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ReportCite this article: Bonarski JT, Checa AG,

Rodriguez-Navarro A, Tarkowski L, Wajda W.

2015 Irregularities of crystallographic

orientation and residual stresses in the

crossed-lamellar shell as a natural functionally

graded material. J. R. Soc. Interface 12:

20150738.

http://dx.doi.org/10.1098/rsif.2015.0738

Received: 18 August 2015

Accepted: 11 November 2015

Subject Areas:environmental science, biomaterials

Keywords:mollusc shell, crossed-lamellar structures,

crystallographic texture, residual stresses,

functionally graded bio-materials

Author for correspondence:Jan T. Bonarski

e-mail: j.bonarski@imim.pl

& 2015 The Author(s) Published by the Royal Society. All rights reserved.

Irregularities of crystallographicorientation and residual stresses in thecrossed-lamellar shell as a naturalfunctionally graded material

Jan T. Bonarski1, Antonio G. Checa2, Alejandro Rodriguez-Navarro3,Leszek Tarkowski1 and Wojciech Wajda1

1Institute of Metallurgy and Materials Science of the Polish Academy of Sciences, 25 Reymonta Strasse,Krakow 30-059, Poland2Departamento de Estratigrafıa y Paleontologıa, Facultad de Ciencias, Universidad de Granada,Avenida Fuentenueva s/n, Granada, Spain3Departamento de Mineralogıa y Petrologıa, Universidad de Granada, Campus de Fuentenueva, Granada, Spain

The microstructures of different groups of molluscs are characterized by

preferential orientations of crystallites (texture), leading to a significant aniso-

tropy of the physical properties of the shells. A complementary characteristic,

usually neglected, is the distribution of the residual stresses existing within the

shell wall. By means of X-ray diffraction, we study the distribution of stresses

with thickness in the shell wall of the gastropod Conus marmoreus, which has a

microstructure of the crossed-lamellar type. The results revealed an extraordi-

nary texture inhomogeneity and the existence of tensional residual stresses

along the shell thickness, the origins of which are unknown. Some of the

observed changes in textural parameters and stresses coincide with the tran-

sitions between shell layers, although other features are of unknown origin.

Our results provide insight into the microstructural regularities that govern

the mesoscale construction of shells, such as that of C. marmoreus.

1. IntroductionNatural shells, such as those of the gastropod mollusc Conus marmoreus, are

multi-phase light composites characterized by relatively high mechanical

toughness and hardness at low ductility. The biomechanical parameters pro-

vide suitable bio-resistance to the destructive influences of the environment

and developed during the evolution of these organisms. They constitute effec-

tive solutions from both the material- and structural-engineering viewpoint.

This efficiency is the result of a specific spatial arrangement of both the individ-

ual components (lamellae, fibres and grains) of the calcium carbonate minerals

and the organic components (membranes and interspersed matrix). The three-

dimensional arrangements of crystallites and organic material are limited and

appear recurrently in the different groups of molluscs. These arrangements

are termed microstructures [1]. Microstructures are characterized by preferential

orientations of crystallites (texture), which lead to significant anisotropy of the

physical properties of the shell.

The shells of the genus Conus consist of several layers with crossed-lamellar

microstructure (figure 1a–d). This microstructure is composed of aragonitic

fibres that are rectangular in cross-section, which are called third-order lamellae.

These third-order lamellae are arranged in planes, with the longest dimension of

their cross-section in the plane, thus forming second-order lamellae. Second-

order lamellae, and their constituent third-order lamellae, are arranged into

irregularly shaped parallelepipedic bundles which elongate perpendicular to the

planes of the second-order lamellae and to the shell surfaces. These are called

first-order lamellae. Within each first-order lamella, lower-order lamellae dip at a

high angle to the shell surface, although the dipping angle is opposite in alternating

OL

ML404 µm

424 µm

1496 µm 1598 µm1576 µm 1649 µm

IL

500 µm 200 µm 500 µm 500 µm

2 µm5 µm0.5 µm5 µm

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

(h)(e) ( f ) (g)

Figure 1. Crossed-lamellar microstructure of the shell of the genus Conus. (a) Radial fracture of the shell wall of the C. marmoreus specimen studied. It is composedof a radial OL, a comarginal ML and a radial IL. (b – d ) Close-up views of the outer (b), middle (c) and inner (d ) layers, with some thickness values (taken directlyunder SEM) indicated. (e) The outer shell layer of Conus omaria, showing the different inclination of the second- and third-order lamellae within alternating first-order lamellae. ( f ) Detail of the third-order lamellae and their arrangement into second-order lamellae in C. omaria. (g) The transition between the outer andmiddle layers in Conus striatus, where the first-order lamellae rotate by 908 to become comarginal. (h) Detail of g ( framed area in g) showing the change inorientation of the third-order lamellae.

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first-order lamellae (and identical every two first-order

lamellae). The orientation of the first-order lamellae with respect

to the margin changes by 908 (e.g. from comarginal to

antimarginal) at the transition between shell layers (figure 1).

Despite their general structural similarity, the micro-

structures grouped under the same term (e.g. nacre,

crossed-lamellar), but belonging to different groups of

molluscs, are characterized by different crystallographic tex-

tures (e.g. [2] and references therein). The scanning electron

microscope (SEM)/transmission electron microscope (TEM)

analysis of the crossed-lamellar structures, such as that of the

shell of C. marmoreus, enabled us to identify areas where inten-

sive morphological transformations occur. However, the

texture development in the shell of C. marmoreus has still not

been fully recognized. Rodrıguez-Navarro et al. [3] carried

out an in-depth study of the crystallography of the shell of

this species and formulated a consistent crystallographic

model. Nevertheless, the identification of areas with dominat-

ing specific crystallographic orientations, which are created

during the growth process, is still rather intuitive. Thus, we

might ask what the real range of the most intensive spatial

rearrangements is within the Conus shell and how areas with

specific orientations of lamellae are distributed within the

Conus shell. Seeking to answer the above questions, we ana-

lysed the thickness profile of the evolution of the

crystallographic texture and residual stresses in the shell of

C. marmoreus. Based on experimental data registered by

means of X-ray diffraction, and supported by the SEM obser-

vations, suitable textural and stress characteristics of the

microstructure of the material were identified. The present

work describes the experimental procedures and interpret-

ation of the results, revealing the micro-scale irregularities of

both kinds of characteristics of the aforementioned shell as a

natural functionally graded material (FGM), which is charac-

terized by gradually changing properties. Moreover, the

development of residual stresses related to the shape of the

mollusc shell contributes to the mechanical toughness of its

wall [4]. Our preliminary studies on the shells of the gastropod

C. marmoreus revealed that especially intensive texture and

possible fields of residual stresses can be expected near both

the outer and inner surfaces of the mollusc shell walls. These

microstructure-derived features may be functional in the

living organism [4,5].

2. Material and methodsThe crystallographic texture and residual stresses along the shell

thickness were identified in one specimen of C. marmoreus,purchased from Conchology Inc. The experimental tests were per-

formed by X-ray diffraction (radiation used: CuKa series). First,

a shell strip was cut parallel to the aperture and subsequently sec-

tioned along a plane slightly oblique to the shell surface (figure 2).

We measured 64 circular areas of ca 1.5 mm in diameter, which

were aligned and distributed at a step size of ca 1 mm along this sur-

face (figure 2). However, to eliminate the overlap between the

subareas measured, we finally considered only one of every two

(exactly 32þ 2 additional; inner and outer surface) in the present

analysis. Two additional analyses, i.e. one of the outer and another

of the inner surface, were performed. In this way, the measurements

were densely distributed from the outer to the inner surface. Given

the 4.28 slope of the wedge-shaped sample, the ca 2 mm distances on

the sectioned sample surface correspond to thickness steps of ca200 mm. Assuming a regular and continuous microstructure of the

mollusc shell (assessed by SEM), the above procedure enabled an

analysis of the complete thickness profile of the microstructural

characteristics (i.e. crystallographic texture and residual stresses) in

the shell of C. marmoreus with a high linear resolution.

In the crossed-lamellar material, the amount of organic matter

is relatively small; it accounts for 1.7% of the total shell weight

in the related gastropod genus Murex [6]. Since aragonite is the

only mineral component of the shell examined, the texture/stress

analysis was performed under the assumption of an orthorhombic

outer surface

GD

ND

RD

sample surface withmeasurement areas

1 mm

4.2º

inner surface

25 mm

~200

µm

Figure 2. Scheme of the obliquely sectioned shell strip and related growth (GD), radial (RD) and normal (ND, perpendicular to the shell surface) directions. Thesketch on the right shows the distances between 62 measurement points along the section surface of the sample, although the results presented concern only 31 ofthe 62 subareas. (Online version in colour.)

111

021

innersurface

outersurface

2q angle (˚)

200

100

0

10

80706050403025

002

012

200

+10

2

112

130

132

113

231

inte

nsity

(cp

s)

no.

mea

s. p

oint

Figure 3. Three-dimensional set of selected diffraction patterns registered in the individual measurement areas (located between the outer and inner surfaces of thetilted section of the C. marmoreus shell shown in figure 2). Filtered CuKa radiation used.

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lattice (symmetry: 2/m2/m2/m) and parameters of pure arago-

nite; a0 ¼ 4.9623 A, b0 ¼ 7.9680 A, c0 ¼ 5.7439 A [7]. The X-ray

experiments were made by means of a D8 Discover Bruker diffract-

ometer equipped with an Euler cradle, PolyCap parallel beam

optics and a specially designed sample holder attached to the

x–y–z sample stage (housed at the Institute of Metallurgy and

Materials Science, IMIM, Krakow, Poland).

Crystallographic orientations along the shell thickness were

determined by the quantitative three-dimensional texture analy-

sis based on the incomplete back-reflection pole figures of (111),

(012) and (002) lattice planes registered in each of the 34 analysed

areas. A discrete ADC method [8,9] to calculate the orientation

distribution function (ODF) [10] and the LaboTex package [11]

was applied.

The distribution of the residual stress components sGD and

sRD (in the growth and longitudinal directions, respectively) was

analysed by the sin2c method [12]. The following parameters

were used for the calculations: Young modulus of E ¼ 107 GPa, a

Poisson ratio of n ¼ 0.25, as well as tensor anisotropic elastic con-

stants of Yamamoto et al. [13]: c11¼ 165.2, c21¼ 39.1, c22¼ 73.4,

c31¼ 19.8, c32¼ 24.6, c33¼ 89.2, c44¼ 23.2, c55 ¼ 17.3, c66¼ 24.1

[1010 dyn cm22]. In the stress analysis, we applied a dedicated

Stress package by Baczmanski [14] based on 111-reflections of ara-

gonite, as well as a MAUD package [15] based on the incomplete

(111)-pole figures.

The microhardness test was performed by means of appar-

atus from CSM Instruments SA. This enabled verification of the

level of residual stresses in the examined sample area.

3. Results3.1. Differences in intensityThe thickness profile of the diffraction patterns registered for the

examined shell strip of C. marmoreus is presented in figure 3. The

diffraction patterns collected show essential differences along

the thickness of the shell studied. Under the assumption of a

homogeneous phase composition of the shell (e.g. [2]), the

observed differences in the intensity of diffraction reflections

diff

ract

ion

inte

nsity

(cp

s)

0 500 1000 1500 2000 2500 3000

thickness of the mollusc mantle (mm)outersurface

innersurface

111-peak

111-peak

112-peak

200-peak

012-peak

002-peak200-peak

35000

500

1000

1500

2000

2500

3000

3500

4000 4500 5000 5500 6000 6500

outer-surfacezone

inner-surfacezoneA-zone B-zone C-zone

Figure 4. Plot of peak intensity of the selected diffraction reflections between the outer and inner shell surfaces of the C. marmoreus sample studied. Filtered CuKaradiation used. The marked A-, B- and C zones indicate the most intense changes of the diffraction intensities of 111, 002 and 200 peaks.

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indicate actual changes in the spatial orientation of crystallites

throughout the shell thickness. A similar conclusion can be

drawn based on a thickness profile of the peak intensity of

selected reflections presented in figure 4.

We have distinguished a few areas (denoted as outer-

surface, A-, B-, C- and inner-surface zones) in the diffrac-

tion-peak profiles (figure 4), where particularly intense

changes in trend or slope are evident. Some of the zones

clearly correspond to the boundaries between crossed-

lamellar layers visible in figures 1a–d and 5. This is true of

most drastic changes of 012 and 200 profiles (zone B),

which correspond to the transition between the middle and

inner crossed-lamellar layers, these having been estimated

by SEM, after slight etching, to be at about 3060 mm directly

on the examined shell strip. The origins of the relatively smal-

ler perturbations identified in the A and C zone are difficult

to explain solely by examining the microstructure, although

the former might be related to the transition from the outer

to the middle layers (MLs) (approx. 325 mm deep). Both

extreme zones (outer and inner surface) are characterized

by particularly high intensities of the 111-peak profile,

which reflects a strong texture development in these zones.

The texture irregularities of the profile examined can be

further inspected by the complete and inverse pole figures cal-

culated from the numerically determined ODF [10]. Selected

(012) pole figures of aragonite of the different subareas are

presented in figure 5.

The changes in the pole figures (i.e. crystallographic

orientations) examined in depth clearly fit the successive

crossed-lamellar layers forming the shell of C. marmoreus(figures 1a–d and 5). These changes have been discussed in

detail in Rodrıguez-Navarro et al. [3]. The presented set of

(012) pole figures reflects the spatial distribution of the f012gplanes in the frame of the shell reference system (GD, RD,

ND). Besides the notable differences in arrangement from the

outer to the inner surface, there is a strong preferential orien-

tation, which is manifested in the almost parallel alignment of

the f012g planes with respect to the shell surface. This dominant

texture is present throughout the entire shell thickness. A distinct

908 rotation of the spreading of the central maximum of the pole

figures takes place at mid-shell thickness, exactlyat the transition

from the middle to the inner layers (ILs). A similar though less

notable change occurs at the transition from the outer to the

ML (figures 1b and 5). In this way, the elongation of the central

maximum remains parallel to the elongation of the first-order

lamellae [3].

A general change in texture intensity with thickness is

shown in figure 6. We used the normalized texture index

(Jn [ [0, 1]) [10,16], which is representative of the texture

sharpness. Avalue of Jn ¼ 1 corresponds to an ideal single crys-

tal, whereas Jn ¼ 0 would correspond to a completely random

distribution of crystallographic orientations (e.g. powdered

polycrystalline materials). The Jn thickness profile provides a

quantitative measure tendency of changes in the spatial

arrangement of crystallites (lamellas). Note that the profile

closely fits that of diffraction reflections (figure 4). The

Jn-thickness plot reveals that the transitions between layers

are marked by sharp (transition outer-ML) to moderate

(transition outer-ML) drops in Jn values.

The results of the quantitative texture analysis provide pre-

cise information on the dominant texture components

throughout the shell thickness. Figure 7 presents the integrated

skeleton profiles of the ODF throughout the shell section

examined. The skeleton profiles (maximal ODF-values inte-

grated within +58 spreading in the orientation space)

enabled us to identify the dominant individual (hkl)[uvw]

orientations (texture components) of the C. marmoreus shell.

A distinct difference was noted in the type and intensity

of the texture components identified between the outer and

inner shell surfaces. The f001gk100l orientation type domi-

nates and attains its maximal intensity close to the inner

shell surface, whereas the outer surface area is dominated

by the f001gk2� 10l type of orientation. The middle zone

of the shell is characterized by several distinct components,

such as f114gk221l, f114gk311l or f001gk650l types. Details

of the orientation indices are indicated in figure 7. The texture

distribution reveals significant differences in the ultrastruc-

ture arrangement between shell sublayers. In particular, the

areas close to the outer and inner surfaces clearly differ

from the central shell areas.

GDGD

GD

GD

GD

GD

GD

GDGD

2 mm

innersurface

outersurface

RDRD

RD

RD

levels

7.0515.9154.7783.6422.6902.3051.5371.1530.768

min. = 0.044max. = 7.520

RD

RD

RD

RDRD

012012

012

012

012

012

012012

012

Figure 5. SEM view of a complete transverse comarginal fracture of the C. marmoreus shell. Some selected (012) pole figures (among the 32 cases analysed) areshown, together with their approximate position on the fracture surface (not the actual sample analysed). The growth (GD) and radial (RD) directions are indicated.The central maximum elongates in parallel with the first-order lamellae.

1.00

0.95

0.90

0.85

inde

x of

text

ure

(Jn)

[ar

b. u

nits

]

0.80

0.750 500 1000 1500 2000 2500 3000

thickness of the mollusc mantle (mm)outersurface

outer-surfacezone

inner-surfacezone

real profiletrend (Jn)

A-zone B-zone C-zone

innersurface

3500 4000 4500 5000 5500 6000 6500

Figure 6. Normalized texture index Jn versus thickness for the shell sample examined.

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3.2. Thickness profile of residual stressesOwing to the growth process of the shell of C. marmoreus,

some residual stresses could be generated and still be

maintained within the shell. To verify the stress state of the

shell microstructure, suitable X-ray diffraction measurements

by a common sin2c method [12] were performed.

(111

)[12

3]

(001

)[10

0]

(001

)[56

0]–

––

––

–

–

––

(001

)[21

0]

(114

)[13

1]

(114

)[22

1]

(101

)[10

1]

outersurface

innersurface shell-wall thickness (mm)

j 1 angle (˚)

orie

ntat

ion

dens

ity (

t.o.r.

)45

40

35

30

25

20

15

10

5

00

6.5

6.0

5.5

5.0

4.5

4.0

3.5

3.0

2.5

2.0

1.5

0.51.0

0

10

20

30

4050

6070

8090

100 110120

130 140 150 160 170 180

Figure 7. Three-dimensional view of skeleton profiles (maximal orientation density versus w1 angle of Euler’s orientation space) of the texture function (ODF)identified in the sectioned shell of C. marmoreus.

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The residual stresses were calculated for the mutually per-

pendicular directions GD and RD (denoted as sGD and sRD),

at the 34 positions analysed. The plot of the residual stresses

versus thickness is presented in figure 8. The results show

that both stress components exhibit a tensional (positive) char-

acter. Except for the areas close to the outer and near inner

surfaces, the residual stresses maintained a rather constant

level of ca 1300–1600 MPa, although the relation sGD , sRD

was maintained throughout almost the entire shell thickness.

The stresses at both the outer and inner zones changed

drastically. For both sGD and sRD, there was a sharp and

almost parallel increase from the outer surface towards the

interior, with the difference that sGD increased faster, starting

from compressive values (figure 8). Close to the internal sur-

face, sGD and sRD values decreased and then rapidly rose.

Later trends differed, because sGD increased drastically to maxi-

mum values of nearly 4000 MPa, whereas sRD again decreased

to former mean values. The only exception to the observed

regularity of the stress field corresponded to the central zone

of the shell (where sGD . sRD), located at ca 1500–3000 mm

below the outer surface (figure 8). The opposite trend detected

in this part was consistent with the sharp changes in the

orientations of crystallites recorded.

The two most immediate possible sources of positive

internal stresses were (i) tensions developed between crystals

during growth or (ii) extra- and intracrystalline tensions due

to the accommodation of organic matrices or to the occlusion

of intracrystalline organic macromolecules. At present, it is

not possible to determine which, if any of the above, was

the origin of the stress distribution observed.

Lower values of the sGD, as compared with the sRD com-

ponent (by ca 300 MPa), can be attributed to a natural ability

of C. marmoreus to grow faster in the growth than in the

radial direction. We hypothesize that C. marmoreus produce

higher stresses in the growth direction than in the radial one,

tending to possible intensive growth of its mantle in a rather

strongly curved wall developed along the GD direction. How-

ever, each step of the directional growth of the stressed

microstructure causes a momentary relaxation of the stresses

(decreasing its value) which can be rebuilt again in the living

organism. In the examined shell of the dead C. marmoreus,the level of relaxed sGD stresses may appear lower than the

sRD stresses due to the lack of vital forces, as documented in

figure 8.

However, the question of the origin of the identified stres-

ses during the growth process is still open. The observed

tendency to develop compressive stresses in the outer layer

(OL) may be caused by increasing mechanical strength (hard-

ness) of the armour, which might protect the animal from

predators. In that configuration, the tensional stresses main-

tained in the IL may result from the need to compensate

for the compressive stresses in the OL.

The interpretation presented is only an attempt to explain

the observed relation in directional stresses identified by the

X-ray diffraction technique. Our hypothesis needs further

testing with more sophisticated techniques.

To recognize the component sND of the stress field (parallel

to the normal direction, ND, in figure 2; figure 9), we measured

selected areas located on the ND–GD plane. Any influence of

stress relaxation on both sides of the shell was avoided

(figure 8) by assuming that the values of the sRN stress com-

ponent close to the outer and inner surfaces was close to

zero. Therefore, the determination of the sLN component was

restricted to areas located in the central zone of the shell

3200

2400

outerlayer

innerlayer

stresses ll GD

stresses ll RD

transition zone1600

800

shell-wall thickness (µm)

10000 2000 3000 4000 5000

resi

dual

str

esse

s (M

Pa)

0

–800

Figure 8. Thickness profile of residual stresses in the growth (sGD) and radial (sRD) directions for the whole shell thickness. The difference in uncertainty of theidentified sGD and sRD stresses is caused by the varying profile of intensity of the hkl-reflection (used in the stress measurement), the spatial positions of whichcorrespond to the (hkl)-pole figure in the GD and RD directions, respectively. The consequence of this diversity in the pole figures is unequal fitting errors of theestimated intensities and peak positions regarded in the stress analysis.

sND

com

pres

sion

com

pres

sion

tension

tension

tension

tension

sND

s RD

s RD

sGD

sGD

Figure 9. Schematic chart of the stress field components within the shell of C. marmoreus.

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sample. The measurement was made in a few areas chosen

along the radial direction of the shell sample. The values

found for sLN ranged from 2510 to 2470 MPa and revealed

the presence of an essentially compressive normal stress

component in the shell of C. marmoreus (figure 9).

A complementary characteristic of the stress analysis is

the plot of the hardness versus thickness of the central part

of the examined shell sample (figure 10).

Because of the natural anisotropy in elasticity of the

aragonite crystals, a global (macro-scale) response of the

550

scan line no. 1

scan line no. 2

averaged hardness

B-zone

hard

ness

(H

V)

500

450

400

350

300

2500

subarea locatedclose to innersurface

subarea locatedclose to outersurface

distance (mm)

0.25 0.50 0.75 1.00 1.25 1.50 1.75 2.00

Figure 10. Hardness – thickness profile of the central part of the C. marmoreus shell analysed (the transition area, shaded, corresponds to the B-zone in figures 4 and 6).

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C. marmoreus material to external loading is moderated by its

resulting texture. Based on the results, we conclude that both

halves of the shell thickness show rather symmetrical distri-

butions of the microstructure characteristics (residual

stresses, texture intensity (Jn index)) with respect to the

middle zone, where it varied notably (especially hardness,

above 30%). The reason is most probably the changes in

spatial arrangement (texture) of the aragonite fibres at the

middle shell thickness, where the transition between the

middle and ILs occurs, also registered in the diffraction

signal (figure 4).

4. DiscussionThe crossed-lamellar microstructure, such as that of the shell of

C. marmoreus, has evolved in geological time (usually measured

in millions of years), repeatedly in different molluscan groups

(bivalves, gastropods, polyplacophorans and scaphopods) in

order to fit to the adaptive requirements of the animal. It is, by

far, the most common type of microstructure among molluscs.

The layered structure of the shell constitutes a natural FGM,

which has to withstand mechanical loadings imposed by

environmental circumstances. Mechanical properties such as

toughness and hardness of the external and internal surface

layers must play an important role during the animal’s life.

For example, brittle surface layers are not well suited to resist

dynamical loadings.

A good illustration of the above-discussed relations in arti-

ficial engineered materials is the so-called white etching layer

(WEL) commonly seen, for example, on the surface of rail

tracks. The WEL is a severely deformed steel layer resulting

from the rolling friction of train wheels under high contact

pressure. It is extremely hard but brittle and susceptible to

crack formation [17,18]. On the other hand, the residual stresses

of compressive character existing within the WEL favour the

durability of the surface layer of the rail track due to resistance

to micro-crack propagation. A similar tendency in the distri-

bution of the residual stresses is observed in the marine

mollusc shell investigated here, especially in the growth

direction (sGD plot, figure 8).

The thickness profiles of the two analysed microstructural

characteristics, texture and residual stresses, have been related

to particular shell directions distinguished in the C. marmoreusshell examined (figure 2). In this species, the shell is made of

three crossed-lamellar layers: an OL (with antimarginal first-

order lamellae), an ML (with comarginal lamellae) and an

internal layer (with antimarginal first-order lamellae). There-

fore, there is a 908 rotation of the first-order lamellae at the

transitions between layers, implying drastic changes of the

spatial arrangement of crystallites. In particular, there is a

908 rotation in the orientation of all microstructural elements

(first- to third-order lamellae; figure 1). These changes are

adaptive in that they deflect fractures (which, in the crossed-

lamellar microstructure, run along the boundaries between

first-order lamellae; [19]), thus contributing to energy dissipa-

tion. The changes also influence differential hardness

throughout the shell thickness.

4.1. Texture characteristicsThe skeleton profiles of the texture function (figure 7) have

been supplemented with the crystallographic orientations

identified. They reveal significant qualitative and quantitative

differences in the spatial arrangement of crystallites. The high-

est texture differences were identified between the f001gk100land k560l orientations, which dominated in the area close to

the inner surface, and the f001gk210l and f114gk221l types of

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orientations, which reach their highest values in the area close

to the outer shell surface. Also, a relatively strong f101gk110ltype of orientation was found towards the outer surface,

while this orientation was insignificant close to the inner one.

This feature is particularly important with regard to the mech-

anical properties of the natural shell, as confirmed by the

hardness plot (figure 10).

4.2. Stress characteristicsThe above-documented observations concerning the changes

of texture with thickness are consistent with changes of

the residual stress distribution. Strongly texturized areas

(figure 6) are characterized by higher levels of residual stress

(figure 8). This feature may be related to crystal growth pro-

cesses occurring at both shell surfaces. Special attention is

paid to the zone close to the inner surface, where the tensional

character of the sGD stress component is extremely high

(figure 8), whereas an opposite tendency of the sRD component

is observed. This agrees with the stress level reported in nacre

by Cortie et al. [4]. Such a configuration of stresses may indicate

different growth trends along different anatomical directions of

the shell, although the origin is not clear. The compressive

character of the sGD stress component in the outer zone can

be interpreted as resulting from a balance between both

stress components on the outer surface shell.

Some differences in stress values and trends may again

be related to the change in microstructure, from a middle

zone (significantly spread) with comarginally oriented first-

order lamellae to an internal layer with radially oriented

first-order lamellae.

5. ConclusionThe results presented here offer valuable information on the

crystallographic texture and residual stresses of the crossed-

lamellar shell of the gastropod C. marmoreus. Some changes

can easily be related to the transitions between crossed-lamellar

layers, where the first-order lamellae drastically change their

orientation from antimarginal to comarginal and vice versa.

Our approach constitutes an initial step in recognizing the bio-

mechanical implications of microstructural changes existing in

such sophisticated natural FGMs, such as marine shells.

Competing interests. We declare we have no competing interests.

Funding. We received no funding for this study.

Acknowledgements. The results presented in this paper pertain to theproject CGL2013-48247-P of the Spanish Ministerio de Ciencia e Inno-vacion, and RNM6433 of the Andalusian Consejerıa de InnovacionCiencia y Tecnologıa, as well as the Research Group RNM363(Junta de Andalucıa).

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