# Effect of grain morphology and interface on the toughness of nacre-like aluminas

Victoria Vilchez, Shelley Rawson, Shitong Zhou, Jamie McGregor, Matthew Lawson, Alexander Rack, Yunhui Chen, Philip J. Withers, Florian Bouville

► To cite this version:

Victoria Vilchez, Shelley Rawson, Shitong Zhou, Jamie McGregor, Matthew Lawson, et al.. Effect of grain morphology and interface on the toughness of nacre-like aluminas. Acta Materialia, 2024, 280, pp.120338. 10.1016/j.actamat.2024.120338. hal-05128569

HAL Id: hal-05128569

https://hal.science/hal-05128569v1

Submitted on 25 Jun 2025

HAL is a multi-disciplinary open access
archive for the deposit and dissemination of sci-
entific research documents, whether they are pub-
lished or not. The documents may come from
teaching and research institutions in France or
abroad, or from public or private research centers.

L'archive ouverte pluridisciplinaire HAL, est
destinée au dépôt et à la diffusion de documents
scientifiques de niveau recherche, publiés ou non,
émanant des établissements d'enseignement et de
recherche français ou étrangers, des laboratoires
publics ou privés.

<figure><img src="image_1.png" /></figure>
<figure><img src="image_2.png" /></figure>

<figure><img src="image_3.png" /></figure>

# Effect of grain morphology and interface on the toughness of nacre-like aluminas

Victoria Vilchez<sup>a</sup>, Shelley Rawson<sup>b</sup>, Shitong Zhou<sup>a</sup>, Jamie McGregor<sup>b</sup>, Matthew Lawson<sup>b</sup>, Alexander Rack<sup>c</sup>, Yunhui Chen<sup>b,c,1</sup>, Philip J. Withers<sup>b</sup>, Florian Bouville<sup>a,*</sup>

## ARTICLE INFO

### Keywords:

Bioinspired ceramics

Toughness

In situ synchrotron tomography

## ABSTRACT

Ceramic composites that are both tough and strong are needed for extreme environments, ranging from aerospace and nuclear, to medical applications. Bioinspired ceramic composites tackle this challenge by mimicking tough natural structures. Nacre-like aluminas (NLAs) are ceramics processed using advanced colloidal techniques to obtain a microstructure resembling the brick-and-mortar structure of nacre. NLAs can achieve flexural strengths up to 600 MPa and fracture toughnesses ranging from 5 MPa·m<sup>1/2</sup> up to 16 MPa·m<sup>1/2</sup> after crack propagation. These high values mainly rely on deflection mechanisms; these can operate at temperatures up to 1200°C and under impact testing. The fracture properties have been found to be highly dependent on the mortar composition and processing technique used. However, we still don't know how far we can extend the structural properties of NLAs by changing their mortar strength and brick morphology. In this study, we combine mode I wedge splitting testing and *in situ* synchrotron X-ray microtomography of mixed-mode SENB fracture testing along with a kinked crack analytical formulation to study the microstructure-properties relationship in NLAs having two mortar compositions/morphologies. We compare the toughness values obtained in mode I and II with deflection models and study the effect of mode-mixity on the NLA toughness. Our findings show the grain morphology strongly influences the fracture behaviour, with the longer grain material showing longer stable crack deflection which could be further optimised going forwards. By contrast the mortar properties which provide deflection and local toughening mechanisms may be nearing their optimal strength.

## 1. Introduction

Ceramics are the materials of choice for applications in extreme environments, when high resistance to high temperatures, strong radiation levels, or corrosive/oxidative environments for instance is needed [1]. However, complications arise when structural loads are added to the mix, as most ceramics are intrinsically brittle [2]. To solve this issue, numerous solutions have been developed in the last decades to increase the fracture toughness of high-performance ceramics. Tough zirconia-based composites use microstructure engineering and transformation toughening to make safe-to-use biomedical devices [3]. MAX phases [4], Si₃N₄ or SiC with elongated grains are other examples of minerals that have been intensely researched due to their promise of high toughness and strength [5]. So far, ceramic matrix composites

(CMCs) are among the toughest ceramics ever made, with their use of woven continuous fibres able to withstand large loads and bridge cracks even when the matrix is extensively cracked [6]. In all these cases, the arrangement of the different phases and the presence of controlled interfaces are important. Taking CMCs as an example, the interface between the matrix and fibre has to be weak enough to break and introduce crack deflection around the fibres, but strong enough to avoid losing too much strength in the composite overall [7].

Bioinspired structural composites are a fertile ground to study, both in themselves, and to generate guiding principles about the link between materials microstructure and fracture properties [8–10]. There are numerous examples of natural structures that present toughening mechanisms directly encoded in the way the mineral and organic phase are spatially arranged and interact with each other [11]. Of all the

<footnote><sup>a</sup> Centre for Advanced Structural Ceramics, Department of Materials, Imperial College London, Exhibition Rd, London SW7 2AZ, United Kingdom</footnote>

<footnote><sup>b</sup> Henry Royce Institute, Department of Materials, The University of Manchester, Oxford Road, Manchester, M13 9PL, United Kingdom</footnote>

<footnote><sup>c</sup> ESRF, The European Synchrotron Radiation Facility, 71 Avenue des Martyrs, CS40220, 38043 Grenoble Cedex 9, France</footnote>

<footnote>* Corresponding author.</footnote>

<footnote>E-mail address: f.bouville@imperial.ac.uk (F. Bouville).</footnote>

<footnote n="1">¹ Present address: RMIT Centre for Additive Manufacturing, RMIT University, 124 La Trobe Street, Melbourne 3000, Australia.</footnote>
bioinspired structures, the ones presenting the highest strength and toughness up to now are inspired by nacre, a highly mineralized composite present in the inner part of most seashells. At the micron-scale, nacre resembles a brick-and-mortar structure in which the micron-scale bricks are made of calcium carbonate and the mortar is composed of an intimate mixture of protein, chitin and mineral asperities [12,13]. This brick-and-mortar structure develops multiple reinforcing mechanisms that stem directly from the microstructure. The crack path deflects around the bricks, triggering local deflection, bridging and pull-out mechanisms. In addition, the complex interface strain hardens thereby creating a large damage zone in front of the crack tip [14–17]. This large damage zone is responsible for an increase in toughness of almost two orders of magnitude between aragonite and nacre at crack initiation, and three orders of magnitude at the highest point of the R-Curve when the toughness is expressed in terms of the energy release rate [18]. The role of the microstructure and interface in this biocomposite has been highlighted in numerous publications, along with that for other natural materials [19].

These studies provide guidelines that can be followed to design better synthetic composites based on stronger and tougher mineral and organic components than those used naturally [20]. There are multiple strategies for fabricating nacre-like composite microstructures, using for instance ice-templating [21,22], additive manufacturing [23,24], tape casting [25], lamination [26], or magnetically assisted slip casting (MASC) [27]. In addition, there is considerable freedom to optimise the composition of the interface [28].

Perhaps surprisingly, the toughest and strongest compositions so far are fully ceramic and often called nacre-like aluminas (NLAs), with alumina micron-sized bricks and a mineral mortar. The reasons behind these excellent properties have been explained in terms of the strong bonding present between the mortar and the bricks; stronger between two ceramics compared with ceramics/metals or ceramic/polymers [28]. The other reason is that the toughening mechanisms developed in NLAs do not rely on the presence of ductile deformation of the interface but instead are based on crack deflection over large angles and lengths along with local crack bridging and brick pull-out. Because these mechanisms and composition are compatible with high temperature operation, NLAs have been observed to display good toughness up to 1200°C [28]. Finally, the incremental improvement in the properties of NLAs has been obtained by adopting stronger mineral mortars [29], or by adding zirconia particles to introduce residual stresses [30].

To continue improving these promising structural ceramics, it is now important to develop a deeper understanding of the link between microstructure and the role of interface properties on the toughening mechanisms. Several steps have already been made in that direction; first by developing advanced models of fracture propagation in NLAs. Models can be based on discrete element models for a higher fidelity of the representation of the real microstructure [31] or finite fracture type formulations [32,33], on lattice Tension-Shear-Coupling and their refinement for broad material and size parameter sweeps [3,4], or on FEM with idealised microstructure and interface properties that can model the mortar plasticity [5]. These models point toward the importance of the toughness of the interface with respect to the bricks and its role on the development of local toughening mechanisms' development. Second, our team recently proposed a better way to quantify the local toughness by using a kinked crack formulation validated by J-integral based finite element modelling (FEM) [34]. This approach provides sample size independent toughness values and allows the quantification of the local mode I/mode II fracture mode-mixity, as well as assessing the presence of local toughening mechanisms in addition to the global deflection. Even with all these recent developments, one of the most significant questions remains: can we further tailor the interface structural properties to improve the toughness of NLAs?

In this study, our goal is two-fold: firstly, to measure the toughness of the interface in NLAs, then to use these newfound data to consider the crack propagation observed in 3D with synchrotron X-ray

microtomography (µCT) to obtain a quantifiable microstructure- properties relationship. To this end we have fabricated two NLAs with different interface compositions, one based on boron oxide and the other based on yttrium oxide so as to quantify the effect of mortar composition on the microstructure and then the effect of these microstructural changes on the fracture behaviour. We then use the wedge splitting test to propagate a stable crack in mode I along the interface in the two NLA compositions in order to derive the fracture toughness of the interface. Finally, we use *in situ* X-ray synchrotron computed tomography to follow the crack propagation for both compositions in 3D to study the effect of the microstructure on the local toughness.

These new data reveal that the interface toughness triggers local toughening mechanisms even in pure mode I, while the microstructure is identified as playing a defining role in the potency of the toughening mechanisms.

## 2. Materials and methods

### 2.1. Sample preparation

The nacre-like aluminas were fabricated by adopting a magnetically assisted slip casting (MASC) procedure. To elucidate the effect of brick morphology and mortar properties on fracture propagation, two brick-and-mortar microstructures were designed in this study having different brick morphologies and mortar toughnesses. The platelets purchased are made of α-alumina and present an average diameter around 10 µm and an average thickness around 500 nm (see Fig. S1). First, alumina platelets were functionalised with superparamagnetic iron oxide nanoparticles to induce a magnetic response. To this end, alumina platelets (Ronaflair, white sapphire, Merck) were dispersed in deionised water at 0.63 vol%, then a solution of water-based ferrofluid (EMG 705, Ferrotech) diluted at 0.37 vol% in deionised water was slowly added. The quantity of ferrofluid was calculated to be 15 % in regard to the volume of platelets. The solution was left under magnetic stirring for at least 2 days. Once the supernatant was clear, the functionalised platelets were filtered under vacuum and dried at 110°C overnight. Slip casting slurries were prepared with different compositions to vary the secondary phase, using either boric acid as a precursor for aluminium borate (NLA-B) or yttrium nitrate as a precursor for yttria (NLA-Y). All slurries were prepared with a powder fraction of around 20 vol%. Typically, water and dispersant (Dolapix CA, Zschimmer & Schwartz) at a concentration of 0.5 wt% of dry powders were mixed together, then boric acid (Ph. Eur., BP, NF, Merck) or yttrium(III) nitrate hexahydrate (Merck) were added in quantities calculated to obtain 1.5 vol% of secondary phase in the final material, i.e. boron oxide or yttrium oxide. Alumina nanoparticles (SMA6, Baikowski) were added to bridge alumina platelets during sintering, with 3 wt% with regard to the alumina platelets. While their exact role is not fully resolved, the addition of 3wt.% of alumina nanoparticles has been reported [3] to trigger crack deflection during fracture when a mortar phase is added. Nanoparticles can be observed in the final samples in between some, but not all, alumina grains in the final sample (Fig. S2), probably due to the low amount added. Alumina nanoparticles were dispersed using a sonication probe (UP200S, SciMed) for 10 minutes at 50% of the maximum amplitude and with ½ time working cycles. The functionalised alumina platelets were added and the slurry sonicated using the same parameters. Finally, polyvinylpyrrolidone (Mw = 360,000 g/mol, Merck) was added in quantity of 4 wt% of alumina platelets and the slurries were left to stir overnight. Prior to slip casting, slurries were degassed in a vacuum desiccator. For the MASC, slurries were poured in a 30 mm diameter cylindrical mould placed over a flat plate of gypsum. A neodymium iron boron magnet (NIBL 00954, N38H grade, Magnet Sales) was set up on an overhead mechanical stirrer and rotated at 200 rpm next to the gypsum plate to align the alumina platelets with the magnetic field. After complete casting, the green bodies containing boric acid were fired at 500°C for 4 hours using a ramp of 5°C/min to burn out the organic compounds
and dehydrate the boric acid. For green bodies containing the yttria precursor, the organic burnout was conducted at 550°C to ensure the complete decomposition of the yttrium nitrate into yttria. Finally, the green bodies were hot pressed in 30 mm diameter graphite dies under argon atmosphere. A loading rate of 3.7 kN/min was applied up to 42kN, then a heating rate of 15°C/min up to 1350°C or 1400°C with a dwell time of 30 minutes. In both cases the mortar represent 1.5 vol% of the sample, following the results obtained in a previous study [35]. The two mortar compositions led to dense samples after sintering, with NLA-B sintered at 1350°C and NLA-Y at 1400°C to promote the formation of YAG following the alumina-yttria phase diagram [36].

## 2.2. SEM and grain size analysis

The microstructure and fracture paths after mechanical testing were imaged by scanning electron microscopy (SEM) at an acceleration voltage of 5 kV when using the secondary electron detector and at 10 kV for the backscattered electron detector (Auriga Crossbeam, Zeiss). To reveal the interphase and grain boundaries, sample surfaces were polished using a broad argon ion beam system (PECS II, Gatan) for 2 hours at 6 keV and 6°. A conductive coating of 10 nm of chromium was sputter coated (Q150T S, Quorum) on the samples prior to imaging. In order to quantify grain growth and morphology, the grain structure was analysed from SEM images using the MorpholibJ [37] plugin in ImageJ [38]. Starting from the SEM cross-sectional images, grain edges were detected using the ‘Find Edges’ feature, then the images were binarized. Grain boundaries were closed using a morphological filter and manually corrected to ensure individual grains were labelled separately from neighbouring grains. Grain shape was analysed by fitting inscribed ellipses. Ellipse elongation was quantified in terms of the grain aspect ratio, r. The maximum Ferret diameter was used to represent the grain length, L, and thickness t was quantified as $t = L/r$. The top surface of the sample was imaged after broad argon ion beam followed by a thermal etching step in a furnace in air at 1200°C for 1h, with a heating rate of 10°C/min, to reveal the grain boundary. We used the linear intercept procedure according to ASTM E112-13 (2021) to extract the average grain size. Four to six blindly selected straight lines were drawn on the SEM images, resulting in over 400 intersections being counted.

## 2.3. Elastic constants measurement with instrumented indentation

The in-plane and out-of-plane Young's moduli of the composite were measured using instrumented indentation. The surfaces of the samples were polished down to 1 µm with diamond suspensions. They were mounted in the nanoindenter (NanoTest Vantage, Micro Materials) equipped with a diamond Berkovich tip (Young's modulus $E_i = 1141$ GPa, Poisson's ratio $v_i = 0.07$, Micro Materials). Load-depth data was acquired by indenting the samples to a 30 N load using a loading time of 20 s and unloading time of 10 s. The highest load was selected to probe the largest volume of materials and thus obtain averaged elastic properties. 10 indents per sample were performed. The acquired load-depth curves were processed using the Oliver-Pharr method [39]. The stiffness S of the material can be deducted by fitting the upper part of the unloading curve with a power law and taking its derivative. Then the reduced Young's modulus $E_r$ can be calculated and the Young's modulus of the sample $E_s$ is linked to $E_r$ by:

$$ \frac{1}{E_r} = \frac{(1 - v_s^2)}{E_s} + \frac{(1 - v_t^2)}{E_t} \quad (1) $$

where $v_s$ is the Poisson's ratio of sample (0.24 for alumina), see Fig. S3 for the results.

## 2.4. SENB Fracture toughness sample setup

Plane strain fracture toughness testing was performed in line with

ASTM D5045, using a Deben CT500 tensile/compression testing stage (Deben UK Ltd., Suffolk, UK) in order to monitor crack growth under mixed-mode loading. Single edged notched bending (SENB) samples of 10 mm (length) x 2 mm (width) x 1mm (breadth) were cut from the sintered disks using a diamond blade. A central notch was produced using a 300 µm thick diamond blade, and the bottom of the notch was then sharpened using a razor blade and diamond paste with a grain size of 1 µm (Diamond Compound, Kemet). Custom-made steel 3-point bending clamps were produced with pins of 1.5 mm diameter positioned 8 mm apart. Three-point bending was performed at a loading rate of 0.1 mm/min at room temperature using a 500 N load cell. Force and displacement were recorded at a sampling rate of 200 ms. Three specimens per composition were tested for statistical significance.

The local mode I and mode II stress intensity factors $K_i^k$ and $K_{II}^k$ were calculated using the Cotterell and Rice approach [40]. For an infinitesimal crack length $c \to 0$, the higher order terms contributing in $c$ can be neglected and the first order approximation on the stress state gives:

$$ K_i^k = \frac{1}{4} \left( 3\cos\frac{\theta}{2} + \cos\frac{3\theta}{2} \right) \times K_i + \mathcal{O}(\sqrt{c}) \quad (2) $$

$$ K_{II}^k = \frac{1}{4} \left( \sin\frac{\theta}{2} + \sin\frac{3\theta}{2} \right) \times K_i + \mathcal{O}(\sqrt{c}) \quad (3) $$

With the stress intensity factor, $K_i$, calculated using the initial crack length and following the ASTM standard E1820 [41]:

$$ K_i = \left[ \frac{FS}{BW^{3/2}} \right] \times f\left(\frac{a_0}{W}\right) \quad (4) $$

where F is the force, S the support span, B the thickness and W the height of the specimen, $a_0$ is the parent notch length, and f is given by:

$$ f\left(\frac{a_0}{W}\right) = \frac{3\left(\frac{a_0}{W}\right)^{1/2} \times \left[ 1.99 - \frac{a_0}{W} \left(1 - \frac{a_0}{W}\right) \left(2.15 - 3.93\frac{a_0}{W} + 2.7\left(\frac{a_0}{W}\right)^2\right) \right]}{2\left(1 + 2\frac{a_0}{W}\right)\left(1 - \frac{a_0}{W}\right)^{3/2}} \quad (5) $$

## 2.5. Wedge Splitting test (WST)

Bars with approximate dimensions of $H \times w \times 2d = 20 \times 2 \times 2$ mm³ were used, with a pre-notch of 0.3 mm width and around 1.5 mm length that was further sharpened using a razor blade with a diamond suspension of 1 µm. In the WST geometry, the elastic energy stored in each arm and energy release rate can be estimated from beam theory using the crack length $a$, Young's modulus $E$, arm height $d$ and displacement $\delta_y$. In practice, this estimation needs to be corrected to take into account shear in the arms for short crack lengths, as well as a rotation correction at the base of the beam and leads to the final equation [42,43]:

$$ G = \frac{3\delta_y^2 E d^3}{8(a + \chi d)^4} \left[ 1 + (1 + \nu) \left( \frac{d}{a + \chi d} \right)^2 \right] \quad (6) $$

where $\chi$ is the rotation correction factor suggested by Williams [44]. For isotropic materials, $\chi$ is equal to 0.67. $\chi$ can be as large as 2.5 for materials with marked orthotropy (compliance tensor components of $a_{66}/a_{11} > 50$), but remains around 0.67 in less anisotropic materials ($a_{66}/a_{11} \approx 2$). In the case of nacre-like alumina, the anisotropy ratio is largely < 2, hence we use $\chi = 0.67$. The Young's modulus, $E$, was taken as the modulus in the transverse direction measured through nano-indentation, with $E_t^B = 239 \pm 29$ GPa for NLA-B and $E_t^Y = 209 \pm 23$ GPa for NLA-Y.

The wedge has an angle of 42° and was moved at the lowest speed of 0.1 mm/min. Optical images were recorded with a custom-made system using a 31-megapixel camera (Oryx 10GigE, Teledyne FLIR) and a high resolution telecentric lens (resolution 1 µm/px, field of view 6.46×4.85
mm², VS-LTC3.3-45/FS, VS Technology). The specimen was illuminated using a low angle diffused ring light (VL-LRD73100W, VS Technology) and photographs were recorded at a frame rate of 2 Hz. Images were processed using ImageJ to perform a drift correction [45] and background subtraction, as well as contrast and brightness correction.

## 2.6. In situ synchrotron µCT imaging

Samples were imaged in situ within the Deben rig in SENB setup, as described in the previous section. Displacement was applied until 2 N of preload was reached, then the initial ‘unloaded’ tomogram was acquired. Samples were then loaded to 8 N before taking the second tomogram. Loading was then applied in increments of 3 N with a tomogram being taken after every load increment until the sample fully fractured (identified as > 75% drop in load). Samples were then retained for high resolution post-fracture SEM.

µCT Imaging was performed using the ID19 beamline at the European Synchrotron Radiation Facility (ESRF), using a 5x front lens and 0.14 numerical aperture resulting in an isotropic voxel size of 1.3 µm. A 250 µm thick single crystal scintillator, cerium doped (LuAG:Ce, Crytur, Czech Republic) and pco.edge camera (PCO AG, Germany) were used alongside a U13 single-harmonic undulator (~1% bandwidth) and an energy of 26.1 keV. The sample to detector distance was 200 mm, enabling some propagation-based phase contrast. 4000 projections were taken at 50 ms per projection through 180° of rotation. Tomographic reconstruction was carried out by means of standard filtered-back projection using ESRF inhouse-software (no beam hardening filter required) combined with single-distance phase retrieval (Paganin method with a δ/β value of 25).

## 2.7. Post fracture high resolution µCT imaging

One sample of each material was µCT scanned ex situ post-fracture on the same beamline (ID19) as the in situ measurements, using a 10x front lens and 0.3 numerical aperture resulting in an isotropic voxel size of 0.65 µm. An LSO:Tb 8.7 µm thick scintillator was used alongside a U13 single-harmonic undulator (~1% bandwidth) and an energy of 26.1 keV. The sample to detector distance was 11 mm. 5000 projections were taken at 50 ms per projection through 180° of rotation. Tomographic reconstruction was carried out by means of standard filtered-back projection using ESRF in-house software (since the beam was monochromatic no beam hardening filter was required) combined with single-distance phase retrieval (Paganin method with a δ/β value of 25).

## 2.8. Finite Element Modelling

FEA was performed with the Abaqus software (Abaqus/CAE 2020, Dassault Systèmes). A 2D planar model with plane-strain conditions was set up using the true dimensions measured on each beam tested in Wedge Splitting. The material model used was linear elastic, transversely isotropic. We used Abaqus notation for the transversely isotropic constitutive model:

$$ \begin{bmatrix} \epsilon_{11} \\ \epsilon_{22} \\ \epsilon_{33} \\ \gamma_{12} \\ \gamma_{13} \\ \gamma_{23} \end{bmatrix} = \begin{bmatrix} 1/E_p & -\nu_p/E_p & -\nu_{tp}/E_t & 0 & 0 & 0 \\ -\nu_p/E_p & 1/E_p & -\nu_{tp}/E_t & 0 & 0 & 0 \\ -\nu_{tp}/E_p & -\nu_{tp}/E_p & 1/E_t & 0 & 0 & 0 \\ 0 & 0 & 0 & 1/G_p & 0 & 0 \\ 0 & 0 & 0 & 0 & 1/G_t & 0 \\ 0 & 0 & 0 & 0 & 0 & 1/G_t \end{bmatrix} \begin{bmatrix} \sigma_{11} \\ \sigma_{22} \\ \sigma_{33} \\ \sigma_{12} \\ \sigma_{13} \\ \sigma_{23} \end{bmatrix} \quad (7) $$

The transversely isotropic model uses three different values of Poisson’s ratio; $\nu_p$ representing the link between in-plane contraction strain generated by in-plane extension, $\nu_{tp}$ and $\nu_{tp}$ representing the link between out-of-plane-strain and in-plane-extension and the link

between in-plane-strain and out-of-plane-extension respectively. This model also uses two Young’s moduli $E_p$ and $E_t$ and two shear moduli $G_p$ and $G_t$ to define the material’s rigidity in-plane and out-of-plane respectively. We used $E_p^B = 327 \pm 19$ GPa, $E_t^B = 239 \pm 29$ GPa for NLA-B and $E_p^Y = 335 \pm 23$ GPa, $E_t^Y = 209 \pm 23$ GPa for NLA-Y, obtained from instrumented microindentation (see Fig. S3). The Poisson’s ratios $\nu_{pt}^B$, $\nu_{pt}^Y$ and $\nu_{tp}^B$, $\nu_{tp}^Y$ for both compositions were approximated to 0.24 and $\nu_{tp}^B$, $\nu_{tp}^Y$ were approximated to 0.22 which are common values measured in alumina [46]. Then, $G_p$ is given by the relation $G_p = \frac{E_p}{2(1+\nu_p)}$, leading to $G_p^B = 132$ GPa, $G_p^Y = 135$ GPa and $G_t$ was approximated as $G_t = \frac{E_t}{2(1+\nu_t)}$, leading to $G_t^B = 96$ GPa, $G_t^Y = 84$ GPa.

Quadratic elements were used for the mesh to allow for J-integral computation, and the mesh was refined in the vicinity of the cracks down to 4 µm, with 20 contours used to ensure a path independence of the J-integral at each step. Cracks were introduced in the model by defining seams with the values of crack length and angle of deflection measured from optical images iteratively for each image recorded. Time correspondence between the load-displacement curve and the images was used to access the load on the specimen corresponding to the current iteration.

# 3. Results

## 3.1. Microstructure characterisation of NLAs from the SENB tests

The microstructure of the nacre-like alumina comprises alumina bricks aligned through advanced colloidal processing techniques held together with a small amount of mortar. As a results of this highly textured microstructure, it fractures with multiple highly deflected cracks (Fig. 1a). During fracture, the cracks progress in a step-like fashion around the platelets introducing local toughening mechanisms including crack branching and bridging (Fig. 1b), with the step-like propagation of the crack indicating a possible link between the crack propagation angle and the brick morphology. The complex crack trajectories lead to a high level of mode-mixity between mode I and mode II at the crack tip (Fig 1a), and the local level of stress intensity at which the crack propagated has been demonstrated [28,35,47] to be dependent of the mortar crack resistance. So far, crack propagation in nacre-inspired composites has mostly been studied by looking at 2D profiles on the outer surfaces. However, the crack trajectories can be influenced by the sample boundary conditions, notably plane-strain or plane-stress conditions. Here µCT shows that within the bulk the crack is strongly deflected by the microstructure (Fig 1c) and suggests that the crack is also deflected at a finer grain scale.

The grain morphology of the two sintered NLAs can be inferred by SEM observation of the fracture surfaces (Fig. 2). While the mortar can not be directly identified in the SEM micrographs due to its low amount, its influence on the microstructure is clear (Fig. 2) in particular affecting the grain size and aspect ratio.

In the NLA-B case, the addition of boric acid triggers the formation of a boron oxide $B_2O_3$ glass during heating, which in turns leads to the formation of aluminum borate during the pressure-assisted sintering. This mortar has been used in previous studies and led to an increase in strength and fracture toughness compared with NLA where no mortar was used [35]. With NLA-Y, a similar strategy was adopted, using soluble yttrium nitrate that transforms into yttrium oxide $Y_2O_3$ upon heating. Then, during pressure-assisted sintering, yttrium oxide was expected to react with alumina to form an yttrium aluminium garnet mortar ($Y_3Al_5O_{12}$, YAG).

It is apparent from the Fig. 2b that the addition of yttrium oxide in NLA leads to a similar grain length $L$ to that for the addition of boron oxide, with $L_{50}$ of 5.1 µm and 3.9 µm for the yttrium oxide and boron oxide respectively (Fig. 2b), but with an almost two-fold increase in thickness, with $t_{50}$ of 2.2 µm and 1.2 µm for the yttrium oxide and boron
<figure><img src="image_4.png" /><figcaption>**Fig. 1.** Fracture in nacre-like alumina (NLA) guided by the 3D stress state and microstructure. a) Schematic of macroscopic SENB test in NLA with multiple deflected cracks leading to local toughening mechanisms and mode-mixity in the brick-and-mortar architecture. b) SEM image of an ion-beam polished NLA with a borate interphase (NLA-B) showing the microstructure local to the crack-tip. c) Mid-thickness synchrotron µCT slice of NLA-B during an in situ SENB test.</figcaption></figure>

<figure><img src="image_5.png" /><figcaption>**Fig. 2.** NLA with different microstructures and mortar compositions. a) SEM images of the fracture surface of NLA with NLA-B aluminum borate mortar (top) and NLA-Y yttrium oxide mortar (bottom). b-d) Distribution of the grain morphological parameters from image analysis for both mortar compositions with b) the grain length L, c) grain thickness *t* and d) grain aspect ratio *r* = *L*/*t*. Solid lines represent lognormal fit of the data.</figcaption></figure>

oxide respectively (Fig. 2c). This change in grain morphology can be further highlighted by the fact that the aspect ratio is 20% smaller for yttrium oxide, with *r*<sub>50</sub> equal to 2.9 and 3.6 for the yttrium oxide and boron oxide respectively (Fig. 2d). These trends are not only seen in the median dimensions but across all the distribution (Table S1). In addition to the grain morphology characterisation in the NLA cross section, we performed SEM on the top surface of samples from both compositions. On the top surface, the grain morphology is equiaxed (Fig. S4) for both NLA-B and NLA-Y. The average grain size in this orientation also increases with the presence of yttrium, with an average grain size of 11±3 µm and 13±4 µm for NLA-B and NLA-Y, further confirming the trends observed in the cross-sections.

This change in aspect ratio points to a larger mobility of the grain boundary associated with the alumina basal plane in the presence of yttrium compared with boron. While both boron and yttrium additions are generally linked with a reduction in grain growth in alumina and an increase in densification kinetics at intermediate temperatures [48], this destabilization effect on specific grain boundaries has not been observed before and deserves further study. Irrespective of the mechanism, it is clear that the two NLAs exhibit different mortar compositions and grain morphologies, enabling an assessment of the influence of the micro-structure on the crack geometry/toughening.
## 3.2. Wedge splitting testing

It is well established that using 3-pt bending SENB tests on samples with such anisotropic fracture behaviour as in the NLA leads to a mixed-mode fracture toughness having high mode-mixity, i.e. $K_I \approx K_{II}$ at the crack tip [34]. While this crack deflection and local mode-mixity are responsible for the high global toughness obtained in NLA, they also make the toughness value harder to link to the toughness of the mortar/grain boundaries. To this end, we decided to test the fracture of NLA in pure local mode I by propagating a crack along the grain length (Fig. 3a) using the wedge splitting test. This geometry presents several advantages: it is a simple geometry that allows stable propagation of the crack regardless of the presence of reinforcing mechanisms, thereby limiting the influence of the notch machining and sharpness, the test is relatively easy to perform and it can be used to control the propagation of the crack along the long axis of the grains in our anisotropic sample, giving access to the mortar or grain boundary fracture toughness.

The toughness was measured from the energy release rate using the displacement of the arms rather than the force to avoid any artefact from friction between the indenter and the arms. While we illustrate the methodology here with NLA-B, the results obtained for both compositions are provided below. Because NLA ceramics are stiff, the arm displacements $\delta$, plotted in Fig. 3b, are in the tens of micron range and thus necessitate the use of high spatial resolution and large field optical measurements to be measured in situ (Fig. 3c). The maximum displacement in the opening direction of each arm ($\delta_y^{top}$ and $\delta_y^{bottom}$) rises to around 15-20 µm, while the displacements along the sample length ($\delta_x^{top}$ and $\delta_x^{bottom}$), never exceed 2 µm, supporting the inference that the crack opening force is only applied in the y direction without inducing compression in the x direction. However, two caveats should be considered. First, due to difficulty in centering the notch and sharpening the crack within a sample less than 2mm in width, the arms were not perfectly symmetrical. This slight asymmetrical displacement can

influence crack propagation and mode-mixity by driving the crack to deflect further in the direction of the arm moving the most (Fig. 3c). Secondly, the analytical calculation of the critical energy release rate from the arm displacement assumes the notch to be infinitely narrow hence the arms have a constant thickness. But the machining of the notch means that the thickness at the crack $d_{bulk}$ is different from that at the notch, $d_{arm}$ (Fig. 3a). The analytical formula used to calculate the energy release rate during WST is based on the following hypothesis: the material should be homogeneous and isotropic; the crack propagates in a straight line and the arms providing the loading to the crack tip have a constant thickness. In our composites, while the anisotropic material properties can be included using a correction factor, we don't have corrective factors for crack deflection and variations in thickness of the arms. Considering that $G_{WST} \propto d_{arm}^2$, we decided to use a FEM model to obtain more accurate values of the energy release rate in our sample where there is a significant increase in arm thickness due to testing and machining constraints [8].

To estimate the error introduced by only using the analytical formula, we compare the analytical estimation to a finite element model, using a J-integral calculation. This strategy has already been employed to confirm the local mode-mixity measured analytically for SENB of NLA in a previous study [34] and is based on the long use of FEM in fracture mechanics to correct analytical formulas, see for instance ASTM standard E180 [7] or [8]. Briefly, the FE model uses a linear elastic anisotropic material model for the NLA and the boundary conditions from the image analysis, including sample geometry, arm displacement, crack length and deflection angle. A J-integral approach is used to calculate the toughness from the stress state (Fig. 3d) at different crack lengths and arm displacements. Because the material used is linear elastic, we can use the $J = G$ equality [49], $J$ being the energy release rate calculated by the J-integral and $G$ the energy release rate as defined by Griffith. The obtained energy release rate $G$ can be further decomposed into local stress intensity factors in mode I and mode II, named $K_I$ and $K_{II}$ respectively, using the pre-logarithmic factor matrix approach

<figure><img src="image_6.png" /><figcaption>**Fig. 3.** Fracture testing along the bricks in NLA using the wedge splitting technique. a) Schematic of the wedge splitting fracture testing for NLA and orientation of the bricks. b) Displacement of each arm in the x and y direction obtained by image analysis from one NLA-B sample. c) High-definition in situ optical measurement of an NLA-B sample during wedge splitting test. d) Example of FEM simulation results corresponding the sample depicted in c). e) Representative value of critical energy release rate $G$ and decomposition in stress intensity factors $K_I$ and $K_{II}$ obtained from J-integral based calculation of FEM results on the sample of NLA-B at the crack length shown in c).</figcaption></figure>
[50]. The model confirms that $K_I$ is more than 8 times higher than $K_{II}$ (Fig. 3e) for most of the crack propagation, despite the asymmetry and slight angle present in the crack propagation direction.

The validated wedge splitting test and its numerical complement was then used to drive and quantify crack propagation in a low mode-mixity configuration in the direction of the grain length in NLA, opening up the characterisation of the mortar properties in more detail.

The R-curves of the energy release rate as a function of crack length calculated by the analytical expression and the J-integral FE model in wedge splitting are plotted in Fig. 4 for both mortar compositions. The change in arm thickness between $d_{bulk}$ and $d_{arm}$ was accounted for in the calculation of G by defining an error envelope. The small end arm thickness $d_{arm}$ was used as the lower bound of the shaded area in Fig. 4 while the upper bound was obtained with the larger end of the arm $d_{bulk}$. Because the J-integral approach directly includes the change in stress state and energy release rate from the different arm thickness, the anisotropy of the materials and the small deflection of the crack, they will be used as the energy release rate in mode I over the ones measured from the analytical formula for the rest of the text. Whereas the stress state values calculated from the FEM are accurate, the error in measuring displacement of the arms and the crack length optically can have a strong influence on the energy release rate, as $G_{WST} \propto d_{arm}^2 \cdot a^4$. We estimated the error on the values obtained with the J-integral by including the error made on the measurement of the arm displacements and crack lengths, adding a total variation $\delta_{res} = 0.5 \mu m$ on the values. $\delta_{res}$ was estimated as half the resolution of our optical measurement setup.

The energy release rate for NLA-B increases from around $3 \pm 1$ J/m$^2$ up to $8 \pm 1$ J/m$^2$ after 2 mm of stable crack propagation (Fig. 4a), while the energy release rate for NLA-Y is initially lower at $0.01 \pm 1$ J/m$^2$ rising to $15 \pm 1$ J/m$^2$ after 3 mm of stable crack propagation (Fig. 4b). We hypothesize the increase in energy release rate as the crack propagates to be due either from the inherent difficulty in accurately measuring smaller arm displacements and crack lengths at the beginning of the test, or to the setup itself. This limitation of the accuracy of energy release rate for short cracks has been observed before in similar wedge splitting configurations and is directly due to the error on the determination of small displacement and crack length [15].

According to the analytical model, the final energy release rates

appear to be broadly similar for both compositions, due to the large confidence bounds due to the variation in arm thickness. The more accurate value obtained from the J-Integral method shows the same trend as the analytical formula, with the J-Integral value initially closer to the lower bound corresponding to the value calculated with $d = d_{arm}$ but then getting closer to the higher bound corresponding to $d = d_{bulk}$ as the crack length increases.

Considering that the crack in this configuration propagates predominantly along the interface between the bricks and that it is mostly in mode I, we started with the hypothesis that the energy release rate obtained corresponds to the critical energy release rate of the mortar. The toughness of the mortar is a fundamental parameter guiding the fracture of the structure; it needs to be low enough to guide the crack at the interface and trigger toughening mechanisms such as deflection and branching, while also being high enough to achieve the highest toughness and strength in the structure.

The stable value of $G_{WST}$ of 8-15 J/m$^2$ obtained here is close to the one usually obtained for non-textured polycrystalline alumina with a similar grain size at around 15 J/m$^2$. These values on polycrystalline alumina also includes the effect of the microstructure, such as local deflection around grains. As a benchmark, the fracture toughness of monocrystalline alumina has been found to be highly anisotropic, with critical energy release rate of around 40 J/m$^2$ or above when cleaving along the c-plane (normal direction (0001)) but ranging from 7 to 24 J/m$^2$ when cleaving along the a-plane or m-plane (normal direction (1210) and (1\bar{1}00)) [51,52]. However, we can see in Fig. 4 that the measured energy release rates for both compositions are increasing with the crack extension. The determination of the crack length and arm displacements at the beginning of the test can be inaccurate due to the small values reached and could explain part of the increase. It is still difficult to rule out the effect of the microstructure entirely on the measured energy release rate, especially given that we know some micro fracturing can happen in NLAs (Fig. 1c). More potent crack bridging is possible when the grain size increases [16], which could explain why NLA-Y $G_{WST}^Y$ is still increasing after more than 3 mm of crack extension.

The energy release rate obtained in alumina monocrystal can be used to estimate how much the interfacial toughness can be further increased. Using the He and Hutchinson approach for crack deflection [53] based on the toughness of the interface, the system can be described by the two

<figure><img src="image_7.png" /><figcaption>**Fig. 4.** Energy release rate as a function of crack length obtained by wedge splitting calculated by the analytical and J-integral FEM-based approaches for a) NLA-B and b) NLA-Y. The upper boundary and lower boundary of the shaded area correspond to energy release rate calculated with arm thickness $d_{bulk}$ and $d_{arm}$ respectively, while the errors on the value obtained by FEM arise from the uncertainty on the arm displacement value measured optically.</figcaption></figure>
layers of alumina with a modulus $E_{brick}$ and toughness $G_{brick}$, separated by a horizontal interface ($\theta = 90^{\circ}$) of modulus $E_{mortar}$ and toughness $G_{mortar}$. In this case, the Dundur's parameter $\alpha = \frac{E_{brick} - E_{mortar}}{E_{brick} + E_{mortar}} = 0$ and so the transition from the case where a crack coming from the top layer deflects at the interface to the case where the crack penetrates the bottom layer and break through platelets is obtained for $\frac{G_{mortar}^m}{G_{brick}} \approx 0.26$.

Using the critical energy release rate when cleaving along the c-plane of alumina we obtain a maximum interface toughness of $G_{mortar}^m = 10 \text{ J/m}^2$ to stop deflection at the interface. The values we measured by wedge splitting on NLAs ~ 8–15 J/m² are in a similar range. If we rule out the effect of the microstructure and local toughening, it will mean we are already close to the optimum interface toughness. However, because of the possible local toughening effect included in the measurements, we can only say that the current mortar compositions energy release rates are low enough to still trigger deflection and that the local toughening effect can be the reason behind the similarity in values we obtained. The next step to further our conclusions would be to use wedge splitting at the platelet level to rule out the effect of the microstructure on the values but these would be delicate measurements to perform given the platelet size.

### 3.3. SENB testing

Having characterised the toughness of the mortar and the toughness of the mortar/interfaces in mode I, the two NLAs were then studied in mixed-mode SENB fracture testing to characterise the role of the microstructure on the fracture behaviour.

The NLAs develop complex crack patterns in SENB fracture, with multiple large scale deflected cracks and crack branching. Until now these mechanisms have only been observed on the surface of sample by optical imaging. However, the stress state in SENB testing changes within the sample thickness, with a lower stress tri-axiality on the surface compared with the centre. In metals, it is known that the higher triaxiality of stresses can influence the crack length and toughening behaviour in addition to possibly leading to an overestimation of the toughness based on surface measurements [54]. The crack may deflect differently in different locations through thickness giving rise to additional crack shielding. As a result, it is important to study the cracking in 3D. Here the two compositions of NLA were tested in SENB and the crack propagation observed in situ by X-ray microtomography at high spatial and temporal resolution (1.3 µm voxel size). This has allowed us to follow the stable crack propagation in 3D and evaluate the shape of the crack through the thickness of the SENB sample as the crack progresses (Fig. 5).

The volume renderings from the CT tomograms in Fig. 5 show sub-surface crack propagation in NLA-B that is similar to what has been typically observed on the surface using optical microscopy, with two cracks deflected at an angle ranging from 70° to 85° from the maximum opening stress direction and that propagate in a stable manner. It is evident that the crack front is not straight but bows through the sample thickness, with a crack ~200-300 µm longer in the centre compared to

the sides in the most extreme cases. This bowing starts at crack initiation and continues throughout the whole stable crack propagation process, which seemingly indicates a sensitivity to plane-stress/plane-strain conditions and possible influence on R-curve toughness values. These observations suggests that surface observations will underestimate the extent of cracking.

Crack bowing was observed in all the samples, with the crack longer in the centre compared to the front and back in 60% of the samples. To quantify the effect of the deflected crack bowing on the calculation of local stress intensity factors, the crack length and deflected angled were measured on three different cross-sections through the thickness of the sample: at the front, centre and back.

The crack length *c* and deflection angle *θ* measured at different positions within the sample were then used to calculate the local stress intensity factors. We used the kinked crack formulation from Cotterell and Rice [40] which allows the stress intensity factors in mode I and mode II, respectively $K_I^k$ and $K_{II}^k$, to be calculated for a deflected crack growing from a parent notch loaded in pure mode I. This method has been described in a previous study, and was shown to give accurate stress intensity factors for deflected cracks of length up to the 2 millimetres by comparing the analytical solution with J-integral based FEM calculations. Then, the local stress intensity factors $K_I^k$ and $K_{II}^k$ can be further summarised by an effective stress intensity factor acting on the crack tip $K_{eff} = \sqrt{(K_I^k)^2 + (K_{II}^k)^2}$.

Fig. 6b represents an R-curve with $K_{eff}$ measured at different cross-

<figure><img src="image_8.png" /></figure>

Fig. 6. Effective mixed-mode stress intensity factor calculated at three different positions within the thickness and with an average of the crack length taken as the average of the crack length over the three slices for each scan.

<figure><img src="image_9.png" /></figure>

Fig. 5. A sequence of volume renderings obtained by in situ µCT of an NLA-B sample tested in situ under SENB with the alumina rendered translucent and crack red during stable crack propagation.
section positions within the sample as a function of the deflected crack length. It can be seen that the stress intensity factor tends to be higher on the sample surface than in the centre for a given crack length, which can in turn lead to a slight overestimation of the R-curve. However, these differences in R-curve are rather small, within 10%, hence were deemed acceptable to describe the general behaviour of the material.

We were somewhat surprised to find crack bowing considering ceramics are typically assumed insensitive to shear, and do not follow the Von Mises criterion for failure but rather the Rankine criterion under which deformation stresses are independent of the bi- or triaxiality of the constraint [55]. We thus hypothesise that another criterion better describes the behaviour of nacre-like alumina, such as Mohr-Coulomb which has been typically employed to describe concrete and rocks. In the Mohr-Coulomb model, the sensitivity to shear stresses has typically been linked to the nucleation of microcracks in the structure during plastic deformation [56], such as those observed in Fig. 1b.

The mid-thickness slices taken from the tomograms (Fig. 7) show crack propagation in NLA-B that is similar to what has been typically observed on the surface using optical microscopy, with two cracks deflected at an angle ranging from 70° to 85° from the maximum opening stress direction and that propagate in a stable manner (Fig 7b). Once the deflected cracks extend by several millimetres, a third unstable crack propagates rapidly through the height of the sample causing brittle failure (Fig. 7c).

In order to study the local microstructure of the cracks in more detail, following the *in situ* X-ray tomography measurements, the crack geometries were further analysed by conducting post-fracture *ex situ* tomography at a higher spatial resolution. At the higher resolution (0.65 µm voxel size), only the crack-tip region could be imaged because of the smaller field of view. The mid-thickness slices in Fig. 8 of the region of interest reveal that, in addition to the large-scale deflection which is typically observed in NLA samples imaged at the macroscale, crack bridging, local brick and mortar scale deflection and diffuse damage arise at the crack fronts. Crack bridging is similar to what is usually observed in elongated grain ceramics, with some grains still being attached and providing friction during the opening. In addition, the crack front in NLA-B also exhibits diffuse damage, with a few small cracks seemingly growing simultaneously. While the spatial resolution of the tomography is not high enough to provide further quantification, this mid-thickness work is consistent with the SEM images in Fig 1 that show a localised region of microcracking within a 10 µm radius of the main crack.

There is a visible difference between Fig. 8a and 8b in the tip opening displacement and the tortuosity of the crack path. This seems to indicate that the morphology of the brick-and-mortar structure influences the crack path in NLA. To further quantify the role of the microstructure on the local toughening mechanisms acting at the crack tip, the R-curves of NLA-B and NLA-Y were compared with regards to the grain morphology.

Fig. 9 presents the data extracted from *in situ* SENB X-ray microtomography to quantify the effect of the microstructural changes in NLA-B and NLA-Y on the fracture toughness using the deflection angle $\theta$

(Fig. 9a), the calculated local stress intensity factors in mode I and II, $K_I^k$ and $K_{II}^k$ (Fig. 9b), and the corresponding stress energy release rate for three different specimens per composition. All the data presented in Fig. 9 are extracted up until the end of the stable crack growth.

It can be observed from Fig. 9a that the deflection angle starts at around 70° for both compositions but ends up at $83 \pm 1°$ for NLA-B and $73 \pm 4°$ for NLA-Y at the end of the stable crack propagation. The crack length at the end of the stable crack propagation is also influenced by the change in composition, with an average final crack length for NLA-B and NLA-Y of $1209 \pm 191$ µm and $433 \pm 193$ µm respectively. Switching one of the mortar elements from boron to yttrium significantly changes the crack propagation, with a decrease of deflection angle by 12% only but a decrease of stable crack length by almost a factor 3. Given that the critical energy release rate in mode I of both mortars was measured to be similar, we hypothesise that this change in fracture behaviour is related to the minute changes in microstructure (Fig. 2), with the grain aspect ratio of NLA-Y being 1.25 times smaller than NLA-B.

Assuming that the crack propagation follows the shape of the grain on average (cf. Fig. 1), we can estimate an expected deflection angle $\theta_e$ based on the grain shape with $\theta_e(r) = 90 - \tan^{-1}(r/L) = 90 - \tan^{-1}(1/r)$, with $t$ the grain thickness, $L$ the grain length, and $r$ the grain aspect ratio.

As the grain dimension distributions follow a log-normal distribution, it is possible to calculate a range of expected deflection angles. In this regard, we found that for both NLA-B and NLA-Y, the experimental deflection angle measured $\theta_m$ always lies between the expected deflection calculated from the 50% and 90% of the aspect ratio distribution, i. e. $\theta_e(r_{50}) < \theta_m < \theta_e(r_{90})$. While this analysis is based only on grain shape and a more representative one but more complex to formulate would also include a grain overlap parameter, the trend matches well.

It thus appears that the change in composition influences the grain morphology, which in turns has an impact on crack propagation. However, this change does not significantly influence the local stress intensity factors. Indeed, the local stress intensity factors (Fig. 9b) start at around $1.5 \text{ MPa.m}^{1/2}$ for both compositions, then increase with a similar slope up to around 3 MPa.m$^{1/2}$ for NLA-B and only to around 2 MPa.m$^{1/2}$ for NLA-Y. This lower fracture toughness reached for NLA-Y is a direct consequence of the lower stable crack length reached, and thus the grain morphology. The change in deflection angle also slightly impacts the local mode-mixity $\beta = K_I^k/(K_I^k+K_{II}^k)$ from a value of $0.54 \pm 0.01$ for NLA-B to $0.57 \pm 0.02$ for NLA-Y.

The fact that the R-curves for both compositions present a similar slope suggests that similar reinforcing mechanisms are acting in the microstructure to slow down crack progression. Given that the effect of the global deflection is not included in this local analysis, this further confirms that both grain bridging and local diffuse cracking at the crack front (Fig. 8) are acting in the two NLA compositions with similar efficacy.

Finally, the local energy release rate obtained in SENB loading under mixed-mode conditions was compared with the energy release rate

<figure><img src="image_10.png" /><figcaption>**Fig. 7.** In-situ 3D crack propagation in NLA-B using Synchrotron X-ray microtomography. a-c) X-ray CT virtual cross section taken at the centre of an NLA-B sample during both the stable and unstable crack propagation.</figcaption></figure>
<figure><img src="image_11.png" /><figcaption>**Fig. 8.** High spatial resolution *ex situ* virtual CT slices from mid thickness showing the crack tip for a) NLA-B and b) NLA-Y. The red arrows are pointing to visible crack branching and the blue arrow shows the diffuse crack front.</figcaption></figure>

<figure><img src="image_12.png" /><figcaption>**Fig. 9.** Local toughness for both NLA types calculated from *in situ* SENB X-ray µCT and kinked crack theory. a) Deflection angle, b) local stress intensity factors in mode I $K_I^k$ and mode II $K_{II}^k$, and c) local energy release rate $G^k$ as a function of crack extension of the left and right crack.</figcaption></figure>

measured in the wedge splitting test in mode I (Fig. 4). The local energy release rate in mixed-mode was obtained from the local stress intensity factors and the linear elastic fracture mechanics framework [57] leading to $G^k = G_I^k + G_{II}^k = (K_I^{k2} + K_{II}^{k2})/E'$, with $E' = E/(1 - \nu^2)$. The local energy release rates are plotted in Fig. 9c, along with energy release rate obtained in wedge splitting test $G_{WST} \approx 8-15$ J/m². The local energy release rates are starting at around 13-15 J/m² for both NLA-B and NLA-Y, which is on the order of $G_{WST}$, although 40% higher in the case of NLA-B. This increase suggests an effect of the mode-mixity on the toughness of the NLA, with higher mode-mixity leading to higher toughness. This effect has been documented on bulk ceramics and glasses before and is known as the Shetty mixed-mode fracture criterion [58]. While alumina usually doesn't show this sensitivity to mixed-mode fracture, both nacre-like compositions do. We hypothesize this originates from preferential orientation of the grain boundaries compared to bulk equi-axed grain polycrystalline alumina, but a deeper study would be needed to confirm or refute this.

## 4. Conclusions

In this paper we used a combination of the wedge splitting test (predominantly mode I), SENB testing (cracking under mixed mode I and II) observed *in situ* by X-ray microtomography and microstructure control to study the influence of the mortar composition and brick morphology on the complex fracture behaviour in bioinspired brick-and-mortar ceramic composites. We designed two nacre-like aluminas (NLA) having different mortar compositions; one based on boron oxide (NLA-B), and one based on yttrium oxide (NLA-Y). The addition of yttrium and the use of a slightly higher sintering temperature changed the brick morphology, essentially doubling the brick thickness while retaining a similar brick length. Both show extensive crack deflection along the mortar.

Using wedge splitting testing supported by J-integral FEM-based calculations, we found that both compositions present similar mode I
toughness when the crack propagates primarily along the brick length, leading to an estimated mortar critical energy release rate of 8 J/m² and up to 15 J/m² for NLA-B and NLA-Y respectively. Comparing this value with the critical energy release rate of alumina, we found that while the energy release rate is on the order of the maximum value that would theoretically allow crack deflection but couldn't rule out the effect of the possible local toughening mechanisms. The presence of residual stresses in both phases could however change this conclusion and provide a possible way to activate deflection with higher mortar strength, but this would need further research.

The 3D imaging results obtained from X-ray synchrotron micro-
tomography indicate that NLA toughness is sensitive to the tri-axial
stress state, with some crack bowing observed through the thickness.
However, this does not significantly affect the quantification of the local
stress intensity factors measured when observing the surface of the
specimens only.

In SENB mixed-mode fracture testing, the two NLA compositions present similar crack initiation toughness and rising R-curve behaviour, and high spatial resolution tomograms point to the presence of similar toughening mechanisms in both cases, including crack branching and local multiple cracking. The change in composition from NLA-B to NLA-Y triggers a significant reduction in stable crack length, which we link to the decrease in brick aspect ratio that in turn influences the crack deflection angle. In conclusion, deflection acts as potent toughening mechanisms when it is activated in certain loading orientations but the process zone at the tip of each crack is in the tens of microns regime, in line with what was obtained in elongated grains ceramics.

These results suggest that a more promising strategy to increase the toughness of NLA than further optimisation of the mortar lies in the better control of the microstructure. Indeed, simulations point toward a strong effect of the regularity of brick size, shape and overlap on the development of diffuse and delocalised damage, a feature that will be difficult to achieve with the current raw material powders and processing pathways used. Consequently, finding building blocks and processes that allow for a precise control of the brick-and-mortar structure appears to be a topic worthy of further exploration.

CRediT authorship contribution statement

**Victoria Vilchez:** Writing – review & editing, Methodology, Investigation, Formal analysis, Data curation, Conceptualization. **Shelley Rawson:** Writing – review & editing, Methodology, Funding acquisition, Formal analysis, Data curation. **Shitong Zhou:** Writing – review & editing, Methodology, Formal analysis, Data curation. **Jamie McGregor:** Data curation. **Matthew Lawson:** Data curation. **Alexander Rack:** Writing – review & editing, Methodology, Data curation. **Yunhui Chen:** Writing – review & editing, Methodology, Data curation. **Philip J. Withers:** Writing – review & editing, Supervision, Funding acquisition, Formal analysis, Conceptualization. **Florian Bouville:** Writing – review & editing, Writing – original draft, Supervision, Methodology, Funding acquisition, Formal analysis, Data curation, Conceptualization.

Declaration of competing interest

The authors declare that they have no known competing financial
interests or personal relationships that could have appeared to influence
the work reported in this paper.

Acknowledgements

The authors would like to acknowledge fruitful discussion on wedge
splitting technique with Prof. Finn Giuliani. We acknowledge the Eu-
ropean Synchrotron Radiation Facility (ESRF) for provision of syn-
chrotron radiation facilities under proposal number MA-5067. This
work was supported by the Engineering and Physical Sciences Research
Council (grant EP/R513052/1). FB acknowledge support from the

European Research Council Starting Grant [H2020-ERC-STG grant agreement n°948336] SSTEEL. PJW, SR and YC acknowledge support from the European Research Council Advanced Grant [H2020-ERC-ADG project number 695638] CORREL-CT as well as the Henry Royce Institute for Advanced Materials, founded through EPSRC grants EP/ R00661X/1, EP/S019367/1, EP/ P025021/1 and EP/P025498/1.

**Supplementary materials**

Supplementary material associated with this article can be found, in
the online version, at doi:10.1016/j.actamat.2024.120338.

**References**

[1] S.Eswarappa Prameela, T.M. Pollock, D. Raabe, M.A. Meyers, A. Aitkaliyeva, K. L. Chintersingh, Z.C. Cordero, L. Graham-Brady, Materials for extreme environments, Nat. Rev. Mater. 8 (2023) 81–88, https://doi.org/10.1038/s41578-022-00496-2.

[2] R.O. Ritchie, The conflicts between strength and toughness, Nat. Mater. 10 (2011) 817–822, https://doi.org/10.1038/nmat3115.

[3] J. Chevalier, A. Liens, H. Reveron, F. Zhang, P. Reynaud, T. Douillard, L. Preiss, V. Sergo, V. Lughi, M. Swain, N. Courtois, Forty years after the promise of «ceramic steel»?: Zirconia-based composites with a metal-like mechanical behavior, Journal of the American Ceramic Society 103 (2020) 1482–1513, https://doi.org/10.1111/jace.16903.

[4] M.W. Barsoum, M. Radovic, Elastic and Mechanical Properties of the MAX Phases, Annu Rev. Mater. Res. 41 (2011) 195–227, https://doi.org/10.1146/annurev-matsci-062910-100448.

[5] A.G. Evans, Perspective on the Development of High-Toughness Ceramics, Journal of the American Ceramic Society 73 (1990) 187–206, https://doi.org/10.1111/j.1151-2916.1990.tb06493.x.

[6] N. Bansal, J.L. Lamon, Ceramic matrix composites, Wiley-VCH, 2014.

[7] F. Rebillat, J. Lamon, A. Guette, Concept of a strong interface applied to SiC/SiC composites with a BN interphase, Acta Mater. 48 (2000) 4609–4618, https://doi.org/10.1016/S1359-6454(00)00247-0.

[8] J.W.C. Dunlop, P. Fratzl, Biological Composites, Annu Rev. Mater. Res. 40 (2010) 1–24, https://doi.org/10.1146/annurev-matsci-070909-104421.

[9] M.A. Meyers, J. McKittrick, P.-Y. Chen, Structural biological materials: critical mechanics-materials connections, Science (1979) 339 (2013) 773–779, https://doi.org/10.1126/science.1220854 (1979).

[10] X. Li, Z. Guo, Q. Huang, C. Yuan, Research and application of biomimetic modified ceramics and ceramic composites: A review, Journal of the American Ceramic Society (2023) 1–35, https://doi.org/10.1111/jace.19490.

[11] W. Huang, D. Restrepo, J.Y. Jung, F.Y. Su, Z. Liu, R.O. Ritchie, J. McKittrick, P. D. Zavattieri, D. Kisailus, Multiscale Toughening Mechanisms in Biological Materials and Bioinspired Designs, Advanced Materials 1901561 (2019) 1–37, https://doi.org/10.1002/adma.201901561.

[12] F. Heinemann, M. Launspach, K. Gries, M. Fritz, Gastropod nacre: structure, properties and growth–biological, chemical and physical basics, Biophys. Chem. 153 (2011) 126–153, https://doi.org/10.1016/j.bpc.2010.11.003.

[13] M.I. Lopez, P.Y. Chen, J. McKittrick, M.A. Meyers, Growth of nacre in abalone: Seasonal and feeding effects, Materials Science and Engineering: C 31 (2011) 238–245, https://doi.org/10.1016/j.msec.2010.09.003.

[14] F. Barthelat, Nacre from mollusk shells: A model for high-performance structural materials, Bioinspir. Biomim. 5 (2010), https://doi.org/10.1088/1748-3182/5/3/035001.

[15] H.D. Espinosa, J.E. Rim, F. Barthelat, M.J. Buehler, Merger of structure and material in nacre and bone – Perspectives on de novo biomimetic materials, Prog. Mater. Sci. 54 (2009) 1059–1100, https://doi.org/10.1016/j.pmatsci.2009.05.001.

[16] H.D. Espinosa, A.L. Juster, F.J. Latourte, O.Y. Loh, D. Gregoire, P.D. Zavattieri, Tablet-level origin of toughening in abalone shells and translation to synthetic composite materials, Nat. Commun. 2 (2011) 173, https://doi.org/10.1038/ncomms1172.

[17] H.-C. Loh, T. Divoux, B. Gludovatz, P.U.P.A. Gilbert, R.O. Ritchie, F.-J. Ulm, A. Masic, Nacre toughening due to cooperative plastic deformation of stacks of co-oriented aragonite platelets, Commun. Mater. 1 (2020) 1–10, https://doi.org/10.1038/s43246-020-00078-y.

[18] F. Barthelat, R. Rabiei, Toughness amplification in natural composites, J. Mech. Phys. Solids. 59 (2011) 829–840, https://doi.org/10.1016/j.jmps.2011.01.001.

[19] F. Barthelat, Z. Yin, M.J. Buehler, Structure and mechanics of interfaces in biological materials, Nat. Rev. Mater. (2016) 16007, https://doi.org/10.1038/natrevmats.2016.7.

[20] U.G.K. Wegst, H. Bai, E. Saiz, A.P. Tomsia, R.O. Ritchie, Bioinspired structural materials, Nat. Mater. 14 (2015) 23–36.

[21] F. Bouville, E. Maire, S. Meille, B. Van de Moortèle, A.J. Stevenson, S. Deville, Strong, tough and stiff bioinspired ceramics from brittle constituents, Nat. Mater. 13 (2014) 508–514, https://doi.org/10.1038/nmat3915.

[22] H. Saad, K. Radi, T. Douillard, D. Jauffres, C.L. Martin, S. Meille, S. Deville, A simple approach to bulk bioinspired tough ceramics, Materialia (Oxf) 12 (2020), https://doi.org/10.1016/j.mtla.2020.100807.
[23] E. Feilden, C. Ferraro, Q. Zhang, E. García-Tuñón, E. D'Elia, F. Giuliani, L. J. Vandeperre, E. Saiz, 3D Printing Bioinspired Ceramic Composites, Sci. Rep. 7 (2017) 13759, https://doi.org/10.1038/s41598-017-14236-9.

[24] A.K. Hofer, I. Kraleva, R. Bermejo, Additive manufacturing of highly textured alumina ceramics, Open Ceramics 5 (2021) 100085, https://doi.org/10.1016/j.oceram.2021.100085.

[25] R. Bermejo, Toward seashells under stress": Bioinspired concepts to design tough layered ceramic composites, J. Eur. Ceram. Soc. (2017), https://doi.org/10.1016/j.jeurceramsoc.2017.04.041.

[26] W.J. Clegg, K. Kendall, N.McN. Alford, T.W. Button, J.D. Birchall, A simple way to make tough ceramics, Nature 347 (1990) 455–457, https://doi.org/10.1038/347455a0.

[27] H.Le Ferrand, F. Bouville, T.P. Niebel, André.R. Studart, Magnetically assisted slip casting of bioinspired heterogeneous composites, Nat. Mater. 14 (2015) 1172–1179, https://doi.org/10.1038/nmat4419.

[28] F. Bouville, Strong and tough nacre-like aluminas: Process-structure-performance relationships and position within the nacre-inspired composite landscape, J Mater Res 35 (2020) 1076–1094, https://doi.org/10.1557/jmr.2019.418.

[29] P.I.B.G.B. Pelissari, V.C. Pandolfelli, D. Carnelli, F. Bouville, Refractory interphase and its role on the mechanical properties of boron containing nacre-like ceramic, J. Eur. Ceram. Soc. 40 (2019) 165–172, https://doi.org/10.1016/j.jeurceramsoc.2019.08.034.

[30] R. Henry, H. Saad, S. Dankic-cottrino, S. Deville, S. Meille, L. De Synthèse, U.M.R. C. Saint-gobain, U. De Lyon, U. Claude, B. Lyon, I.L. Matière, Nacre-like alumina composites reinforced by zirconia particles, (n.d.) 1–17.

[31] K. Radi, D. Jauffres, S. Deville, C.L. Martin, Elasticity and fracture of brick and mortar materials using discrete element simulations, J. Mech. Phys. Solids. 126 (2019) 101–116, https://doi.org/10.1016/j.jmps.2019.02.009.

[32] T. Duminy, R. Henry, J. Adrien, A. Doitrand, S. Meille, Anisotropic fracture in nacre-like alumina, Theoretical and Applied Fracture Mechanics 123 (2023) 103710, https://doi.org/10.1016/j.tafmec.2022.103710.

[33] R. Henry, H. Saad, A. Doitrand, S. Deville, S. Meille, Interface failure in nacre-like alumina, J. Eur. Ceram. Soc. 40 (2020) 4694–4699, https://doi.org/10.1016/j.jeurceramsoc.2020.05.068.

[34] V. Vilchez, P.I.B.G.B. Pelissari, V.C. Pandolfelli, F. Bouville, Mixed-mode fracture model to quantify local toughness in nacre-like alumina, J. Eur. Ceram. Soc. 43 (2023) 4472–4481, https://doi.org/10.1016/j.jeurceramsoc.2023.03.044.

[35] P.I.B.G.B. Pelissari, F. Bouville, V.C. Pandolfelli, D. Carnelli, F. Giuliani, A.P. Luz, E. Saiz, André.R. Studart, Nacre-like ceramic refractories for high temperature applications, J. Eur. Ceram. Soc. (2017) 0–1, https://doi.org/10.1016/j.jeurceramsoc.2017.10.042.

[36] A. Ikesue, T. Kinoshita, K. Kamata, K. Yoshida, Fabrication and Optical Properties of High-Performance Polycrystalline Nd:YAG Ceramics for Solid-State Lasers, Journal of the American Ceramic Society 78 (1995) 1033–1040, https://doi.org/10.1111/j.1151-2916.1995.tb08433.x.

[37] D. Legland, I. Arganda-Carreras, P. Andrey, MorphoLibJ: Integrated library and plugins for mathematical morphology with ImageJ, Bioinformatics. 32 (2016) 3532–3534, https://doi.org/10.1093/bioinformatics/btw413.

[38] J. Schindelin, I. Arganda-Carreras, E. Frise, V. Kaynig, M. Longair, T. Pietzsch, S. Preibisch, C. Rueden, S. Saalfeld, B. Schmid, J.-Y.J.-Y. Tinevez, D.J. White, V. Hartenstein, K. Eliceiri, P. Tomancak, A. Cardona, K. Liceiri, P. Tomancak, C. A, Fiji: an open source platform for biological image analysis, Nat. Methods 9 (2012) 676–682, https://doi.org/10.1038/nmeth.2019.Fiji.

[39] W.C. Oliver, G.M. Pharr, An improved technique for determining hardness and elastic modulus using load and displacement sensing indentation experiments, J Mater Res 7 (1992) 1564–1583, https://doi.org/10.1557/JMR.1992.1564.

[40] C. B, R. JR, B. Cotterell, J.R. Rice, Slightly Curved or Kinked Cracks, Int. J. Fract. 16 (1979) 155–169.

[41] ASTM Standard E1820, Standard Test Method for Measurement of Fracture Toughness, ASTM Book of Standards, 2013, pp. 1–54, https://doi.org/10.1520/E1820-13.Copyright.

[42] N. Aldegaither, G. Sernicola, A. Mesgarnejad, A. Karma, D. Balint, J. Wang, E. Saiz, S.J. Shefelbine, A.E. Porter, F. Giuliani, Fracture toughness of bone at the microscale, Acta Biomater. 121 (2021) 475–483, https://doi.org/10.1016/j.actbio.2020.12.007.

[43] G. Sernicola, T. Giovannini, P. Patel, J.R. Kermode, D.S. Balint, T. Ben Britton, F. Giuliani, In situ stable crack growth at the micron scale, Nat. Commun. 8 (2017) 108, https://doi.org/10.1038/s41467-017-00139-w.

[44] J.G. Williams, End corrections for orthotropic DCB specimens, Compos. Sci. Technol. 35 (1989) 367–376, https://doi.org/10.1016/0266-3538(89)90058-4.

[45] A. Parslow, A. Cardona, R.J. Bryson-Richardson, Sample Drift Correction Following 4D Confocal Time-lapse Imaging, Journal of Visualized Experiments (2014) e51086, https://doi.org/10.3791/51086.

[46] H. Saad, K. Radi, T. Douillard, D. Jauffres, C.L. Martin, S. Meille, S. Deville, A simple approach to bulk bioinspired tough ceramics, Materialia (Oxf) 12 (2020), https://doi.org/10.1016/j.mtla.2020.100807.

[47] R. Henry, H. Saad, S. Dankic-Cottrino, S. Deville, S. Meille, Nacre-like alumina composites reinforced by zirconia particles, J. Eur. Ceram. Soc. 42 (2022) 2319–2330, https://doi.org/10.1016/j.jeurceramsoc.2021.12.043.

[48] R. Voytovych, I. MacLaren, M.A. Gülgün, R.M. Cannon, M. Rühle, The effect of yttrium on densification and grain growth in α-alumina, Acta Mater. 50 (2002) 3453–3463, https://doi.org/10.1016/S1359-6454(02)00159-3.

[49] J.R. Rice, A Path Independent Integral and the Approximate Analysis of Strain Concentration by Notches and Cracks, J. Appl. Mech. 35 (1968) 379.

[50] C.F. Shih, R.J. Asaro, Elastic-Plastic Analysis of Cracks on Bimaterial Interfaces: Part I—Small Scale Yielding, J. Appl. Mech. 55 (1988) 299–316, https://doi.org/10.1115/1.3173676.

[51] S. Graça, V. Trabadelo, A. Neels, J. Kuebler, V.Le Nader, G. Gamez, M. Döbeli, K. Wasmer, Influence of mosaicity on the fracture behavior of sapphire, Acta Mater. 67 (2014) 67–80, https://doi.org/10.1016/j.actamat.2013.12.004.

[52] T. Vodenitcharova, L.C. Zhang, I. Zarudi, Y. Yin, H. Domyo, T. Ho, M. Sato, The effect of anisotropy on the deformation and fracture of sapphire wafers subjected to thermal shocks, J. Mater. Process. Technol. 194 (2007) 52–62, https://doi.org/10.1016/j.jmatprotec.2007.03.125.

[53] M.Y.Y. He, J.W.W. Hutchinson, Crack deflection at an interface, Int. J. Solids. Struct. 25 (1989) 1053–1067.

[54] T.L. Anderson, Fracture Mechanics: Fundamentals and Applications, 2012, https://doi.org/10.1016/j.jmps.2010.02.008.

[55] W. Rankine II, On the stability of loose earth, Philos Trans R Soc Lond 147 (1857) 9–27, https://doi.org/10.1098/rstl.1857.0003.

[56] H. Tu, H. Zhou, J. Lu, Y. Gao, L. Shi, Elastoplastic coupling analysis of high-strength concrete based on tests and the Mohr-Coulomb criterion, Constr. Build. Mater. 255 (2020) 119375, https://doi.org/10.1016/j.conbuildmat.2020.119375.

[57] T.L. Anderson, Fracture Mechanics, Third edit, Taylor & Francis Group, 2005.

[58] D.K. Shetty, Mixed-Mode Fracture Criteria for Reliability Analysis and Design With Structural Ceramics, J. Eng. Gas. Turbine Power. 109 (1987) 282–289, https://doi.org/10.1115/1.3240037.