Layered Ceramics

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Chapter 9.7

Layered Ceramics

Raul Bermejo and Marco DelucaInstitut fuer Struktur- und Funktionskeramik (Institute for Structural and Functional Ceramics), Montanuniversitaet Leoben (University of Leoben),

Franz-Josef-Strasse 18, 8700 Leoben, Austria

Chapter Outline1. Introduction 733

2. Residual Stresses in Layered Ceramics 735

3. Mechanical Behavior 739

4. Design Guidelines to Optimize Strength and Toughness 742

5. Outlook 746

References 747

1. INTRODUCTION

The interest for the mechanical behavior of ceramic mate-

rials has been alwaysmotivated by their possible application

as structural components, especially in the cases where

properties such as high hardness, chemical stability, low

density, and high strength, among others, are sought. Due to

their brittleness, ceramics have been used for many decades

as structural elements, but usually under compressive

loading conditions. Nowadays, most of the new engineering

designs need to withstand tensile stresses, which imply

potential limitations for ceramics due to their low fracture

toughness and the sensitivity of their strength to the presence

of defects [1e3]. This is very well known for glass, which is

one of the strongest manufactured materials when the

surfaces are free from flaws (as for the case of glass fibers),

whereas under ordinary conditions “glass” is a synonym for

fragility. The brittle fracture of glasses and ceramics is

a consequence of the material defects located either within

the bulk or at the surface, resulting from the processing and/

or machining procedures [4,5]. Under external applied

stress, the stress concentration associated with those defects

is the common source of failure for ceramic components. If

each defect is considered as a crack or a potential source for

crack initiation, then it becomes clear that the size and type

of these defects determine the mechanical strength of the

material [6]. The distribution of defects within a ceramic

component yields a statistically variable strength which can

be described by the Weibull theory [7,8]. Since flaws are

intrinsic to processing and in most cases unavoidable, the

reliability of ceramic components in terms of strength is

associated with such flaw distribution.

In order to reduce both the defect population and the

defect size, many studies have been devoted in the past to

improve ceramic processing. The use of colloidal routes

has, to some extent, enabled the reduction of the critical

size of the flaw causing the failure of the material, thus

allowing fabrication of advanced ceramics with relatively

high strength [9]. In an attempt to reduce the level of

uncertainty in mechanical strength and to overcome the

lack of toughness of structural and functional ceramics,

several processing routes have arose in the last two decades

which do not utilize the conventional “flaw elimination”

approach, but rather use the implication of energy release

mechanisms to obtain “flaw tolerant” (strength reliable)

materials, with improved fracture toughness [9e26]. In this

regard, the outstanding mechanical behavior of hierarchical

layered structures found in nature has inspired material

scientists to reproduce or mimic some of these architectures

for improving engineering designs [10,15,16,27e32], for

instance, the extraordinary toughness and strength of

mollusk shells (Figure 1), which are related to their fine-

scale structure, namely a laminate of thin calcium

carbonate crystallite layers consisting of 99% calcium

carbonate (CaCO3) and tough biopolymers, arranged in an

energy-absorbing hierarchical microstructure [33]. The

strength and toughness of such layered structures are

significantly higher than those of their constituents [30,34].

In addition to the improvement of mechanical strength,

there is another motivation for the production of layered

ceramics. The demanding requirements for advanced

devices involve in many cases the combination of several

material classes (such as metals and ceramics) to fulfill the

Handbook of Advanced Ceramics. http://dx.doi.org/10.1016/B978-0-12-385469-8.00039-3

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Handbook of Advanced Ceramics, Second Edition, 2013, 733e751


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performance in a given system. The unique mechanical and

functional properties offered by ceramic materials make

them good candidates for many advanced engineering

applications (e.g. solid oxide fuel cells, piezoactuator and

sensor devices, thermal barrier coatings, and conducting

plates for wireless communications). The fabrication of

components having two different materials is here a chal-

lenge from the viewpoint of not only structural integrity

(i.e. mechanical resistance) but also functionality. Multi-

layer piezoelectric actuators, for instance, are constituted

by thin piezoceramic layers with interdigitated metal

electrodes [35,36]. In order to ensure the device function-

ality, the propagation of cracks between adjacent electrodes

must be avoided [37,38]. Another example is the case of

low temperature co-fired ceramics (LTTCs), where the

concept of co-sintering multilayer ceramic substrates,

metal electrodes, and vias at relatively low temperatures

(i.e. ca. 900 �C) has enabled the improvement of wireless

communication systems (e.g. mobile phones and GPS

technology) at relative low costs [39]. In LTCCs the

mechanical reliability of the ceramic substrate (subjected to

thermo-, mechanical-, and electrical loads) relies on

avoiding crack propagation which would reduce or even

completely hinder the performance of the microelectronic

device.

In recent years, as a result of remarkable progress in

terms of microstructural design and advanced processing

[9,31,40,41], toughness and strength of structural ceramics

have been increasingly enhanced by crack shielding from

microstructure-related mechanisms [10,42e48]. A direct

consequence of these energy-dissipating toughening

mechanisms, which aim to reduce the crack driving force at

the crack tip, is the development of an increasing crack

growth resistance as the crack extends, i.e. R-curve

behavior. This concept first arose from studies in metals and

alloys in the 1960s and was later applied to single-phase,

duplex, and laminar ceramics by numerous authors

[11,48e50]. Particular attention has been paid to fiber,

platelets, and layer-reinforced ceramics, where the better

mechanical performance is associated with the second

phase or layer addition as well as with the arrangement of

the fibers or the layer assemblage, respectively [32,45,

51e54]. As an extension of this laminar ceramic/fiber-

reinforced concept, multilayer designs have also been

attempted in many ways aiming to improve both the resis-

tance to crack propagation and the mechanical reliability of

ceramic components [10,11,15,18,20,23,55e58]. This

approach has been demonstrated to be more cost-effective

than the former and more accurate in terms of tailoring

mechanical requirements.

The design of composite materials using such multi-

layer architectures (e.g. ceramic composites such as

aluminaezirconia and mulliteealumina among others) has

been reported to exhibit increased fracture toughness,

higher energy absorption capability, and/or noncatastrophic

fracture behavior in comparison with their constituent

(monolithic) materials. Among the various laminate

designs reported in literature, two main approaches

regarding the fracture energy of the layer interfaces must be

highlighted. On the one hand, laminates designed with

weak interfaces have yielded significant enhanced fracture

energy (failure resistance) through interface delamination

[10,14,25,30,59e68]. The fracture of the first layer would

be followed by crack propagation along the weak interface

or within the weaker interlayer. This is the so-called

“graceful failure,” which prevents the material from cata-

strophic failure e a fracture scenario where maximum

applied load does not lead to unstable crack extension. In

this case, the reinforcement mechanisms during fracture

remind those from natural systems such as mollusk shells

(cf. Figure 1). On the other hand, laminates designed with

strong interfaces present crack growth resistance (R-curve)

behavior through microstructural design (e.g. grain size and

layer composition) and/or due to the presence of

compressive residual stresses, acting as a barrier to crack

propagation [15,16,20,21,24,55,58,69e71]. The increase in

fracture energy in these laminates is associated with

energy-dissipating mechanisms such as crack deflection/

bifurcation phenomena. Within this context, a commonly

used structural design is that associated with the presence

of compressive residual stresses and/or phase trans-

formations. Compressive stresses could develop in the

laminate during cooling from sintering due to differences in

elastic or thermal properties (Young’s modulus, thermal

FIGURE 1 Fracture of a mollusk shell consisting of CaCO3 brittle layers

and tough biopolymers, arranged in a hierarchical microstructure. (Cour-

tesy of Dr. Deville [33]).

734 Handbook of Advanced Ceramics



expansion coefficient, etc.) between the layers [46,56,72].

The specific location of the compressive layers, either at the

surface or internal, is associated with the attempted design

approach, based on either mechanical resistance or damage

tolerance, respectively. In the former case, the effect of the

compressive residual stresses results in a higher, but single-

value, apparent fracture toughness together with enhanced

strength (the main goal) and some improved reliability

[16,49,55]. On the other hand, in the latter case, the internal

compressive layers are designed to rather act as a stopper to

any potential crack growing from processing and/or

machining flaws, at or near the surface layers such that

failure tends to take place under conditions of maximum

crack growth resistance [15,20,24,58]. The utilization of

tailored compressive residual stresses acting as physical

barriers to crack propagation has succeeded in many

ceramic systems, yielding in some cases a so-called

“threshold strength,” i.e. a minimum stress level below

which the material does not fail [15,24,26,58,70,73,74]. In

such layered ceramics, the strength variability of the

ceramic material due to the flaw size distribution in the

component is reduced, leading to a constant value of

strength. The selection of multilayer systems with tailored

compressive stresses either at the surface or in the bulk is

based on the end application, and is determined by the

loading scenarios where the material will work.

The understanding of the conditions under which such

reinforcement and energy-dissipating mechanisms occur

and the influence of the layered architecture on the crack

propagation must be pursued in order to improve modern

structural and functional multilayer devices. The motiva-

tion of this chapter is to review the main approaches

attempted in the field of layered ceramics to improve the

mechanical properties of ceramic materials. Among the

different possibilities to increase strength and toughness in

multilayers, the use of residual stresses as key feature will

be addressed aiming to provide some guidelines to design

more reliable advanced ceramics.

2. RESIDUAL STRESSES IN LAYEREDCERAMICS

In every case where dissimilar materials are sealed together

through a relative strong interface and subsequently

undergo differential dimensional change, stresses arise

between the materials [75]. Hence, a particular challenge in

the processing of ceramic laminates is to understand the

nature of these residual stresses, especially if they are to be

used to enhance their mechanical properties. In ceramic

laminates, residual stresses can be due to different factors:

some of them are due to intrinsic causes such as epitaxial,

variations of density or volume, densification, and oxida-

tion at the surface. Others are extrinsic such as thermal or

thermoplastic strains developed during cooling or by

external forces and momentums. Among them, the aspect

most commonly referred to is the difference in the coeffi-

cients of thermal expansion (CTEs) between adjacent

layers. During sintering of the laminate, it is considered that

stresses between layers are negligible. However, as the

temperature decreases, the differences in the CTE (ai) may

promote a differential strain between layers. In addition to

this differential strain, other strain differences, mainly due

to phase transformations (Dεt) [46,57] or reactions (Dεr)

[72] inside one layer, should also be considered. As a result,

the final differential strain between two given layers A and

B after cooling may be expressed as

Dε ¼ ðaA � aBÞDT þ Dεt þ Dεr (1)

where DT ¼ Tref � T0 is the difference between the refer-

ence temperature, i.e. the temperature at sintering where

residual stresses are negligible, Tref, and the room temper-

ature, T0.

2.1. Analytical Solution

For ideal elastic materials, neglecting the influence of the

external surfaces (where stresses may relax) and consid-

ering the laminate as an infinite plate the stress field can be

determined analytically [12,75,76]. In each layer a homo-

geneous and biaxial residual stress state exists far from the

free edges. The stress magnitude in each layer, sres;i, can be

defined as

sres;i ¼Ei

1� ni

ða� aiÞ DT ¼ Ei

1� ni

Dεi; (2)

where Ei; ni, and ai are material properties of the ith layer

(i.e. Young’s modulus, Poisson’s ratio, and coefficient of

thermal expansion, respectively). Dεi ¼ ða� aiÞDT is the

mismatch strain of the ith layer, where the coefficient a

is given as an averaged expansion coefficient of the

laminate:

a ¼X

N

i¼ 1

Eitiai

1� ni

,

X

N

i¼ 1

Eiti

1� ni

; (3)

with ti being the thickness of the ith layer and N the number

of layers.

Note that the reference temperature Tref is, in practice,

not easy to determine. It is always lower than the sintering

temperature, since e if temperatures are reduced after

sintering e the diffusion, which reduces the strain

mismatch, does not stop abruptly but it becomes slower and

slower. Generally, a normalization based on Eqn (2) and

additional residual stress measurements have to be per-

formed to determine Tref. For typical alumina-based or

silicon-based ceramics, this stress-free empirical tempera-

ture is general between 1200 �C and 1300 �C [76].

735Chapter | 9.7 Layered Ceramics



When only two types of layer materials (A and B) are

represented in the laminate (this is the case we will consider

in the following), Eqn (3) can be written in the form

a ¼

EAaA

1� nA$

X

nA

i¼ 1

tA;i þEBaB

1� nB$

X

nB

i¼ 1

tB;i

!,

EA

1� nA$

X

nA

i¼ 1

tA;i þEB

1� nB$

X

nB

i¼ 1

tB;i

!

: (4)

The magnitude of the residual stresses depends on the

properties of A and B and on the ratio between the total

thickness of the layers of type AðTA ¼P

tA;iÞ and

BðTB ¼P

tB;iÞ. The ratio of total thickness of the layer

materials equals to their volume ratio: TB=TA ¼ VB=VA.

It is interesting to note that the magnitude of residual

stresses only depends on this volume ratio and not on the

thickness of the individual layers i [77]:

sres;i ¼ fi

X

nB

j¼ 1

tB; j

,

X

nA

j¼ 1

tA; j

!

¼ fiðTB=TAÞ

¼ fiðVB=VAÞ: (5)

Finite element simulations of residual stress distributions in

two symmetrical layered systems with the same volume

ratio show the same magnitude of stresses in both cases,

regardless of the combination of layer thicknesses of each

material (see Figure 2). This is a very important aspect,

which can provide the designer with more flexibility in

order to tailor the disposition and thickness of layers when

searching for an optimal design for a given level of residual

stresses.

2.2. Limitations for Design

Although residual stresses can be a key feature to enhance

the mechanical properties of many layered systems, some

negative effects of high residual stresses should be

considered. For instance, while compressive stresses are

beneficial in acting as “shielding” mechanism against crack

advance, tensile stresses will cause the cracking of the layer

if they overcome its strength. A typical example is

“tunneling cracks” that may appear at the surface of the

tensile layers [78e81], and which can affect the structural

integrity of the laminate (see Figure 3a). They can be

avoided by lowering the level of tensile stresses in the

corresponding layers.

Another important aspect is the free surface of the

material. It is well known that stresses at the free surface of

layered materials are different from thosewithin the bulk. In

the region far from the free edges (i.e. in an infinite plate),

biaxial residual stresses parallel to the layer plane exist, and

the stresses perpendicular to the layer plane are negligible

[82]. Near free edges, however, the residual stress state is no

longer biaxial since the edge surface must be traction-free.

As a result, a stress component perpendicular to the layer

plane appears at the free edge [82e87]. This stress has a sign

opposite to that of the biaxial stresses in the interior. Hence,

for a compressive layer sandwiched between two tensile

layers, a tensile residual stress perpendicular to the layer

plane exists near the free surface of the compressive layer.

The amplitude of maximum tensile residual stress at the free

surface is related to the biaxial compressive residual stress in

the interior. Although such tensile residual stress decreases

rapidly from the edge surface to become negligible at

FIGURE 2 Residual stress distribution in two

symmetrical layered systems with different

combination of layer thicknesses but the same

volume ratio. The magnitude of residual stresses in

each layer, i.e. sA and sB, is the same in both cases.

(a) (b)FIGURE 3 (a) Tunneling crack through the tensile layer

in a laminate with high tensile residual stresses, (b) edge

crack in a laminate due to high stresses in the compressive

layers [80].




a distance of the order of the compressive layer thickness,

defects at the surface may be activated so that cracks may be

initiated. An example are the so-called “edge cracks”,

initiating from preexisting flaws, which can be encountered

at the free edges of compressive layers (see Figure 3b).

Preventing edge cracking is important for the structural

integrity of the component and should be considered in the

multilayer design, as it has been attempted by several

authors [23,86,88].

A combined action to avoid both tunneling and edge

cracks may be undertaken by selecting the level of residual

stresses in the design so that the strength of the layers is not

overcome. Such a limit for the magnitude of the residual

stresses depends on eachparticular design and can be selected

according to the properties of the employed materials. An

example of such approach has been derived for aluminae

zirconia-based multilayer ceramics [77]. It is assumed for

both A-layers and B-layers the same elastic constants, frac-

ture toughness, and strength, i.e. EA ¼ EB, nA ¼ nB, KIc,A ¼KIc,B, and sc,A ¼ sc,B ¼ sc. The residual stress difference

between adjacent layers is defined as s0 ¼ sA�sB, with sA

andsBbeing the residual stress inA-layers (compressive) and

B-layers (tensile), respectively, which can be expressed as

sA ¼ s0$VB

VA þ VB(6a)

sB ¼ �s0$VA

VA þ VB(6b)

In order to avoid edge cracks the strength of the layer, sc,

seems to be a reasonable limit for jsAj, i.e. jsAj � sc. If

tunneling cracks are to be avoided jsBj �sc=2 is a reasonablelimit, as derived in Ref. [77]. Using Eqns (6a) and (6b)

a limitings0 to design laminates free of cracks can bederived:

js0j � sc$

�

1þ 1

VB=VA

�

(7)

js0j �sc

2$

�

1þ VB

VA

�

(8)

These two limits (Eqns (7) and (8)) give restrictions on the

magnitude of js0j to avoid edge cracks and tunneling

cracks, respectively, and should be considered for design

purposes. In Figure 4 both conditions are plotted as

a function of VB=VA for a typical characteristic strength

value of sc ¼ 400 MPa. Therefore, a region free of surface

cracks can be estimated by tailoring the volume ratio

between material A and B.

2.3. Experimental Determinationof Residual Stresses

The magnitude of residual stresses within a material or

component can be experimentally determined by either

destructive or nondestructive methods. Mechanical tech-

niques based on the use of a strain gauge are destructive in

the sense that they require the component to be drilled or

cut. Another method which is less invasive but still regar-

ded as destructive is the use of micro-indentations (in

general, Vickers imprints) [89,90]. This procedure is based

on the measurement of the crack lengths arising from the

tip of the imprint in both stressed and nonstressed mate-

rials. The magnitude and profile of the residual stresses are

directly associated with the measured crack length differ-

ence. In Figure 5a a scheme of indentation profiles in inner

and outer layers of an aluminaezirconia laminate is

reported, whereas the results are displayed in Figure 5b. It

becomes clear that the level of stresses involved in the outer

layers is considerably lower. This method proves to be

a quick and low-cost alternative to more complicated

analytical methods (see below). However, since the

indentations are performed at the surface of the specimen,

the use of this technique is limited only to the evaluation of

surface stresses. This effect is displayed in Figure 6 as the

result of FE calculations of the average residual stresses

near surface and at the center of the sample. As could

clearly be seen, notable differences are present between

stresses in the outer and inner layers.

Nondestructive techniques for the measurement of

residual stress in ceramic laminates generally are noncon-

tact methods, namely they make use of an incident radia-

tion (being X-rays, neutrons, or light) to probe the material

surface in a position-resolved fashion. The penetration

depth and the spatial resolution of the technique depend on

the radiation wavelength and energy. In addition, the

physical mechanism (especially the associated ease or

difficulty in data interpretation) and the availability of the

radiation source are very important aspects for the choice of

the analytical technique.

0 2 4 6 8 100

200

400

600

800

1000tunnelling cracks

|0| (M

Pa

)

VB

/VA

(-)

σc

edge cracks

FIGURE 4 Design limits to prevent tunneling and edge cracks for a given

volume ratio VB/VA between two materials in a layered structure. js0j is thedifference between the residual stresses in adjacent layers, sA�sB. The

mean strength of the layers is given by sc.




The most common methods for residual stress

measurements in multilayer ceramics are X-ray [91e93]

and neutron diffraction [94e100]. Both methods are based

on Bragg’s equation, which allows the accurate determi-

nation of atomic spacing and, consequently, elastic strains

in crystalline materials. The main difference between these

two methods (apart from the radiation source) is the fact

that laboratory X-rays have a much shallower penetration

depth (a few microns) and therefore allow only surface

measurements, whereas neutron diffraction enables in-

depth measurements up to some millimeters [92,97]. Both

techniques present significant challenges in case a position-

resolved analysis is needed. In fact, generally, a neutron

beam cannot be focused to a very small size (highest

possible spatial resolution: ~200 mm on the material

surface); on the other hand, traditional X-ray diffraction

(XRD) methods involve rotation or tilt of the specimen

[92], leading to a cumbersome experimental procedure. As

a result, only macroscopic residual stresses are accessible

by these techniques.

In the recent years, synchrotron XRD has emerged as

a powerful analytical method for the study of microscopic

residual stresses in ceramic laminates [101e104]. Due to

the high energy of synchrotron X-rays and the advanced

collimation and focusing equipment available at common

beamlines, this technique allows noncontact measurements

with a very narrow spot size (micron to submicron),

whereas the wavelength tuneability of radiation allows

choosing the penetration depth inside the material. 2D and

3D microscale residual stress measurements are made

possible using special procedures such as the 3D diffraction

microscopy (3DXRD), based on bidimensional detectors

and sample rotation, or Laue microdiffraction, based on

wavelength tuning [93].

An example of residual stress analysis in layered

ceramics is constituted by the work of Leoni et al. [92] on

aluminaezirconia laminates. Figure 7 shows a through-

thickness residual stress profile obtained with synchrotron

XRD and the Laue microdiffraction method on two

alumina and one aluminaezirconia layer. In the central

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5

-700

-600

-500

-400

-300

-200

-100

0

100

200BB B

Interior

Surface

Resid

ual S

tress [

MP

a]

AB

AA A A

Distance in thickness direction [mm]

FIGURE 6 FE calculation of residual stresses after sintering in the center

and at the surface of an aluminaezirconia laminate. A difference in the

average residual stresses between near-surface areas and the center of the

laminate body can be observed.

FIGURE 7 Through-thickness residual stress profile in an aluminae

zirconia laminate: design values (line) and measurement results for

alumina (open dots) and zirconia (squares). The average stress is also

shown (stars). (Courtesy of Dr. Sglavo [92]).

B

A

300 m

B

A

Indentation

imprints

0 100 200 300 400 500 6000

20

40

60

80

100

120

140

A outer layer

Re

sid

ua

l S

tre

ss [

MP

a]

Distance to any A/B interface [ m]

A inner layer

(a) (b)FIGURE 5 (a) Scheme of the indentation

profile in both inner and outer alumina layers of

an aluminaezirconia multilayer, (b) plot of the

experimentally measured residual stress profile.




alumina-zirconia layer, stress values belonging to both

phases (calculated with isotropic elastic constants) are

reported. The measurement was performed by varying the

depth of the diffraction gauge volume. Examples of

residual stress analyses in nanometer-sized layers also

appeared recently in the literature [104], which prove the

high suitability of synchrotron XRD also for the new trends

in microelectronics and materials science.

The need for a synchrotron X-ray or a neutron source,

however, makes these techniques seldom available and not

always cost-effective. These difficulties could be overcome

by another method capable of position-resolved residual

stress measurement on the microscale: Raman spectros-

copy. This technique is based on the Raman effect, namely

the inelastic scattering of monochromatic light (a laser) by

a crystal. Raman spectroscopy is noncontact and nonde-

structive, and common spectrometers are laboratory-size

equipment [105]. The spatial resolution (spot size and

penetration depth) depends on the wavelength of the inci-

dent laser, on the choice of the objective lens, and on the

absorption properties of the investigated material

[106e109]. In common ceramics such as alumina, a spot

size of ~1 mm and a penetration depth of ~15 mm can be

achieved [108], which makes the technique surface-

sensitive in comparison to the aforementioned XRD and

neutron diffraction. The interpretation of the relationship

between the Raman spectral shift and stress (piezo-

spectroscopy) is nontrivial [110,111], but has been well

established in the past for a wide range of materials (silicon

[112,113], zirconia [114], and silicon nitride [115e118],

among others). In the case of alumina, the influence of

residual stress on the luminescence signal of intrinsic Cr3þ

impurities in the ceramic body, induced by the laser and

detected in the Raman spectrometer (photoluminescence,

PL, henceforth), is used [87,111,119e122]. The physical

mechanism in this case is different, in the sense that it is not

based on the modification of the force constants of lattice

vibrations (Raman piezo-spectroscopy), but rather on the

shift in the position of the energy levels of Cr3þ impurities

under the influence of a macroscopic stress [111]. Gener-

ally, a convolution of the calculated stress values by

a suitable stress model and the probe response function is

done within the probe size, which leads then to a good

approximation of the measured stress values [121]. An

example of residual stress measurement performed with

this method is provided in Figure 8 [122]; here the PL probe

was scanned through alumina and aluminaezirconia

layers, allowing to obtain different values of measured

stresses for different layer configurations and thicknesses.

It has to be noted that the stress values measured with the

PL technique are generally lower than those predicted

inside the layers [87]. This is associated with the free

surface effect and also with the fact that the PL probe gives

information only on the sum of principal stresses. There-

fore, only mean stresses (trace of the stress tensor) can be

measured at the surface.

In the recent years, alternative techniques emerged in

the scientific community, which could be useful in the

future for analyses in ceramic laminates. They are electron

back-scattered diffraction (EBSD) [123] and positron

annihilation lifetime spectroscopy (PALS) [124]. The first

technique can be carried out in an electron microscope, and

provides very local (nanometer-scale) strain measurements.

It is however only a surface-based technique and the

methodology to avoid charging effects in ceramic materials

is currently under development. PALS has already been

used together with nanoindentation in aluminaezirconia

laminates to study the influence of stress on localized

defects. The technique has a relatively high penetration

depth (~100 mm), and thus could be a valid alternative to

neutron diffraction measurements.

3. MECHANICAL BEHAVIOR

The response of a monolithic ceramic material to an

external applied load can be characterized by its mechan-

ical strength and its crack growth resistance. Both strength

and toughness have proved to be enhanced using layered

architectures with tailored properties (i.e. interface tough-

ness, strength and toughness of each layer, composition and

disposition of the layers, residual stresses, etc). Following

the two main approaches in the design of ceramic

FIGURE 8 Stress profiles and micrographs of the cross section in multilayered AeAZ specimens with different thickness ratios among the layers. Each

profile refers to the specimen showed on the right. Only half of the stress profile is plotted. (Courtesy of Dr. de Portu [121]).




laminates, systems with weak or with strong interfaces can

show a different response to fracture.

3.1. Laminates with Weak Interfaces

Multilayer systems designed with weak interfaces or

interlayers are aimed to prevent the component from

catastrophic failure by guiding the crack along the interface

or propagating the crack within the interlayer, and thus

dissipating energy during the fracture process. The fracture

process is based on the failure of the (stiffer) layers, and the

strength of the system is associated with the mechanical

resistance of such layers. Key works on this kind of

multilayer material are those from Clegg et al. [10,14,125].

As an example, the fracture toughness of a silicon carbide

monolithic ceramic is compared with that of a SiC

multilayer containing graphite interlayers [125]. The so-

called “graceful failure” of the material can be seen in the

loadedeflection curve in Figure 9. The failure of one layer

does not imply the catastrophic failure of the entire

component, raising the apparent fracture toughness from

3.6 to 17.7 Mpa m1/2.

A special case is that of porous interlayers, where crack

deflection within the layer can occur under bending if the

layer has a minimum volume fraction of porosity

[14,63,65,126]. The crack path (i.e. deflection within

the interlayer or along the interface) is dependent on the

composition of the interlayer [59]. Models to predict the

deflection of cracks within weak interlayers of laminates

loaded under bending have been developed based on energy

criteria. This has enabled optimizing the fracture energy of

suchmultilayer systems as a function of interface toughness,

strength of the layers, and Young’s modulus [127e130].

The particular case of a crack deflecting along a weak

interface between two materials (having different elastic

and/or mechanical properties) was first studied by He,

Hutchinson, and Evans based on the type of loading and on

the properties of the layers and interfaces (i.e. fracture

energy of interface and layers, elastic constants of the

individual layers, etc.) [131e133]. The tendency of a crack

to deflect along or penetrate into the next layer depends on

the relations between the involved fracture energies (of the

material layers A and B, Glayer, and of the interface Gi) and

the relevant energy release rates (of deflecting and pene-

trating cracks, Gd and Gp, respectively). This is also influ-

enced by the combination of elastic properties of layers

A and B, as described by the Dundurs parameters [134]. In

Figure 10 a diagram showing the regions prone to crack

deflection and to crack penetration is represented depend-

ing on the angle of crack propagation.

The curves given by the ratio Gd/Gp limit both regions.

When a crack propagates normal to the interface, it tends to

lam

inat

e

mon

olith

ic

0 Deflection

Load

0

FIGURE 9 Typical loadedeflection diagram of a layered structure with

weak interfaces. The steps show the failure of individual layers and the

crack propagation along the interface. A schematic side view of a broken

specimen showing crack deflection into the weak layers is shown in the

inset. The failure of a monolithic is also shown for comparison.

-1.0 -0.5 0.0 0.5 1.0

0.5

1.0

1.5

B1)

30°

45°

60°

Gi/G

laye

r

= (E '2

-E '1

) / (E '2

+ E '1

)

penetration

deflection

Gd/Gp

90°

A2)

AB

A1) B2)

BA

FIGURE 10 Diagram to predict crack

penetration into or deflection along the

interface in a multilayer structure. When

the crack propagates straight toward the

interface (left) crack penetration occurs. If

crack bifurcation takes place, the low angle

with which the crack approaches the inter-

face favors interface delamination (right).




penetrate, whereas cracks propagating with an inclined

angle may favor interface delamination, as shown in

Figure 10. It has been derived that the type of applied load

(i.e. tensile or bending), the presence of residual stresses,

and/or the angle of the approaching crack are key features

conditioning the crack path. This has also been validated

experimentally in different systems [14,25,60,62,68,135],

even for multilayers with relatively strong interfaces

[136,137].

3.2. Laminates with Strong Interfaces

Multilayer architectures designed with strong interfaces

can be subdivided into those with and without residual

stresses in the layers. The mechanical behavior of the latter

is enhanced by the different microstructures in the adjacent

layers (i.e. composition, fine or large grain size, etc.),

yielding crack branching or crack bridging as energy-

dissipating mechanisms [50,138]. More significant,

however, is the mechanical response of laminates with

residual stresses. In this case, two multilayered designs,

regarding the location of the compressive stresses either at

the surface or within the bulk material, have been exten-

sively investigated in order to tailor particular structural

applications. Laminates with compressive stresses on the

surface have proved to be useful for improving fracture

strength as well as increasing wear resistance to contact

damage [19,46,49,55,73,139e143]. On the other hand, if

the compressive layers are internal, mechanical behavior

enhancement is rather achieved in terms of flaw tolerance

and energy-dissipation mechanisms occurring at fracture

[11,15,20,21,24,70,78,79,144e149]. From this perspec-

tive, attainment of a threshold strength, i.e. a failure stress

that is independent of the original processing or machining

flaw size, is a reliable evidence of the potential effective-

ness of this approach [15,20,24]. An example of the

mechanical response of both configurations is shown in

Figures 11 and 12, respectively. In Figure 11a the bending

strength distribution of an aluminaezirconia multilayer

with external compressive stresses is plotted in a Weibull

diagram and compared with the strength corresponding to

a monolithic alumina-based ceramic. Due to the compres-

sive stresses in the outer layer (this layer is subjected to

tensile stresses under bending), the strength is enhanced

with respect to the monolithic material (without compres-

sive stresses). A slight improvement in the Weibull

modulus can also be observed. The fracture path in these

specimens is shown in Figure 11b. The presence of

compressive stresses slightly deviates the crack from

propagating straight. However, the propagation takes place

under unstable conditions. In Figure 12a indentation

strength results of similar aluminaezirconia multilayers are

plotted together with an alumina monolithic material. For

the latter the typical strength dependence with critical flaw

size (indentation crack) can be observed as for brittle

materials; the larger is the indentation crack introduced, the

lower is the failure stress. On the other hand, the strength on

the multilayer remains constant regardless of the initial

indentation flaw size. A minimum failure stress is obtained

for the different crack lengths introduced (threshold

100 μm

1

10

20

30

50

63

80

90

99

99,9

3300 386 472 558 644 730-6

-5

-4

-3

-2

-1

0

1

2

A

m = 10,4

0 = 492 MPa

A/AZ

m = 18,1

0 = 650 MPa

ln ln

1/

(1-F

)

pro

ba

bility o

f fa

ilu

re %

strength [MPa]

(a) (b) FIGURE 11 (a) Bending strength distri-

bution of aluminaezirconia (A/AZ) lami-

nates designed with compressive stresses in

the external layers. The strength is

compared to monolithic material (A) of the

external layers. (b) Crack propagation

through the layered structure; slight crack

deflection is observed due to the compres-

sive stresses in the layers.




strength). This is associated with the initial growth of

cracks during bending until they reach the compressive

(stopper) layer as can be seen in Figure 12b. The failure of

the structure occurs when the crack propagates through the

compressive layer. In such a case, the fracture takes place

through deflection and/or bifurcation of the crack (see

Figure 12c), which enhances significantly the fracture

energy of the system.

The design and use of multilayer systems with either

external or internal compressive stresses should be moti-

vated by the end application, as described in the Intro-

duction. The design optimization of such structures in

terms of strength and fracture resistance should also be

regarded according to the property which is to be improved,

as we will see below.

4. DESIGN GUIDELINES TO OPTIMIZESTRENGTH AND TOUGHNESS

Layered ceramics designed with strong interfaces have

proved to increase the strength and toughness of monolithic

ceramics by tailoring residual stresses in the layers. Much

effort has been focused on the optimization of symmetrical

laminates with a given layer thickness ratio between

adjacent layers [26]. Recent research has shown that the

distribution of layers of different materials can enhance

significantly the fracture response of the laminate while

maintaining a constant level of residual stresses [77]. Some

design guidelines based on fracture mechanics criteria and

experiments will be addressed in this section.

4.1. Fracture Mechanics Approach

The fracture criterion of brittle materials is described by the

linear elastic fracture mechanics (LEFM) based on the

well-known Griffith/Irwin equation [1]:

K � KIc (9)

where K is the stress intensity factor and KIc is the fracture

toughness of the monolithic material which can be exper-

imentally determined using the standardized single-edge V-

notch beam (SEVNB) method [150]. For an external

applied stress, sappl, an applied stress intensity factor, Kappl,

can be defined as

KapplðaÞ ¼ sapplYffiffiffiffiffiffi

pap

(10)

where Y is a geometric factor depending on the crack shape

and loading configuration and a is the crack length. The

10 15 20 25 3080

100

120

140

160

180

200

Square root of initial flaw size, c1/2 [ m1/2

]

Failu

re s

tress,

f [M

Pa

]

Monolith: A

Laminate: A/B

cra

ck

200 μm

(a) (b)

(c)

FIGURE 12 (a) Indentation strength results in aluminaezirconia laminates (A/B) designed with internal compressive stresses. The strength is compared

to monolithic material (A) of the external layers. (b) Arrest of an indentation crack due to the high compressive stresses in the approached layer.

(c) Fracture pattern through bifurcation mechanisms, enhancing the toughness of the system.




crack propagation is possible if the stress intensity factor at

the crack tip, Ktip, equals or exceeds the intrinsic material

toughness. The resistance to crack propagation in mono-

lithic materials is measured normal to the direction of

applied stress (mode I). However, in multilayer ceramics,

especially those designed with residual stresses, the stress

intensity factor at the crack tip as a function of the crack

length, Ktip (a), can be given as the externally applied stress

intensity factor Kappl (a) plus the contribution of the

residual stresses, given by Kres (a). In these cases, an

“apparent fracture toughness” as a function of the position

of the crack within the layered structure is evaluated, which

requires alternative approaches. In general, the effect

caused by the residual stresses can be described by

considering these stresses to be an additional external

stress, thus adding a term Kres, to the stress intensity factor

at the crack tip, Ktip, which reads

KtipðaÞ ¼ KapplðaÞ þ KresðaÞ (11)

Thus, solving Eqn (11) for Kappl, the Griffith/Irwin criterion

described by Eqn (9) now becomes

KapplðaÞ � KIc � KresðaÞ ¼ KRðaÞ (12)

where KR (a) is the “apparent fracture toughness”. For

Kres < 0, as it holds for the action of compressive stresses,

KRðaÞ � KIc, what is called an increasing crack growth

resistance curve (R-curve). This describes the “shielding”

effect associated with the compressive stresses. If tensile

residual stresses are acting, “anti-shielding” occurs and KR

decreases with increasing crack extension.

The evaluation of the fracture toughness (or fracture

energy) of layered structures has been attempted by theo-

retical means using different approaches. One general

procedure for the determination of Kres(a) is the finite

element (FE) method. An FE model has to be created in

order to compute the stress intensity factor at the crack tip

under applied external stress for every position of the crack

within the multilayer. Although there is, in general,

a singularity problem at the interface, methods such as the

J-integral can approximate the solution to the problem up to

certain distance from the interface [151]. In order to

describe the propagation of the crack along or through the

interface, methods based on the LEFM have been devel-

oped such as the “finite fracture mechanics” approach,

where the crack path near an interface between two

different materials can be described [152]. Such methods

can be used to describe the crack propagation resistance in

linear elastic monolithic materials. However, the applica-

tion to composites or layered structures combining

different classes of materials (e.g. metaleceramic and

ceramicepolymer) with different elastic constants should

be carried out with care. In this regard, a new approach is

the configurational forces (CF), which considers a material

inhomogeneity (e.g. second phase and layer) as an

additional defect in the material (besides the crack)

inducing an additional contribution to the crack driving

force. This contribution is called the material inhomoge-

neity term Cinh. The thermodynamic force at the crack tip,

denominated as the local, near-tip crack driving force Jtip, is

the sum of the nominally applied far-field crack driving

force Jfar (classical J-integral of fracture mechanics) and the

material inhomogeneity term Cinh [153e155]. This method

allows, for instance, taking into account the contribution of

the different compliance of the layers to the crack propa-

gation resistance. For the case of ceramic laminates with

layers having relatively similar elastic constants, an alter-

native method to account for the term Kres(a) is the weight

function (WF) approach. This allows us to calculate the

apparent toughness KR(a) for an edge crack of length a for

an arbitrary stress distribution acting normal to the

prospective fracture path as [156]

KRðaÞ ¼ K0 �Z

a

0

hðx; aÞsresðxÞdx (13)

where K0 is the intrinsic fracture toughness of each indi-

vidual layer, x is the distance along the crack length

measured from the surface, a is the crack length, and h(a,x)

is theweight function, which has been developed for an edge

crack in a bar under different loading configurations [157].

The methods described above give very similar results

and correlate with experimental findings for layered

ceramics with residual stresses [77] (see Figure 13).

Therefore, any of them can be used for K-value or J-inte-

gral calculations. Through comparison of the computa-

tional effort factors of the FE method, the CF method, and

the WF method, it can be stated that the WF approach is

much less time-consuming and thus is recommended when

optimization processes of laminates are to be performed.

0.0 0.1 0.2 0.3 0.4 0.5 0.60

40

80

120

160

200

240

J ap

pt (

J/m

2 )

a (mm)

A-layer B-layer A-layer

Weight function (Bermejo et al.)

FEM (Sestakova et al.)

Configurational forces (Chen et al.)

SEVNB-Experiments (Pascual et al.)

FIGURE 13 Comparison of the apparent J-integral, Jappt, as a function of

the crack length a, calculated using experimental as well as analytical and

numerical methods, for an aluminaezirconia laminate with compressive

residual stresses in the external layers [26,77,158,159].




This will be used below to compare and optimize the

mechanical properties of layered ceramics with external or

internal compressive stresses.

4.2. Optimal Laminates with ExternalCompressive Stresses

In this section, the design optimization in terms of tough-

ness and strength of an aluminaezirconia laminate with

external compressive stress (ECS) is illustrated. Material

properties used in this study are based on typical values for

aluminaezirconia periodic laminates (i.e. all layers of

material A have the same thickness; the same holds for

material B) [23]. Hence, elastic properties are chosen as

E ¼ 390 GPa, n ¼ 0.22, and coefficients of thermal expan-

sion between layers asDa¼ 1� 10�6K�1. In Figure 14 the

qualitative behavior of ECS laminates is shown (the data

correspond to laminates with s0 ¼ �590 MPa).

For the determination of the apparent toughness, the

WF method has been employed. Plotted are the R-curves

versus the crack length parameter Yffiffiffiffiffiffi

pap

for the first two

layers of two laminates having a different material volume

ratio VB=VA (i.e. for ECS1: VB=VA ¼ 7=3 and for ECS2:

VB=VA ¼ 9=1). The geometric factor Y is taken as 1.12 for

an edge crack. Therefore, the stress magnitudes in the

layers of the two laminates are also different (i.e. for ECS1:

sA ¼ �413 MPa, sB ¼ þ177 MPa and for ECS2: sA ¼�531 MPa, sB ¼ þ59 MPa). It is assumed that the thick-

ness of the first two layers is constant ðtA þ tB ¼ 1 mmÞfor both laminates. In the laminate ECS1, the compressive

outer A-layer is thicker ðtAÞ than in laminate ECS2 but the

magnitude of the compressive stresses is lower. The second

(tensile) B-layer is thinner ðtBÞ in ECS1 but the stress

magnitude is higher than in ECS2. The shielding effect

of the compressive residual stresses causing a rise of the

R-curve within the first layer can clearly be recognized. In

the analyzed region (the first two layers) maximum

shielding is always achieved at the first A/B interface of the

external compressive A-layer, i.e. the length of the crack

having a maximum shielding is a ¼ tA.

For this case, the influence of the compressive residual

stresses in the outer A layer can easily be determined.

It simply holds: KRðaÞja�tA¼ 1:12$sA

ffiffiffiffiffiffi

pap

with sA ¼s0$VB=ðVA þ VBÞzs0$tB=ðtA þ tBÞ. Maximum shielding

is reached if a ¼ tA. Therefore, the peak toughness is

KR;peak ¼ K0 � 1:12ffiffiffiffi

pp

$s0$tBffiffiffiffiffi

tAp

=ðtA þ tBÞ (14)

Note that s0 is a negative number. Therefore, for a given s0,

the peak toughness is maximum, if tBffiffiffiffiffi

tAp

=ðtA þ tBÞ is

maximum. For ðtA þ tBÞ ¼ constant, this value has its

maximum for tB=tA ¼ 2.

Figure 15 shows the peak toughness KR;peak versus

tA=ðtA þ tBÞ for laminates with different values of

ðtA þ tBÞ. It can be recognized that the maximum always

occurs for tB=tA ¼ 2, i.e. tA=ðtA þ tBÞ ¼ 1=3, with the

toughness increasing with tA þ tB.

Additionally to the optimization of the apparent

toughness, the strength of the laminate must also be

regarded. The strength depends on the size of the fracture

origins (the flaws where fracture starts), considered as the

depth of the through-thickness edge crack. The typical

range of flaw sizes occurring in a ceramic material depends

on the processing conditions. For technical state-of-the-art

materials, the typical size of a volume flaw is about 30 mm

(about 10 mm for surface flaws) [8]. A typical range of

fracture origins is indicated in Figure 14 (shaded bar).

However, larger flaws may also occur, causing the strength

scatter in that type of ceramics [3,160]. Indeed, in a lami-

nate system, no processing flaws larger than the layer

thickness ðtAÞ can occur. In order to interpret the

0.0 0.2 0.4 0.6 0.8 1.0

3

6

9

12

15

18

tA + t

B = 100 μm

tA + t

B = 200 μm

tA + t

B = 1000 μm

KR

,pea

k (M

Pa

.m1

/2)

tA/(t

A+t

B) (-)

(tA + t

B) increases

1/3

FIGURE 15 Peak toughness as a function of the thickness ratio tA/tAþ tBfor different total thicknesses of the first two layers tA þ tB. A maximum

toughness value is obtained independent of the tA þ tB selected.

0.00 0.01 0.02 0.03 0.04 0.05 0.060

3

6

9

12

15

18

21

KIc

234

tA,ECS1tA,ECS2

1

appl

KR,peak

Kappl

tA + t

B

ECS2

ECS1

Ap

pa

ren

t to

ug

hn

ess, K

R (

MP

a.m

1/2

)

Crack length parameter, 1.12( a)1/2

(m1/2

)

FIGURE 14 Apparent fracture toughness of laminates designed with

external compressive stresses. The peak toughness, KR, peak, depends on

the thickness of the first layer. The range of typical defect sizes is repre-

sented as a shaded bar.




implications of the design in strength, the dependence of

KapplðaÞ on the crack length parameter 1:12ffiffiffiffiffiffi

pap

is repre-

sented in Figure 14 as lines through the origin. Lines with

different slopes refer to different values of applied stress

(lines 1e4). Hence, for an applied stress intensity factor

corresponding to lines 1 and 2 and for cracks having

a length in the shaded bar, it holds Kappl < KR for ECS1 as

well as for ECS2. This indicates that the driving force is too

small to extend these cracks. At higher stresses (line 3) and

for the largest flaw in the laminate ECS1, Kappl ¼ KR holds.

This crack (and larger cracks, if they exist) may propagate

but the smaller cracks may not. In the laminate ECS2

cracks having a length corresponding to the shaded bar are

still too small to propagate. If we increase the applied stress

to the slope of line 4, the Griffith criterion is also fulfilled

for the largest flaw in the shaded area for ECS2. In that case

the right end border of the shaded bar corresponds to the

A/B interface, and the corresponding crack length will be

tA. This case defines a lower limit (a threshold value) for the

strength of ECS2. It is interesting to note that although

laminate ECS1 has higher peak toughness than ECS2, the

strength of ECS2 is higher than that of ECS1.

A comparison of the strength of the monolithic ceramic

(material A) and the laminates is also possible. Since the

monolithic ceramic has no increasing R-curve, its fracture

toughness KIc corresponds to the horizontal dashed line in

Figure 14. For the flaws in the shaded area, the lowest

strength value of the monolithic material is given by line 1.

It is obvious that the strength of both laminates is signifi-

cantly higher than that of the monolith.

In general, the size of the largest possible processing flaw

in a laminate is limited to the thickness of the outer A-layer.

Then the threshold for the strength depends on the height of

the peak toughness and on the layer thickness, as givenbelow:

sth ¼ KR;peak

1:12ffiffiffiffiffiffiffiffi

ptAp ¼ Kc

1:12ffiffiffiffiffiffiffiffi

ptAp � s0

tB

tA þ tB(15)

The first term of Eqn (15) increases as tA is reduced. It is

obvious that this threshold stress can be increased by

decreasing the layer thickness, but, for technological

reasons, laminates with layers thinner than 5e10 mm can,

today, hardly be processed. Then the contribution of the first

term to the threshold can reach the characteristic strength of

the material if the cracks are as large as the thickness of the

first layer. The second term is positive and, for tA<<tB, it

reaches js0j, which can be of the order of magnitude of the

characteristic strength of material A. Compared to mono-

lithic ceramics where failure may occur at any stress, the

occurrence of a threshold stress causes a significant increase

in mechanical reliability (at stresses lower than the

threshold) and can thus be used for safe design.

In ECS laminates the key parameter is the thickness of

the first layer (with compressive stresses), which should be

as thin as possible but thick enough to contain the largest

processing flaws. This can be achieved by designing non-

periodic laminates where the thickness of the layers in the

center of the architecture corresponding to material A can

compensate the small thickness of the very first layer in

order to tailor the residual stresses (associated with VB/VA),

which will maximize the peak toughness predicted by Eqn

(14) (see Ref. [77] for more details).

4.3. Optimal Laminates with InternalCompressive Stresses

For ICS laminates (internal compressive stress, the outer

layer is under tension) simple analytical solutions as for

ECS laminates do not apply and the apparent toughness

(the R-curve) has to be determined using approximation

methods such as the WF method. The apparent toughness

of a periodic aluminaezirconia ICS laminate according to

Eqn 13 is shown in Figure 16. The R-curve is represented as

a function of the crack length parameter 1:12ffiffiffiffiffiffi

pap

in the

region of maximum shielding (peak toughness), which is

achieved for a crack length of a ¼ tA þ tB. Due to the

tensile residual stresses the R-curve decreases in the outer

A-layer and increases again in the following B-layer, which

contains compressive residual stresses. In this kind of

laminate, two regions can be distinguished as a function of

the flaw (crack) size. For very small flaws having a size in

region I unstable crack propagation occurs, which causes

catastrophic failure. This happens at relatively high applied

stresses (see the slope of line 1). On the other hand, larger

cracks in region II first pop in to an even greater size if

stress is applied (section of line 3 with the decreasing

R-curve) and then stop (intersection point of line 3 with the

increasing part of the R-curve in layer B). This is caused by

the shielding effect of the compressive layer. If the stress is

0.00 0.01 0.02 0.03 0.04 0.05 0.06

-3

0

3

6

9

ΚR,peak

appl

2

sta

ble

unstable3

I

th

(unstable + stable + unstable)

(unstable)

K c

Ap

pa

ren

t to

ug

hn

ess, K

R (

MP

a.m

1/2

)

Crack length parameter, 1.12( a)1/2

(m1/2

)

1

II

FIGURE 16 Apparent fracture toughness of laminates designed with

internal compressive stresses. The peak toughness, KR,peak, depends on the

thickness of the first two layers. Regions of stable and unstable crack

growth can be found as a function of the initial defect size. The threshold

strength can be derived from the peak toughness.




further increased, stable crack growth up to the crack length

of a ¼ tA þ tB occurs. Line 2 intersects the R-curve of the

laminate at a stress level at which these cracks become

unstable again and where catastrophic failure occurs. This

determines a threshold for the strength of the laminate,

which is given by: sth ¼ KR;peak=1:12ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

pðtA þ tBÞp

. Note

that only the first two layers of ICS laminates are important

for the assessment of the crack resistance of such a lami-

nate. Considering tA þ tB ¼ constant an optimal design for

maximal shielding can be found. Figure 17 shows the peak

toughness KR, peak versus tA=ðtA þ tBÞ for laminates with

different values of tA þ tB. It can be seen that the maximum

always occurs for tA=ðtA þ tBÞz0:8 (which corresponds totB=tAz0:25) and the toughness values also increase with

tA þ tB. Similar behavior can be observed for the threshold

strength, which reaches its maximum for the same ratio

tB=tAz0:25 and increases with tA þ tB. In order to enhance

the threshold strength one could also increase the number

of layers. However, the peak toughness would be signifi-

cantly reduced. In this regard, improvements may still be

possible for nonperiodic laminates trying to optimize the

first two layers and then tailoring the internal structure in

order to accommodate the residual stresses.

In Figure 18 the apparent fracture toughness of a periodic

ICS laminate (ICS1) is compared to that of a nonperiodic one

(ICS2), which has been designed with a thin first (tensile)

layer and a thicker second (compression) layer. Both lami-

nates have the same tensile and compressive residual stresses

in the layers (the same VB=VA ratio). It can be observed that

by decreasing the thickness of the first A layer the threshold

strength can be improved and by increasing the thickness of

the next layer (layer B) the peak toughness is also enhanced.

Summarizing, the optimal design for ICS laminates with

nonperiodic layers lies in the combination of both concepts:

(i) first make the tensile layer (A) as thin as possible and (ii)

the compressive layer (B) as thick as possible. This design

ensures a low decrease ofKR in the first thin tensile layer and

a high increase of KR within the second thick compressive

layer. When both steps are adopted in a unique nonperiodic

design, the mechanical properties of the system can be

significantly enhanced with respect to monolithic materials.

4.4. Search for New Design Concepts

The potential of layered designs to improve the mechanical

properties of ceramics is based on the capability of the layers

to arrest or deflect potential cracks in thematerial aswell as to

increase the strength reliability of the system through tailored

residual stresses. The role of the interface in the fracture

process must also be taken into account. For instance, the

combined effect of laminates with residual stresses and at the

same time relatively weak interfaces can significantly

enhance the resistance to crack propagation in the material

[161]. This has been recently shown in an aluminaezirconia

layered system designed with high compressive residual

stresses. The magnitude of such stresses and the thickness of

the compressive layer induced crack bifurcation during

bending, thus increasing the fracture energy of the system.

Additionally, the low bifurcation angle, the different elastic

constants of the layers, and the interface fracture energy

could also promote interface delamination (see Figure 10).

The combination of layers with high compressive residual

stresses and weak interfaces can be a promising strategy to

combine the benefits of both approaches.

5. OUTLOOK

The production and implementation of layered ceramic

structures in advanced material science are either motivated

by the need for a composite material whose mechanical

0.0 0.2 0.4 0.6 0.8 1.0

3

4

5

6

7

8

9

10

tA + t

B = 200 μm

tA + t

B = 100 μm

tA + t

B = 1000 μm

KR

,pe

ak (

MP

a.m

1/2

)

tA/(t

A+t

B) (-)

(tA + t

B) increases

4/5

FIGURE 17 Peak toughness as a function of the thickness ratio tA/(tAþ tB)

for different total thicknesses of the first two layers tA þ tB. A maximum

toughness value is obtained independent of the tA þ tB selected.

0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14

-4

0

4

8

12

16

20

24 Periodic laminate

Non-periodic laminate

ICS1-periodic

ICS2-non-periodic

th

Kth

Ap

pa

ren

t to

ug

hn

ess, K

R (

MP

a.m

1/2

)

Crack length parameter, Y ( a)1/2

(m1/2

)

FIGURE 18 Apparent fracture toughness of a periodic (ICS1) and

nonperiodic (ICS2) laminate, with the same tensile and compressive

residual stresses in the layers. The nonperiodic disposition shows higher

peak toughness and threshold strength.




properties surpass those of its constituents or driven by the

material’s special applications. The concept of layered

ceramics and functionally graded materials allows in fact

tailoring of the surface and bulk properties of advanced

engineering components with the purpose of enhancing

their structural integrity as well as adding multi-

functionality, which would translate into higher efficiency

and better performance of these components.

Vast industrial sectors involving, for instance, aero-

nautics, biomedicine, communications, and automotive

(among others) could benefit from the development of such

advanced materials. Specific examples of applications are

thermal barrier coatings, which provide thermal protection

for gas turbine blades and combustion chambers of aero-

engines, dental crowns and hip prostheses for biomedical

replacements, multilayer stacks in actuators for a reduction

of emissions and the better performance of diesel engines,

and hard layers in cutting tools. Also in the communication

industry the development of reliable layered composites

suitable for ultra-THz filters for wireless communications

(e.g. mobile phones) is becoming necessary because the

increasing demand for bandwidth is pushing the wireless

short-range network into the THz frequency. Another

example is the miniaturization of SOFCs (e.g. to be used as

hybrid batteries in laptops or PDAs), where the perfor-

mance of the system relies on the structural integrity of the

multilayer structure.

The replication of architectural features that are found

in nature, at the micro- and nanoscales, into real macroscale

structural and functional engineering materials at

a reasonable cost is expected to be the future leading

concept for layered ceramics. This is generally due to the

fact that production facilities for such materials are already

available or could be easily scaled up (i.e. the tape-casting

process). The main challenge regarding these structures

resides in the careful tailoring of all materials parameters in

order to induce crack deflection and graceful failure. In

addition, it is necessary to build these high toughness

architectural features by using more durable materials since

they should possess additional functional and/or structural

properties as, for example, high-temperature stability and

specific functionality (i.e. metaleceramic composites in

the case of piezoelectric actuators). Another challenge is

the integration of materials with different structures and

phases, such as the multilayer packages for microelec-

tronics, which include single crystalline and polycrystalline

silicon, amorphous polymer layers, and metals.

The use of advanced ceramic-based multilayer archi-

tectures in engineering systems will be feasible when the

mechanisms responsible for the outstanding mechanical

behavior of natural systems would be completely under-

stood. The use of bio-inspired multilayer structures on

systems of different kinds (e.g. ceramiceceramic and

ceramicemetal) should contribute to material innovation

designs within the field of material science and engineering

for the next decades.

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