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Delivered by Ingenta toRice University Fondren Library
IP 16871277Mon 06 Sep 2010 113147
RESEARCH
ARTIC
LE
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
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
Delivered by Ingenta toRice University Fondren Library
IP 16871277Mon 06 Sep 2010 113147
RESEARCH
ARTIC
LE
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
6454 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 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
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
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)
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
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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
Delivered by Ingenta toRice University Fondren Library
IP 16871277Mon 06 Sep 2010 113147
RESEARCH
ARTIC
LE
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
6454 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 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
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
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)
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 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
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
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)
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
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
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)
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
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)
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
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)
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)
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