn27864 47924plusmn128201500 76422plusmn14534 42665plusmn45442 36504plusmn19134 48023plusmn162601750 76038plusmn5328 36778plusmn43280 23134plusmn14506 42119plusmn134802000 77272plusmn23380 22735plusmn27700 39590plusmn7578 30254plusmn161022250 73014plusmn19526 47414plusmn38834 42094plusmn14534 45706plusmn111322500 75154plusmn33076 44930plusmn30546 43432plusmn10366 41823plusmn67182750 70583plusmn10536 36824plusmn43588 45395plusmn29766 41752plusmn142163000 70721plusmn9954 52850plusmn23208 47465plusmn31962 34445plusmn232063250 73558plusmn22002 36969plusmn30768 54583plusmn13252 27997plusmn241803500 65840plusmn13386 43234plusmn28390 57026plusmn37038 16880plusmn125543750 64727plusmn25580 38552plusmn28978 69721plusmn38238 16070plusmn145024000 65531plusmn22600 51139plusmn35480 54157plusmn29638 16375plusmn8452

Matrix mean values and standard deviations (CM) Conus Mediterraneus (PJ) Pecten Jacobeus (VV) Venus Verrucosa (PN) Pinna Nobilis

020406080

100120140160180

(a)

0 500 1000 1500 2000 2500 3000 3500 4000

Indentation depth [nm]

You

ngprimes

mod

ulus

[G

Pa]

CM PJ VV PN CM PJ VV PN

(b) CM PJ VV PN CM PJ VV PN

05

101520253035404550

0 500 1000 1500 2000 2500 3000 3500 4000

Indentation depth [nm]

You

ngprimes

mod

ulus

[G

Pa]

(c) CM PJ VV PN CM PJ VV PN

You

ngprimes

mod

ulus

[G

Pa]

0102030405060708090

100

0 500 1000 1500 2000 2500 3000 3500 4000

Indentation depth [nm]

Fig 6 Continued

(d) CM PJ VV PN CM PJ VV PN

You

ngprimes

mod

ulus

[G

Pa]

Indentation depth [nm]

01020304050607080

0 500 1000 1500 2000 2500 3000 3500 4000

(e) CM PJ VV PN CM PJ VV PN

You

ngprimes

mod

ulus

[G

Pa]

Indentation depth [nm]

0102030405060708090

0 500 1000 1500 2000 2500 3000 3500 4000

Fig 6 (a) Results obtained for Youngrsquos modulus regarding tests per-formed on the inner surface of the four shells (b) Results obtained forYoungrsquos modulus regarding tests performed on the cross section innerzone of the four shells (c) Results obtained for Youngrsquos modulus regard-ing tests performed on the cross section middle zone of the four shells(d) Results obtained for Youngrsquos modulus regarding tests performed onthe cross section outer zone of the four shells (e) Results obtainedfor Youngrsquos modulus regarding tests performed on the outer surface ofthe four shells (CM) Conus Mediterraneus (PJ) Pecten Jacobeus (VV)Venus Verrucosa (PN) Pinna Nobilis

6458 J Nanosci Nanotechnol 10 6453ndash6460 2010

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Bignardi et al Nanoindentations on Conch Shells

or point on Figures 5 6 represents the average value ofthe indentation matrixThe 3200 tests have been analysed applying an ad hoc

modification of the Weibull Statistics8 ie interpreting thecumulative probability function F of finding zones withnanohardness (Youngrsquos modulus) smaller than HE at anindentation depth h according to

F lt H= 1minus eminushh0nHH0

m

(1)

where H0 is the nominal nanohardness (or E0 is the nom-inal Youngrsquos modulus ie corresponding to F = 63for hh0

n = 1 h0 is a reference indentation depth(eg 1 m) m is the Weibull moduls and nm is the size-effect exponent Classically Weibull Statistics is appliedconsidering H as the material strength h as a characteris-tic size defined as the cubic root of the specimen volume(or square root of the specimen surface) and thus n = 3(or n = 2) for volume (or surface) predominant defectsAlternatively Nanoscale Weibull Statistics9 specificallydeveloped for nearly defect-free structures considersn= 0 Thus we note that our modification proposed inEq (1) describes in addition to the nanohardness (Youngrsquosmodulus) distribution also the indentation size-effect in

Nanohardness perpendicular to the internal surfaces (IS)

y = 57387xndash55553R2 = 0938

ndash4

ndash3

ndash2

ndash1

0

1

2(a)

(b)

03 04 05 06 07 08 09 1 11 12

ln(hh0)

ln(ln

(1(

1ndashF

)))

Nanohardness parallel to the internal surface (CI)

y = 93303x+20516

R2 = 09028

ndash10

ndash8

ndash6

ndash4

ndash2

0

2

4

6

8

ndash3 ndash28 ndash26 ndash24 ndash22 ndash2 ndash18 ndash16 ndash14

ln (hh0)

ln(ln

(1(

1ndashF

)))ndash

3ln

(hh

0)

Fig 7 (a) Statistical data analysis on nanohardness measured on theinner surface of the Conus Mediterraneus shell (n = 0) (b) Statisticaldata analysis on nanohardness measured on the cross section of the innersurface of the Conus Mediterraneus shell (n= 3)

the form of H prop hminusnm (E prop hminusnm Similar results areobtained for the different shells as an example we focusour attention on the Conus meditteraneous conch10 In ourtests a negligible indentation size-effect has been revealedthus suggesting n= 0 for which in fact the highest statisti-cal correlation (coefficient of correlation R2 is found Anexception for the softer anisotropic inner layer is observedfor which we found the maximum statistical correlationfor n = 3 suggesting that the size-effect is governed byvolume-dominated process such as dislocation sliding Infact n = 0 would correspond for the nanohardness dataanalysis to R2n = 0 = 07232 whereas R2n = 1 =08755 R2n= 2= 09020 R2n= 3= 09028 R2n=4 = 08981 thus with a maximum for n = 3 A sim-ilar trend is observed for the Youngrsquos modulus As anexample the Weibull plots for the nanohardness measuredalong the two considered orthogonal directions of the inneranisotropic layer are shown in Figure 7 We note that theproposed modification of the Weibull Statistics is powerfulin treating nanoindentation experimentsOur analysis supports the idea that super-composites or

super-armors could be realized in the near future mimick-ing nacre11 with anisotropic and hierarchical architecturescomposed by hard surfaces and tough volumes in order toincrease the material fracture toughness12ndash16

4 DISCUSSION AND CONCLUSIONS

We have performed 3200 nanoindentations on four dif-ferent representative types of conch shells belonging tothe two biggest classes of molluscs Gastropoda andBivalvia in order to compare nanohardness and Youngrsquosmodulus with respect to their microstructural anisotropicarchitecture The following considerations can be drawn(i) a strong anisotropy of the inner layer is present inall the four investigated shells nanohardness and Youngrsquosmodulus increase by one order of magnitude from thecross-section to the surface(ii) nanohardness and Youngrsquos modulus grow from theinner to the outer side for the Gastropoda Conus mediter-raneus and Bivalvia Pinna nobilis shells but an oppositetrend is found for the Pecten jacobeus and Venus verru-cosa Bivalvia shells(iii) no sensible difference has been observed as regardsto the nanoindentation depth with the exception of thesofter inner anisotropic layer of the Gastropoda Conusmediterraneus for which we have statistically deduced avolume-dominated dislocation sliding This suggests a nat-ural evolution against external attacks from outside forthe first two shells or during the ldquoopenrdquo critical phase forthe last two Bivalvia shells

Acknowledgments Nicola M Pugno acknowl-edges the financial support from the Piemonte

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Nanoindentations on Conch Shells Bignardi et al

Region ldquoConverging Technologiesrdquo BiotechnologyndashNanotechnology METREGEN 2008 ldquoMetrology ona cellular and macromolecular scale for regenerativemedicinerdquo

References and Notes

1 S Kamat H Kessler R Ballarini M Nassirou and A H HeuerActa Mater 52 2395 (2004)

2 A Y M Lin M A Meyers and K S Vecchio Mater Sci Eng C26 1380 (2006)

3 R Menig M H Meyers M A Meyers and K S Vecchio MaterSci Eng A 297 203 (2001)

4 D F Hou G S Zhou and M Zheng Biomaterials 25 751(2004)

5 C Linnaeligus Systema naturaelig per regna tria naturaelig secundumclasses ordines genera species cum characteribus differentiis

synonymis locis Tomus I Editio Decima Reformata 10th ednHolmiaelig (Stockholm) (Laurentii Salvii) (1758)

6 J G Bruguiegravere and C H Hwass Encyc Meacuteth Hist Nat des Vers2 690 (1792)

7 W C Oliver and G M Pharr J Mater Res 7 1564 (1992)8 W Weibul J Appl Mech 18 293 (1951)9 N Pugno and R Ruoff J Appl Phys 99 024301 (2006)10 C Bignardi M Petraroli and N M Pugno The Nanomechanics

in Italy edited by N M Pugno Research Signpost Kerala India(2007) p 125

11 N Pugno Nanotechnology 17 5480 (2006)12 N Pugno Int J of Fracture 140 159 (2006)13 M Ippolito A Mattoni L Colombo and N Pugno Phys Rev B

73 104111-1 (2006)14 N Pugno B Peng and H D Espinosa Int J of Solids and

Structures 42 647 (2004)15 A Carpinteri and N Pugno Powder Technology 131 93 (2003)16 A Carpinteri F Ciola and N Pugno Computers and Structures

79 389 (2001)

Received 7 July 2009 Accepted 22 September 2009

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RESEARCH

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Nanoindentations on Conch Shells Bignardi et al

Fig 1 Schematic diagram of crossed-lamellar three layered anisotropicarchitecture of conch shell

rather thinner or eventually disappear Each lamella con-sists of lath-like crystals The hierarchical lamellae havedifferent orientations Moreover the lamellae are rotated inthe ldquolamellar planerdquo of an angle about 70ndash90 with respectto their neighbour layerlayers The complete microscopicplywood sketch map of conch shell is shown in Figure 1In this paper we have investigated the nanomechanical

anisotropic properties of the shells with a nanoindentermaking 3200 tests then treated with an ah hoc modifica-tion of the Weibull Statistics

2 NANOINDENTATION EXPERIMENTS

Nanoindentation method has been used to explore atthe nanoscale the mechanical properties of four differ-ent representative types of conch shells belonging to thetwo biggest classes of molluscs Gastropoda and Bivalviain order to compare nanohardness and Youngrsquos moduluswith respect to the microstructural anisotropic architectureThe conch shells chosen are Pecten jacobeus (Linnaeus1758)5 Pinna nobilis (Linnaeus 1758) Venus verru-cosa (Linnaeus 1758) and Conus mediterraneus (Hwass1792)6 Figure 2

For the experimental tests a Nano Indenter XP (MTSNano Instruments Oak Ridge TN) has been used Themechanical tests have been carried out on the inneroutersurfaces of each shell and on three zones along their crosssection (inner middle and outer) in order to determinethe nanohardness and Youngrsquos modulus by varying posi-tion and orientation Figure 3 Specimens were incorpo-rated inside a resin support Figure 4 and those of the

(a) (b) (c) (d)

Fig 2 (a) Conus mediterraneus conch (b) Pecten jacobeus conch(c) Venus verrucosa conch and (d) Pinna nobilis conch

Inner or outer (back)surfaces

Cross sectionrsquos outer zone

Cross sectionrsquos middle zone

Cross sectionrsquos inner zone

Fig 3 Example of indentation zones on Conus mediterraneus conch

(a) (b) (c)

Fig 4 Some of the specimens used (a) outer surface of the Conusmediterraneus conch shell (b) cross section zones of the Venus verrucosaconch shell (c) inner surface of the Pinna nobilis conch shell

cross-section have been lapped in order to obtain a flatsurface On each of these surfaces the indentation has beenperformed at different maximum depth from 250 nm to4 m with a step of 250 nm Both on the innerouter sur-faces and on each cross-sectional zone every test consistedof an indentation matrix 2times 5 thus globally 3200 inden-tations have been performed 800 for each conch shell Inthe choice of the area to indent it has been taken careto avoid the nanoindentation-boundary interaction and foreach matrix the distance between the indentation pointshas been increased by increasing the indentation depth inorder to avoid their self-interactions tooThe Oliver-Pharr model was used for data extraction7

According to this method a loadingndashunloading cycle isapplied and the maximum force measured averaged on thecorresponding indentation area gives the nanohardness ofthe specimen while from the slope of the unloading curveits Youngrsquos modulus can be derived Each indentation wasmade using a diamond Berkovich tip

3 STATISTICAL DATA TREATMENT

Results obtained for nanohardness are reported in Table Iand Figure 5 or for Youngrsquos modulus in Table II andFigure 6 Each table or Figure is related to one of the fivesurfaces tested and shows nanohardness or Youngrsquos modu-lus at 16 different depths Each data reported in Tables I II

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RESEARCH

ARTIC

LE

Bignardi et al Nanoindentations on Conch Shells

Table I(a)ndash(e) (a) Nanohardness measurements on the inner surface (b) Nanohardness measurements on the cross section inner zone (c) Nanohard-ness measurements on the cross section middle zone (d) Nanohardness measurements on the cross section outer zone (e) Nanohardness measurementson the outer surface

Depth [nm] CM PJ VV PN

(a) Inner surface-Nanohardness [GPa]250 2960plusmn1938 6648plusmn6060 2983plusmn3530 1612 plusmn1608500 2355plusmn1828 1470plusmn1754 3901plusmn3226 2258plusmn1894750 2715plusmn1110 2167plusmn2548 2878plusmn2214 2657plusmn30101000 2466plusmn0612 1806plusmn1654 2449plusmn1748 2383plusmn15661250 2813plusmn0762 1238plusmn1908 2215plusmn1396 2491plusmn11261500 1549plusmn1678 2759plusmn0888 2556plusmn2140 2010plusmn16181750 1456plusmn2204 2587plusmn2040 2669plusmn2056 2119plusmn10742000 2631plusmn0406 2938plusmn0624 3289plusmn1542 2482plusmn10302250 2067plusmn2530 2795plusmn0792 3352plusmn1616 2384plusmn07862500 2766plusmn0760 2655plusmn0514 3299plusmn1510 2144plusmn07102750 2443plusmn1028 1333plusmn1806 2691plusmn2656 2415plusmn12623000 2208plusmn1360 0719plusmn1458 3363plusmn1764 2488plusmn08863250 2642plusmn1278 1647plusmn1678 3355plusmn1432 2411plusmn07343500 2366plusmn1838 1722plusmn1874 3097plusmn1852 2256plusmn08243750 2431plusmn1280 2421plusmn0568 2789plusmn2566 2615plusmn06424000 3064plusmn1292 2321plusmn0926 3335plusmn0862 2858plusmn0788

(b) Cross section inner zone-Nanohardness [GPa]250 0225plusmn0044 0736plusmn1050 0302plusmn0440 0080 plusmn0242500 0140plusmn0096 1073plusmn1468 0253plusmn0152 0440plusmn1132750 0105plusmn0066 1086plusmn1602 0216plusmn0110 0419plusmn05481000 0118plusmn0106 0785plusmn0478 0203plusmn0106 0580plusmn05821250 0097plusmn0034 1030plusmn0612 0217plusmn0110 0629plusmn06661500 0061plusmn0032 0977plusmn0672 0218plusmn0100 0602plusmn08761750 0096plusmn0036 1132plusmn0360 0230plusmn0074 0601plusmn06102000 0080plusmn0044 0825plusmn0468 0240plusmn0076 0570plusmn06142250 0074plusmn0036 0737plusmn0266 0189plusmn0054 0722plusmn05602500 0085plusmn0048 0804plusmn0310 0215plusmn0064 1016plusmn06142750 0082plusmn0038 0759plusmn0302 0221plusmn0062 1220plusmn04563000 0068plusmn0030 0632plusmn0190 0220plusmn0066 1499plusmn06943250 0071plusmn0034 0674plusmn0330 0325plusmn0256 1334plusmn08883500 0073plusmn0020 0655plusmn0544 0205plusmn0036 0877plusmn10703750 0071plusmn0022 0584plusmn0440 0223plusmn0044 1111plusmn08644000 0060plusmn0024 0652plusmn0246 0201plusmn0064 1086plusmn0722

(c) Cross section middle zone-Nanohardness [GPa]250 2308plusmn2458 2413plusmn2222 2023plusmn3482 1301plusmn2022500 2045plusmn1236 2580plusmn1970 3600plusmn1594 1029plusmn1914750 3178plusmn1376 3889plusmn3012 4001plusmn1938 1275plusmn18161000 3786plusmn2900 3936plusmn1872 3940plusmn2350 2794plusmn16641250 3520plusmn1878 3879plusmn1636 2842plusmn1892 2503plusmn17701500 3090plusmn2320 3892plusmn1112 2851plusmn1056 2702plusmn18281750 3587plusmn0996 4008plusmn1096 1817plusmn1734 2739plusmn09482000 3610plusmn2276 3964plusmn1060 2984plusmn1752 2975plusmn08462250 3664plusmn1538 3799plusmn0716 1673plusmn1742 2702plusmn05342500 3253plusmn0554 4142plusmn1072 2281plusmn1912 1802plusmn13662750 3691plusmn1594 3683plusmn0720 2794plusmn1122 2002plusmn07023000 3590plusmn0860 3921plusmn0708 2621plusmn0814 1799plusmn04083250 3823plusmn0482 3872plusmn0894 1370plusmn1548 1935plusmn11723500 3676plusmn0718 3438plusmn0588 1931plusmn1230 1881plusmn05403750 3675plusmn0664 3850plusmn0766 2646plusmn1230 1620plusmn07324000 3551plusmn0986 3839plusmn1262 2747plusmn1024 1789plusmn0598

(d) Cross section outer zone-Nanohardness [GPa]

250 1891plusmn1664 0308plusmn0136 3623plusmn2564 1020plusmn1192500 2005plusmn1944 1028plusmn1392 3212plusmn2672 1118plusmn1504750 2461plusmn1862 1599plusmn0898 3205plusmn1490 0347plusmn02921000 2922plusmn1382 2149plusmn1470 3199plusmn1576 0303plusmn06761250 1863plusmn1978 1893plusmn1338 3543plusmn0504 1015plusmn13881500 2947plusmn0784 2289plusmn0956 3341plusmn0558 1021plusmn14781750 2924plusmn2816 1269plusmn1282 2976plusmn1188 0590plusmn0680

Continued

J Nanosci Nanotechnol 10 6453ndash6460 2010 6455

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RESEARCH

ARTIC

LE

Nanoindentations on Conch Shells Bignardi et al

Table I(a)ndash(e) Continued

Depth [nm] CM PJ VV PN

2000 3344plusmn0830 1065plusmn1508 2872plusmn1386 0834plusmn07862250 4000plusmn0822 1011plusmn0900 3292plusmn1098 0905plusmn09302500 4257plusmn1084 0612plusmn0772 2945plusmn1072 1079plusmn08122750 3422plusmn1126 1114plusmn0620 3095plusmn1096 0476plusmn03003000 2837plusmn0838 1026plusmn0516 2998plusmn0856 0821plusmn10863250 3846plusmn1288 0818plusmn1266 2224plusmn2254 0015plusmn00263500 3332plusmn1212 0781plusmn1056 1295plusmn1794 0371plusmn05983750 3395plusmn0940 0903plusmn0926 0490plusmn0490 0221plusmn01884000 2893plusmn0442 0366plusmn0402 0497plusmn0448 0200plusmn0152

(e) Outer surface-Nanohardness [GPa]250 4585plusmn3238 1586plusmn3270 1492plusmn2174 3880plusmn0540500 4198plusmn3616 0877plusmn1236 0894plusmn0534 3398plusmn1240750 4471plusmn2134 0362plusmn0560 0783plusmn0612 3669plusmn14781000 4473plusmn2740 0567plusmn0676 0575plusmn0286 2576plusmn14661250 3043plusmn3058 0898plusmn0710 0498plusmn0188 2666plusmn14221500 4485plusmn1770 0707plusmn0972 0492plusmn0228 2938plusmn16241750 4635plusmn0742 0578plusmn1018 0374plusmn0212 2156plusmn11522000 4043plusmn3270 0420plusmn0656 0504plusmn0106 0777plusmn09122250 3926plusmn2394 0745plusmn1170 0472plusmn0204 2334plusmn12222500 3940plusmn3792 0857plusmn0968 0433plusmn0126 2119plusmn06382750 3992plusmn1368 0518plusmn1002 0442plusmn0336 2085plusmn14183000 3652plusmn1678 1592plusmn1590 0646plusmn0674 1671plusmn16203250 4296plusmn2304 0665plusmn0908 1121plusmn0844 1241plusmn14703500 3418plusmn1926 0869plusmn1102 1229plusmn1246 0427plusmn04263750 3334plusmn2788 0592plusmn0812 0658plusmn0646 0533plusmn12544000 3557plusmn2474 1178plusmn1404 0627plusmn0668 0346plusmn0336

Matrix mean values and standard deviations (CM) Conus Mediterraneus (PJ) Pecten Jacobeus (VV) Venus Verrucosa (PN) Pinna Nobilis

01234567

(a)

0 500 1000 1500 2000 2500 3000 3500 4000

Indentation depth [nm]

Nan

ohar

dnes

s [G

Pa] CM PJ VV PN

CM PJ VV PN

(c)

Nan

ohar

dnes

s [G

Pa]

005

115

225

335

445

0 500 1000 1500 2000 2500 3000 3500 4000

Indentation depth [nm]

CM PJ VV PN CM PJ VV PN

(b)

002040608

1121416

0 500 1000 1500 2000 2500 3000 3500 4000

Indentation depth [nm]

CM PJ VV PN CM PJ VV PN

Nan

ohar

dnes

s [G

Pa]

Fig 5 Continued

(d) CM PJ VV PN CM PJ VV PN

005

115

225

335

445

0 500 1000 1500 2000 2500 3000 3500 4000

Indentation depth [nm]

(e)CM PJ VV PN CM PJ VV PN

005

115

225

335

445

5

0 500 1000 1500 2000 2500 3000 3500 4000

Indentation depth [nm]

Nan

ohar

dnes

s [G

Pa]

Nan

ohar

dnes

s [G

Pa]

Fig 5 (a) Results obtained for nanohardness regarding tests performedon the inner surface of the four shells (b) Results obtained for nanohard-ness regarding tests performed on the cross section inner zone of the fourshells (c) Results obtained for nanohardness regarding tests performedon the cross section middle zone of the four shells (d) Results obtainedfor nanohardness regarding tests performed on the cross section outerzone of the four shells (e) Results obtained for nanohardness regard-ing tests performed on the outer surface of the four shells (CM) ConusMediterraneus (PJ) Pecten Jacobeus (VV) Venus Verrucosa (PN) PinnaNobilis

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RESEARCH

ARTIC

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Bignardi et al Nanoindentations on Conch Shells

Table II(a)ndash(e) (a) Youngrsquos modulus measurements on the inner surface (b) Youngrsquos modulus measurements on the cross section inner zone(c) Youngrsquos modulus measurements on the cross section middle zone (d) Youngrsquos modulus measurements on the cross section outer zone (e) Youngrsquosmodulus measurements on the outer surface

Depth [nm] CM PJ VV PN

(a) Inner surfacendashYoungrsquos modulus [GPa]250 81279plusmn17816 158140plusmn41988 76077plusmn46928 43722plusmn25560500 74370plusmn18576 63099plusmn32914 102189plusmn47702 51170plusmn22662750 72426plusmn10712 70070plusmn29798 83247plusmn38488 49904plusmn272481000 68667plusmn7910 68301plusmn24380 74024plusmn18026 44490plusmn130961250 70714plusmn6768 54039plusmn43578 74393plusmn21308 42212plusmn81141500 52981plusmn32346 75782plusmn8228 76652plusmn23400 37870plusmn110721750 49288plusmn29130 70110plusmn36068 76038plusmn21730 37314plusmn78242000 63450plusmn2448 73509plusmn6724 88814plusmn19330 38703plusmn53522250 52015plusmn34358 71831plusmn9854 85201plusmn20594 37627plusmn44862500 59701plusmn5894 69745plusmn6844 84908plusmn19012 36027plusmn48142750 56869plusmn13532 51203plusmn34800 73265plusmn34562 36980plusmn82943000 55101plusmn12122 45240plusmn29758 79923plusmn18584 38371plusmn48003250 60612plusmn12366 54518plusmn25204 76997plusmn10844 37617plusmn45123500 54667plusmn13148 57345plusmn27006 76154plusmn17686 38309plusmn35143750 55266plusmn12908 63713plusmn6658 73751plusmn39782 39307plusmn39224000 60041plusmn8536 62636plusmn11576 73211plusmn11726 41351plusmn4806

(b) Cross section inner zonendashYoungrsquos modulus [GPa]250 1148plusmn0370 36575plusmn40406 4984plusmn3260 1130plusmn2282500 0811plusmn0168 42990plusmn38016 4741plusmn1862 26457plusmn38744750 0616plusmn0136 40620plusmn39684 4608plusmn1456 19404plusmn256561000 0553plusmn0208 34607plusmn19128 4315plusmn1474 26832plusmn177261250 0461plusmn0070 39035plusmn11178 4717plusmn1464 27574plusmn83401500 0352plusmn0084 39460plusmn14116 4629plusmn0946 23686plusmn228841750 0377plusmn0054 41777plusmn13302 4816plusmn0982 24590plusmn174362000 0325plusmn0086 36470plusmn12830 5445plusmn3578 23728plusmn160822250 0309plusmn0050 32501plusmn3210 4231plusmn0766 30475plusmn104982500 0288plusmn0092 34194plusmn4866 4440plusmn0956 40052plusmn128742750 0260plusmn0076 33637plusmn4934 4649plusmn0972 42492plusmn114903000 0240plusmn0060 32064plusmn8040 4519plusmn0748 47624plusmn104223250 0235plusmn0066 30021plusmn9272 11864plusmn20064 44846plusmn105203500 0235plusmn0052 33249plusmn19940 4266plusmn0426 36853plusmn220023750 0222plusmn0058 30588plusmn12498 4424plusmn0612 41776plusmn152504000 0212plusmn0042 29249plusmn8166 4118plusmn0662 39905plusmn10018

(c) Cross section middle zonendashYoungrsquos modulus [GPa]250 71655plusmn48894 81889plusmn40584 54291plusmn58910 40942plusmn42484500 71315plusmn27448 78443plusmn28356 76019plusmn22378 36495plusmn45432750 74650plusmn14360 88513plusmn31648 71383plusmn11840 47723plusmn358101000 78856plusmn28222 85835plusmn21426 65405plusmn15322 74669plusmn239281250 73304plusmn20580 83654plusmn16882 53780plusmn11834 70897plusmn282321500 61911plusmn25920 80019plusmn12346 49263plusmn5284 71225plusmn255021750 71338plusmn9928 81225plusmn13060 42051plusmn9480 71729plusmn149442000 71174plusmn22840 77939plusmn11126 46813plusmn7454 75633plusmn151522250 71822plusmn14384 75745plusmn8120 34226plusmn16398 69159plusmn80162500 65045plusmn6768 77914plusmn15054 41678plusmn10780 60981plusmn274922750 69830plusmn13836 73380plusmn6586 42704plusmn6046 61925plusmn97323000 67038plusmn10758 74489plusmn7376 41666plusmn4306 56636plusmn119943250 66316plusmn2820 72934plusmn9862 32498plusmn11618 61709plusmn160063500 63516plusmn6200 67930plusmn5954 35910plusmn7720 57928plusmn106703750 62770plusmn6102 72175plusmn10096 38138plusmn5982 52967plusmn151384000 62323plusmn8710 70002plusmn8232 36956plusmn5812 53883plusmn10218

(d) Cross section outer zonendashYoungrsquos modulus [GPa]250 67321plusmn32026 5135plusmn1982 71345plusmn26300 29613plusmn33994500 64372plusmn40712 28634plusmn35434 67633plusmn16862 45177plusmn30642750 66923plusmn27956 45858plusmn7546 61235plusmn15370 19371plusmn128221000 72572plusmn18380 47969plusmn19354 56635plusmn9426 20492plusmn377941250 56387plusmn27206 36296plusmn20492 53308plusmn4172 46354plusmn339141500 69231plusmn15104 38056plusmn11456 48775plusmn1900 43150plusmn358961750 68175plusmn28194 25664plusmn16456 43905plusmn6624 33701plusmn248022000 70863plusmn10676 23729plusmn15744 60831plusmn7902 41386plusmn20218

Continued

J Nanosci Nanotechnol 10 6453ndash6460 2010 6457

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RESEARCH

ARTIC

LE

Nanoindentations on Conch Shells Bignardi et al

Table II(a)ndash(e) Continued

Depth [nm] CM PJ VV PN

2250 67929plusmn6502 25842plusmn14930 40776plusmn5028 46703plusmn220282500 69148plusmn8270 21603plusmn21340 38759plusmn3532 50566plusmn188562750 60788plusmn6416 38125plusmn12594 36877plusmn3832 34328plusmn177243000 62926plusmn9312 37966plusmn12296 34495plusmn2750 42746plusmn360603250 58085plusmn8288 27762plusmn31224 28957plusmn11436 0634plusmn12283500 54617plusmn9722 22801plusmn24670 24200plusmn9742 28779plusmn200263750 52964plusmn7564 27527plusmn22962 17267plusmn5692 15918plusmn285864000 62467plusmn4316 16159plusmn24342 16020plusmn7052 15395plusmn15930

(e) Outer surfacendashYoungrsquos modulus [GPa]250 83946plusmn36172 34904plusmn33518 26146plusmn12810 58133plusmn8366500 75668plusmn28860 29083plusmn32668 30066plusmn21320 50565plusmn15452750 80058plusmn15162 21090plusmn32514 53334plusmn37128 53672plusmn102601000 79559plusmn20274 29378plusmn42356 50011plusmn25766 45708plusmn116021250 74599plusmn46044 41159plusmn12902 37239plusmn27864 47924plusmn128201500 76422plusmn14534 42665plusmn45442 36504plusmn19134 48023plusmn162601750 76038plusmn5328 36778plusmn43280 23134plusmn14506 42119plusmn134802000 77272plusmn23380 22735plusmn27700 39590plusmn7578 30254plusmn161022250 73014plusmn19526 47414plusmn38834 42094plusmn14534 45706plusmn111322500 75154plusmn33076 44930plusmn30546 43432plusmn10366 41823plusmn67182750 70583plusmn10536 36824plusmn43588 45395plusmn29766 41752plusmn142163000 70721plusmn9954 52850plusmn23208 47465plusmn31962 34445plusmn232063250 73558plusmn22002 36969plusmn30768 54583plusmn13252 27997plusmn241803500 65840plusmn13386 43234plusmn28390 57026plusmn37038 16880plusmn125543750 64727plusmn25580 38552plusmn28978 69721plusmn38238 16070plusmn145024000 65531plusmn22600 51139plusmn35480 54157plusmn29638 16375plusmn8452

Matrix mean values and standard deviations (CM) Conus Mediterraneus (PJ) Pecten Jacobeus (VV) Venus Verrucosa (PN) Pinna Nobilis

020406080

100120140160180

(a)

0 500 1000 1500 2000 2500 3000 3500 4000

Indentation depth [nm]

You

ngprimes

mod

ulus

[G

Pa]

CM PJ VV PN CM PJ VV PN

(b) CM PJ VV PN CM PJ VV PN

05

101520253035404550

0 500 1000 1500 2000 2500 3000 3500 4000

Indentation depth [nm]

You

ngprimes

mod

ulus

[G

Pa]

(c) CM PJ VV PN CM PJ VV PN

You

ngprimes

mod

ulus

[G

Pa]

0102030405060708090

100

0 500 1000 1500 2000 2500 3000 3500 4000

Indentation depth [nm]

Fig 6 Continued

(d) CM PJ VV PN CM PJ VV PN

You

ngprimes

mod

ulus

[G

Pa]

Indentation depth [nm]

01020304050607080

0 500 1000 1500 2000 2500 3000 3500 4000

(e) CM PJ VV PN CM PJ VV PN

You

ngprimes

mod

ulus

[G

Pa]

Indentation depth [nm]

0102030405060708090

0 500 1000 1500 2000 2500 3000 3500 4000

Fig 6 (a) Results obtained for Youngrsquos modulus regarding tests per-formed on the inner surface of the four shells (b) Results obtained forYoungrsquos modulus regarding tests performed on the cross section innerzone of the four shells (c) Results obtained for Youngrsquos modulus regard-ing tests performed on the cross section middle zone of the four shells(d) Results obtained for Youngrsquos modulus regarding tests performed onthe cross section outer zone of the four shells (e) Results obtainedfor Youngrsquos modulus regarding tests performed on the outer surface ofthe four shells (CM) Conus Mediterraneus (PJ) Pecten Jacobeus (VV)Venus Verrucosa (PN) Pinna Nobilis

6458 J Nanosci Nanotechnol 10 6453ndash6460 2010

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IP 16871277Mon 06 Sep 2010 113147

RESEARCH

ARTIC

LE

Bignardi et al Nanoindentations on Conch Shells

or point on Figures 5 6 represents the average value ofthe indentation matrixThe 3200 tests have been analysed applying an ad hoc

modification of the Weibull Statistics8 ie interpreting thecumulative probability function F of finding zones withnanohardness (Youngrsquos modulus) smaller than HE at anindentation depth h according to

F lt H= 1minus eminushh0nHH0

m

(1)

where H0 is the nominal nanohardness (or E0 is the nom-inal Youngrsquos modulus ie corresponding to F = 63for hh0

n = 1 h0 is a reference indentation depth(eg 1 m) m is the Weibull moduls and nm is the size-effect exponent Classically Weibull Statistics is appliedconsidering H as the material strength h as a characteris-tic size defined as the cubic root of the specimen volume(or square root of the specimen surface) and thus n = 3(or n = 2) for volume (or surface) predominant defectsAlternatively Nanoscale Weibull Statistics9 specificallydeveloped for nearly defect-free structures considersn= 0 Thus we note that our modification proposed inEq (1) describes in addition to the nanohardness (Youngrsquosmodulus) distribution also the indentation size-effect in

Nanohardness perpendicular to the internal surfaces (IS)

y = 57387xndash55553R2 = 0938

ndash4

ndash3

ndash2

ndash1

0

1

2(a)

(b)

03 04 05 06 07 08 09 1 11 12

ln(hh0)

ln(ln

(1(

1ndashF

)))

Nanohardness parallel to the internal surface (CI)

y = 93303x+20516

R2 = 09028

ndash10

ndash8

ndash6

ndash4

ndash2

0

2

4

6

8

ndash3 ndash28 ndash26 ndash24 ndash22 ndash2 ndash18 ndash16 ndash14

ln (hh0)

ln(ln

(1(

1ndashF

)))ndash

3ln

(hh

0)

Fig 7 (a) Statistical data analysis on nanohardness measured on theinner surface of the Conus Mediterraneus shell (n = 0) (b) Statisticaldata analysis on nanohardness measured on the cross section of the innersurface of the Conus Mediterraneus shell (n= 3)

the form of H prop hminusnm (E prop hminusnm Similar results areobtained for the different shells as an example we focusour attention on the Conus meditteraneous conch10 In ourtests a negligible indentation size-effect has been revealedthus suggesting n= 0 for which in fact the highest statisti-cal correlation (coefficient of correlation R2 is found Anexception for the softer anisotropic inner layer is observedfor which we found the maximum statistical correlationfor n = 3 suggesting that the size-effect is governed byvolume-dominated process such as dislocation sliding Infact n = 0 would correspond for the nanohardness dataanalysis to R2n = 0 = 07232 whereas R2n = 1 =08755 R2n= 2= 09020 R2n= 3= 09028 R2n=4 = 08981 thus with a maximum for n = 3 A sim-ilar trend is observed for the Youngrsquos modulus As anexample the Weibull plots for the nanohardness measuredalong the two considered orthogonal directions of the inneranisotropic layer are shown in Figure 7 We note that theproposed modification of the Weibull Statistics is powerfulin treating nanoindentation experimentsOur analysis supports the idea that super-composites or

super-armors could be realized in the near future mimick-ing nacre11 with anisotropic and hierarchical architecturescomposed by hard surfaces and tough volumes in order toincrease the material fracture toughness12ndash16

4 DISCUSSION AND CONCLUSIONS

We have performed 3200 nanoindentations on four dif-ferent representative types of conch shells belonging tothe two biggest classes of molluscs Gastropoda andBivalvia in order to compare nanohardness and Youngrsquosmodulus with respect to their microstructural anisotropicarchitecture The following considerations can be drawn(i) a strong anisotropy of the inner layer is present inall the four investigated shells nanohardness and Youngrsquosmodulus increase by one order of magnitude from thecross-section to the surface(ii) nanohardness and Youngrsquos modulus grow from theinner to the outer side for the Gastropoda Conus mediter-raneus and Bivalvia Pinna nobilis shells but an oppositetrend is found for the Pecten jacobeus and Venus verru-cosa Bivalvia shells(iii) no sensible difference has been observed as regardsto the nanoindentation depth with the exception of thesofter inner anisotropic layer of the Gastropoda Conusmediterraneus for which we have statistically deduced avolume-dominated dislocation sliding This suggests a nat-ural evolution against external attacks from outside forthe first two shells or during the ldquoopenrdquo critical phase forthe last two Bivalvia shells

Acknowledgments Nicola M Pugno acknowl-edges the financial support from the Piemonte

J Nanosci Nanotechnol 10 6453ndash6460 2010 6459

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RESEARCH

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Nanoindentations on Conch Shells Bignardi et al

Region ldquoConverging Technologiesrdquo BiotechnologyndashNanotechnology METREGEN 2008 ldquoMetrology ona cellular and macromolecular scale for regenerativemedicinerdquo

References and Notes

1 S Kamat H Kessler R Ballarini M Nassirou and A H HeuerActa Mater 52 2395 (2004)

2 A Y M Lin M A Meyers and K S Vecchio Mater Sci Eng C26 1380 (2006)

3 R Menig M H Meyers M A Meyers and K S Vecchio MaterSci Eng A 297 203 (2001)

4 D F Hou G S Zhou and M Zheng Biomaterials 25 751(2004)

5 C Linnaeligus Systema naturaelig per regna tria naturaelig secundumclasses ordines genera species cum characteribus differentiis

synonymis locis Tomus I Editio Decima Reformata 10th ednHolmiaelig (Stockholm) (Laurentii Salvii) (1758)

6 J G Bruguiegravere and C H Hwass Encyc Meacuteth Hist Nat des Vers2 690 (1792)

7 W C Oliver and G M Pharr J Mater Res 7 1564 (1992)8 W Weibul J Appl Mech 18 293 (1951)9 N Pugno and R Ruoff J Appl Phys 99 024301 (2006)10 C Bignardi M Petraroli and N M Pugno The Nanomechanics

in Italy edited by N M Pugno Research Signpost Kerala India(2007) p 125

11 N Pugno Nanotechnology 17 5480 (2006)12 N Pugno Int J of Fracture 140 159 (2006)13 M Ippolito A Mattoni L Colombo and N Pugno Phys Rev B

73 104111-1 (2006)14 N Pugno B Peng and H D Espinosa Int J of Solids and

Structures 42 647 (2004)15 A Carpinteri and N Pugno Powder Technology 131 93 (2003)16 A Carpinteri F Ciola and N Pugno Computers and Structures

79 389 (2001)

Received 7 July 2009 Accepted 22 September 2009

6460 J Nanosci Nanotechnol 10 6453ndash6460 2010

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RESEARCH

ARTIC

LE

Bignardi et al Nanoindentations on Conch Shells

Table I(a)ndash(e) (a) Nanohardness measurements on the inner surface (b) Nanohardness measurements on the cross section inner zone (c) Nanohard-ness measurements on the cross section middle zone (d) Nanohardness measurements on the cross section outer zone (e) Nanohardness measurementson the outer surface

Depth [nm] CM PJ VV PN

(a) Inner surface-Nanohardness [GPa]250 2960plusmn1938 6648plusmn6060 2983plusmn3530 1612 plusmn1608500 2355plusmn1828 1470plusmn1754 3901plusmn3226 2258plusmn1894750 2715plusmn1110 2167plusmn2548 2878plusmn2214 2657plusmn30101000 2466plusmn0612 1806plusmn1654 2449plusmn1748 2383plusmn15661250 2813plusmn0762 1238plusmn1908 2215plusmn1396 2491plusmn11261500 1549plusmn1678 2759plusmn0888 2556plusmn2140 2010plusmn16181750 1456plusmn2204 2587plusmn2040 2669plusmn2056 2119plusmn10742000 2631plusmn0406 2938plusmn0624 3289plusmn1542 2482plusmn10302250 2067plusmn2530 2795plusmn0792 3352plusmn1616 2384plusmn07862500 2766plusmn0760 2655plusmn0514 3299plusmn1510 2144plusmn07102750 2443plusmn1028 1333plusmn1806 2691plusmn2656 2415plusmn12623000 2208plusmn1360 0719plusmn1458 3363plusmn1764 2488plusmn08863250 2642plusmn1278 1647plusmn1678 3355plusmn1432 2411plusmn07343500 2366plusmn1838 1722plusmn1874 3097plusmn1852 2256plusmn08243750 2431plusmn1280 2421plusmn0568 2789plusmn2566 2615plusmn06424000 3064plusmn1292 2321plusmn0926 3335plusmn0862 2858plusmn0788

(b) Cross section inner zone-Nanohardness [GPa]250 0225plusmn0044 0736plusmn1050 0302plusmn0440 0080 plusmn0242500 0140plusmn0096 1073plusmn1468 0253plusmn0152 0440plusmn1132750 0105plusmn0066 1086plusmn1602 0216plusmn0110 0419plusmn05481000 0118plusmn0106 0785plusmn0478 0203plusmn0106 0580plusmn05821250 0097plusmn0034 1030plusmn0612 0217plusmn0110 0629plusmn06661500 0061plusmn0032 0977plusmn0672 0218plusmn0100 0602plusmn08761750 0096plusmn0036 1132plusmn0360 0230plusmn0074 0601plusmn06102000 0080plusmn0044 0825plusmn0468 0240plusmn0076 0570plusmn06142250 0074plusmn0036 0737plusmn0266 0189plusmn0054 0722plusmn05602500 0085plusmn0048 0804plusmn0310 0215plusmn0064 1016plusmn06142750 0082plusmn0038 0759plusmn0302 0221plusmn0062 1220plusmn04563000 0068plusmn0030 0632plusmn0190 0220plusmn0066 1499plusmn06943250 0071plusmn0034 0674plusmn0330 0325plusmn0256 1334plusmn08883500 0073plusmn0020 0655plusmn0544 0205plusmn0036 0877plusmn10703750 0071plusmn0022 0584plusmn0440 0223plusmn0044 1111plusmn08644000 0060plusmn0024 0652plusmn0246 0201plusmn0064 1086plusmn0722

(c) Cross section middle zone-Nanohardness [GPa]250 2308plusmn2458 2413plusmn2222 2023plusmn3482 1301plusmn2022500 2045plusmn1236 2580plusmn1970 3600plusmn1594 1029plusmn1914750 3178plusmn1376 3889plusmn3012 4001plusmn1938 1275plusmn18161000 3786plusmn2900 3936plusmn1872 3940plusmn2350 2794plusmn16641250 3520plusmn1878 3879plusmn1636 2842plusmn1892 2503plusmn17701500 3090plusmn2320 3892plusmn1112 2851plusmn1056 2702plusmn18281750 3587plusmn0996 4008plusmn1096 1817plusmn1734 2739plusmn09482000 3610plusmn2276 3964plusmn1060 2984plusmn1752 2975plusmn08462250 3664plusmn1538 3799plusmn0716 1673plusmn1742 2702plusmn05342500 3253plusmn0554 4142plusmn1072 2281plusmn1912 1802plusmn13662750 3691plusmn1594 3683plusmn0720 2794plusmn1122 2002plusmn07023000 3590plusmn0860 3921plusmn0708 2621plusmn0814 1799plusmn04083250 3823plusmn0482 3872plusmn0894 1370plusmn1548 1935plusmn11723500 3676plusmn0718 3438plusmn0588 1931plusmn1230 1881plusmn05403750 3675plusmn0664 3850plusmn0766 2646plusmn1230 1620plusmn07324000 3551plusmn0986 3839plusmn1262 2747plusmn1024 1789plusmn0598

(d) Cross section outer zone-Nanohardness [GPa]

250 1891plusmn1664 0308plusmn0136 3623plusmn2564 1020plusmn1192500 2005plusmn1944 1028plusmn1392 3212plusmn2672 1118plusmn1504750 2461plusmn1862 1599plusmn0898 3205plusmn1490 0347plusmn02921000 2922plusmn1382 2149plusmn1470 3199plusmn1576 0303plusmn06761250 1863plusmn1978 1893plusmn1338 3543plusmn0504 1015plusmn13881500 2947plusmn0784 2289plusmn0956 3341plusmn0558 1021plusmn14781750 2924plusmn2816 1269plusmn1282 2976plusmn1188 0590plusmn0680

Continued

J Nanosci Nanotechnol 10 6453ndash6460 2010 6455

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RESEARCH

ARTIC

LE

Nanoindentations on Conch Shells Bignardi et al

Table I(a)ndash(e) Continued

Depth [nm] CM PJ VV PN

2000 3344plusmn0830 1065plusmn1508 2872plusmn1386 0834plusmn07862250 4000plusmn0822 1011plusmn0900 3292plusmn1098 0905plusmn09302500 4257plusmn1084 0612plusmn0772 2945plusmn1072 1079plusmn08122750 3422plusmn1126 1114plusmn0620 3095plusmn1096 0476plusmn03003000 2837plusmn0838 1026plusmn0516 2998plusmn0856 0821plusmn10863250 3846plusmn1288 0818plusmn1266 2224plusmn2254 0015plusmn00263500 3332plusmn1212 0781plusmn1056 1295plusmn1794 0371plusmn05983750 3395plusmn0940 0903plusmn0926 0490plusmn0490 0221plusmn01884000 2893plusmn0442 0366plusmn0402 0497plusmn0448 0200plusmn0152

(e) Outer surface-Nanohardness [GPa]250 4585plusmn3238 1586plusmn3270 1492plusmn2174 3880plusmn0540500 4198plusmn3616 0877plusmn1236 0894plusmn0534 3398plusmn1240750 4471plusmn2134 0362plusmn0560 0783plusmn0612 3669plusmn14781000 4473plusmn2740 0567plusmn0676 0575plusmn0286 2576plusmn14661250 3043plusmn3058 0898plusmn0710 0498plusmn0188 2666plusmn14221500 4485plusmn1770 0707plusmn0972 0492plusmn0228 2938plusmn16241750 4635plusmn0742 0578plusmn1018 0374plusmn0212 2156plusmn11522000 4043plusmn3270 0420plusmn0656 0504plusmn0106 0777plusmn09122250 3926plusmn2394 0745plusmn1170 0472plusmn0204 2334plusmn12222500 3940plusmn3792 0857plusmn0968 0433plusmn0126 2119plusmn06382750 3992plusmn1368 0518plusmn1002 0442plusmn0336 2085plusmn14183000 3652plusmn1678 1592plusmn1590 0646plusmn0674 1671plusmn16203250 4296plusmn2304 0665plusmn0908 1121plusmn0844 1241plusmn14703500 3418plusmn1926 0869plusmn1102 1229plusmn1246 0427plusmn04263750 3334plusmn2788 0592plusmn0812 0658plusmn0646 0533plusmn12544000 3557plusmn2474 1178plusmn1404 0627plusmn0668 0346plusmn0336

Matrix mean values and standard deviations (CM) Conus Mediterraneus (PJ) Pecten Jacobeus (VV) Venus Verrucosa (PN) Pinna Nobilis

01234567

(a)

0 500 1000 1500 2000 2500 3000 3500 4000

Indentation depth [nm]

Nan

ohar

dnes

s [G

Pa] CM PJ VV PN

CM PJ VV PN

(c)

Nan

ohar

dnes

s [G

Pa]

005

115

225

335

445

0 500 1000 1500 2000 2500 3000 3500 4000

Indentation depth [nm]

CM PJ VV PN CM PJ VV PN

(b)

002040608

1121416

0 500 1000 1500 2000 2500 3000 3500 4000

Indentation depth [nm]

CM PJ VV PN CM PJ VV PN

Nan

ohar

dnes

s [G

Pa]

Fig 5 Continued

(d) CM PJ VV PN CM PJ VV PN

005

115

225

335

445

0 500 1000 1500 2000 2500 3000 3500 4000

Indentation depth [nm]

(e)CM PJ VV PN CM PJ VV PN

005

115

225

335

445

5

0 500 1000 1500 2000 2500 3000 3500 4000

Indentation depth [nm]

Nan

ohar

dnes

s [G

Pa]

Nan

ohar

dnes

s [G

Pa]

Fig 5 (a) Results obtained for nanohardness regarding tests performedon the inner surface of the four shells (b) Results obtained for nanohard-ness regarding tests performed on the cross section inner zone of the fourshells (c) Results obtained for nanohardness regarding tests performedon the cross section middle zone of the four shells (d) Results obtainedfor nanohardness regarding tests performed on the cross section outerzone of the four shells (e) Results obtained for nanohardness regard-ing tests performed on the outer surface of the four shells (CM) ConusMediterraneus (PJ) Pecten Jacobeus (VV) Venus Verrucosa (PN) PinnaNobilis

6456 J Nanosci Nanotechnol 10 6453ndash6460 2010

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RESEARCH

ARTIC

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Bignardi et al Nanoindentations on Conch Shells

Table II(a)ndash(e) (a) Youngrsquos modulus measurements on the inner surface (b) Youngrsquos modulus measurements on the cross section inner zone(c) Youngrsquos modulus measurements on the cross section middle zone (d) Youngrsquos modulus measurements on the cross section outer zone (e) Youngrsquosmodulus measurements on the outer surface

Depth [nm] CM PJ VV PN

(a) Inner surfacendashYoungrsquos modulus [GPa]250 81279plusmn17816 158140plusmn41988 76077plusmn46928 43722plusmn25560500 74370plusmn18576 63099plusmn32914 102189plusmn47702 51170plusmn22662750 72426plusmn10712 70070plusmn29798 83247plusmn38488 49904plusmn272481000 68667plusmn7910 68301plusmn24380 74024plusmn18026 44490plusmn130961250 70714plusmn6768 54039plusmn43578 74393plusmn21308 42212plusmn81141500 52981plusmn32346 75782plusmn8228 76652plusmn23400 37870plusmn110721750 49288plusmn29130 70110plusmn36068 76038plusmn21730 37314plusmn78242000 63450plusmn2448 73509plusmn6724 88814plusmn19330 38703plusmn53522250 52015plusmn34358 71831plusmn9854 85201plusmn20594 37627plusmn44862500 59701plusmn5894 69745plusmn6844 84908plusmn19012 36027plusmn48142750 56869plusmn13532 51203plusmn34800 73265plusmn34562 36980plusmn82943000 55101plusmn12122 45240plusmn29758 79923plusmn18584 38371plusmn48003250 60612plusmn12366 54518plusmn25204 76997plusmn10844 37617plusmn45123500 54667plusmn13148 57345plusmn27006 76154plusmn17686 38309plusmn35143750 55266plusmn12908 63713plusmn6658 73751plusmn39782 39307plusmn39224000 60041plusmn8536 62636plusmn11576 73211plusmn11726 41351plusmn4806

(b) Cross section inner zonendashYoungrsquos modulus [GPa]250 1148plusmn0370 36575plusmn40406 4984plusmn3260 1130plusmn2282500 0811plusmn0168 42990plusmn38016 4741plusmn1862 26457plusmn38744750 0616plusmn0136 40620plusmn39684 4608plusmn1456 19404plusmn256561000 0553plusmn0208 34607plusmn19128 4315plusmn1474 26832plusmn177261250 0461plusmn0070 39035plusmn11178 4717plusmn1464 27574plusmn83401500 0352plusmn0084 39460plusmn14116 4629plusmn0946 23686plusmn228841750 0377plusmn0054 41777plusmn13302 4816plusmn0982 24590plusmn174362000 0325plusmn0086 36470plusmn12830 5445plusmn3578 23728plusmn160822250 0309plusmn0050 32501plusmn3210 4231plusmn0766 30475plusmn104982500 0288plusmn0092 34194plusmn4866 4440plusmn0956 40052plusmn128742750 0260plusmn0076 33637plusmn4934 4649plusmn0972 42492plusmn114903000 0240plusmn0060 32064plusmn8040 4519plusmn0748 47624plusmn104223250 0235plusmn0066 30021plusmn9272 11864plusmn20064 44846plusmn105203500 0235plusmn0052 33249plusmn19940 4266plusmn0426 36853plusmn220023750 0222plusmn0058 30588plusmn12498 4424plusmn0612 41776plusmn152504000 0212plusmn0042 29249plusmn8166 4118plusmn0662 39905plusmn10018

(c) Cross section middle zonendashYoungrsquos modulus [GPa]250 71655plusmn48894 81889plusmn40584 54291plusmn58910 40942plusmn42484500 71315plusmn27448 78443plusmn28356 76019plusmn22378 36495plusmn45432750 74650plusmn14360 88513plusmn31648 71383plusmn11840 47723plusmn358101000 78856plusmn28222 85835plusmn21426 65405plusmn15322 74669plusmn239281250 73304plusmn20580 83654plusmn16882 53780plusmn11834 70897plusmn282321500 61911plusmn25920 80019plusmn12346 49263plusmn5284 71225plusmn255021750 71338plusmn9928 81225plusmn13060 42051plusmn9480 71729plusmn149442000 71174plusmn22840 77939plusmn11126 46813plusmn7454 75633plusmn151522250 71822plusmn14384 75745plusmn8120 34226plusmn16398 69159plusmn80162500 65045plusmn6768 77914plusmn15054 41678plusmn10780 60981plusmn274922750 69830plusmn13836 73380plusmn6586 42704plusmn6046 61925plusmn97323000 67038plusmn10758 74489plusmn7376 41666plusmn4306 56636plusmn119943250 66316plusmn2820 72934plusmn9862 32498plusmn11618 61709plusmn160063500 63516plusmn6200 67930plusmn5954 35910plusmn7720 57928plusmn106703750 62770plusmn6102 72175plusmn10096 38138plusmn5982 52967plusmn151384000 62323plusmn8710 70002plusmn8232 36956plusmn5812 53883plusmn10218

(d) Cross section outer zonendashYoungrsquos modulus [GPa]250 67321plusmn32026 5135plusmn1982 71345plusmn26300 29613plusmn33994500 64372plusmn40712 28634plusmn35434 67633plusmn16862 45177plusmn30642750 66923plusmn27956 45858plusmn7546 61235plusmn15370 19371plusmn128221000 72572plusmn18380 47969plusmn19354 56635plusmn9426 20492plusmn377941250 56387plusmn27206 36296plusmn20492 53308plusmn4172 46354plusmn339141500 69231plusmn15104 38056plusmn11456 48775plusmn1900 43150plusmn358961750 68175plusmn28194 25664plusmn16456 43905plusmn6624 33701plusmn248022000 70863plusmn10676 23729plusmn15744 60831plusmn7902 41386plusmn20218

Continued

J Nanosci Nanotechnol 10 6453ndash6460 2010 6457

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RESEARCH

ARTIC

LE

Nanoindentations on Conch Shells Bignardi et al

Table II(a)ndash(e) Continued

Depth [nm] CM PJ VV PN

2250 67929plusmn6502 25842plusmn14930 40776plusmn5028 46703plusmn220282500 69148plusmn8270 21603plusmn21340 38759plusmn3532 50566plusmn188562750 60788plusmn6416 38125plusmn12594 36877plusmn3832 34328plusmn177243000 62926plusmn9312 37966plusmn12296 34495plusmn2750 42746plusmn360603250 58085plusmn8288 27762plusmn31224 28957plusmn11436 0634plusmn12283500 54617plusmn9722 22801plusmn24670 24200plusmn9742 28779plusmn200263750 52964plusmn7564 27527plusmn22962 17267plusmn5692 15918plusmn285864000 62467plusmn4316 16159plusmn24342 16020plusmn7052 15395plusmn15930

(e) Outer surfacendashYoungrsquos modulus [GPa]250 83946plusmn36172 34904plusmn33518 26146plusmn12810 58133plusmn8366500 75668plusmn28860 29083plusmn32668 30066plusmn21320 50565plusmn15452750 80058plusmn15162 21090plusmn32514 53334plusmn37128 53672plusmn102601000 79559plusmn20274 29378plusmn42356 50011plusmn25766 45708plusmn116021250 74599plusmn46044 41159plusmn12902 37239plusmn27864 47924plusmn128201500 76422plusmn14534 42665plusmn45442 36504plusmn19134 48023plusmn162601750 76038plusmn5328 36778plusmn43280 23134plusmn14506 42119plusmn134802000 77272plusmn23380 22735plusmn27700 39590plusmn7578 30254plusmn161022250 73014plusmn19526 47414plusmn38834 42094plusmn14534 45706plusmn111322500 75154plusmn33076 44930plusmn30546 43432plusmn10366 41823plusmn67182750 70583plusmn10536 36824plusmn43588 45395plusmn29766 41752plusmn142163000 70721plusmn9954 52850plusmn23208 47465plusmn31962 34445plusmn232063250 73558plusmn22002 36969plusmn30768 54583plusmn13252 27997plusmn241803500 65840plusmn13386 43234plusmn28390 57026plusmn37038 16880plusmn125543750 64727plusmn25580 38552plusmn28978 69721plusmn38238 16070plusmn145024000 65531plusmn22600 51139plusmn35480 54157plusmn29638 16375plusmn8452

Matrix mean values and standard deviations (CM) Conus Mediterraneus (PJ) Pecten Jacobeus (VV) Venus Verrucosa (PN) Pinna Nobilis

020406080

100120140160180

(a)

0 500 1000 1500 2000 2500 3000 3500 4000

Indentation depth [nm]

You

ngprimes

mod

ulus

[G

Pa]

CM PJ VV PN CM PJ VV PN

(b) CM PJ VV PN CM PJ VV PN

05

101520253035404550

0 500 1000 1500 2000 2500 3000 3500 4000

Indentation depth [nm]

You

ngprimes

mod

ulus

[G

Pa]

(c) CM PJ VV PN CM PJ VV PN

You

ngprimes

mod

ulus

[G

Pa]

0102030405060708090

100

0 500 1000 1500 2000 2500 3000 3500 4000

Indentation depth [nm]

Fig 6 Continued

(d) CM PJ VV PN CM PJ VV PN

You

ngprimes

mod

ulus

[G

Pa]

Indentation depth [nm]

01020304050607080

0 500 1000 1500 2000 2500 3000 3500 4000

(e) CM PJ VV PN CM PJ VV PN

You

ngprimes

mod

ulus

[G

Pa]

Indentation depth [nm]

0102030405060708090

0 500 1000 1500 2000 2500 3000 3500 4000

Fig 6 (a) Results obtained for Youngrsquos modulus regarding tests per-formed on the inner surface of the four shells (b) Results obtained forYoungrsquos modulus regarding tests performed on the cross section innerzone of the four shells (c) Results obtained for Youngrsquos modulus regard-ing tests performed on the cross section middle zone of the four shells(d) Results obtained for Youngrsquos modulus regarding tests performed onthe cross section outer zone of the four shells (e) Results obtainedfor Youngrsquos modulus regarding tests performed on the outer surface ofthe four shells (CM) Conus Mediterraneus (PJ) Pecten Jacobeus (VV)Venus Verrucosa (PN) Pinna Nobilis

6458 J Nanosci Nanotechnol 10 6453ndash6460 2010

Delivered by Ingenta toRice University Fondren Library

IP 16871277Mon 06 Sep 2010 113147

RESEARCH

ARTIC

LE

Bignardi et al Nanoindentations on Conch Shells

or point on Figures 5 6 represents the average value ofthe indentation matrixThe 3200 tests have been analysed applying an ad hoc

modification of the Weibull Statistics8 ie interpreting thecumulative probability function F of finding zones withnanohardness (Youngrsquos modulus) smaller than HE at anindentation depth h according to

F lt H= 1minus eminushh0nHH0

m

(1)

where H0 is the nominal nanohardness (or E0 is the nom-inal Youngrsquos modulus ie corresponding to F = 63for hh0

n = 1 h0 is a reference indentation depth(eg 1 m) m is the Weibull moduls and nm is the size-effect exponent Classically Weibull Statistics is appliedconsidering H as the material strength h as a characteris-tic size defined as the cubic root of the specimen volume(or square root of the specimen surface) and thus n = 3(or n = 2) for volume (or surface) predominant defectsAlternatively Nanoscale Weibull Statistics9 specificallydeveloped for nearly defect-free structures considersn= 0 Thus we note that our modification proposed inEq (1) describes in addition to the nanohardness (Youngrsquosmodulus) distribution also the indentation size-effect in

Nanohardness perpendicular to the internal surfaces (IS)

y = 57387xndash55553R2 = 0938

ndash4

ndash3

ndash2

ndash1

0

1

2(a)

(b)

03 04 05 06 07 08 09 1 11 12

ln(hh0)

ln(ln

(1(

1ndashF

)))

Nanohardness parallel to the internal surface (CI)

y = 93303x+20516

R2 = 09028

ndash10

ndash8

ndash6

ndash4

ndash2

0

2

4

6

8

ndash3 ndash28 ndash26 ndash24 ndash22 ndash2 ndash18 ndash16 ndash14

ln (hh0)

ln(ln

(1(

1ndashF

)))ndash

3ln

(hh

0)

Fig 7 (a) Statistical data analysis on nanohardness measured on theinner surface of the Conus Mediterraneus shell (n = 0) (b) Statisticaldata analysis on nanohardness measured on the cross section of the innersurface of the Conus Mediterraneus shell (n= 3)

the form of H prop hminusnm (E prop hminusnm Similar results areobtained for the different shells as an example we focusour attention on the Conus meditteraneous conch10 In ourtests a negligible indentation size-effect has been revealedthus suggesting n= 0 for which in fact the highest statisti-cal correlation (coefficient of correlation R2 is found Anexception for the softer anisotropic inner layer is observedfor which we found the maximum statistical correlationfor n = 3 suggesting that the size-effect is governed byvolume-dominated process such as dislocation sliding Infact n = 0 would correspond for the nanohardness dataanalysis to R2n = 0 = 07232 whereas R2n = 1 =08755 R2n= 2= 09020 R2n= 3= 09028 R2n=4 = 08981 thus with a maximum for n = 3 A sim-ilar trend is observed for the Youngrsquos modulus As anexample the Weibull plots for the nanohardness measuredalong the two considered orthogonal directions of the inneranisotropic layer are shown in Figure 7 We note that theproposed modification of the Weibull Statistics is powerfulin treating nanoindentation experimentsOur analysis supports the idea that super-composites or

super-armors could be realized in the near future mimick-ing nacre11 with anisotropic and hierarchical architecturescomposed by hard surfaces and tough volumes in order toincrease the material fracture toughness12ndash16

4 DISCUSSION AND CONCLUSIONS

We have performed 3200 nanoindentations on four dif-ferent representative types of conch shells belonging tothe two biggest classes of molluscs Gastropoda andBivalvia in order to compare nanohardness and Youngrsquosmodulus with respect to their microstructural anisotropicarchitecture The following considerations can be drawn(i) a strong anisotropy of the inner layer is present inall the four investigated shells nanohardness and Youngrsquosmodulus increase by one order of magnitude from thecross-section to the surface(ii) nanohardness and Youngrsquos modulus grow from theinner to the outer side for the Gastropoda Conus mediter-raneus and Bivalvia Pinna nobilis shells but an oppositetrend is found for the Pecten jacobeus and Venus verru-cosa Bivalvia shells(iii) no sensible difference has been observed as regardsto the nanoindentation depth with the exception of thesofter inner anisotropic layer of the Gastropoda Conusmediterraneus for which we have statistically deduced avolume-dominated dislocation sliding This suggests a nat-ural evolution against external attacks from outside forthe first two shells or during the ldquoopenrdquo critical phase forthe last two Bivalvia shells

Acknowledgments Nicola M Pugno acknowl-edges the financial support from the Piemonte

J Nanosci Nanotechnol 10 6453ndash6460 2010 6459

Delivered by Ingenta toRice University Fondren Library

IP 16871277Mon 06 Sep 2010 113147

RESEARCH

ARTIC

LE

Nanoindentations on Conch Shells Bignardi et al

Region ldquoConverging Technologiesrdquo BiotechnologyndashNanotechnology METREGEN 2008 ldquoMetrology ona cellular and macromolecular scale for regenerativemedicinerdquo

References and Notes

1 S Kamat H Kessler R Ballarini M Nassirou and A H HeuerActa Mater 52 2395 (2004)

2 A Y M Lin M A Meyers and K S Vecchio Mater Sci Eng C26 1380 (2006)

3 R Menig M H Meyers M A Meyers and K S Vecchio MaterSci Eng A 297 203 (2001)

4 D F Hou G S Zhou and M Zheng Biomaterials 25 751(2004)

5 C Linnaeligus Systema naturaelig per regna tria naturaelig secundumclasses ordines genera species cum characteribus differentiis

synonymis locis Tomus I Editio Decima Reformata 10th ednHolmiaelig (Stockholm) (Laurentii Salvii) (1758)

6 J G Bruguiegravere and C H Hwass Encyc Meacuteth Hist Nat des Vers2 690 (1792)

7 W C Oliver and G M Pharr J Mater Res 7 1564 (1992)8 W Weibul J Appl Mech 18 293 (1951)9 N Pugno and R Ruoff J Appl Phys 99 024301 (2006)10 C Bignardi M Petraroli and N M Pugno The Nanomechanics

in Italy edited by N M Pugno Research Signpost Kerala India(2007) p 125

11 N Pugno Nanotechnology 17 5480 (2006)12 N Pugno Int J of Fracture 140 159 (2006)13 M Ippolito A Mattoni L Colombo and N Pugno Phys Rev B

73 104111-1 (2006)14 N Pugno B Peng and H D Espinosa Int J of Solids and

Structures 42 647 (2004)15 A Carpinteri and N Pugno Powder Technology 131 93 (2003)16 A Carpinteri F Ciola and N Pugno Computers and Structures

79 389 (2001)

Received 7 July 2009 Accepted 22 September 2009

6460 J Nanosci Nanotechnol 10 6453ndash6460 2010

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IP 16871277Mon 06 Sep 2010 113147

RESEARCH

ARTIC

LE

Nanoindentations on Conch Shells Bignardi et al

Table I(a)ndash(e) Continued

Depth [nm] CM PJ VV PN

2000 3344plusmn0830 1065plusmn1508 2872plusmn1386 0834plusmn07862250 4000plusmn0822 1011plusmn0900 3292plusmn1098 0905plusmn09302500 4257plusmn1084 0612plusmn0772 2945plusmn1072 1079plusmn08122750 3422plusmn1126 1114plusmn0620 3095plusmn1096 0476plusmn03003000 2837plusmn0838 1026plusmn0516 2998plusmn0856 0821plusmn10863250 3846plusmn1288 0818plusmn1266 2224plusmn2254 0015plusmn00263500 3332plusmn1212 0781plusmn1056 1295plusmn1794 0371plusmn05983750 3395plusmn0940 0903plusmn0926 0490plusmn0490 0221plusmn01884000 2893plusmn0442 0366plusmn0402 0497plusmn0448 0200plusmn0152

(e) Outer surface-Nanohardness [GPa]250 4585plusmn3238 1586plusmn3270 1492plusmn2174 3880plusmn0540500 4198plusmn3616 0877plusmn1236 0894plusmn0534 3398plusmn1240750 4471plusmn2134 0362plusmn0560 0783plusmn0612 3669plusmn14781000 4473plusmn2740 0567plusmn0676 0575plusmn0286 2576plusmn14661250 3043plusmn3058 0898plusmn0710 0498plusmn0188 2666plusmn14221500 4485plusmn1770 0707plusmn0972 0492plusmn0228 2938plusmn16241750 4635plusmn0742 0578plusmn1018 0374plusmn0212 2156plusmn11522000 4043plusmn3270 0420plusmn0656 0504plusmn0106 0777plusmn09122250 3926plusmn2394 0745plusmn1170 0472plusmn0204 2334plusmn12222500 3940plusmn3792 0857plusmn0968 0433plusmn0126 2119plusmn06382750 3992plusmn1368 0518plusmn1002 0442plusmn0336 2085plusmn14183000 3652plusmn1678 1592plusmn1590 0646plusmn0674 1671plusmn16203250 4296plusmn2304 0665plusmn0908 1121plusmn0844 1241plusmn14703500 3418plusmn1926 0869plusmn1102 1229plusmn1246 0427plusmn04263750 3334plusmn2788 0592plusmn0812 0658plusmn0646 0533plusmn12544000 3557plusmn2474 1178plusmn1404 0627plusmn0668 0346plusmn0336

Matrix mean values and standard deviations (CM) Conus Mediterraneus (PJ) Pecten Jacobeus (VV) Venus Verrucosa (PN) Pinna Nobilis

01234567

(a)

0 500 1000 1500 2000 2500 3000 3500 4000

Indentation depth [nm]

Nan

ohar

dnes

s [G

Pa] CM PJ VV PN

CM PJ VV PN

(c)

Nan

ohar

dnes

s [G

Pa]

005

115

225

335

445

0 500 1000 1500 2000 2500 3000 3500 4000

Indentation depth [nm]

CM PJ VV PN CM PJ VV PN

(b)

002040608

1121416

0 500 1000 1500 2000 2500 3000 3500 4000

Indentation depth [nm]

CM PJ VV PN CM PJ VV PN

Nan

ohar

dnes

s [G

Pa]

Fig 5 Continued

(d) CM PJ VV PN CM PJ VV PN

005

115

225

335

445

0 500 1000 1500 2000 2500 3000 3500 4000

Indentation depth [nm]

(e)CM PJ VV PN CM PJ VV PN

005

115

225

335

445

5

0 500 1000 1500 2000 2500 3000 3500 4000

Indentation depth [nm]

Nan

ohar

dnes

s [G

Pa]

Nan

ohar

dnes

s [G

Pa]

Fig 5 (a) Results obtained for nanohardness regarding tests performedon the inner surface of the four shells (b) Results obtained for nanohard-ness regarding tests performed on the cross section inner zone of the fourshells (c) Results obtained for nanohardness regarding tests performedon the cross section middle zone of the four shells (d) Results obtainedfor nanohardness regarding tests performed on the cross section outerzone of the four shells (e) Results obtained for nanohardness regard-ing tests performed on the outer surface of the four shells (CM) ConusMediterraneus (PJ) Pecten Jacobeus (VV) Venus Verrucosa (PN) PinnaNobilis

6456 J Nanosci Nanotechnol 10 6453ndash6460 2010

Delivered by Ingenta toRice University Fondren Library

IP 16871277Mon 06 Sep 2010 113147

RESEARCH

ARTIC

LE

Bignardi et al Nanoindentations on Conch Shells

Table II(a)ndash(e) (a) Youngrsquos modulus measurements on the inner surface (b) Youngrsquos modulus measurements on the cross section inner zone(c) Youngrsquos modulus measurements on the cross section middle zone (d) Youngrsquos modulus measurements on the cross section outer zone (e) Youngrsquosmodulus measurements on the outer surface

Depth [nm] CM PJ VV PN

(a) Inner surfacendashYoungrsquos modulus [GPa]250 81279plusmn17816 158140plusmn41988 76077plusmn46928 43722plusmn25560500 74370plusmn18576 63099plusmn32914 102189plusmn47702 51170plusmn22662750 72426plusmn10712 70070plusmn29798 83247plusmn38488 49904plusmn272481000 68667plusmn7910 68301plusmn24380 74024plusmn18026 44490plusmn130961250 70714plusmn6768 54039plusmn43578 74393plusmn21308 42212plusmn81141500 52981plusmn32346 75782plusmn8228 76652plusmn23400 37870plusmn110721750 49288plusmn29130 70110plusmn36068 76038plusmn21730 37314plusmn78242000 63450plusmn2448 73509plusmn6724 88814plusmn19330 38703plusmn53522250 52015plusmn34358 71831plusmn9854 85201plusmn20594 37627plusmn44862500 59701plusmn5894 69745plusmn6844 84908plusmn19012 36027plusmn48142750 56869plusmn13532 51203plusmn34800 73265plusmn34562 36980plusmn82943000 55101plusmn12122 45240plusmn29758 79923plusmn18584 38371plusmn48003250 60612plusmn12366 54518plusmn25204 76997plusmn10844 37617plusmn45123500 54667plusmn13148 57345plusmn27006 76154plusmn17686 38309plusmn35143750 55266plusmn12908 63713plusmn6658 73751plusmn39782 39307plusmn39224000 60041plusmn8536 62636plusmn11576 73211plusmn11726 41351plusmn4806

(b) Cross section inner zonendashYoungrsquos modulus [GPa]250 1148plusmn0370 36575plusmn40406 4984plusmn3260 1130plusmn2282500 0811plusmn0168 42990plusmn38016 4741plusmn1862 26457plusmn38744750 0616plusmn0136 40620plusmn39684 4608plusmn1456 19404plusmn256561000 0553plusmn0208 34607plusmn19128 4315plusmn1474 26832plusmn177261250 0461plusmn0070 39035plusmn11178 4717plusmn1464 27574plusmn83401500 0352plusmn0084 39460plusmn14116 4629plusmn0946 23686plusmn228841750 0377plusmn0054 41777plusmn13302 4816plusmn0982 24590plusmn174362000 0325plusmn0086 36470plusmn12830 5445plusmn3578 23728plusmn160822250 0309plusmn0050 32501plusmn3210 4231plusmn0766 30475plusmn104982500 0288plusmn0092 34194plusmn4866 4440plusmn0956 40052plusmn128742750 0260plusmn0076 33637plusmn4934 4649plusmn0972 42492plusmn114903000 0240plusmn0060 32064plusmn8040 4519plusmn0748 47624plusmn104223250 0235plusmn0066 30021plusmn9272 11864plusmn20064 44846plusmn105203500 0235plusmn0052 33249plusmn19940 4266plusmn0426 36853plusmn220023750 0222plusmn0058 30588plusmn12498 4424plusmn0612 41776plusmn152504000 0212plusmn0042 29249plusmn8166 4118plusmn0662 39905plusmn10018

(c) Cross section middle zonendashYoungrsquos modulus [GPa]250 71655plusmn48894 81889plusmn40584 54291plusmn58910 40942plusmn42484500 71315plusmn27448 78443plusmn28356 76019plusmn22378 36495plusmn45432750 74650plusmn14360 88513plusmn31648 71383plusmn11840 47723plusmn358101000 78856plusmn28222 85835plusmn21426 65405plusmn15322 74669plusmn239281250 73304plusmn20580 83654plusmn16882 53780plusmn11834 70897plusmn282321500 61911plusmn25920 80019plusmn12346 49263plusmn5284 71225plusmn255021750 71338plusmn9928 81225plusmn13060 42051plusmn9480 71729plusmn149442000 71174plusmn22840 77939plusmn11126 46813plusmn7454 75633plusmn151522250 71822plusmn14384 75745plusmn8120 34226plusmn16398 69159plusmn80162500 65045plusmn6768 77914plusmn15054 41678plusmn10780 60981plusmn274922750 69830plusmn13836 73380plusmn6586 42704plusmn6046 61925plusmn97323000 67038plusmn10758 74489plusmn7376 41666plusmn4306 56636plusmn119943250 66316plusmn2820 72934plusmn9862 32498plusmn11618 61709plusmn160063500 63516plusmn6200 67930plusmn5954 35910plusmn7720 57928plusmn106703750 62770plusmn6102 72175plusmn10096 38138plusmn5982 52967plusmn151384000 62323plusmn8710 70002plusmn8232 36956plusmn5812 53883plusmn10218

(d) Cross section outer zonendashYoungrsquos modulus [GPa]250 67321plusmn32026 5135plusmn1982 71345plusmn26300 29613plusmn33994500 64372plusmn40712 28634plusmn35434 67633plusmn16862 45177plusmn30642750 66923plusmn27956 45858plusmn7546 61235plusmn15370 19371plusmn128221000 72572plusmn18380 47969plusmn19354 56635plusmn9426 20492plusmn377941250 56387plusmn27206 36296plusmn20492 53308plusmn4172 46354plusmn339141500 69231plusmn15104 38056plusmn11456 48775plusmn1900 43150plusmn358961750 68175plusmn28194 25664plusmn16456 43905plusmn6624 33701plusmn248022000 70863plusmn10676 23729plusmn15744 60831plusmn7902 41386plusmn20218

Continued

J Nanosci Nanotechnol 10 6453ndash6460 2010 6457

Delivered by Ingenta toRice University Fondren Library

IP 16871277Mon 06 Sep 2010 113147

RESEARCH

ARTIC

LE

Nanoindentations on Conch Shells Bignardi et al

Table II(a)ndash(e) Continued

Depth [nm] CM PJ VV PN

2250 67929plusmn6502 25842plusmn14930 40776plusmn5028 46703plusmn220282500 69148plusmn8270 21603plusmn21340 38759plusmn3532 50566plusmn188562750 60788plusmn6416 38125plusmn12594 36877plusmn3832 34328plusmn177243000 62926plusmn9312 37966plusmn12296 34495plusmn2750 42746plusmn360603250 58085plusmn8288 27762plusmn31224 28957plusmn11436 0634plusmn12283500 54617plusmn9722 22801plusmn24670 24200plusmn9742 28779plusmn200263750 52964plusmn7564 27527plusmn22962 17267plusmn5692 15918plusmn285864000 62467plusmn4316 16159plusmn24342 16020plusmn7052 15395plusmn15930

(e) Outer surfacendashYoungrsquos modulus [GPa]250 83946plusmn36172 34904plusmn33518 26146plusmn12810 58133plusmn8366500 75668plusmn28860 29083plusmn32668 30066plusmn21320 50565plusmn15452750 80058plusmn15162 21090plusmn32514 53334plusmn37128 53672plusmn102601000 79559plusmn20274 29378plusmn42356 50011plusmn25766 45708plusmn116021250 74599plusmn46044 41159plusmn12902 37239plusmn27864 47924plusmn128201500 76422plusmn14534 42665plusmn45442 36504plusmn19134 48023plusmn162601750 76038plusmn5328 36778plusmn43280 23134plusmn14506 42119plusmn134802000 77272plusmn23380 22735plusmn27700 39590plusmn7578 30254plusmn161022250 73014plusmn19526 47414plusmn38834 42094plusmn14534 45706plusmn111322500 75154plusmn33076 44930plusmn30546 43432plusmn10366 41823plusmn67182750 70583plusmn10536 36824plusmn43588 45395plusmn29766 41752plusmn142163000 70721plusmn9954 52850plusmn23208 47465plusmn31962 34445plusmn232063250 73558plusmn22002 36969plusmn30768 54583plusmn13252 27997plusmn241803500 65840plusmn13386 43234plusmn28390 57026plusmn37038 16880plusmn125543750 64727plusmn25580 38552plusmn28978 69721plusmn38238 16070plusmn145024000 65531plusmn22600 51139plusmn35480 54157plusmn29638 16375plusmn8452

Matrix mean values and standard deviations (CM) Conus Mediterraneus (PJ) Pecten Jacobeus (VV) Venus Verrucosa (PN) Pinna Nobilis

020406080

100120140160180

(a)

0 500 1000 1500 2000 2500 3000 3500 4000

Indentation depth [nm]

You

ngprimes

mod

ulus

[G

Pa]

CM PJ VV PN CM PJ VV PN

(b) CM PJ VV PN CM PJ VV PN

05

101520253035404550

0 500 1000 1500 2000 2500 3000 3500 4000

Indentation depth [nm]

You

ngprimes

mod

ulus

[G

Pa]

(c) CM PJ VV PN CM PJ VV PN

You

ngprimes

mod

ulus

[G

Pa]

0102030405060708090

100

0 500 1000 1500 2000 2500 3000 3500 4000

Indentation depth [nm]

Fig 6 Continued

(d) CM PJ VV PN CM PJ VV PN

You

ngprimes

mod

ulus

[G

Pa]

Indentation depth [nm]

01020304050607080

0 500 1000 1500 2000 2500 3000 3500 4000

(e) CM PJ VV PN CM PJ VV PN

You

ngprimes

mod

ulus

[G

Pa]

Indentation depth [nm]

0102030405060708090

0 500 1000 1500 2000 2500 3000 3500 4000

Fig 6 (a) Results obtained for Youngrsquos modulus regarding tests per-formed on the inner surface of the four shells (b) Results obtained forYoungrsquos modulus regarding tests performed on the cross section innerzone of the four shells (c) Results obtained for Youngrsquos modulus regard-ing tests performed on the cross section middle zone of the four shells(d) Results obtained for Youngrsquos modulus regarding tests performed onthe cross section outer zone of the four shells (e) Results obtainedfor Youngrsquos modulus regarding tests performed on the outer surface ofthe four shells (CM) Conus Mediterraneus (PJ) Pecten Jacobeus (VV)Venus Verrucosa (PN) Pinna Nobilis

6458 J Nanosci Nanotechnol 10 6453ndash6460 2010

Delivered by Ingenta toRice University Fondren Library

IP 16871277Mon 06 Sep 2010 113147

RESEARCH

ARTIC

LE

Bignardi et al Nanoindentations on Conch Shells

or point on Figures 5 6 represents the average value ofthe indentation matrixThe 3200 tests have been analysed applying an ad hoc

modification of the Weibull Statistics8 ie interpreting thecumulative probability function F of finding zones withnanohardness (Youngrsquos modulus) smaller than HE at anindentation depth h according to

F lt H= 1minus eminushh0nHH0

m

(1)

where H0 is the nominal nanohardness (or E0 is the nom-inal Youngrsquos modulus ie corresponding to F = 63for hh0

n = 1 h0 is a reference indentation depth(eg 1 m) m is the Weibull moduls and nm is the size-effect exponent Classically Weibull Statistics is appliedconsidering H as the material strength h as a characteris-tic size defined as the cubic root of the specimen volume(or square root of the specimen surface) and thus n = 3(or n = 2) for volume (or surface) predominant defectsAlternatively Nanoscale Weibull Statistics9 specificallydeveloped for nearly defect-free structures considersn= 0 Thus we note that our modification proposed inEq (1) describes in addition to the nanohardness (Youngrsquosmodulus) distribution also the indentation size-effect in

Nanohardness perpendicular to the internal surfaces (IS)

y = 57387xndash55553R2 = 0938

ndash4

ndash3

ndash2

ndash1

0

1

2(a)

(b)

03 04 05 06 07 08 09 1 11 12

ln(hh0)

ln(ln

(1(

1ndashF

)))

Nanohardness parallel to the internal surface (CI)

y = 93303x+20516

R2 = 09028

ndash10

ndash8

ndash6

ndash4

ndash2

0

2

4

6

8

ndash3 ndash28 ndash26 ndash24 ndash22 ndash2 ndash18 ndash16 ndash14

ln (hh0)

ln(ln

(1(

1ndashF

)))ndash

3ln

(hh

0)

Fig 7 (a) Statistical data analysis on nanohardness measured on theinner surface of the Conus Mediterraneus shell (n = 0) (b) Statisticaldata analysis on nanohardness measured on the cross section of the innersurface of the Conus Mediterraneus shell (n= 3)

the form of H prop hminusnm (E prop hminusnm Similar results areobtained for the different shells as an example we focusour attention on the Conus meditteraneous conch10 In ourtests a negligible indentation size-effect has been revealedthus suggesting n= 0 for which in fact the highest statisti-cal correlation (coefficient of correlation R2 is found Anexception for the softer anisotropic inner layer is observedfor which we found the maximum statistical correlationfor n = 3 suggesting that the size-effect is governed byvolume-dominated process such as dislocation sliding Infact n = 0 would correspond for the nanohardness dataanalysis to R2n = 0 = 07232 whereas R2n = 1 =08755 R2n= 2= 09020 R2n= 3= 09028 R2n=4 = 08981 thus with a maximum for n = 3 A sim-ilar trend is observed for the Youngrsquos modulus As anexample the Weibull plots for the nanohardness measuredalong the two considered orthogonal directions of the inneranisotropic layer are shown in Figure 7 We note that theproposed modification of the Weibull Statistics is powerfulin treating nanoindentation experimentsOur analysis supports the idea that super-composites or

super-armors could be realized in the near future mimick-ing nacre11 with anisotropic and hierarchical architecturescomposed by hard surfaces and tough volumes in order toincrease the material fracture toughness12ndash16

4 DISCUSSION AND CONCLUSIONS

We have performed 3200 nanoindentations on four dif-ferent representative types of conch shells belonging tothe two biggest classes of molluscs Gastropoda andBivalvia in order to compare nanohardness and Youngrsquosmodulus with respect to their microstructural anisotropicarchitecture The following considerations can be drawn(i) a strong anisotropy of the inner layer is present inall the four investigated shells nanohardness and Youngrsquosmodulus increase by one order of magnitude from thecross-section to the surface(ii) nanohardness and Youngrsquos modulus grow from theinner to the outer side for the Gastropoda Conus mediter-raneus and Bivalvia Pinna nobilis shells but an oppositetrend is found for the Pecten jacobeus and Venus verru-cosa Bivalvia shells(iii) no sensible difference has been observed as regardsto the nanoindentation depth with the exception of thesofter inner anisotropic layer of the Gastropoda Conusmediterraneus for which we have statistically deduced avolume-dominated dislocation sliding This suggests a nat-ural evolution against external attacks from outside forthe first two shells or during the ldquoopenrdquo critical phase forthe last two Bivalvia shells

Acknowledgments Nicola M Pugno acknowl-edges the financial support from the Piemonte

J Nanosci Nanotechnol 10 6453ndash6460 2010 6459

Delivered by Ingenta toRice University Fondren Library

IP 16871277Mon 06 Sep 2010 113147

RESEARCH

ARTIC

LE

Nanoindentations on Conch Shells Bignardi et al

Region ldquoConverging Technologiesrdquo BiotechnologyndashNanotechnology METREGEN 2008 ldquoMetrology ona cellular and macromolecular scale for regenerativemedicinerdquo

References and Notes

1 S Kamat H Kessler R Ballarini M Nassirou and A H HeuerActa Mater 52 2395 (2004)

2 A Y M Lin M A Meyers and K S Vecchio Mater Sci Eng C26 1380 (2006)

3 R Menig M H Meyers M A Meyers and K S Vecchio MaterSci Eng A 297 203 (2001)

4 D F Hou G S Zhou and M Zheng Biomaterials 25 751(2004)

5 C Linnaeligus Systema naturaelig per regna tria naturaelig secundumclasses ordines genera species cum characteribus differentiis

synonymis locis Tomus I Editio Decima Reformata 10th ednHolmiaelig (Stockholm) (Laurentii Salvii) (1758)

6 J G Bruguiegravere and C H Hwass Encyc Meacuteth Hist Nat des Vers2 690 (1792)

7 W C Oliver and G M Pharr J Mater Res 7 1564 (1992)8 W Weibul J Appl Mech 18 293 (1951)9 N Pugno and R Ruoff J Appl Phys 99 024301 (2006)10 C Bignardi M Petraroli and N M Pugno The Nanomechanics

in Italy edited by N M Pugno Research Signpost Kerala India(2007) p 125

11 N Pugno Nanotechnology 17 5480 (2006)12 N Pugno Int J of Fracture 140 159 (2006)13 M Ippolito A Mattoni L Colombo and N Pugno Phys Rev B

73 104111-1 (2006)14 N Pugno B Peng and H D Espinosa Int J of Solids and

Structures 42 647 (2004)15 A Carpinteri and N Pugno Powder Technology 131 93 (2003)16 A Carpinteri F Ciola and N Pugno Computers and Structures

79 389 (2001)

Received 7 July 2009 Accepted 22 September 2009

6460 J Nanosci Nanotechnol 10 6453ndash6460 2010

Delivered by Ingenta toRice University Fondren Library

IP 16871277Mon 06 Sep 2010 113147

RESEARCH

ARTIC

LE

Bignardi et al Nanoindentations on Conch Shells

Table II(a)ndash(e) (a) Youngrsquos modulus measurements on the inner surface (b) Youngrsquos modulus measurements on the cross section inner zone(c) Youngrsquos modulus measurements on the cross section middle zone (d) Youngrsquos modulus measurements on the cross section outer zone (e) Youngrsquosmodulus measurements on the outer surface

Depth [nm] CM PJ VV PN

(a) Inner surfacendashYoungrsquos modulus [GPa]250 81279plusmn17816 158140plusmn41988 76077plusmn46928 43722plusmn25560500 74370plusmn18576 63099plusmn32914 102189plusmn47702 51170plusmn22662750 72426plusmn10712 70070plusmn29798 83247plusmn38488 49904plusmn272481000 68667plusmn7910 68301plusmn24380 74024plusmn18026 44490plusmn130961250 70714plusmn6768 54039plusmn43578 74393plusmn21308 42212plusmn81141500 52981plusmn32346 75782plusmn8228 76652plusmn23400 37870plusmn110721750 49288plusmn29130 70110plusmn36068 76038plusmn21730 37314plusmn78242000 63450plusmn2448 73509plusmn6724 88814plusmn19330 38703plusmn53522250 52015plusmn34358 71831plusmn9854 85201plusmn20594 37627plusmn44862500 59701plusmn5894 69745plusmn6844 84908plusmn19012 36027plusmn48142750 56869plusmn13532 51203plusmn34800 73265plusmn34562 36980plusmn82943000 55101plusmn12122 45240plusmn29758 79923plusmn18584 38371plusmn48003250 60612plusmn12366 54518plusmn25204 76997plusmn10844 37617plusmn45123500 54667plusmn13148 57345plusmn27006 76154plusmn17686 38309plusmn35143750 55266plusmn12908 63713plusmn6658 73751plusmn39782 39307plusmn39224000 60041plusmn8536 62636plusmn11576 73211plusmn11726 41351plusmn4806

(b) Cross section inner zonendashYoungrsquos modulus [GPa]250 1148plusmn0370 36575plusmn40406 4984plusmn3260 1130plusmn2282500 0811plusmn0168 42990plusmn38016 4741plusmn1862 26457plusmn38744750 0616plusmn0136 40620plusmn39684 4608plusmn1456 19404plusmn256561000 0553plusmn0208 34607plusmn19128 4315plusmn1474 26832plusmn177261250 0461plusmn0070 39035plusmn11178 4717plusmn1464 27574plusmn83401500 0352plusmn0084 39460plusmn14116 4629plusmn0946 23686plusmn228841750 0377plusmn0054 41777plusmn13302 4816plusmn0982 24590plusmn174362000 0325plusmn0086 36470plusmn12830 5445plusmn3578 23728plusmn160822250 0309plusmn0050 32501plusmn3210 4231plusmn0766 30475plusmn104982500 0288plusmn0092 34194plusmn4866 4440plusmn0956 40052plusmn128742750 0260plusmn0076 33637plusmn4934 4649plusmn0972 42492plusmn114903000 0240plusmn0060 32064plusmn8040 4519plusmn0748 47624plusmn104223250 0235plusmn0066 30021plusmn9272 11864plusmn20064 44846plusmn105203500 0235plusmn0052 33249plusmn19940 4266plusmn0426 36853plusmn220023750 0222plusmn0058 30588plusmn12498 4424plusmn0612 41776plusmn152504000 0212plusmn0042 29249plusmn8166 4118plusmn0662 39905plusmn10018

(c) Cross section middle zonendashYoungrsquos modulus [GPa]250 71655plusmn48894 81889plusmn40584 54291plusmn58910 40942plusmn42484500 71315plusmn27448 78443plusmn28356 76019plusmn22378 36495plusmn45432750 74650plusmn14360 88513plusmn31648 71383plusmn11840 47723plusmn358101000 78856plusmn28222 85835plusmn21426 65405plusmn15322 74669plusmn239281250 73304plusmn20580 83654plusmn16882 53780plusmn11834 70897plusmn282321500 61911plusmn25920 80019plusmn12346 49263plusmn5284 71225plusmn255021750 71338plusmn9928 81225plusmn13060 42051plusmn9480 71729plusmn149442000 71174plusmn22840 77939plusmn11126 46813plusmn7454 75633plusmn151522250 71822plusmn14384 75745plusmn8120 34226plusmn16398 69159plusmn80162500 65045plusmn6768 77914plusmn15054 41678plusmn10780 60981plusmn274922750 69830plusmn13836 73380plusmn6586 42704plusmn6046 61925plusmn97323000 67038plusmn10758 74489plusmn7376 41666plusmn4306 56636plusmn119943250 66316plusmn2820 72934plusmn9862 32498plusmn11618 61709plusmn160063500 63516plusmn6200 67930plusmn5954 35910plusmn7720 57928plusmn106703750 62770plusmn6102 72175plusmn10096 38138plusmn5982 52967plusmn151384000 62323plusmn8710 70002plusmn8232 36956plusmn5812 53883plusmn10218

(d) Cross section outer zonendashYoungrsquos modulus [GPa]250 67321plusmn32026 5135plusmn1982 71345plusmn26300 29613plusmn33994500 64372plusmn40712 28634plusmn35434 67633plusmn16862 45177plusmn30642750 66923plusmn27956 45858plusmn7546 61235plusmn15370 19371plusmn128221000 72572plusmn18380 47969plusmn19354 56635plusmn9426 20492plusmn377941250 56387plusmn27206 36296plusmn20492 53308plusmn4172 46354plusmn339141500 69231plusmn15104 38056plusmn11456 48775plusmn1900 43150plusmn358961750 68175plusmn28194 25664plusmn16456 43905plusmn6624 33701plusmn248022000 70863plusmn10676 23729plusmn15744 60831plusmn7902 41386plusmn20218

Continued

J Nanosci Nanotechnol 10 6453ndash6460 2010 6457

Delivered by Ingenta toRice University Fondren Library

IP 16871277Mon 06 Sep 2010 113147

RESEARCH

ARTIC

LE

Nanoindentations on Conch Shells Bignardi et al

Table II(a)ndash(e) Continued

Depth [nm] CM PJ VV PN

2250 67929plusmn6502 25842plusmn14930 40776plusmn5028 46703plusmn220282500 69148plusmn8270 21603plusmn21340 38759plusmn3532 50566plusmn188562750 60788plusmn6416 38125plusmn12594 36877plusmn3832 34328plusmn177243000 62926plusmn9312 37966plusmn12296 34495plusmn2750 42746plusmn360603250 58085plusmn8288 27762plusmn31224 28957plusmn11436 0634plusmn12283500 54617plusmn9722 22801plusmn24670 24200plusmn9742 28779plusmn200263750 52964plusmn7564 27527plusmn22962 17267plusmn5692 15918plusmn285864000 62467plusmn4316 16159plusmn24342 16020plusmn7052 15395plusmn15930

(e) Outer surfacendashYoungrsquos modulus [GPa]250 83946plusmn36172 34904plusmn33518 26146plusmn12810 58133plusmn8366500 75668plusmn28860 29083plusmn32668 30066plusmn21320 50565plusmn15452750 80058plusmn15162 21090plusmn32514 53334plusmn37128 53672plusmn102601000 79559plusmn20274 29378plusmn42356 50011plusmn25766 45708plusmn116021250 74599plusmn46044 41159plusmn12902 37239plusmn27864 47924plusmn128201500 76422plusmn14534 42665plusmn45442 36504plusmn19134 48023plusmn162601750 76038plusmn5328 36778plusmn43280 23134plusmn14506 42119plusmn134802000 77272plusmn23380 22735plusmn27700 39590plusmn7578 30254plusmn161022250 73014plusmn19526 47414plusmn38834 42094plusmn14534 45706plusmn111322500 75154plusmn33076 44930plusmn30546 43432plusmn10366 41823plusmn67182750 70583plusmn10536 36824plusmn43588 45395plusmn29766 41752plusmn142163000 70721plusmn9954 52850plusmn23208 47465plusmn31962 34445plusmn232063250 73558plusmn22002 36969plusmn30768 54583plusmn13252 27997plusmn241803500 65840plusmn13386 43234plusmn28390 57026plusmn37038 16880plusmn125543750 64727plusmn25580 38552plusmn28978 69721plusmn38238 16070plusmn145024000 65531plusmn22600 51139plusmn35480 54157plusmn29638 16375plusmn8452

Matrix mean values and standard deviations (CM) Conus Mediterraneus (PJ) Pecten Jacobeus (VV) Venus Verrucosa (PN) Pinna Nobilis

020406080

100120140160180

(a)

0 500 1000 1500 2000 2500 3000 3500 4000

Indentation depth [nm]

You

ngprimes

mod

ulus

[G

Pa]

CM PJ VV PN CM PJ VV PN

(b) CM PJ VV PN CM PJ VV PN

05

101520253035404550

0 500 1000 1500 2000 2500 3000 3500 4000

Indentation depth [nm]

You

ngprimes

mod

ulus

[G

Pa]

(c) CM PJ VV PN CM PJ VV PN

You

ngprimes

mod

ulus

[G

Pa]

0102030405060708090

100

0 500 1000 1500 2000 2500 3000 3500 4000

Indentation depth [nm]

Fig 6 Continued

(d) CM PJ VV PN CM PJ VV PN

You

ngprimes

mod

ulus

[G

Pa]

Indentation depth [nm]

01020304050607080

0 500 1000 1500 2000 2500 3000 3500 4000

(e) CM PJ VV PN CM PJ VV PN

You

ngprimes

mod

ulus

[G

Pa]

Indentation depth [nm]

0102030405060708090

0 500 1000 1500 2000 2500 3000 3500 4000

Fig 6 (a) Results obtained for Youngrsquos modulus regarding tests per-formed on the inner surface of the four shells (b) Results obtained forYoungrsquos modulus regarding tests performed on the cross section innerzone of the four shells (c) Results obtained for Youngrsquos modulus regard-ing tests performed on the cross section middle zone of the four shells(d) Results obtained for Youngrsquos modulus regarding tests performed onthe cross section outer zone of the four shells (e) Results obtainedfor Youngrsquos modulus regarding tests performed on the outer surface ofthe four shells (CM) Conus Mediterraneus (PJ) Pecten Jacobeus (VV)Venus Verrucosa (PN) Pinna Nobilis

6458 J Nanosci Nanotechnol 10 6453ndash6460 2010

Delivered by Ingenta toRice University Fondren Library

IP 16871277Mon 06 Sep 2010 113147

RESEARCH

ARTIC

LE

Bignardi et al Nanoindentations on Conch Shells

or point on Figures 5 6 represents the average value ofthe indentation matrixThe 3200 tests have been analysed applying an ad hoc

modification of the Weibull Statistics8 ie interpreting thecumulative probability function F of finding zones withnanohardness (Youngrsquos modulus) smaller than HE at anindentation depth h according to

F lt H= 1minus eminushh0nHH0

m

(1)

where H0 is the nominal nanohardness (or E0 is the nom-inal Youngrsquos modulus ie corresponding to F = 63for hh0

n = 1 h0 is a reference indentation depth(eg 1 m) m is the Weibull moduls and nm is the size-effect exponent Classically Weibull Statistics is appliedconsidering H as the material strength h as a characteris-tic size defined as the cubic root of the specimen volume(or square root of the specimen surface) and thus n = 3(or n = 2) for volume (or surface) predominant defectsAlternatively Nanoscale Weibull Statistics9 specificallydeveloped for nearly defect-free structures considersn= 0 Thus we note that our modification proposed inEq (1) describes in addition to the nanohardness (Youngrsquosmodulus) distribution also the indentation size-effect in

Nanohardness perpendicular to the internal surfaces (IS)

y = 57387xndash55553R2 = 0938

ndash4

ndash3

ndash2

ndash1

0

1

2(a)

(b)

03 04 05 06 07 08 09 1 11 12

ln(hh0)

ln(ln

(1(

1ndashF

)))

Nanohardness parallel to the internal surface (CI)

y = 93303x+20516

R2 = 09028

ndash10

ndash8

ndash6

ndash4

ndash2

0

2

4

6

8

ndash3 ndash28 ndash26 ndash24 ndash22 ndash2 ndash18 ndash16 ndash14

ln (hh0)

ln(ln

(1(

1ndashF

)))ndash

3ln

(hh

0)

Fig 7 (a) Statistical data analysis on nanohardness measured on theinner surface of the Conus Mediterraneus shell (n = 0) (b) Statisticaldata analysis on nanohardness measured on the cross section of the innersurface of the Conus Mediterraneus shell (n= 3)

the form of H prop hminusnm (E prop hminusnm Similar results areobtained for the different shells as an example we focusour attention on the Conus meditteraneous conch10 In ourtests a negligible indentation size-effect has been revealedthus suggesting n= 0 for which in fact the highest statisti-cal correlation (coefficient of correlation R2 is found Anexception for the softer anisotropic inner layer is observedfor which we found the maximum statistical correlationfor n = 3 suggesting that the size-effect is governed byvolume-dominated process such as dislocation sliding Infact n = 0 would correspond for the nanohardness dataanalysis to R2n = 0 = 07232 whereas R2n = 1 =08755 R2n= 2= 09020 R2n= 3= 09028 R2n=4 = 08981 thus with a maximum for n = 3 A sim-ilar trend is observed for the Youngrsquos modulus As anexample the Weibull plots for the nanohardness measuredalong the two considered orthogonal directions of the inneranisotropic layer are shown in Figure 7 We note that theproposed modification of the Weibull Statistics is powerfulin treating nanoindentation experimentsOur analysis supports the idea that super-composites or

super-armors could be realized in the near future mimick-ing nacre11 with anisotropic and hierarchical architecturescomposed by hard surfaces and tough volumes in order toincrease the material fracture toughness12ndash16

4 DISCUSSION AND CONCLUSIONS

We have performed 3200 nanoindentations on four dif-ferent representative types of conch shells belonging tothe two biggest classes of molluscs Gastropoda andBivalvia in order to compare nanohardness and Youngrsquosmodulus with respect to their microstructural anisotropicarchitecture The following considerations can be drawn(i) a strong anisotropy of the inner layer is present inall the four investigated shells nanohardness and Youngrsquosmodulus increase by one order of magnitude from thecross-section to the surface(ii) nanohardness and Youngrsquos modulus grow from theinner to the outer side for the Gastropoda Conus mediter-raneus and Bivalvia Pinna nobilis shells but an oppositetrend is found for the Pecten jacobeus and Venus verru-cosa Bivalvia shells(iii) no sensible difference has been observed as regardsto the nanoindentation depth with the exception of thesofter inner anisotropic layer of the Gastropoda Conusmediterraneus for which we have statistically deduced avolume-dominated dislocation sliding This suggests a nat-ural evolution against external attacks from outside forthe first two shells or during the ldquoopenrdquo critical phase forthe last two Bivalvia shells

Acknowledgments Nicola M Pugno acknowl-edges the financial support from the Piemonte

J Nanosci Nanotechnol 10 6453ndash6460 2010 6459

Delivered by Ingenta toRice University Fondren Library

IP 16871277Mon 06 Sep 2010 113147

RESEARCH

ARTIC

LE

Nanoindentations on Conch Shells Bignardi et al

Region ldquoConverging Technologiesrdquo BiotechnologyndashNanotechnology METREGEN 2008 ldquoMetrology ona cellular and macromolecular scale for regenerativemedicinerdquo

References and Notes

1 S Kamat H Kessler R Ballarini M Nassirou and A H HeuerActa Mater 52 2395 (2004)

2 A Y M Lin M A Meyers and K S Vecchio Mater Sci Eng C26 1380 (2006)

3 R Menig M H Meyers M A Meyers and K S Vecchio MaterSci Eng A 297 203 (2001)

4 D F Hou G S Zhou and M Zheng Biomaterials 25 751(2004)

5 C Linnaeligus Systema naturaelig per regna tria naturaelig secundumclasses ordines genera species cum characteribus differentiis

synonymis locis Tomus I Editio Decima Reformata 10th ednHolmiaelig (Stockholm) (Laurentii Salvii) (1758)

6 J G Bruguiegravere and C H Hwass Encyc Meacuteth Hist Nat des Vers2 690 (1792)

7 W C Oliver and G M Pharr J Mater Res 7 1564 (1992)8 W Weibul J Appl Mech 18 293 (1951)9 N Pugno and R Ruoff J Appl Phys 99 024301 (2006)10 C Bignardi M Petraroli and N M Pugno The Nanomechanics

in Italy edited by N M Pugno Research Signpost Kerala India(2007) p 125

11 N Pugno Nanotechnology 17 5480 (2006)12 N Pugno Int J of Fracture 140 159 (2006)13 M Ippolito A Mattoni L Colombo and N Pugno Phys Rev B

73 104111-1 (2006)14 N Pugno B Peng and H D Espinosa Int J of Solids and

Structures 42 647 (2004)15 A Carpinteri and N Pugno Powder Technology 131 93 (2003)16 A Carpinteri F Ciola and N Pugno Computers and Structures

79 389 (2001)

Received 7 July 2009 Accepted 22 September 2009

6460 J Nanosci Nanotechnol 10 6453ndash6460 2010

Delivered by Ingenta toRice University Fondren Library

IP 16871277Mon 06 Sep 2010 113147

RESEARCH

ARTIC

LE

Nanoindentations on Conch Shells Bignardi et al

Table II(a)ndash(e) Continued

Depth [nm] CM PJ VV PN

2250 67929plusmn6502 25842plusmn14930 40776plusmn5028 46703plusmn220282500 69148plusmn8270 21603plusmn21340 38759plusmn3532 50566plusmn188562750 60788plusmn6416 38125plusmn12594 36877plusmn3832 34328plusmn177243000 62926plusmn9312 37966plusmn12296 34495plusmn2750 42746plusmn360603250 58085plusmn8288 27762plusmn31224 28957plusmn11436 0634plusmn12283500 54617plusmn9722 22801plusmn24670 24200plusmn9742 28779plusmn200263750 52964plusmn7564 27527plusmn22962 17267plusmn5692 15918plusmn285864000 62467plusmn4316 16159plusmn24342 16020plusmn7052 15395plusmn15930

(e) Outer surfacendashYoungrsquos modulus [GPa]250 83946plusmn36172 34904plusmn33518 26146plusmn12810 58133plusmn8366500 75668plusmn28860 29083plusmn32668 30066plusmn21320 50565plusmn15452750 80058plusmn15162 21090plusmn32514 53334plusmn37128 53672plusmn102601000 79559plusmn20274 29378plusmn42356 50011plusmn25766 45708plusmn116021250 74599plusmn46044 41159plusmn12902 37239plusmn27864 47924plusmn128201500 76422plusmn14534 42665plusmn45442 36504plusmn19134 48023plusmn162601750 76038plusmn5328 36778plusmn43280 23134plusmn14506 42119plusmn134802000 77272plusmn23380 22735plusmn27700 39590plusmn7578 30254plusmn161022250 73014plusmn19526 47414plusmn38834 42094plusmn14534 45706plusmn111322500 75154plusmn33076 44930plusmn30546 43432plusmn10366 41823plusmn67182750 70583plusmn10536 36824plusmn43588 45395plusmn29766 41752plusmn142163000 70721plusmn9954 52850plusmn23208 47465plusmn31962 34445plusmn232063250 73558plusmn22002 36969plusmn30768 54583plusmn13252 27997plusmn241803500 65840plusmn13386 43234plusmn28390 57026plusmn37038 16880plusmn125543750 64727plusmn25580 38552plusmn28978 69721plusmn38238 16070plusmn145024000 65531plusmn22600 51139plusmn35480 54157plusmn29638 16375plusmn8452

Matrix mean values and standard deviations (CM) Conus Mediterraneus (PJ) Pecten Jacobeus (VV) Venus Verrucosa (PN) Pinna Nobilis

020406080

100120140160180

(a)

0 500 1000 1500 2000 2500 3000 3500 4000

Indentation depth [nm]

You

ngprimes

mod

ulus

[G

Pa]

CM PJ VV PN CM PJ VV PN

(b) CM PJ VV PN CM PJ VV PN

05

101520253035404550

0 500 1000 1500 2000 2500 3000 3500 4000

Indentation depth [nm]

You

ngprimes

mod

ulus

[G

Pa]

(c) CM PJ VV PN CM PJ VV PN

You

ngprimes

mod

ulus

[G

Pa]

0102030405060708090

100

0 500 1000 1500 2000 2500 3000 3500 4000

Indentation depth [nm]

Fig 6 Continued

(d) CM PJ VV PN CM PJ VV PN

You

ngprimes

mod

ulus

[G

Pa]

Indentation depth [nm]

01020304050607080

0 500 1000 1500 2000 2500 3000 3500 4000

(e) CM PJ VV PN CM PJ VV PN

You

ngprimes

mod

ulus

[G

Pa]

Indentation depth [nm]

0102030405060708090

0 500 1000 1500 2000 2500 3000 3500 4000

Fig 6 (a) Results obtained for Youngrsquos modulus regarding tests per-formed on the inner surface of the four shells (b) Results obtained forYoungrsquos modulus regarding tests performed on the cross section innerzone of the four shells (c) Results obtained for Youngrsquos modulus regard-ing tests performed on the cross section middle zone of the four shells(d) Results obtained for Youngrsquos modulus regarding tests performed onthe cross section outer zone of the four shells (e) Results obtainedfor Youngrsquos modulus regarding tests performed on the outer surface ofthe four shells (CM) Conus Mediterraneus (PJ) Pecten Jacobeus (VV)Venus Verrucosa (PN) Pinna Nobilis

6458 J Nanosci Nanotechnol 10 6453ndash6460 2010

Delivered by Ingenta toRice University Fondren Library

IP 16871277Mon 06 Sep 2010 113147

RESEARCH

ARTIC

LE

Bignardi et al Nanoindentations on Conch Shells

or point on Figures 5 6 represents the average value ofthe indentation matrixThe 3200 tests have been analysed applying an ad hoc

modification of the Weibull Statistics8 ie interpreting thecumulative probability function F of finding zones withnanohardness (Youngrsquos modulus) smaller than HE at anindentation depth h according to

F lt H= 1minus eminushh0nHH0

m

(1)

where H0 is the nominal nanohardness (or E0 is the nom-inal Youngrsquos modulus ie corresponding to F = 63for hh0

n = 1 h0 is a reference indentation depth(eg 1 m) m is the Weibull moduls and nm is the size-effect exponent Classically Weibull Statistics is appliedconsidering H as the material strength h as a characteris-tic size defined as the cubic root of the specimen volume(or square root of the specimen surface) and thus n = 3(or n = 2) for volume (or surface) predominant defectsAlternatively Nanoscale Weibull Statistics9 specificallydeveloped for nearly defect-free structures considersn= 0 Thus we note that our modification proposed inEq (1) describes in addition to the nanohardness (Youngrsquosmodulus) distribution also the indentation size-effect in

Nanohardness perpendicular to the internal surfaces (IS)

y = 57387xndash55553R2 = 0938

ndash4

ndash3

ndash2

ndash1

0

1

2(a)

(b)

03 04 05 06 07 08 09 1 11 12

ln(hh0)

ln(ln

(1(

1ndashF

)))

Nanohardness parallel to the internal surface (CI)

y = 93303x+20516

R2 = 09028

ndash10

ndash8

ndash6

ndash4

ndash2

0

2

4

6

8

ndash3 ndash28 ndash26 ndash24 ndash22 ndash2 ndash18 ndash16 ndash14

ln (hh0)

ln(ln

(1(

1ndashF

)))ndash

3ln

(hh

0)

Fig 7 (a) Statistical data analysis on nanohardness measured on theinner surface of the Conus Mediterraneus shell (n = 0) (b) Statisticaldata analysis on nanohardness measured on the cross section of the innersurface of the Conus Mediterraneus shell (n= 3)

the form of H prop hminusnm (E prop hminusnm Similar results areobtained for the different shells as an example we focusour attention on the Conus meditteraneous conch10 In ourtests a negligible indentation size-effect has been revealedthus suggesting n= 0 for which in fact the highest statisti-cal correlation (coefficient of correlation R2 is found Anexception for the softer anisotropic inner layer is observedfor which we found the maximum statistical correlationfor n = 3 suggesting that the size-effect is governed byvolume-dominated process such as dislocation sliding Infact n = 0 would correspond for the nanohardness dataanalysis to R2n = 0 = 07232 whereas R2n = 1 =08755 R2n= 2= 09020 R2n= 3= 09028 R2n=4 = 08981 thus with a maximum for n = 3 A sim-ilar trend is observed for the Youngrsquos modulus As anexample the Weibull plots for the nanohardness measuredalong the two considered orthogonal directions of the inneranisotropic layer are shown in Figure 7 We note that theproposed modification of the Weibull Statistics is powerfulin treating nanoindentation experimentsOur analysis supports the idea that super-composites or

super-armors could be realized in the near future mimick-ing nacre11 with anisotropic and hierarchical architecturescomposed by hard surfaces and tough volumes in order toincrease the material fracture toughness12ndash16

4 DISCUSSION AND CONCLUSIONS

We have performed 3200 nanoindentations on four dif-ferent representative types of conch shells belonging tothe two biggest classes of molluscs Gastropoda andBivalvia in order to compare nanohardness and Youngrsquosmodulus with respect to their microstructural anisotropicarchitecture The following considerations can be drawn(i) a strong anisotropy of the inner layer is present inall the four investigated shells nanohardness and Youngrsquosmodulus increase by one order of magnitude from thecross-section to the surface(ii) nanohardness and Youngrsquos modulus grow from theinner to the outer side for the Gastropoda Conus mediter-raneus and Bivalvia Pinna nobilis shells but an oppositetrend is found for the Pecten jacobeus and Venus verru-cosa Bivalvia shells(iii) no sensible difference has been observed as regardsto the nanoindentation depth with the exception of thesofter inner anisotropic layer of the Gastropoda Conusmediterraneus for which we have statistically deduced avolume-dominated dislocation sliding This suggests a nat-ural evolution against external attacks from outside forthe first two shells or during the ldquoopenrdquo critical phase forthe last two Bivalvia shells

Acknowledgments Nicola M Pugno acknowl-edges the financial support from the Piemonte

J Nanosci Nanotechnol 10 6453ndash6460 2010 6459

Delivered by Ingenta toRice University Fondren Library

IP 16871277Mon 06 Sep 2010 113147

RESEARCH

ARTIC

LE

Nanoindentations on Conch Shells Bignardi et al

Region ldquoConverging Technologiesrdquo BiotechnologyndashNanotechnology METREGEN 2008 ldquoMetrology ona cellular and macromolecular scale for regenerativemedicinerdquo

References and Notes

1 S Kamat H Kessler R Ballarini M Nassirou and A H HeuerActa Mater 52 2395 (2004)

2 A Y M Lin M A Meyers and K S Vecchio Mater Sci Eng C26 1380 (2006)

3 R Menig M H Meyers M A Meyers and K S Vecchio MaterSci Eng A 297 203 (2001)

4 D F Hou G S Zhou and M Zheng Biomaterials 25 751(2004)

5 C Linnaeligus Systema naturaelig per regna tria naturaelig secundumclasses ordines genera species cum characteribus differentiis

synonymis locis Tomus I Editio Decima Reformata 10th ednHolmiaelig (Stockholm) (Laurentii Salvii) (1758)

6 J G Bruguiegravere and C H Hwass Encyc Meacuteth Hist Nat des Vers2 690 (1792)

7 W C Oliver and G M Pharr J Mater Res 7 1564 (1992)8 W Weibul J Appl Mech 18 293 (1951)9 N Pugno and R Ruoff J Appl Phys 99 024301 (2006)10 C Bignardi M Petraroli and N M Pugno The Nanomechanics

in Italy edited by N M Pugno Research Signpost Kerala India(2007) p 125

11 N Pugno Nanotechnology 17 5480 (2006)12 N Pugno Int J of Fracture 140 159 (2006)13 M Ippolito A Mattoni L Colombo and N Pugno Phys Rev B

73 104111-1 (2006)14 N Pugno B Peng and H D Espinosa Int J of Solids and

Structures 42 647 (2004)15 A Carpinteri and N Pugno Powder Technology 131 93 (2003)16 A Carpinteri F Ciola and N Pugno Computers and Structures

79 389 (2001)

Received 7 July 2009 Accepted 22 September 2009

6460 J Nanosci Nanotechnol 10 6453ndash6460 2010

Delivered by Ingenta toRice University Fondren Library

IP 16871277Mon 06 Sep 2010 113147

RESEARCH

ARTIC

LE

Bignardi et al Nanoindentations on Conch Shells

or point on Figures 5 6 represents the average value ofthe indentation matrixThe 3200 tests have been analysed applying an ad hoc

modification of the Weibull Statistics8 ie interpreting thecumulative probability function F of finding zones withnanohardness (Youngrsquos modulus) smaller than HE at anindentation depth h according to

F lt H= 1minus eminushh0nHH0

m

(1)

where H0 is the nominal nanohardness (or E0 is the nom-inal Youngrsquos modulus ie corresponding to F = 63for hh0

n = 1 h0 is a reference indentation depth(eg 1 m) m is the Weibull moduls and nm is the size-effect exponent Classically Weibull Statistics is appliedconsidering H as the material strength h as a characteris-tic size defined as the cubic root of the specimen volume(or square root of the specimen surface) and thus n = 3(or n = 2) for volume (or surface) predominant defectsAlternatively Nanoscale Weibull Statistics9 specificallydeveloped for nearly defect-free structures considersn= 0 Thus we note that our modification proposed inEq (1) describes in addition to the nanohardness (Youngrsquosmodulus) distribution also the indentation size-effect in

Nanohardness perpendicular to the internal surfaces (IS)

y = 57387xndash55553R2 = 0938

ndash4

ndash3

ndash2

ndash1

0

1

2(a)

(b)

03 04 05 06 07 08 09 1 11 12

ln(hh0)

ln(ln

(1(

1ndashF

)))

Nanohardness parallel to the internal surface (CI)

y = 93303x+20516

R2 = 09028

ndash10

ndash8

ndash6

ndash4

ndash2

0

2

4

6

8

ndash3 ndash28 ndash26 ndash24 ndash22 ndash2 ndash18 ndash16 ndash14

ln (hh0)

ln(ln

(1(

1ndashF

)))ndash

3ln

(hh

0)

Fig 7 (a) Statistical data analysis on nanohardness measured on theinner surface of the Conus Mediterraneus shell (n = 0) (b) Statisticaldata analysis on nanohardness measured on the cross section of the innersurface of the Conus Mediterraneus shell (n= 3)

the form of H prop hminusnm (E prop hminusnm Similar results areobtained for the different shells as an example we focusour attention on the Conus meditteraneous conch10 In ourtests a negligible indentation size-effect has been revealedthus suggesting n= 0 for which in fact the highest statisti-cal correlation (coefficient of correlation R2 is found Anexception for the softer anisotropic inner layer is observedfor which we found the maximum statistical correlationfor n = 3 suggesting that the size-effect is governed byvolume-dominated process such as dislocation sliding Infact n = 0 would correspond for the nanohardness dataanalysis to R2n = 0 = 07232 whereas R2n = 1 =08755 R2n= 2= 09020 R2n= 3= 09028 R2n=4 = 08981 thus with a maximum for n = 3 A sim-ilar trend is observed for the Youngrsquos modulus As anexample the Weibull plots for the nanohardness measuredalong the two considered orthogonal directions of the inneranisotropic layer are shown in Figure 7 We note that theproposed modification of the Weibull Statistics is powerfulin treating nanoindentation experimentsOur analysis supports the idea that super-composites or

super-armors could be realized in the near future mimick-ing nacre11 with anisotropic and hierarchical architecturescomposed by hard surfaces and tough volumes in order toincrease the material fracture toughness12ndash16

4 DISCUSSION AND CONCLUSIONS

We have performed 3200 nanoindentations on four dif-ferent representative types of conch shells belonging tothe two biggest classes of molluscs Gastropoda andBivalvia in order to compare nanohardness and Youngrsquosmodulus with respect to their microstructural anisotropicarchitecture The following considerations can be drawn(i) a strong anisotropy of the inner layer is present inall the four investigated shells nanohardness and Youngrsquosmodulus increase by one order of magnitude from thecross-section to the surface(ii) nanohardness and Youngrsquos modulus grow from theinner to the outer side for the Gastropoda Conus mediter-raneus and Bivalvia Pinna nobilis shells but an oppositetrend is found for the Pecten jacobeus and Venus verru-cosa Bivalvia shells(iii) no sensible difference has been observed as regardsto the nanoindentation depth with the exception of thesofter inner anisotropic layer of the Gastropoda Conusmediterraneus for which we have statistically deduced avolume-dominated dislocation sliding This suggests a nat-ural evolution against external attacks from outside forthe first two shells or during the ldquoopenrdquo critical phase forthe last two Bivalvia shells

Acknowledgments Nicola M Pugno acknowl-edges the financial support from the Piemonte

J Nanosci Nanotechnol 10 6453ndash6460 2010 6459

Delivered by Ingenta toRice University Fondren Library

IP 16871277Mon 06 Sep 2010 113147

RESEARCH

ARTIC

LE

Nanoindentations on Conch Shells Bignardi et al

Region ldquoConverging Technologiesrdquo BiotechnologyndashNanotechnology METREGEN 2008 ldquoMetrology ona cellular and macromolecular scale for regenerativemedicinerdquo

References and Notes

1 S Kamat H Kessler R Ballarini M Nassirou and A H HeuerActa Mater 52 2395 (2004)

2 A Y M Lin M A Meyers and K S Vecchio Mater Sci Eng C26 1380 (2006)

3 R Menig M H Meyers M A Meyers and K S Vecchio MaterSci Eng A 297 203 (2001)

4 D F Hou G S Zhou and M Zheng Biomaterials 25 751(2004)

5 C Linnaeligus Systema naturaelig per regna tria naturaelig secundumclasses ordines genera species cum characteribus differentiis

synonymis locis Tomus I Editio Decima Reformata 10th ednHolmiaelig (Stockholm) (Laurentii Salvii) (1758)

6 J G Bruguiegravere and C H Hwass Encyc Meacuteth Hist Nat des Vers2 690 (1792)

7 W C Oliver and G M Pharr J Mater Res 7 1564 (1992)8 W Weibul J Appl Mech 18 293 (1951)9 N Pugno and R Ruoff J Appl Phys 99 024301 (2006)10 C Bignardi M Petraroli and N M Pugno The Nanomechanics

in Italy edited by N M Pugno Research Signpost Kerala India(2007) p 125

11 N Pugno Nanotechnology 17 5480 (2006)12 N Pugno Int J of Fracture 140 159 (2006)13 M Ippolito A Mattoni L Colombo and N Pugno Phys Rev B

73 104111-1 (2006)14 N Pugno B Peng and H D Espinosa Int J of Solids and

Structures 42 647 (2004)15 A Carpinteri and N Pugno Powder Technology 131 93 (2003)16 A Carpinteri F Ciola and N Pugno Computers and Structures

79 389 (2001)

Received 7 July 2009 Accepted 22 September 2009

6460 J Nanosci Nanotechnol 10 6453ndash6460 2010

Delivered by Ingenta toRice University Fondren Library

IP 16871277Mon 06 Sep 2010 113147

RESEARCH

ARTIC

LE

Nanoindentations on Conch Shells Bignardi et al

Region ldquoConverging Technologiesrdquo BiotechnologyndashNanotechnology METREGEN 2008 ldquoMetrology ona cellular and macromolecular scale for regenerativemedicinerdquo

References and Notes

1 S Kamat H Kessler R Ballarini M Nassirou and A H HeuerActa Mater 52 2395 (2004)

2 A Y M Lin M A Meyers and K S Vecchio Mater Sci Eng C26 1380 (2006)

3 R Menig M H Meyers M A Meyers and K S Vecchio MaterSci Eng A 297 203 (2001)

4 D F Hou G S Zhou and M Zheng Biomaterials 25 751(2004)

5 C Linnaeligus Systema naturaelig per regna tria naturaelig secundumclasses ordines genera species cum characteribus differentiis

synonymis locis Tomus I Editio Decima Reformata 10th ednHolmiaelig (Stockholm) (Laurentii Salvii) (1758)

6 J G Bruguiegravere and C H Hwass Encyc Meacuteth Hist Nat des Vers2 690 (1792)

7 W C Oliver and G M Pharr J Mater Res 7 1564 (1992)8 W Weibul J Appl Mech 18 293 (1951)9 N Pugno and R Ruoff J Appl Phys 99 024301 (2006)10 C Bignardi M Petraroli and N M Pugno The Nanomechanics

in Italy edited by N M Pugno Research Signpost Kerala India(2007) p 125

11 N Pugno Nanotechnology 17 5480 (2006)12 N Pugno Int J of Fracture 140 159 (2006)13 M Ippolito A Mattoni L Colombo and N Pugno Phys Rev B

73 104111-1 (2006)14 N Pugno B Peng and H D Espinosa Int J of Solids and

Structures 42 647 (2004)15 A Carpinteri and N Pugno Powder Technology 131 93 (2003)16 A Carpinteri F Ciola and N Pugno Computers and Structures

79 389 (2001)

Received 7 July 2009 Accepted 22 September 2009

6460 J Nanosci Nanotechnol 10 6453ndash6460 2010