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Journal of the European Ceramic Society 35 (2015) 631–640

Design of alumina-zirconia composites with spatially tailored

strength and toughness

Yunfei Chang a, Raul Bermejo b, Oldrich Sevecek c, Gary L. Messing a,∗

a Department of Materials Science and Engineering, Pennsylvania State University, University Park, PA, 16802, United Statesb Institut für Struktur-und Funktionskeramik, Montanuniversität Leoben, Leoben, Austria

c Institute of Solid Mechanics, Mechatronics and Biomechanics, Brno University of Technology, Brno, Czech Republic

Received 16 July 2014; received in revised form 3 September 2014; accepted 9 September 2014

Available online 27 September 2014

Abstract

Composites of Al2O3–5 vol.% t-ZrO2 (ATZ) and Al2O3–30 vol.% m-ZrO2 (AMZ) layers were designed with 3–1 connectivity to explore the effect

of spatially-dependent residual stress and layer distribution on mechanical behavior. ATZ composites with ‘shallow’ and ‘deep’ regions of AMZ,

defined relative to the distance from the surface, were fabricated. Four-point bending tests on indented 3–1 composites showed crack arrest in the

first compressive AMZ layer and a fracture strength nearly independent of indent size (i.e. minimum strength); the failure occurring in the region

with thicker outer ATZ layers (‘deep’ region). Region dependent crack growth resistance was measured on SEVNB specimens and compared

to theoretical predictions using a fracture mechanics model. Spatially tailored constant strengths were obtained, ranging between 148 MPa and

470 MPa; the maximum value corresponding to a ‘shallow’ region with a relatively thicker AMZ compressive layer embedded close to the tensile

ATZ surface. The 3–1 design concept allows the fabrication of ‘deep’ and ‘shallow’ embedded regions within a unique composite architecture,

thus providing a preferential path for crack propagation, opening new possibilities for design of composite structures with spatially-tailored crack

growth resistance.

© 2014 Elsevier Ltd. All rights reserved.

Keywords: Connectivity; Composites; Residual stresses; Fracture strength; Toughness

1. Introduction

The variable strength in brittle materials such as glasses

and ceramics is related to the different size of critical defects,

from specimen to specimen, introduced during processing, from

machining or occurring in service. The strength cannot be char-

acterized as a single value but as a distribution function, which

is related to the defect size distribution in the material.1 Increas-

ing strength in glasses and ceramics can be attained by reducing

the size of critical defects (e.g. through colloidal processing)2 or

introducing surface compressive residual stresses (e.g. strength-

ening in glass)3,4 to enhance the resistance of the material to

∗ Corresponding author. Tel.: +01 814 865 2262; fax: +01 814 865 8262.

E-mail addresses: messing@ems.psu.edu, messing@matse.psu.edu

(G.L. Messing).

crack propagation. However, significant reduction of strength

variability may not be achieved. Rather than reducing critical

flaw size, a “flaw-tolerant” approach has been developed to build

ceramic composites by combining layers of two different materi-

als/microstructures in a periodic architecture with 2–2 multilayer

connectivityd.5–13 Two main approaches regarding the fracture

energy of the layer interfaces are particularly useful, which aim

to generate “weak” or “strong” interfaces. In particular, 2–2

layered composites designed with strong interfaces can present

enhanced mechanical behavior through microstructural design

d Connectivity is defined as the number of dimensions in which each com-

ponent (e.g. material or microstructure) is self-connected.5 In two-component

composites, a 2–2 composite is one in which both components are self-connected

in two dimensions, i.e. a laminate. More details on the connectivity and its

schematic illustration are available in the supplemental file.

http://dx.doi.org/10.1016/j.jeurceramsoc.2014.09.017

0955-2219/© 2014 Elsevier Ltd. All rights reserved.

632 Y. Chang et al. / Journal of the European Ceramic Society 35 (2015) 631–640

(e.g. grain size, layer composition) and/or due to the presence of

compressive residual stresses, acting as a barrier to crack propa-

gation. Under certain conditions, the compressive stresses may

arrest the propagation of surface cracks, yielding a so-called

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

failure does not occur despite the presence of relatively large

cracks.

Threshold strength was first reported for alumina-mullite lay-

ered composites, where the propagation of indentation cracks

under bending was arrested between two compressive layers.14

The concept of designing ceramics with a “minimum strength”

was further extended to other alumina-based 2–2 layered com-

posites (e.g. alumina–Si3N4, alumina–zirconia) under different

loading configurations.7,8,10,11 In alumina–zirconia systems,

high compressive stresses in the embedded layers are devel-

oped during cooling from the sintering temperature because of

the differences in thermal expansion coefficients between lay-

ers of different composition.15 The profile of the tensile and

compressive stresses can be tailored by combinations of com-

position, stacking sequence and layer thickness.7,10,15–17 Recent

advances in fracture mechanics modeling have shown that an

optimized non-periodic 2–2 layered architecture can result in

pronounced crack growth resistance and minimum strength

using thin outer tensile layers and thicker internal compres-

sive layers.18 Although much progress has been achieved in

improving the resistance to crack propagation in 2–2 multilayer

composites, the potential of complex architectural design has not

been sufficiently exploited or explored. This is very important

because spatial control and composite connectivity of the indi-

vidual layers of a composite are ultimately the key to developing

and controlling useful and unique properties.

From the functional point of view, the dependence of prop-

erties on connectivity is especially pronounced in ceramic

components that are fabricated with complex connectivities for

piezoelectric transducer, magnetic field sensor, low temperature

co-fired electronic package and solid oxide fuel cell applications

etc.5,19–22 However, from the structural integrity point of view,

residual stresses related to the combination of different mate-

rials (e.g. metal electrodes, ceramic parts) may initiate cracks,

which can propagate during service and reduce the component

functionality.23 The development of structural composites with

various connectivities (e.g. 3–1, 1–1) in three-dimensional struc-

tures might allow access to unique mechanical properties never

before achieved in 2–2 composites. To our knowledge, few stud-

ies focused on designing and understanding the properties of

structural composites with such higher levels of complexity are

available in the literature.

In this work, we explore novel 3–1 connected composites to

understand how this connectivity can be used to affect the resis-

tance to crack propagation and fracture behavior in a ceramic

composite. Alumina–zirconia was chosen as the model system

due to its highly useful mechanical properties that warrant fur-

ther exploration. Four types of 3–1 connected alumina–zirconia

based composites with ‘shallow’ and ‘deep’ regions, defined rel-

ative to the distance of the embedded compressive layers from

the surface, were fabricated. Crack propagation was investigated

by four-point bending of indented 3–1 specimens and compared

to that of 2–2 composites. The effects of location and thickness

of the embedded compressive layers on the fracture strength

and fracture toughness of 3–1 composites were determined.

A fracture mechanics model, based on a weight function analy-

sis, was implemented to interpret the results.

2. Experimental

The 3–1 connected alumina–zirconia composites consist

of two components: layers of 95 vol% alumina and 5 vol%

Y2O3-stabilized zirconia (ATZ), and embedded layers of

70 vol% alumina and 30 vol% monoclinic zirconia (AMZ). In

3–1 connected alumina–zirconia composites, ATZ and AMZ

components are self-connected in three and one dimensions,

respectively. The addition of 5 vol% tetragonal zirconia in ATZ

has the effect of limiting alumina grain growth during sinter-

ing. The 30 vol% of monoclinic zirconia was used in the AMZ

layers to generate a large strain mismatch between the AMZ

and ATZ layers as a result of the ∼5% volume change dur-

ing the tetragonal-monoclinic transformation at ∼730 ◦C upon

cooling,24 and thus induce a high residual compressive stress

when embedded in the ATZ matrix.24,25

The composite was assembled with a symmetric and

non-periodic distribution of the embedded AMZ layers. The

symmetric architecture of the composite avoids warpage dur-

ing sintering. The non-periodic design enables the distribution

of layers at different locations and depths within a particular

region, while having a constant total volume ratio between the

two materials. The design and properties of the four types of

composites, including the AMZ layer thicknesses (tAMZ) and

the corresponding first layer thickness ratios (t1stATZ:t1st

AMZ),

are shown in Fig. 1 and listed in Table 1. The total volume ratio of

ATZ:AMZ materials is 12.0 ± 0.2 for all 3–1 composites stud-

ied. Two main regions can be defined in each 3–1 composite,

hereinafter referred to ‘shallow’ and ‘deep’ regions, associated

with the distance (t1stATZ) from the surface to the first AMZ

embedded layer. The nomenclature used for the four types of

3–1 composites is AF, BE, CD and GH, where the regions

A, B, C, D, E, F, G and H correspond to depths (t1stATZ) of

1222 �m, 802 �m, 458 �m, 382 �m, 382 �m, 382 �m, 382 �m

and 150 �m for the first AMZ embedded layers, respectively.

The AMZ layer is 75 �m thick in all cases except for GH where

the AMZ layers are 150 �m thick in region H.

2.1. Fabrication of 3–1 alumina–zirconia composites

Composites were produced from 0.28 �m �-Al2O3 powders

(AKP50, Sumitomo Chemical Co. Ltd., Tokyo, Japan), 0.60 �m

yttria stabilized zirconia powder (TZ-3Y, Tosoh, Yamaguchi,

Japan), and 0.30 �m monoclinic zirconia powder (TZ-0, Tosoh,

Yamaguchi, Japan). The ATZ and AMZ tape casting slurries

were prepared by ball milling the powders for 48 h in a 50:50

(weight ratio) xylenes ± ethanol solution containing blown men-

haden fish oil. Binder and plasticizers (polyvinyl butyral, butyl

benzyl phthalate, and polyalkylene glycol) were then added,

followed by an additional 24 h milling/mixing step.26

Y. Chang et al. / Journal of the European Ceramic Society 35 (2015) 631–640 633

Fig. 1. Schematics of the four types of 3–1 composites (xz plane) studied.

Table 1

Properties of 3–1 composites with an ATZ:AMZ volume ratio of 12.0 ± 0.2 as a function of AMZ layer location and thickness.

Composite Region tAMZ (�m) t1stATZ:t1st

AMZ σf (MPa) Kapt (MPa m1/2) Kmax# (MPa m1/2)

AF A 75 16.3:1 – 2.7 ± 0.1 6.8

F 75 5.1:1 259 ± 4 10.1 ± 0.3 11.0

BE B 75 10.7:1 148 ± 3 6.4 ± 0.1 9.0

E 75 5.1:1 250 ± 9 9.5 ± 0.2 11.0

CD C 75 6.1:1 218 ± 4 8.0 ± 0.1 10.6

D 75 5.1:1 250 ± 9 9.4 ± 0.2 11.0

GH G 75 5.1:1 299 ± 13 11.0 ± 0.3 11.0

H 150 1.0:1 470 ± 8 – 17.6

# Maximum fracture toughness as predicted by the fracture mechanics model.

Single ATZ tapes were prepared by tape casting.26 The

ATZ and AMZ slurries were co-cast27,28 with the component

interfaces parallel to the length of the single tape. Each co-

cast tape was composed of three segments with the two outer

segments having the same composition. The cast and co-cast

tapes were dried, cut, and stacked to obtain the four types of

3–1 ATZ–AMZ composites shown in Fig. 1 and illustrated in

Fig. 2a for a BE composite. The stacked tapes were laminated at

75 ◦C and 20 MPa to fabricate the green composites. The binder

was removed by heating the composites in air at 0.2 ◦C/min to

600 ◦C for 3 h. After cold isostatic pressing at 200 MPa, green

composites were heated at 5 ◦C/min in air to 1550 ◦C and held

for 4 h. Composite plates of approximately 45 mm by 45 mm

by 3.9 mm were obtained for the four types of 3–1 composites

studied. An optical micrograph of the x–z plane of the 3–1 BE

composite and an SEM image of the interface between the ATZ

Fig. 2. BE type 3–1 composites: (a) schematic of stacking sequence, (b) optical micrograph of part of the xz plane, and (c) SEM image of the ATZ and AMZ interface.

634 Y. Chang et al. / Journal of the European Ceramic Society 35 (2015) 631–640

and AMZ components in the composite are shown in Figs. 2b

and c, respectively.

2.2. Residual stress determination

The differential thermal strain, �ε, between ATZ and AMZ

was estimated by thermomechanical analysis (TMA) of sin-

tered ATZ and AMZ monoliths using a differential dilatometer

(PT1000, Linseis GmbH, Selb, Germany). The thermal cycle

consisted of heating at 2 ◦C/min until 1250 ◦C, where the temper-

ature was held for around 20 min, followed by cooling to room

temperature at the same rate. Assuming 1200 ◦C as the reference

temperature, Tref, above which the composite is considered to be

stress-free, the corresponding coefficients of thermal expansion

(CTE) of ATZ and AMZ components are αATZ = 9.8 ± 0.1 ppm

and α AMZ= 8.0 ± 0.1 ppm between 25 ◦C and 1200 ◦C. The

lower average CTE of AMZ monolith is a consequence of the

compensating expansion of the phase transformation and ther-

mal contraction during cooling.

The residual stress distribution in the 3–1 composites was cal-

culated under plain strain conditions with a 2D parametric finite

element model (FEM) using ANSYS 14.0. Stresses calculated

in regions far from the junctions were compared with analytical

calculations corresponding to 2–2 ATZ–AMZ composites (far

from the free edges) in order to validate the model. The analyt-

ical calculation considers a homogeneous and biaxial residual

stress state in the interior of the layers. The stress magnitude

σres,i in layer i can be calculated as8

σres,i =Ei

1 − νi

(α − αi) �T (1)

where Ei, vi and αi are the elastic modulus, Poisson ratio and

CTE of the ith layer, respectively, and α is the average thermal

expansion coefficient for the composite. For a layered composite

consisting of A and B materials, α of the composite is given by18

α =

(

EAαA1−νA

×∑nA

i=1tA,i +EBαB1−νB

×∑nB

i=1tB,i

)

(

EA1−νA

×∑nA

i=1tA,i +EB

1−νB×

∑nBi=1tB,i

) (2)

where nA and nB are the numbers of layers of materials A and

B, respectively, and tA and tB are the thicknesses of the A and

B layers, respectively.

2.3. Indentation–strength test of 3–1 composites

The 3–1 composites were cut perpendicular to the y-direction

to obtain 3–1 bend bars (Fig. 3). To study the effects of the inner

compressive layer position and thickness on the fracture behav-

ior of the 3–1 composites, at least 48 bend bars of each type

of composites were prepared. One surface and one lateral face

of the bending bars were polished to a 3 �m finish, and the

other surface was ground. The following combinations of Vick-

ers indents were placed longitudinally on composite surfaces

with a separation distance of 2.5 mm to avoid crack interaction29:

(1) 20, 50, 100 N; (2) 20, 100, 50 N; (3) 50, 100, 20 N; (4) 50,

20, 100 N; (5) 100, 20, 50 N; (6) 100, 50, 20 N; (7) 50, 100,

Fig. 3. The orientation of the sample cuts for BE type 3–1 composite.

200 N; (8) 50, 200, 100 N; (9) 100, 50, 200 N; (10) 100, 200,

50 N (11) 200, 50, 100 N (12) 200, 100, 50 N (13) 20, 20, 20 N

(14) 50, 50, 50 N (15) 100, 100, 100 N; (16) 200, 200, 200 N.

For each combination of three indents noted above, the middle

indent was above the junction region, while the outer indents

were above the two different 2–2 regions and far from the junc-

tion region, respectively. In all cases, the set of three indents

was within the inner span used during four-point bending, and

thus under constant bending moment. Cracks emanating from

the corner of the indentations were measured with an optical

microscope. The pre-crack sizes c induced by the indentation

loads of 20 N, 50 N, 100 N, 200 N were (at the surface) approx-

imately 52 ± 3 �m, 98 ± 7 �m, 152 ± 9 �m and 243 ± 16 �m,

respectively. Based on earlier observations of indentation cracks

in ATZ layers of 2–2 composites,30 the crack-shape was assumed

to be semi-elliptical, with c/a ≈ 1.25; a being the crack depth.

All indented samples were fractured under four-point bending at

0.1 mm/min on a screw-driven universal testing machine (model

5866, Instron Ltd. Grove City, PA) at 25 ◦C and 40% relative

humidity. The fracture strength σf was determined according to

ASTM C-1161.31

The 2–2 composites were also fabricated for indentation-

strength measurements by cutting 3–1 composites perpendicular

to the x-direction (Fig. 3). The following combinations of Vick-

ers indents were placed longitudinally on each specimen surface:

(1) 20, 20, 20 N; (2) 50, 50, 50 N; (3) 100, 100, 100 N; (4)

200, 200, 200 N. The pre-crack sizes were similar to those mea-

sured in the 3–1 composites. All samples were fractured under

four-point bending at 0.1 mm/min.

2.4. Apparent fracture toughness assessment of 3–1

composites

The apparent fracture toughness Kapt was experimentally

determined using the Single Edge V-Notch Beam method

(SEVNB) specimens according to the ISO 23146 standard

procedure.32 A pre-notch, made with a thin high speed diamond

saw (150 �m thick blade), was sharpened with an automatic

razor blade machine to a radius of ≤10 �m to minimize the

influence of notch radius on KIc.33 Notched 3–1 bend bars were

loaded to fracture in four-point bending at 0.1 mm/min on a

screw-driven universal testing machine (model 5866, Instron

Ltd. Grove City, PA) at ambient conditions (i.e. 25 ◦C and 40%

relative humidity). The same procedure was conducted on the

2–2 composite bars. A total of eight specimens were tested for

each composite design.

Y. Chang et al. / Journal of the European Ceramic Society 35 (2015) 631–640 635

Fig. 4. Residual stress distribution (σxx in-plane and σzz out-of-plane) through the thickness of the BE 3–1 composite in region E, region B and junction BE. The

contour plot shows the stress distribution in the x-direction, indicating compressive and tensile stresses in the AMZ and ATZ materials, respectively.

3. Results and discussion

3.1. Residual stress profile in 3–1 composites

The predicted stress distribution in the 3–1 BE composite

is shown as an example in Fig. 4. The ATZ layers are under

a nominal (in-plane) constant tensile stress of +65 MPa, while

the embedded AMZ layers are under a constant (in-plane) com-

pressive stress of −720 MPa. The thermal expansion mismatch

between the ATZ and AMZ components also causes a residual

stress near the junction regions. The graphs in Fig. 4 represent

the in-plane and out-of-plane stresses (σxx parallel to the layer

plane, and σzz perpendicular to the layers) in the ATZ and AMZ

layers in region B, region E and junction BE, respectively. It can

be seen that the in-plane stresses in the ATZ and AMZ layers of

both regions are the same. In these two regions the stress perpen-

dicular to the layers, σzz, is negligible. However, the stresses in

the junction BE are different from those in the B and E regions.

The stress component parallel to the layers, σxx, in the junction is

negligible because there is no thermo-elastic material mismatch

along this path, whereas the tensile stress perpendicular to the

layers, σzz, reaches a maximum of +90 MPa. The “ruffle” seen

in the stress distribution in the junction region (Fig. 4) is associ-

ated with the alternating ATZ and AMZ layers in that region; the

maximum σzz value near the edge of the AMZ layers decreases

when entering the ATZ material.

A tensile stress of around 65 ± 2 MPa in the ATZ layers

and a compressive stress of ∼720 ± 5 MPa in the AMZ layers

were predicted using Eq. 1, considering a “mean” volume ratio

VATZ/VAMZ = 12.0 ± 0.2. The low scatter in the average stresses

for the composites is a result of the small variation in the vol-

ume ratios between the different 3–1 composites tested. These

values are in good agreement with the maximal stresses calcu-

lated by FEM for the ATZ and AMZ layers as shown in Fig. 4.

As described in the literature,18 if the influence of the external

surfaces is neglected, and the 2–2 composite is assumed to be

an infinite plate in x and y-directions, then the magnitude of

the residual stresses depends only on the total volume ratio of

the two components and not on the individual layer thicknesses.

Since the total volume ratio between ATZ and AMZ of the eight

regions (i.e. A to H) in the four types of 3–1 composites is the

same, the residual stresses in each ATZ and AMZ material must

be the same, respectively.

3.2. Indentation-strength results of 3–1 composites

Different combinations of Vickers indents were placed on the

surface of the ATZ monoliths and the 3–1 composites. Examina-

tion of broken ATZ monolith after four-point bending showed

that failure occurred from the largest pre-crack, generated by

the largest indentation load (i.e. larger critical flaw size), as

expected for brittle materials. However, failure in the 3–1 com-

posites occurred from one of the three indentation pre-cracks and

was not necessarily associated with the highest indentation load.

All AF, BE and GH 3–1 composites failed from the indents in

regions A, B or G, respectively (i.e. where the first ATZ tensile

layer is thicker), and independent of the original combination

of Vickers indents listed in Section 2.3. A similar outcome was

observed in the indented CD composites, where most of the spec-

imens failed in region C and only a small number of samples

failed in region D.

The variation of the fracture strength, σf, with the indenta-

tion load, P, is logarithmically plotted in Fig. 5a for the A, B,

C and G regions (‘deep’ regions) in AF, BE, CD and GH 3–1

composites, and for the ATZ monolith, respectively. The fracture

strength is the average of 12 specimens per 3–1 composite tested.

A linear regression analysis of the strengths in Fig. 5a shows

that fracture strength, σf, of the ATZ monolith decreases with

increasing indentation load, P, following a power law charac-

teristic of brittle materials, σf ∝ P−k, with k = 0.30.34 For region

A in AF composites, with the first ATZ layer around 1222 �m

in thickness, the fracture strength also decreases with increasing

indentation load (i.e. increasing initial flaw size) and region A

fails at a lower fracture strength at each indentation load than

the ATZ monolith. The lower strength is a consequence of the

residual tensile stress in the ATZ layers. Region B in the BE

636 Y. Chang et al. / Journal of the European Ceramic Society 35 (2015) 631–640

Fig. 5. The variation of the average fracture strength of 12 specimens per composite type with the indentation load (P) (plotted logarithmically) for (a) indented 3–1

AF, BE, CD and GH composites failed in ‘deep’ regions (i.e. A, B, C and G) and (b) indented 3–1 D, E, F and H composites. Indented ATZ monolith is also shown

for comparison. The error bars represent the standard deviation for each sample.

composite, with a ∼802 �m thick first ATZ layer, has a frac-

ture strength of ∼148 MPa that is nearly independent of the

original indentation flaw size. Region C of the CD composites,

with a thickness of around 458 �m for the first ATZ layer, has

almost constant fracture strength of ∼218 MPa. Compared with

the monolith, most of the fracture strengths are higher for the

CD composites, pointing out the enhanced mechanical behav-

ior of the composites. Region G of the GH composites, with a

thickness of around 382 �m, has the highest average strength of

∼299 MPa. The fracture strengths (σf) with the standard devi-

ations corresponding to the A, B, C and G regions of the 3–1

composites are listed in Table 1.

In order to analyze the fracture behavior in D, E, F, and H

regions (i.e. ‘shallow’ regions), 2–2 indented composites were

also tested. The variation of the average fracture strengths, σf,

is plotted as a function of the logarithm of indentation load, P,

in Fig. 5b. Results for the ATZ monolith are plotted for compar-

ison. The samples have the same indentation-size independence

as observed for the 3–1 composites. All 2–2 composites have

higher fracture strengths than the monoliths at each indent size.

It is worth pointing out that in regions D, E, and F (i) the

first AMZ compressive layer is 75 �m thick, (ii) the first ATZ

layer thickness is the same (382 �m), and (iii) only the loca-

tions of the second AMZ layer are different. For these particular

regions, a nearly constant strength was measured, ranging from

∼250 MPa to ∼259 MPa. This result indicates that the inter-

nal structure beyond the first two layers does not significantly

influence the indentation-strengths of the 2–2 composites. For

2–2 H composites, the first ATZ/AMZ layer thickness ratio is

around 1.0:1, and the thickness of the first AMZ compressive

layer is 150 �m or twice that in the D, E and F regions. The

almost constant strength of 2–2 bars reached ∼470 MPa, which

is much higher than those obtained in the other three regions.

The average strengths (σf) with the standard deviations corre-

sponding to the D, E, F and H 2–2 composites are also listed in

Table 1.

In summary, the 3–1 composites have fracture strengths

nearly independent of indentation crack size and the strengths

are strongly influenced by the distribution of the AMZ com-

pressive layers in the composites. It is shown that placing the

Fig. 6. Typical stress–displacement curves of ATZ monolith, and 3–1 CD and

GH composites failed at 100 N indentation load. The “pop-in” events in the

CD and GH composites correspond to the propagation of the initial indentation

(200 N, 100 N, and 50 N) cracks.

first AMZ compressive layer closer to the surface increases the

indentation strength of the composites.

3.3. Analysis of crack arrest in 3–1 composites

Fig. 6 shows typical stress–displacement curves of the 3–1

CD and GH indented composites (with 100 N, 50 N and 200 N

indents) which failed in the C and G regions, respectively. Data

for an indented ATZ monolith is also plotted for comparison. The

ATZ monolith failed at a lower stress than the composites and

in a brittle manner. However, the 3–1 CD and GH composites

showed “pop-in” events in the stress-displacement curves, i.e.

load drops, associated with the propagation of indentation cracks

during loading, as observed in other 2–2 multilayer systems.18

The mechanical behavior of the 3–1 composites as observed

in Fig. 6 can be described as follows: During four-point bending

of indented specimens, every indentation crack rapidly grew

through the tensile layer normal to the first ATZ layer at a stress

corresponding to the “pop-in” events in the stress-displacement

curves. The stress at which the “pop-in” event occurs depends

on the size of the indentation crack. The three “pop-in” events

observed in each composite curve correspond to propagation of

the 200 N, 100 N and 50 N indentation cracks, respectively. An

Y. Chang et al. / Journal of the European Ceramic Society 35 (2015) 631–640 637

Fig. 7. Stress intensity factor (Kappl) and calculated material fracture toughness

(KR) as a function of the crack length in indented C region. The crack propa-

gation of three pre-cracks (indents) under applied stress σappl is schematically

represented. “Pop-in” events in the load–displacement curves are defined as the

intersects between Kappl and KR for a given initial pre-crack size.

instantaneous drop in load can be observed right after the abrupt

growth of each indentation crack. It is noteworthy that the “pop-

in” events in the CD and GH composites occur at similar stress

levels. This can be explained by the fact that the residual tensile

stress in the ATZ layers containing the indents is the same in

both systems. In contrast to the catastrophic failure of the ATZ

monolith, the sudden indentation crack extensions in the first

ATZ layer do not result in failure of the composite.

In order to interpret the initial propagation of indentation

cracks and explain the different strengths obtained in the dif-

ferent regions of the 3–1 composites a linear elastic fracture

mechanics model, based on a weight function approach,35,36 was

implemented. The “apparent” fracture toughness in a multilayer

system with residual stresses, KR, depends on the location of the

crack tip within the layers. If the crack tip is in the layer with

tensile residual stresses, KR(a) decreases with the crack length,

a; if the crack tip is in the compressive layer, shielding occurs

and KR(a) increases with a. Thus, KR(a) can be expressed as

follows:

KR(a) = KIc −

a∫

0

h(a, x)σres(x)dx (3)

where KIc is the intrinsic fracture toughness of each individual

layer, x is the distance along the crack length measured from the

surface, a is the crack length, and h(a,x) is the weight function.

To account for the contribution of the residual stresses in a mul-

tilayer (Kres), the stress distribution, σres, of the corresponding

layer needs be introduced into Eq. (3). The weight function h(a,

x) is considered the same for all four multilayers, as given in

Ref. [36].

For the calculation of KR in a specific region of a 3–1 com-

posite, we consider the corresponding geometry and the residual

stress distribution as calculated with the FE model. Fig. 7 repre-

sents the applied stress intensity factor (Kappl) and the calculated

material fracture toughness (KR) as a function of the crack length

for indented C region as an example. For simplicity, only a dis-

tance corresponding to the first four layers is plotted. The crack

length parameter, â = Y(a)1/2, enables the representation of the

applied stress intensity factor, Kappl, as a straight line, the slope

corresponding to the applied stress, σappl, as inferred from the

Griffith/Irwin equation37:

Kappl(a) = σapplY (a)1/2 (4)

where Y is a geometric factor corresponding to four-point bend-

ing for the SEVNB geometry.

In Fig. 7, it can be observed that toughness KR decreases in the

ATZ layers with a tensile residual stress state and increases very

significantly within the AMZ layers with compressive resid-

ual stresses (something like steeply R-curve behavior) as â

increases. The conditions for stable/unstable crack growth in

region C can be directly established in Fig. 7 (see Ref. [10] for

more details). For the 50 N indent (as an example), according to

the Griffth criterion, when Kappl reaches KR (i.e. Kappl ≥ KR) the

indentation crack corresponding to the 50 N indent will experi-

ence unstable propagation in the tensile ATZ layer. This occurs

when one of the represented Kappl lines intersects KR (Fig. 7).

However, the propagation does not lead to catastrophic fail-

ure. This is observed in Fig. 6 as a drop in the applied load

(i.e. pop-in). The reason by which the load-drop does not go

to zero (i.e. specimen failure) is that the “unstable” growth of

the initial indentation crack is hindered and gets arrested by the

compressive AMZ layer. Under this situation, the propagating

crack would require additional applied stress to further propa-

gate. Indeed, the same reasoning applies for the 20 N, 100 N and

200 N indentation cracks.

The propagation of the initial indentation cracks occurs

at different applied stress levels (represented in Fig. 7 as

σpop-in,20N, σpop-in,50N and σpop-in,100N), as measured experimen-

tally (Fig. 6). We caution the reader that the pop-in stress values

predicted by the model (i.e. slope of the curve at the intersect

Kappl = KR) were slightly different than those in Fig. 6. This

can be due to: (i) the model considers an “edge crack” and not

an “indent crack”, and (ii) the sub-critical growth of the indent

before pop-in is not taken into account. Once the crack has been

arrested at the compressive layer, further propagation (now sta-

ble propagation) requires increasing the applied stress, σappl.

According to Griffith criterion, when Kappl overcomes the max-

imum KR, the crack will unstably propagate up to failure, which

corresponds to the maximum stress intensity factor (Kmax), and

thus maximum applied stress measured in Fig. 5. Below such

stress level, the indentation cracks cannot cause catastrophic fail-

ure. The maximum applied stress can be defined as a “minimum

strength” (σmin), as was found in most of the 3–1 regions of the

composites investigated.

3.4. Crack growth resistance in different regions of 3–1

composites: Experiments and modeling

The fracture toughness Kapt was determined experimentally

with the SEVNB method for each region and is given in Table 1.

638 Y. Chang et al. / Journal of the European Ceramic Society 35 (2015) 631–640

Fig. 8. Apparent fracture toughness, KR, versus crack length parameter, Y(a)1/2, for all the regions of different 3–1 composites: (a) AF, (b) BE, (c) CD, and (d)

GH. The straight lines represent the applied stress intensity factor, Kappl, the slope being the applied stress, σappl. Post-fracture optical micrographs of indented 3–1

composites are also shown.

It can be seen that the fracture toughness in the 3–1 compos-

ites is strongly influenced by the location of the compressive

layers in the different regions. Decreasing the thickness of the

first tensile ATZ layer significantly enhances the fracture tough-

ness of the composites. For instance, a Kapt of ∼11.0 MPa m1/2

was obtained in region G with the first ATZ/AMZ layer thick-

ness ratio of around 5.1:1, which is much higher than the

3.2 MPa m1/2 of the ATZ monolith. Due to the thinness of the

first ATZ layer in region H (i.e. ca. 150 �m) it was not possible

to measure Kapt experimentally via the SEVNB method in that

region.

In order to compare the different regions in all four multi-

layer systems, the apparent toughness, KR, calculated according

to Eq. (3), is represented in Fig. 8 as a function of a crack

length parameter Y(a)1/2. Fig. 8a–d represents the crack growth

resistance in regions AF, BE, CD and GH, respectively. The min-

imum strength (σmin) and the maximum crack growth resistance

(Kmax) can be derived, which differ from laminate to laminate

and region to region (see Fig. 8). The calculated Kmax values

for the eight regions are listed in Table 1. As predicted by Ses-

takova et al.,18 the thicknesses of the first ATZ tensile and AMZ

compressive layers mainly influence the maximal toughness and

minimum strength in a layered system. The highest KR values

can be obtained in designs which have thin (tensile) outer lay-

ers (in our case the ATZ layer) followed by a relatively thicker

compressive layer (in this case the AMZ layer). In Fig. 8a and b,

regions F and E have a thickness ratio between the first two lay-

ers of ATZ:AMZ = 5.1:1, whereas regions A and B have higher

ratios, of ATZ:AMZ = 16.3:1 and ATZ:AMZ = 10.7:1, respec-

tively (see Table 1). That is, the first ATZ tensile layers in regions

A and B (‘deep’ regions) are significantly thicker than those in

regions F and E (‘shallow’ regions). As a result, regions F and

E lead to higher Kmax values (i.e. Kmax,F and Kmax,E) as well

as higher minimum strengths (i.e. σmin,F and σmin,E). As a con-

sequence, failure will occur through the “deep” regions (A and

B), as observed experimentally. In the case of region A, due

to the relatively thick first ATZ layer, no minimum strength was

found for the sizes of indentation cracks introduced in these sam-

ples. In system CD, both regions have a similar thickness ratio

between the first two layers (i.e. ATZ:AMZ = 6.1:1 for region C

and ATZ:AMZ = 5.1:1 for region D). As a consequence, similar

Kmax and σmin are expected (see Fig. 8c). This is also the reason

that some 3–1 indented specimens in system CD failed through

the C region and others through the D region, as reported above.

The Kmax values predicted by the model corresponding to

regions F, E and D, are around 11 MPa m1/2 (see Fig. 8),

Y. Chang et al. / Journal of the European Ceramic Society 35 (2015) 631–640 639

which is in good agreement (although slightly overestimated)

with the SEVNB measurements in such regions, as reported

in Table 1. Minimum strengths calculated from Eq. (3) for the

maximal toughness values at the corresponding crack length

(i.e. a = tATZ + tAMZ) ranges between 275 and 300 MPa, which

is also in agreement with the measured minimum strength (i.e.

∼250 MPa) in these three regions, as reported in Table 1.

In region H, significantly higher Kmax and σmin (compared

to regions F, E and D) can be observed (see Fig. 8d), where the

first ATZ layer is as thin as ∼150 �m and the first AMZ layer is

as thick as ∼150 �m (see Table 1). In this case, Kmax values of

approx. 17 MPa m1/2 and σmin as high as 530 MPa are predicted

with the model. Although experimental values for KR could not

be measured (according to the SEVNB standards32) due to the

thinness of the first ATZ layer, a fracture strength of ∼470 MPa

was experimentally obtained (see Table 1) in the H region; in

good agreement with the predicted minimum strength value.

Very interesting is the KR distribution in region G (see Fig. 8d).

In this region the first peak in the KR curve (obtained at the end

of the first compressive AMZ layer) does not correspond to the

maximum value of KR for region G (see Kmax G and K∗max G in

Fig. 8d). According to this calculation a higher apparent tough-

ness could be achieved at the second compressive AMZ layer

(see Fig. 8d). This might also lead to slightly higher minimum

strength (as the slope of the straight line up to the second AMZ

layer, i.e. σ∗min,G, slightly increases compared to σmin,G). In fact,

the measured fracture strength for the G region is ∼300 MPa

(in contrast to 250 MPa for regions F, E and D), although all of

them have the same layer thickness ratio of the first two layers

(see Table 1). This suggests the possible presence of a second

crack arrest (at the second AMZ compressive layer). This finding

raises the question about whether such a combination of com-

pressive layers may yield higher performance (in terms of flaw

tolerance) than provided by a single-crack-arrest configuration,

and will be investigated in future work.

Post-fracture optical micrographs of indented 3–1 compos-

ites are presented in Fig. 8. It can be seen that each 3–1 composite

failed in the region with the thicker first tensile layer (i.e.

‘deep’ region), as predicted by the model. In addition, a typ-

ical step-wise fracture can be observed in the composites, as

compared to the straight character typically exhibited during

fracture of monolithic ceramic materials. This is associated with

the compressive stresses in all AMZ layers, hindering and/or

deviating the crack propagation, as found in other 2–2 layered

composites.30

From the above results, it can be summarized that the fig-

ures of merit of the 2–2 composites, such as significantly

enhanced fracture toughness and the existence of minimum

strength, are also applicable to 3–1 composites. In addi-

tion, 3–1 composites have some unique characteristics that

2–2 composites do not possess. In particular, fracture in

2–2 laminates may occur from any potential surface defect

which propagates toward the compressive layer. In con-

trast, the fracture location of the 3–1 composites can be

tailored by the appropriate location of the embedded com-

pressive layers. The ‘deep’ region in the 3–1 composites

(i.e. the region with lower crack growth resistance) provides

the preferential path for cracks (initiated at the surface) to

propagate, thus protecting potential features which may be

located in the ‘shallow’ regions. The improved fracture tough-

ness and strength, and more importantly, the spatially-dependent

fracture behavior make 3–1 composites good candidates for

structural applications.

4. Conclusions

A new design concept based on 3–1 connectivity of two dif-

ferent components was tested in alumina-zirconia composites

consisting of a higher thermal expansion matrix (ATZ) and inter-

persed regions of lower thermal expansion (AMZ) which led to

tensile stresses in the matrix of +65 MPa and internal compres-

sive residual stresses up to −720 MPa. The 3–1 composites were

fabricated by altering the stacking sequence of patterned and

unpatterned tapes, thus allowing different regions within a 3–1

composite by tailoring of the spatial distribution and thickness

of the internal AMZ layers. Four-point bending tests on indented

3–1 composites showed crack arrest in the first AMZ compres-

sive layer and a fracture strength independent of indent size (i.e.

minimum strength). Failure occurred in the region with thicker

outer ATZ layers (‘deep’ region). A minimum strength as high as

470 MPa was achieved in a region with a relatively thicker AMZ

compressive layer located close to the tensile surface (‘shallow’

region). The 3–1 design concept is based on the placement of

‘deep’ and ‘shallow’ embedded regions to tailor the associated

stress distribution, and consequently, to manipulate preferential

locations/surfaces for crack propagation. We believe this work

demonstrates that 3–1 and other composite connectivities open

new possibilities for design of multilayer structures with tailored

crack growth resistance.

Appendix A. Supplementary data

Supplementary data associated with this article can be

found, in the online version, at http://dx.doi.org/10.1016/

j.jeurceramsoc.2014.09.017.

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