# Liquid metal embrittlement of Cu-30%Zn by EGaIn: Microscale fracture toughness by in situ SEM testing

Marco Ezequiel, Eva Héripré, Ingrid Proriol Serre, Thierry Auger

► To cite this version:

Marco Ezequiel, Eva Héripré, Ingrid Proriol Serre, Thierry Auger. Liquid metal embrittlement of Cu-30%Zn by EGaIn: Microscale fracture toughness by in situ SEM testing. Engineering Fracture Mechanics, 2025, Engineering Fracture Mechanics, 327, pp.111505. 10.1016/j.engfracmech.2025.111505. hal-05241301

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# Liquid Metal Embrittlement of Cu-30%Zn by EGaIn: Microscale Fracture Toughness by In Situ SEM Testing

Marco Ezequiel¹)*, Eva Héripré²,³), Ingrid Proriol Serre¹), Thierry Auger²)*

1) Univ. Lille, CNRS, INRAE, Centrale Lille, UMR 8207 - UMET - Unité Matériaux et Transformations, F-59000 Lille, France

2) PIMM/Arts et Métiers Technology Institute, CNRS, CNAM, 151 Bd de l'hôpital 75013 Paris, France

3) Université Paris-Saclay, CentraleSupélec, ENS Paris-Saclay, CNRS, Laboratoire de Mécanique Paris-Saclay, 91190 Gif-sur-Yvette, France.

## Abstract

Liquid Metal Embrittlement (LME) of Cu-30%Zn brass induced by liquid Ga-In eutectic (EGaIn) is investigated through a novel approach that combines *in situ* scanning electron microscopy (SEM) and micromechanical testing. Unlike macroscopic measurements, at a small scale, the crack initiation process can be sufficiently monitored such that a crack initiation fracture toughness can be derived using Finite Element Modeling (FEM) both at the continuum level or within a Crystal Plasticity framework (CPFEM). Using this new analysis methodology, the measured fracture initiation toughness values, $K_{Ic} = 2.00$ (FEM) and 2.36 MPa·m$^{1/2}$ (CPFEM), are found to be considerably lower than the ones previously measured in the LME literature, thanks to the minimization of plastic zone size effects. These results highlight the critical role of real-time observations in capturing crack nucleation and open a pathway for direct comparison with atomistic fracture models.

<footnote>* marco.ezequiel@lspm.cnrs.fr</footnote>

<footnote>• thierry.auger@ensam.eu</footnote>
Nomenclature

<table><tr><td>a</td><td>Notch length</td></tr><tr><td>a<sup>su</sup></td><td>Interaction matrix between the slip systems s and u</td></tr><tr><td>B</td><td>Height of the sample</td></tr><tr><td>b</td><td>Norm of the Burgers vector</td></tr><tr><td>BSE</td><td>Backscattered Electrons</td></tr><tr><td>C<sub>ii</sub></td><td>Elastic constants</td></tr><tr><td>CPFEM</td><td>Crystal Plasticity Finite Element Method</td></tr><tr><td>DIC</td><td>Digital Image Correlation</td></tr><tr><td>E</td><td>Young's Modulus</td></tr><tr><td>EBID</td><td>Electron-Beam Induced Deposition</td></tr><tr><td>EBSD</td><td>Electron Backscattered Diffraction</td></tr><tr><td>EGaIn</td><td>Ga-In eutectic</td></tr><tr><td>FCC</td><td>Face-centered cubic</td></tr><tr><td>FEM</td><td>Finite Element Method</td></tr><tr><td>FIB</td><td>Focus ion beam</td></tr><tr><td>J</td><td>J-integral</td></tr><tr><td>K</td><td>Fracture Toughness</td></tr><tr><td>LEFM</td><td>Linear Elastic Fracture Mechanics Approach</td></tr><tr><td>LME</td><td>Liquid Metal Embrittlement</td></tr><tr><td>n</td><td>stress sensitivity parameter</td></tr><tr><td>ND</td><td>Normal Direction</td></tr><tr><td>RD</td><td>Rolling Direction</td></tr><tr><td>SEM</td><td>Scanning Electron Microscopy</td></tr><tr><td>SIF</td><td>Stress Intensity Factor</td></tr><tr><td>TD</td><td>Transverse Direction</td></tr><tr><td>TEM</td><td>Transmission Electron Microscopy</td></tr><tr><td>T<sub>i</sub></td><td>Traction components</td></tr><tr><td>u<sub>i</sub></td><td>Displacement components</td></tr><tr><td>W</td><td>Width of the sample</td></tr><tr><td>w</td><td>Density of Strain Energy</td></tr><tr><td>γ̇<sub>0</sub></td><td>Reference shear rate</td></tr><tr><td>γ̇<sup>s</sup></td><td>Rate-dependent slip rate</td></tr><tr><td>γ<sub>c</sub></td><td>Material's fit parameter</td></tr><tr><td>μ</td><td>Isotropic shear modulus</td></tr><tr><td>ν</td><td>Poisson's ratio</td></tr><tr><td>ρ<sup>u</sup></td><td>Internal dislocation density in the slip system u</td></tr><tr><td>ρ<sub>0</sub></td><td>Dislocation density</td></tr></table>
$\dot{\rho}^s$ Stored dislocation density

$\sigma_y$ Yield strength

$\tau_0$ Lattice friction stress

$\tau^s$ Resolved shear stress

$\tau_c^s$ Critical shear stress

$\Gamma$ Contour around the crack

# 1 Introduction

Liquid metal embrittlement (LME) is a phenomenon in which a normally ductile material fractures in a brittle manner when it is subject to plastic deformation in contact with liquid metal. Despite extensive research, numerous studies and reviews indicate that LME remains a complex and incompletely understood subject with critical issues hampering further progress [1–5]. One of the issues is that the proposed LME mechanisms are diverse, with various plausible embrittlement scenarios at the atomic scale. The cursor lies between adsorption-induced weakening and modified plastic behavior of the material interfaces, possibly induced by diffusion ahead of the crack tip. Still, none can universally describe the phenomenology in all cases so far [1–3].

Another major issue is that fracture mechanics data are sparse and suffer from an evident scale dependence, making them inoperant compared to modeling at the microscopic scale. The crack initiation stress intensity factor (SIF), which is a key quantity of major interest in environmentally induced fractures, should ultimately allow for comparison with atomistic models, provided that plasticity surrounding the crack tip is correctly accounted for. In this latter modeling type, the crack tip is considered to be separated into a fracture process zone in which one is primarily interested when regarding various fracture mechanisms and a K-dominance zone where linear elasticity rigorously applies (also labeled dislocation-free zone [6]). Ideally, one would like to extract from the experiment the critical SIF in a K-dominance
mode to compare righteously with atomistic modeling. After crack initiation in LME brittle
systems, the crack growth rate is either relatively fast right after initiation (as in the case we
will consider here), or it occurs subcritically, often being strain rate controlled. This latter
phase is complex to model other than empirically in the current state of LME understanding
due to the lack of a good description of the kinetics of crack propagation. Looking at the
previous attempts to measure critical SIF for environmental cracking phenomena limited to
surface effects by adsorption, such as LME, one can notice two trends. The first one uses a
well-defined macroscopic mechanical framework, taking into account the stress concentration
and, eventually, the plastic deformation surrounding the crack tip that invariably occurs in this
type of fracture, being the fracture of an otherwise ductile material. This is exemplified in the
study of the intergranular cracking of the Al/Hg system where critical SIF down to 1.56
MPa·m¹/² was inferred using Moiré interferometry techniques for measuring the surface
displacement field [7]. This technique seems, however, limited to a subset of systems with
extremely large embrittlement effects, so direct measurement is still problematic in many
cases.

The second trend is to miniaturize the test down to microscales attempting to limit plastic
dissipation near the crack tip, such as to be in a situation where one can neglect or rigorously
take into account surrounding confined plasticity, both by computation and using correlation
with scanning electron microscopy (SEM) observations. Two examples of this more recent
trend are provided by the work of Amstrong et al. [8] on the Cu/Bi system and by Yeng et al.
[9,10] on the FeAl/hydrogen system. These studies represent a significant step forward but
have been limited in their analysis either to a linear isotropic elastic framework (neglecting
small-scale plasticity) or using otherwise an isotropic elastoplastic J integral framework.
Furthermore, the Cu/Bi study was notably not a dynamical fracture experiment because
embrittlement resulted from segregation heat treatments before testing that led to greatly
weakened grain boundaries by a bismuth bi-layer segregation structure. Such a procedure
would not allow one to generalize these measurements easily to other systems either.

Among the alternative *in situ* studies that have been carried out at a small scale, Hugo et al.

[11] carried out transmission electron microscopy (TEM) *in situ* observation of the embrittlement of Al by liquid Ga. A work devoted to another class of LME cases where liquid Ga spontaneously penetrates the Al grain boundaries, also referred to as grain boundary wetting by liquid metal. While such an experimental approach is very informative on LME mechanisms, it is hard to quantify the critical SIF by *in situ* TEM due to an undefined mechanical loading condition.

In this article, we address the study of LME through an *in situ* SEM observation approach in a fracture mechanics geometry. To facilitate this investigation, the Ga-In eutectic (EGaIn) was chosen as the liquid metal due to its melting point of 15.5 °C and a negligible vapor pressure inferior to $1.33 \times 10^{-10}$ Pa at 300 °C [12,13], making it suitable for observation in vacuum. The solid selected is a Cu-30 wt.% Zn alloy, known to be sensitive to LME when it undergoes plastic deformation in contact with liquid EGaIn [14]. Studying the Cu-30%Zn/EGaIn ensures that the embrittlement manifests only when the solid is under plastic strain (i.e., no spontaneous grain boundary wetting occurs). Notably, despite being a miscible system in which Cu and Zn atoms dissolve into EGaIn and Cu atoms further react with Ga in the liquid to form intermetallic compounds, LME persists at room temperature across a wide range of mechanical conditions [14]. The LME phenomenon is investigated using an instrumented mechanical test at a micrometric scale machined in a focus ion beam-scanning electron microscope (FIB-SEM). The experimental approach involves a clamped beam bending test on a polycrystalline sample with a careful sample preparation methodology that restrains the possible impact of $Ga^+$ ion implantation and ensures good wetting by the liquid metal. Finally, an elasto-plastic analysis of the data generated from this micrometric test using finite element
method (FEM) employing continuum mechanics (isotropic elastoplastic) and crystal plasticity modeling (anisotropic elastoplastic) is proposed to quantify the crack initiation fracture toughness for crack initiation. The results are commensurate with typical mechanical loading at crack initiation in atomistic cracking models, enabling potentially an easier discussion of various LME scenarios.

# 2 Materials and methods

## 2.1 Materials

The Cu-30 wt.% Zn alloy, supplied by Alfa Aesar in sheet form with a thickness of 2 mm, had a hardness of 142 ± 4 HV and a monophasic microstructure with equiaxed grains of 39 ± 7 µm, indicating a post-rolling annealing. The EGaIn is composed of Ga-24.5 wt.% In, and it was prepared by melting 99.99 wt.% pure Ga, supplied by Mining & Chemical Products, at 80 °C in a crucible, then adding solid 99.99 wt.% pure In, provided by Alfa Aesar, and mixing.

The alloy manipulations were carried out at room temperature using a RAININ micropipette.

The EGaIn drops were deoxidized before their deposition by immersing them in a 1M hydrochloric acid solution, which dissolves the oxides formed at the surface of the liquid [15,16].

## 2.2 Choice of geometry: Double-clamped beam sample preparation

### Rational for test selection

Designing a micrometric mechanical test for *in situ* observation of the liquid metal embrittlement (LME) in Cu-30%Zn/EGaIn requires careful consideration of specific aspects linked to the small-scale testing. First, given the intergranular nature of LME in this system [14], the test must be conducted on a grain boundary. While growing specific bi-crystal is a
possible option, it is time-consuming and barely available nowadays. An alternative is to carry
out the micro-scale mechanical test on a polycrystalline material by selecting a suitable grain
boundary configuration [8].

Second, ensuring that the crack initiates in the zone in contact with liquid EGaIn is crucial to
observe its direct influence on Cu-30%Zn mechanical behavior. For this purpose, the test
should facilitate continuous contact between the grain boundary and the liquid metal, and it
should present high-stress concentration, limiting the influence of other damage mechanisms.
One of the drawbacks of LME tests is that pre-cracking is hardly feasible in a controlled
manner since the initial cracking length cannot be easily monitored by conventional means (a
liquid metal is opaque and conductive).

Furthermore, since the main effect of the LME is to change the fracture behavior, the most
suitable parameter for its quantification is the fracture toughness; hence, the mechanical
testing should be ideally compatible with its measurement. Recent studies have explored
micromechanical tests for measuring fracture toughness, raising concerns about their
reliability. For instance, Jaya et al. [17] compared four geometries for testing Si (100) fracture
toughness at a micrometric scale: double cantilever bending test, pillar splitting, single
cantilever bending, and clamped beam bending. According to them, the double cantilever
bending test is restricted to brittle systems and presents a low success rate, while the pillar
splitting is unsuitable for studying interfaces [17]. Another possible test is the micro-tensile
test on notched specimens. For example, Arnaud et al. [18] studied thin nitride compound
layers using this method to extract their elastic modulus, Poisson's ratio, and fracture
toughness simultaneously. However, in contrast to the notched tensile test, the bending tests
on a notched specimen have a stress concentration zone limited to a single small surface. This
loading mode reduces the possible damage before the fracture apparition and warrants a
controlled localization of the fracture initiation.
Hence, to measure the fracture toughness of Cu-30%Zn in contact with liquid EGaIn, the most suitable tests would be the single cantilever bending and the clamped beam bending. In this work, the clamped beam test was chosen over the single cantilever bending test since preliminary tests showed that the single cantilever bending test had issues with excessive cantilever bending before fracture and slipping of the loading tip.

Saxena et al. [19] presented a workflow with recommendations for calculating fracture toughness at a micrometric scale. From these recommendations, we highlight the choice of a sample size to comply with Eq. (1) to apply elastoplastic fracture mechanics [20], where *B* and *W* are the width and height of the sample, *a* is the notch length, *J* is the J-integral, and *σ*<sub>y</sub> is the yield strength. To prevent overestimation of the material fracture toughness using elastoplastic fracture mechanics, Saxena et al. recommend using notches extending through the entire thickness of the sample rather than bridge notches fabricated only in a central sample volume. These recommendations were followed in this work in machining a suitable geometry.

$$ \{ \begin{matrix} B \\ W-a \end{matrix} \} > 10 \frac{J}{\sigma_y} \qquad (1) $$

## Sample preparation

A 1 × 0.5 mm Cu-30 wt.% Zn sample was mechanically polished on both sides to a final thickness of approximately 60 µm using SiC papers with grades increasing to 2000. The sample was machined using an FEI Helios Nanolab 660 dual-beam FIB-SEM. The instrument featured a Schottky thermal field emission electron gun and a Ga ion source at 52° to the electron beam. It is also equipped with a four-axis micro-manipulator with a W needle (“EasyLift”).

The sample preparation consisted of several steps. First, a transverse cut 500 x 60 µm was milled using a high-intensity ion beam of 65 nA at an acceleration voltage of 30 kV (See
Supplementary Material-A). Then, a grain boundary positioned vertically was selected for the
mechanical testing. Electron backscattered diffraction (EBSD) measurements were performed
to quantify the misorientations of the grains on all accessible faces. The sample was then
milled around the selected grain boundary using sequentially decreasing ion beam intensities
ranging from 65 nA to 80 pA at a constant voltage of 30 kV. A tilt of 2° was employed for the
finishing steps to account for the beam halo and to ensure the parallelism of the opposite
faces. When necessary, the observations with the ion beam were performed at a low intensity
of 40 pA to limit Ga⁺ contamination. The last step of the preparation of the double-clamped
beam consisted of applying a thin W-layer on top of the notch by using electron-beam
induced deposition (EBID); the conditions were chosen to lead to a 20 nm thick deposition,
but this thickness could not be corroborated. The final notch radius was around 2 µm.

Additional details on sample fabrication are given in Supplementary Material-A. The purpose
of this W-layer is to prevent direct contact between the sample and the liquid EGaIn before
the start of the test. If they were to be put in contact before testing, they would react to form
an intermetallic compound at the solid-liquid interface [21]. This would deplete the liquid
metal reservoir and eventually suppress LME. The expected behavior of the W layer is that,
given the intrinsic brittle nature of W, it fractures during the first stages of plastic deformation
of the sample, enabling the liquid EGaIn to come into contact with the Cu-30%Zn only when
the latter is undergoing plastic deformation. Since W has no stable phases with Cu or Ga [22],
it ensures that no chemical evolution occurs between machining and *in situ* testing.

The liquid EGaIn was then deposited using the micro-manipulator equipped with a W needle.
For that purpose, the needle was previously soaked in liquid EGaIn so that many micro-sized
droplets would cover its tip. The needle was moved towards the sample while observing using
the ion and electronic beams to ensure precise positioning for the deposition process. Figure 1
illustrates some key steps during the deposition of the drops. Due to the good wettability of
EGaIn on Cu-30%Zn (contact angle ≈ 40° [14]), the liquid drop remained in contact with the double-clamped beam sample throughout the entire test by capillarity, without dropping or flowing away from the notch. Moreover, the procedure is tolerant towards small localized overflow (see Supplementary Material-A).

Figure 2 presents the sample with its dimensions and the results of an EBSD performed on two faces of the sample. Emerging slip bands and crack initiation at the grain boundary position can be monitored during the test in Backscattered Electrons (BSE) imaging mode. In contrast to other studies [18], no image correlation for sample deformation measurement is used since the required pattern deposition would hinder crystallographic contrast in the BSE images.

## 2.3 Micro-mechanical test and in situ observation

The machine used to carry out the micromechanical test consists of three piezo-stages to ensure the sample displacement in the X, Y, and Z axes and a calibrated 0.5 N load cell to register the force applied to the sample. A W needle milled as a triangular prism is used as a punch for bending (a rotation degree of freedom along the needle axis allows further freedom in positioning). Additional details on the design of this machine can be found in Refs. [18,23].

The micro-mechanical bending test was performed stepwise, with intermittent pauses to capture high-resolution electron micrographs. Throughout the test, the sample underwent observation using an electron beam accelerated at 10 kV with a current of 1.6 nA. The SE detector was used for surface imaging while simultaneously acquiring the crystallographic contrast with the BSE detector (using only the outer circular zone). The latter allows the observation of surface emerging slip bands that are particularly interesting as they indicate when and where the material undergoes plastic deformation.
The force applied to the sample was obtained from the load cell, while the needle real displacement was measured from the SE micrographs.

## 3 Calculation: Finite element modeling with continuum mechanics and crystal plasticity

The micromechanical test was simulated using the finite element method (FEM) with two complementary approaches. The beam material was modeled as an isotropic non-linear elastoplastic material in the first instance. Figure 3 shows the true stress-true strain curve of the Cu-30%Zn alloy, which was obtained by performing a macroscopic tensile test at a constant displacement rate of 0.5 mm/min, combined with 2D digital image correlation (DIC) on a standard flat geometry aligned with the rolling direction (RD). The tensile behavior matches with the literature values of cold rolled Cu-30%Zn [24]. The true stress-true strain relationship was implemented in ABAQUS 6.13 software as a non-linear isotropic behavior along with Young's modulus (E) of 99.7 GPa and a Poisson's ratio (ν) of 0.33 describing the elastic part.

The fracture toughness was calculated using the J-integral [25], which is derived from elastoplastic fracture mechanics and is defined in Eq. (2):

$$J = \int_{\Gamma} (w \, dy - T_i \frac{\partial u_i}{\partial x} \, ds) \qquad (2)$$

where Γ is taken here as a circular strained contour around the crack, w is the density of strain energy, Tᵢ are the traction components, uᵢ are the displacement components, and ds is the incremental length along Γ. Using the converged value of the J-Integral upon reaching the elastic contour, in the case of plane stress, the fracture toughness (Kᵢ) can be approximated using Eq. (3).
$$K_j = \sqrt{E_j} \qquad (3)$$

The J-integral computation is implemented in the ABAQUS software, so the test modeling allows the calculation of the J-integral at the fracture initiation point. In the FEM assemblies, the needle was treated as a rigid body, and zero friction was assumed. Calculation time was reduced by utilizing symmetric conditions of the sample. The assembly, boundary conditions, and meshes (C3D8 elements) for the FEM are depicted in Figure 4.

In a second instance, the clamped beam bending test was also modeled using a crystal plasticity finite element model (CPFEM). To reduce computational complexity, only the central region of the specimen was simulated. The boundary conditions were imposed as displacement fields, designed to replicate the displacements observed experimentally in the SEM images, thereby approximating the actual deformation experienced during the test.

Figure 5a shows a top view of the central part of the modeled clamped beam specimen, segmented according to the grain boundaries identified by EBSD (Figure 5b). Since mapping or imaging the other faces of the sample was experimentally not accessible, the model assumes that only the grains visible on these faces are present. For simplicity, each grain was assigned its average orientation, and the grain structure was assumed to extend straight into the interior of the sample.

Figure 5c shows the cylindrically symmetrized mesh centered at the notch (with a radius of 2 µm), and Figure 5d illustrates the boundary conditions applied to this CPFEM. The RD-axis displacements correspond to the movement executed by the needle in the sample's lower face, and the transversal direction (TD) axis displacements correspond to those imposed by the sample boundary during its deformation. There are no boundary conditions on the normal direction (ND) axis.
The CPFEM was implemented in Abaqus using a User Subroutine UMAT as a constitutive elastoplastic law with dislocation density internal variables, described in Ref. [26]. The critical shear stress ($\tau_c^s$) [27], the rate-dependent slip rate ($\dot{\gamma}^s$) [28], and the rate of evolution of the stored dislocation density ($\dot{\rho}^s$) [29] were respectively defined according to equations (5), (6), and (7).

$$ \tau_c^s = \tau_0 + \mu b \sqrt{\sum_{u=1,12} a^{su} \rho^u} \qquad (5) $$

$$ \dot{\gamma}^s = \begin{cases} \dot{\gamma}_0 \left( \frac{|\tau^s|}{\tau_c^s} \right)^n \operatorname{sign}(\tau^s), & |\tau^s| > \tau_c^s \\ 0, & \text{otherwise} \end{cases} \qquad (6) $$

$$ \dot{\rho}^s = \frac{|\dot{\gamma}^s|}{b} \left[ \frac{\sqrt{\sum_{u \neq s} \rho^u}}{K} - 2y_c \rho^s \right] \qquad (7) $$

where $\tau_0$ is the lattice friction stress, $\mu$ the isotropic shear modulus, $b$ is the norm of the Burgers vector, $a^{su}$ is the interaction matrix between the slip systems $s$ and $u$, $\rho^u$ is the internal dislocation density on the slip system $u$, $\dot{\gamma}_0$ is a reference shear rate, $\tau^s$ is the resolved shear stress, $n$ is the stress sensitivity parameter, $K$ and $y_c$ are material's parameters to fit, and $\rho^s$ is the internal dislocation density on the slip system $s$. This type of modeling is a standard crystal plasticity framework [29].

The three independent elastic constants and the Burgers vector corresponding to the FCC Cu-30%Zn crystal were taken from the work of Jia et al. [30] ($C_{11}$=147 GPa, $C_{12}$=111 GPa, $C_{44}$=72 GPa, and $b=2.56 \times 10^{-7}$ mm). The remaining parameters, including the initial dislocation density ($\rho_0$), were iteratively adjusted by simulating a polycrystalline material until the simulated behavior matched the experimental material's behavior under tensile stress. This simulation was set by modeling a cube composed of 100 grains with different orientations, resulting in an isotropic crystallographic texture. The microstructure was
generated using the open-source Neper software package for polycrystal generation and meshing [31]. The true stress-true strain behavior was averaged over the entire CPFEM model aggregate.

Figure 3 compares the final behavior modeled by CPFEM with the experimental curve. Table 1 lists the parameters finally retained for Cu-30%Zn. Notably, the simulation accurately reproduces the transition from elastic to plastic deformation observed in the experimental test. This agreement supports the chosen value for the critical resolved shear stress, which is close to the value of 94.4 MPa reported in Ref. [32]. The experimental and the simulated curves match up to a strain of 10%. Beyond this point, the simulated material presents a lower strain hardening than the actual material. This divergence at larger plastic deformation most likely comes from the onset of twinning on Cu-30%Zn at high strain levels, which is not described in our CPFEM framework. Since the deformation level reached in the experiment is within the well-fitted range, it was deemed suitable to model the clamped beam bending test near crack initiation. Table 1 Parameters for the CPFEM of the Cu-30 wt.% Zn.

<table><thead><tr><th>γ̇₀ (s⁻¹)</th><th>n</th><th>y_c (mm)</th><th>K</th><th>τ₀ (MPa)</th><th>ρ₀ (mm⁻²)</th><th>a⁰</th><th>a¹</th><th>a²</th><th>a³</th></tr></thead><tbody><tr><td>10⁻⁴</td><td>40</td><td>1.5×10⁻⁵</td><td>100</td><td>110</td><td>1000</td><td>0.02</td><td>0.08</td><td>0.18</td><td>0.3</td></tr></tbody></table>

Modelling frameworks of fracture at the atomic scale typically assume that the crack is asymptotically loaded in K-dominance mode in a small neighbouring ($r < r_K$) such that the stress and strain fields follow asymptotic linear elastic fracture mechanics. One then considers that plastic dissipation is exhausted at the crack tip (in the Dislocation Free Zone) while further away, surrounding plastic activity shields the crack tip from the applied stress concentration. As measured by a J integral, the fracture toughness integrates the plastic area via an independent path integral in the elastic part with the small-scale yielding condition. The J integral, therefore, also contains the effect of plasticity.
# 4 Results

## 4.1 Experimental fracture test

The clamped beam bending test was conducted in various interrupted steps following the methodology described previously. SEM micrographs were captured during these intervals to document the progression of the test. The video of the entire test can be found in the Supplementary Material-Video1.

Figure 6a and b show the crack initiation process, and Figure 6c and d show the step preceding the final failure. Fracture initiation is easier to evidence in the BSE imaging mode. The crack initiation criterion is taken as the appearance of a narrow vertical channel induced by the liquid EGaIn, showing the onset of grain boundary separation. This occurs as the liquid alloy immediately follows the crack tip due to capillarity. Additionally, various fractures appeared near the notch in the later stages of the test.

Following the abrupt failure of the sample, the elastic deformation of the sample and the entire setup relaxed. This recovery generated a quick needle movement towards the sample, leading to significant damage to the fracture surface; a post-mortem fracture assessment is found in Supplementary Material-B for completeness. An alternative clamped beam bending test was subsequently designed to address this issue; however, crack initiation did not proceed in the grain boundary plane, and the test was not included in the analysis. A description of this alternative test is included in Supplementary Material-C.

## 4.2 Assessment of the fracture toughness

Figure 7 shows the comparison between the experimental force-displacement curve and the one computed using isotropic elastoplastic FEM for the micro-bending test. The red circle indicates the fracture initiation in the experiment, corresponding to the initiation step shown
in Figure 6 a,b. The model reproduces the initial portion of the curve well, particularly up to the point of fracture initiation. The onset of plasticity is followed in FEM as a conventional strain hardening curve typical of a material constituted of a few grains (mostly stage I of plasticity).

While the simulations reproduced the experimental force-displacement behavior well up to the point of crack initiation determined by SEM imaging, the role of modeling in this work is to resolve the stress and strain fields at the moment of crack initiation such that ABAQUS computes the corresponding fracture toughness. Therefore, our analysis is restricted to the cracking initiation. This is possible since the liquid EGaIn does not affect the mechanical behavior of Cu-30%Zn before the crack initiation [14].

Figure 8a shows the J-integral, computed from the FEM full simulation and the one computed from the reduced CPFEM modeling, as a function of increasing contours. These values correspond to the displacement at fracture initiation (red circle in Figure 7). The plotted value corresponds to the contour at the sample surface, as cracking was only observed on one face. Averaging over the thickness could introduce errors since neither the 3D shape of the crack nor the full crystallographic structure through the sample thickness is known. The J-integral evaluation converges from the 30th contour, located ≈ 2.8 µm away, indicating that this contour encapsulates all plastically deformed regions. Consequently, the small-scale plasticity condition is fulfilled, and the $K_{Jc}$ values, corresponding to the crack initiation, can be calculated using Eq. (3).

To ensure the independence of the $K_{Jc}$ with the mesh size, additional simulations were performed, varying the mesh size between 11 and 59 nm. The $K_{Jc}$ values were computed by taking the contours at distances > 2.8 µm from the notch. Figure 8b shows these $K_{Jc}$ values, demonstrating that they remain independent of the mesh size across the current simulations.
For further analysis, we selected the simulation with the smallest mesh size, marked by a red rhombus in Figure 8b. Table 2 presents the $K_{Jc}$ values obtained from this mesh for both isotropic elastoplastic material behavior and CPFEM.

<table><caption>Table 2 $K_{Jc}$ values for the clamped beam bending test simulations considering an isotropic elastoplastic material's behavior and using the crystal plasticity model.</caption><thead><tr><th></th><th>Isotropic elastoplastic</th><th>Crystal plasticity</th></tr></thead><tbody><tr><th>K<sub>Jc</sub> (MPa·m<sup>1/2</sup>)</th><td>2.00 ± 0.01</td><td>2.36 ± 0.08</td></tr></tbody></table>

# 5 Discussion

The micro-bending test conducted in the Cu-30 wt.% Zn alloy in contact with the EGAln proves to be a valuable new tool for examining Liquid Metal Embrittlement (LME) by allowing the extraction of LME crack initiation SIF. Indeed, the stress concentration obtained by machining a notch allows for applying standard procedures for fracture toughness measurement at a very small scale. It is to be noted that pre-cracking is not usually applied in LME due to the fast crack propagation at the onset of crack propagation, which generally prevents controlled pre-cracking. Nevertheless, once an intergranular LME crack is initiated, one immediately has a nearly atomically sharp crack tip with limited blunting.

The selection of a vertical grain boundary, achievable by combining SEM imaging and a crystalline orientation map by EBSD, allows the intergranular fracture plane to be kept in a well-defined loading mode along the potential vertical crack path. The micro-bending test in an SEM also provides easy deciphering of the crack initiation moment and its further propagation. The Cu-30%Zn alloy is a normally very ductile material that can exhibit substantial plastic deformation before LME fracture initiation; despite the significant plastic deformation reached before cracking, it is shown here to be amenable to an analysis customarily used for brittle materials. The essential confined small-scale yielding condition
for a fracture toughness measurement is achieved as indicated by the J-integral saturation
going away from the crack tip.

To provide a baseline for comparison in the absence of liquid metal embrittlement, prior
estimates of the J-integral for ductile fracture at the macroscopic scale of Cu-30%Zn range
from 14.42 to 47.24 kJ/m², depending on the degree of cold rolling reduction [24]. These are in
sharp contrast with the significantly lower J values obtained in this study: 0.040 and 0.056 kJ/m²
for the FEM and CPFEM simulations, respectively. This substantial difference indicates the
strong embrittlement of the Cu-30%Zn alloys by the liquid EGaIn. Moreover, the corresponding
K<sub>Jc</sub> values of 2.00 MPa·m¹/² (FEM) and 2.36 MPa·m¹/² (CPFEM) are closer with previous
micromechanical measurements in environmentally assisted cracking studies. The SIF
measurement for crack initiation in the Cu/Bi system is 4.7 MPa·m¹/² on average, estimated
using a linear elastic fracture mechanics approach (LEFM) [8]. In comparison, the lowest
measured value for the FeAl/Hydrogen system is 15 MPa·m¹/² (using a J integral approach)
[10].

Certain complexities of the micro-bending test deserve an in-depth discussion. The measured
fracture toughness values were obtained using a microscale geometry specifically designed to
satisfy K-dominance conditions. However, their extrapolation to macroscale components must
be made with caution. At larger scales, plastic dissipation becomes more significant, which
partially mitigates the embrittlement effect [14]. Therefore, the values reported in this study
should be considered as representative of local fracture behavior under EGaIn exposure and can
be used as a conservative lower bound in macroscale modeling.

One primary issue is that the sample preparation method causes prolonged contact between
liquid EGaIn and Cu-30%Zn. Without an effective measure to prevent direct contact before
the micromechanical test begins, intermetallic compounds would form between copper-zinc
and gallium. This would significantly alter the surface and geometry of the sample or even
deplete the liquid EGaIn. A thin W-layer, deposited at the notch by electron-beam induced deposition (EBID), effectively avoids this by blocking the intermetallic formation. As intended, the W-layer breaks during the test, allowing the liquid EGaIn to come into contact with the strained Cu-30%Zn surface. This contact triggers brittle failure along the grain boundary, which is crucial for studying LME phenomena.

To minimize any mechanical influence while maintaining chemical isolation, the W-layer was deposited with a very low thickness (~20 nm), approximately three orders of magnitude thinner than the sample height (9 µm). This ensured that the coating would not significantly affect the mechanical response while functioning as a diffusion barrier during exposure to liquid EGaIn. In reactive systems like Cu-30%Zn/EGaIn, such a barrier is essential to avoid time-dependent reactions that could compromise test reproducibility and interpretation. As a result, we did not expect embrittlement or liquid metal penetration to occur before deformation.

The methodology developed in this study can be adapted to non-reactive systems, where the pre-exposure time can be systematically varied to assess its influence on embrittlement. Such tests would offer insight into whether LME is governed purely by stress-driven mechanisms or if liquid metal infiltration alone can induce embrittlement over time. However, in reactive systems, this analysis is not possible, as chemical transformation would most likely hinder grain boundary penetration, and it becomes experimentally challenging at the microscale to decouple these effects.

In terms of the sample dimensions, there are two size-related phenomena to consider: limited dislocation sources and dislocation pile-up at the center of the beam. Motz et al. [33] studied these effects on pure Cu by performing single cantilever tests with variable dimensions, revealing a substantial increase in yield strength from 250 to 1000 MPa as sample thickness reduced from 7.5 to 1 µm, with a bulk yielding point at 227 MPa. Similarly, Fleck et al. [34]
reported a lower resistance in a 170 µm diameter Cu wire compared to a 12 µm wire under
torsional testing, and Weiss et al. [35] reported a reduction of fracture strain from 36 to 15 %
when reducing the Cu foil thickness from 250 to 50 µm and a reduction of fracture strain from
16 to 12 % when reducing the Cu wire diameter from 122 to 50 µm. Nevertheless, in our
study, no clear evidence suggests the appearance of any size effect in the micro-bending test
of Cu-30%Zn in contact with EGaIn. Unlike the mechanical tests on pure Cu by Motz et al.
[33] and Kiener et al. [36], the number of dislocation sources in our polycrystalline sample is
not limited. Indeed, multiple slip bands originate from the grain boundaries and the sample's
surface. According to Motz et al., the pile-up effect diminishes when abundant dislocation
sources are available, as dislocations can be more uniformly distributed.

On the other hand, one potential enhancement for the simulations involves implementing a
notch correction to address the roughness introduced by the ion beam, as proposed by Arnaud
et al. [18]. Nevertheless, the W-layer deposited by EBID diminishes the impact of the milling-
induced roughness. However, one clear perspective to enhance the test's modeling is to
address the discrete nature of plastic deformation manifested by well-regularly spaced slip
bands emerging to the surface during the test. To better depict the material behavior, a Crystal
Plasticity framework that accurately describes plastic deformation localization is needed.

The fracture toughness values reported in this study correspond to a single grain boundary.

Though these results provide clear evidence of LME and allow for quantification of fracture toughness, they should not be generalized to all grain boundaries in polycrystalline Cu-30%Zn, given that the LME susceptibility is known to be strongly influenced by the grain boundary properties [2,37]. For instance, experimental studies on Zn-induced embrittlement in Fe have shown that high-angle grain boundaries exhibit higher diffusivity, due to their lower activation energy and activation volume, making them the preferred cracking paths under LME conditions [37].
In parallel, recent atomistic simulations on Fe/Zr have demonstrated that Zn segregation at grain boundaries is strongly dependent on grain boundary energy, with high-energy boundaries accommodating larger amounts of Zn atoms [38]. Furthermore, through their atomistic simulations, the same group identified a novel atomistic mechanism for Zn-induced embrittlement of Fe: Zn facilitates dislocation emission at the crack tip but fails to blunt the crack; instead, Zn atoms infiltrate the newly created crack surfaces via steps formed by dislocation activity, ultimately promoting brittle crack propagation [39].

These findings underscore the need to approach LME as a multiscale phenomenon, where both mechanical and chemical processes at the atomic scale must be considered to fully understand the embrittlement mechanisms. In the specific case of Ga-induced embrittlement of Cu-30%Zn, there are currently no atomistic simulations available to elucidate the underlying interactions at the crack tip or grain boundaries. Nonetheless, the $K_{Jc}$ values for crack initiation obtained in this study can be compared to those reported for the dislocation emission at a crack tip on a Cu-30%Zn monocrystal, $K_{Je}=0.47$ MPa·m$^{1/2}$ [40].

Building on both the simulations and the experimental results, a valuable next step would be to perform new atomistic and multiscale simulations that incorporate grain boundary energy effects within an anisotropic framework. Such an approach would aim to predict fracture toughness while explicitly accounting for grain orientation, local chemistry, and mechanical boundary conditions.

Finally, the methodology developed in this study can be extended to other solid/liquid metal systems. For reactive systems, a suitable diffusion barrier should be employed, one that remains chemically inert to both the solid substrate and the liquid metal. Furthermore, the approach is not limited to room temperature and can be adapted for use at elevated temperatures. In addition to the general precautions required for high-temperature operation in the SEM (which can be found in the literature [41]), it is ideal to ensure that the liquid metal
used has a low vapor pressure at the testing temperature, to avoid vapor generation under
vacuum conditions. This is essential to prevent contamination or damage to the SEM chamber
and ensure stable imaging conditions.

## 6 Conclusions

The present work assesses the fracture toughness of Cu-30 wt.% Zn in contact with liquid EGaIn. Incorporating *in situ* observations during a micrometric mechanical test has proven effective in studying liquid metal embrittlement (LME), offering insights into phenomena such as slip band formation and crack initiation that are elusive with other methods.

Because of the reactive nature of Cu-30%Zn in contact with EGaIn, a thin W-layer was
deposited during sample fabrication to block intermetallic formation at the notch. This
prevented the modification of the solid geometry and the depletion of the liquid before testing.
The successful application of this methodology suggests its potential for studying other
systems, particularly those involving reactive wetting.

By implementing continuum mechanics (isotropic elastoplastic) and crystal plasticity
modeling (anisotropic elastoplastic) of the double-clamped beam test, $K_{Jc}$ values of 2.00 and
2.36 MPa·m$^{1/2}$ were obtained, respectively. These values were calculated using the J-integral
method at the point of experimentally observed fracture initiation. These results demonstrate
that to better correlate experimental observations with small-scale simulations, it is necessary
to employ suitable micromechanical testing in combination with crystal plasticity modeling
that accurately captures the material behavior, including small-scale plasticity and anisotropy.

Moreover, the fracture toughness values reported in this work can serve as a valuable
experimental benchmark for comparison with atomistic simulations, such as those recently
conducted on Cu-30%Zn monocrystals [40]. Integrating these approaches within a multiscale
modeling framework offers a promising path for a deeper understanding of LME mechanisms.

This approach, therefore, opens new avenues for investigating LME crack initiation mechanisms at the micrometric scale, providing a novel perspective on LME research.

Acknowledgments

This work was financed by the French National Research Agency (ANR) under the project ANR Gauguin (N° ANR-18-CE08-0009-01). The authors thank Jean-Baptiste Marijon for the DIC analysis and Vincent Magnier and the University of Lille for the access to the ABAQUS 6.13 license.

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<figure><img src="image_2.png" /><figcaption>Figure 1 a-c) Secondary electron (SE) images and d-f) ion beam scanning imaging showing the EGaIn drop deposition steps in the notch covered by W.</figcaption></figure>

<figure><img src="image_3.png" /><figcaption>Figure 2 a) BSE and b) SE images of the double-clamped beam sample. c) Dimensions of the sample and d) EBSD characterization of two faces.</figcaption></figure>
<figure><img src="image_4.png" /><figcaption>Figure 3 True stress-true strain curves of the experimental Cu-30%Zn and the CPFEM simulation.</figcaption></figure>

<figure><img src="image_5.png" /><figcaption>Figure 4 FEM assemblies, boundary conditions, and mesh for the clamped beam bending test.</figcaption></figure>
<figure><img src="image_6.png" /><figcaption>Figure 5 Simplified CPFEM of the clamped beam bending test: a) mesh partition corresponding to the grains, b) grain orientations acquired through EBSD, c) sample mesh, and d) applied displacement field on the sample (in yellow).</figcaption></figure>

<figure><img src="image_7.png" /><figcaption>Figure 6 a) SE and b) BSE views of the fracture initiation. c) SE and d) BSE views of the last frame before the sample's failure.</figcaption></figure>
<figure><img src="image_8.png" /></figure>

Figure 7 Comparison of experimental and calculated (using the Isotropic elastoplastic modelling) force-displacement curves for the double-clamped beam bending test. The red circle indicates the crack initiation.

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

Figure 8 a) Values of the J-integral across the different contours for the modeling using the isotropic elastoplastic law and the CPFEM. b) Values of K<sub>J</sub> for isotropic elastoplastic simulations with different mesh sizes. The red rhombus indicates the mesh size used for our study.
Liquid Metal Embrittlement of Cu-30%Zn by
EGaln: Microscale Fracture Toughness by In Situ
SEM Testing

Marco Ezequiel¹), Eva Héripré²,³), Ingrid Proriol Serre¹), Thierry Auger²)

1) Univ. Lille, CNRS, INRAE, Centrale Lille, UMR 8207 - UMET - Unité Matériaux et Transformations, F-59000 Lille, France

2) PIMM/Arts et Métiers Technology Institute, CNRS, CNAM, HESAM University, 151 Bd de l'hôpital 75013 Paris, France

3) Université Paris-Saclay, CentraleSupélec, ENS Paris-Saclay, CNRS, Laboratoire de Mécanique Paris-Saclay, 91190, Gif-sur-Yvette, France.

A. Details on the double-clamped beam sample fabrication

Finding a suitable grain boundary orientation for the sample fabrication was crucial. This was achieved by performing extensive transversal milling. Figure A.1a shows this milled area, where the crystallographic contrast generated from ion milling allowed precise microstructure observation with the backscattered electrons (BSE) detector in the scanning electron microscope (SEM). Once a suitable grain boundary was found (Figure A.1b), electron backscattered diffraction (EBSD) measurements were performed to quantify the misorientations of the grains (Figure A.1c).
<figure><img src="image_10.png" /><figcaption>Figure A.1 a) Milling of the sample to find a suitable grain boundary, b) grain boundary selected for the sample preparation, and c) EBSD orientation mapping of the grain boundary.</figcaption></figure>

Once a suitable grain boundary was identified, the sample was milled in several steps. We highlight the milling around the selected grain boundary (Figure A.2a), the fabrication of the double-clamped beam geometry with the desired dimensions (Figure A.2b), the fabrication of the notch (Figure A.2c), and finally, the deposition of the W-layer in the notch (Figure A.2d).

<figure><img src="image_11.png" /><figcaption>Figure A.2 Steps of the fabrication of the clamped beam bending test sample. a) rough milling around the selected zone. b) milling of the double-clamped beam, c) milling of the notch, and d) deposition of the W-layer.</figcaption></figure>
The EGaIn was deposited in the notch using the W manipulator. During deposition, there was a limited overflow of the EGaIn, which then reacted with the solid to form an intermetallic compound (Figures A.3a and A.3d). However, this reaction stopped after a few minutes (Figures A.3b and A.3e). It did not deplete the liquid EGaIn reservoir at the notch (Figures A.3c and A.3f).

<figure><img src="image_12.png" /><figcaption>Figure A.3 EGaIn/Cu-30%Zn interface evolution after overflow: a, d) Immediately post-drop deposition; b, e) 12 minutes post-deposition; and c, f) 20 hours post-deposition. Panels a to c display SE images, d and e ion scanning images, and f is a BSE image.</figcaption></figure>

## B. Post-mortem observation of the double-clamped beam test

Figure B.1a and B.1c depict the step preceding the final failure of the sample. In the next displacement step, the ultimate failure of the sample occurred rapidly during the image capture, here in Figure B.1b and B.1d. The fracture propagated so swiftly that the scanning line in the micrographs shows a disruption, highlighted by a white arrow.
<figure><img src="image_13.png" /><figcaption>Figure B.1 a and c) Views of the frame before the sample's failure. b) and d) Final fracture of the sample. Panels a and b display SE images and c and d BSE images.</figcaption></figure>

After the sample cracked completely, both the sample and the entire setup exhibited an abrupt elastic deformation recovery. Figure presents post-mortem observations of the fracture surface showing this damage. Moreover, it is seen that the W-layer broke, and the fracture occurred homogeneously across the sample thickness.
<figure><img src="image_14.png" /><figcaption>Figure B.2 Views of the fracture surface of the clamped beam bending test sample.</figcaption></figure>

## C. Alternative double-clamped beam test

Given the outcomes of the double-clamped beam test, an alternative sample geometry is proposed in which the notch is positioned on the side of the specimen rather than in the center of the sample. The primary objective of this modification is to prevent the fracture surface from being destroyed by the tip applying the force when the specimen fractures. The zone choice is because, apart from the original notch placement, the stress is maximum in these lateral zones.

The fabrication of this specimen followed the same steps as the other. Figure C.1 shows the main steps: Figure C.1a displays the finding of the grain boundary, Figure C.1b depicts the milling of the sample and the notch around the chosen grain boundary, Figure C.1c illustrates the beam with the W protective layer, and Figure C.1d presents the liquid EGaIn deposited in the notch of the sample. Figure C.2 presents the final sample with its dimensions and the results of an EBSD analysis carried out on two faces of the sample.
<figure><img src="image_15.png" /><figcaption>Figure C.1 Fabrication of the alternative double-clamped beam sample: a) Choose of the grain boundary, b) Creation of the V-notch, c) Deposition of a W-layer by EBID, and d) Deposition of the EGAln in the notch.</figcaption></figure>

<figure><img src="image_16.png" /><figcaption>Figure C.2 a) secondary electrons and c) backscattered electrons images of the double-clamped beam sample. b) dimensions of the sample and d) EBSD characterization</figcaption></figure>

Figure C.3 and Figure C.4 showcase images captured at distinct test intervals utilizing the SE and BSE-Outer detectors, respectively. These images offer insights at key moments: the test's initiation, the instant preceding the sample's final failure, and post-failure.
<figure><img src="image_17.png" /><figcaption>Figure C.3 SE images of the alternative clamped beam bending test, illustrating the test initiation, moment before the final failure, and post-failure.</figcaption></figure>

<figure><img src="image_18.png" /><figcaption>Figure C.4 BSE images of the alternative clamped beam bending test, providing insights into critical test intervals.</figcaption></figure>

Unexpectedly, the sample failed in the middle rather than at the notch, possibly attributed to excessive needle indentation due to the small radius of the tip, causing significant plastic deformation around the contact point. However, during the step of the final sample failure, a fracture emerged near the notch in an interface formed during the sample's deformation.
Potential improvements to enhance the clamped bending tests involve utilizing a smooth manipulator instead of a sharp needle and a stiffer setup.