# Elasticity, plasticity and fracture toughness of REBCO coated conductors characterized via micromechanical tests at room temperature

G. Vernassa, M. Rusinowicz, S. Kalácska, S. Sao-Joao, L. Bottura, H. Felice, B. Bordini, J-M Bergheau, G. Kermouche

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## To cite this version:

G. Vernassa, M. Rusinowicz, S. Kalácska, S. Sao-Joao, L. Bottura, et al., Elasticity, plasticity and fracture toughness of REBCO coated conductors characterized via micromechanical tests at room temperature. IEEE Transactions on Applied Superconductivity, 2025, 35 (5), pp.1 - 5. 10.1109/tasc.2025.3530382. hal-04915557

HAL Id: hal-04915557

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Submitted on 27 Jan 2025

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Distributed under a Creative Commons Attribution 4.0 International License
Elasticity, Plasticity and Fracture Toughness of
REBCO Coated Conductors Characterized via
Micromechanical Tests at Room Temperature

G. Vernassa, M. Rusinowicz, S. Kalácska, S. Sao-Joao, L. Bottura, H. Felice, B. Bordini, J.-M. Bergheau, and G. Kermouche

***Abstract***—REBCO, the leading candidate conductor for ultra high field magnets, is typically produced in the form of thin tapes, consisting of multiple layers of diverse materials with very different natures and properties. Knowledge of the mechanical properties of these different layers is crucial for magnet design. In this paper, we propose a methodology to measure the elasticity, plasticity and fracture toughness of conductor layer materials, at the scale of its constituents, based on nanoindentation, micropillar compression and micropillar splitting techniques. Measurements with these techniques are carried out at room temperature on a commercial conductor, and the results obtained are compared to the values found in the literature and to those specified by the manufacturers.

***Index Terms***—High-temperature superconductors (HTS), Micromechanical properties, Micromechanical testing, REBCO.

# I. INTRODUCTION

Rare-Earth Barium Copper Oxide (REBCO) Coated Conductors (CC) are currently the most promising candidates for manufacturing Ultra High Field (UHF) superconducting magnets [1], [2]. This family of High Temperature Superconductors (HTS) is characterized by high mechanical strength under certain loading orientations [3] and a large electrodynamic stability margin [4], in addition to their high critical temperature ($T_c$ ~ 90 K) and high engineering critical current densities ($I_c$/width ~ 1150 A cm$^{-1}$, at 4.2 K and 19 T parallel field [5]). Recently, REBCO CCs have received large attention for the potential use in coils for compact thermonuclear fusion reactors [6]. This spurred the interest of researchers to look for potential applications of REBCO CC in several other fields such as nuclear magnetic resonance (NMR) magnets [7], HTS motors [8] and cryocooled magnets [9] to name a few. This, has also been accelerated by the recent record field of 45.5 T achieved by the national high magnetic field laboratory (NHMFL) [11] with a 14.4 T REBCO insert coil inside a 31.1 T background resistive solenoid. Mechanical calculations estimated that the coil operated at an average hoop stress level

G. Vernassa is with CERN, CH-1211 Geneva, Switzerland and the École des Mines Saint-Etienne, CNRS, UMR5307 LGF, Centre SMS, 42023 Saint Etienne, France.

M. Rusinowicz, S. Kalácska, S. Sao-Joao, and G. Kermouche are with the École des Mines Saint-Etienne, CNRS, UMR5307 LGF, Centre SMS, 42023 Saint Etienne, France.

L. Bottura, and B. Bordini are with CERN, CH-1211 Geneva, Switzerland.

J.-M. Bergheau is with the Univ Lyon, École Centrale Lyon, CNRS, ENTPE, LTDS, UMR5513, ENISE, F-42023 Saint-Étienne, France.

H. Felice is with the CEA-Saclay, IRFU, Univ. Paris Saclay, F-91191 Gif Sur Yvette, France.

of ~ 1 GPa [12], and peak stress levels as high as 1420 MPa, when considering the effects of screening currents-induced stresses (SCIS) [12]. These high stresses are also expected in a 40-60 T solenoid [13] which is under study at CERN, the European Organization for Nuclear Research, in the context of the technological demonstrators for a future Muon Collider [14], which is where our work finds its context.

For a reliable and detailed design of such systems, accurate knowledge of the mechanical properties of the materials is of paramount importance. However, the complex structure of REBCO CCs, consisting of multiple layers with thicknesses ranging from 1 to 100 µm, makes it impractical or infeasible to characterize each layer independently. As a result, researchers have frequently relied on well-established macroscopic testing methods, adapted to REBCO tapes to inversely determine the mechanical properties of the individual layers [15]. Other approaches within the community include macroscopic measurements on bulk materials, such as the three-point bending test described in [16] or the fracture toughness characterization of REBCO bulks [17]. However, these methodologies are difficult to scale to REBCO CCs due to the size effects peculiar to ceramics [18]. To our knowledge, up to date, the only published mechanical measurements of REBCO's properties at the microscale are those reported in [18], where researchers have characterized the elastic properties and fracture toughness of a GdBCO layer via the microcantilever beam method coupled with a dedicated Finite Element model. This methodology however has never been adopted on other REBCO CCs, and the results of [18] remain an isolated case of application on a specific tape. Given the large variety of architectures commercially available and the importance of the mechanical properties of these materials, we propose the application of small scale mechanical testing to determine the properties of REBCO CCs by performing nano/micromechanical experiments that can be applied directly to the REBCO tape layers. In this paper, we report on our first measurements based on instrumented nanoindentation, micropillar compression and splitting tests conducted on a commercial REBCO CC. Although the end goal is the application of these methodologies at cryogenic temperatures, in this campaign we only focused on deploying them at room temperature. We therefore describe the techniques, discuss the results in terms of elastic, plastic, and fracture properties, and finally compare the obtained values to those available in the literature where applicable.
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<figure><img src="image_4.png" /><figcaption>Fig. 1. (a) SEM image of the multilayer stack in a cross-section of the REBCO tape showing, from bottom to top: Hastelloy substrate, MgO buffer layer, REBCO layer, silver layer, and copper layer. (b) EDS chemical analysis verifying the nature of the layers by the presence of their major constituent element.</figcaption></figure>

## II. MATERIALS AND METHODS

### A. REBCO tape preparation

In this work, the individual layers of a commercial tape from the manufacturer THEVA were studied. These layers consist of a 47 µm thick Hastelloy substrate, a 3.6 µm thick magnesium oxide (MgO) buffer layer, a 3.2 µm thick REBCO (YBCO) layer, a 1.3 µm thick silver (Ag) layer, and a 10.5 µm thick copper (Cu) layer. Fig. 1(a) presents a cross-sectional SEM (scanning electron microscopy) image of the tape, and Fig. 1(b) shows the EDX (energy-dispersive X-ray spectroscopy) chemical analysis performed on this cross-section to clearly identify the layers through their major constituent element.

All nano/micromechanical tests were performed on the individual layers of the tape in cross-section, which was cut with scissors, embedded in cold resin (Buehler EpoThin™ 2 epoxy resin with hardener) to prevent delamination of the layers, and mechanically polished with silicon carbide papers of progressively small particle size, to a finish with colloidal silica of particle size 0.03 µm. The surface layer affected by polishing is expected to be of the same order of magnitude as the finishing particle size, i.e. a few tens of nanometers, meaning that our measurements are not impacted by it since they concern much greater depths, ranging between 150 nm to 1500 nm as it will be seen later. Micropillars were then machined perpendicularly to the cross-sectional cut, i.e. parallel to the surface of the substrate, by focused ion beam (FIB) milling using a FEI Helios NanoLab DualBeam 600i SEM. Initially, high current conditions (30 kV, 2.5 nA) were applied to achieve the overall shape of the pillar, followed by gradually reducing the current down to 80 pA to obtain the final geometry. The dimensions of the pillars measured by SEM are summarized in Table I.

### B. Instrumented nanoindentation

Instrumented nanoindentation involves applying a normal load to a very hard and stiff tip while measuring the penetration depth of the tip during the loading (indentation) and

<table><caption>TABLE I
TOP DIAMETER $d_{top}$, BOTTOM DIAMETER $d_{bot}$, AVERAGE RADIUS $r_{avg}$ AND HEIGHT $h_{pil}$ OF THE PILLARS MACHINED IN THE DIFFERENT MATERIALS FOR COMPRESSION (C) AND SPLITTING (S) TESTS.</caption><thead><tr><th></th><th>Hastelloy (C)</th><th>Copper (C)</th><th>REBCO (C)</th><th>REBCO (S)</th></tr></thead><tbody><tr><td>$d_{top}$ (µm)</td><td>~ 3.3</td><td>~ 2.6</td><td>~ 2.0</td><td>~ 2.0</td></tr><tr><td>$d_{bot}$ (µm)</td><td>~ 3.9</td><td>~ 3.0</td><td>~ 2.4</td><td>~ 2.4</td></tr><tr><td>$r_{avg}$ (µm)</td><td>~ 1.8</td><td>~ 1.4</td><td>~ 1.1</td><td>~ 1.1</td></tr><tr><td>$h_{pil}$ (µm)</td><td>~ 5.0</td><td>~ 4.0</td><td>~ 5.5</td><td>~ 3.0</td></tr></tbody></table>

unloading (retraction) phases. By monitoring the penetration depth $h$, the load $F$ and the contact stiffness $S$ defined as the slope of the $F-h$ curve at the early stage of unloading, the elastic modulus $E$ and hardness $H$ of the material can be measured.

Nanoindentation tests were performed using the load-controlled DCM (dynamic contact module) head of a MTS XP nanoindenter. A diamond Berkovich tip was used, with its geometry calibrated on a fused silica reference sample following the Oliver and Pharr method [19] to obtain the area function relating the projected contact area $A_c$ to the contact depth $h_c$. The tests were conducted with a targeted loading rate of $\dot{F}/F = 0.05 \text{ s}^{-1}$ (indentation strain rate $h/h \approx 0.025 \text{ s}^{-1}$) up to a maximum load of 15 mN. The continuous stiffness measurement (CSM) mode was employed to measure the contact stiffness as a function of penetration depth, allowing continuous extraction of the elastic modulus and hardness during indentation. A matrix of 49 indents was made in the relatively thick Hastelloy substrate, while individual indents were targeted in the much thinner layers, using a 40× optical objective, resulting in a total of 5–10 indents per layer for Cu, MgO and REBCO. Fig. 2(a) shows an optical microscopy overview of the residual indentation imprints in the different layers, and Fig. 2(b)-(c) show SEM images of some representative imprints. The mechanical properties presented hereafter were extracted at a depth of 150 nm to strike a balance between minimizing tip defect effect at shallow depths and limiting the composite effect of surrounding layers at greater depths.

In terms of post-processing, the elastic modulus $E$ and
<figure><img src="image_5.png" /><figcaption>Fig. 2. (a) Optical image of the residual indentation imprints in the Hastelloy, copper, MgO (blue arrows) and REBCO (green arrows) layers. Red arrows indicate tests rejected due to being too close to other layers because of poor targeting. (b) SEM images of the residual indentation imprints in the REBCO and MgO layers. (c) SEM images of the residual indentation imprints in the Hastelloy layer.</figcaption></figure>

hardness *H* of the materials were determined using Sneddon's equation and Meyer's definition, respectively:

$$E^* = \frac{\sqrt{\pi}}{2} \frac{S}{\sqrt{A_c}} , \quad \frac{1}{E^*} = \frac{1 - \nu_t^2}{E_t} + \frac{1 - \nu^2}{E} \quad (1)$$

$$H = \frac{F}{A_c} \quad (2)$$

with $E^*$ the reduced elastic modulus, $E_t = 1141$ GPa and $\nu_t = 0.07$ the elastic modulus and Poisson's ratio of the diamond tip, $\nu$ the Poisson's ratio of the tested material, and $A_c$ the projected contact area between the tip surface and the sample surface. Given the very different natures of the materials in the multilayer stack (ductile metals, brittle ceramics), the contact area was estimated using Loubet's model [20], which captures both sink-in and pile-up rheologies:

$$h_c = 1.2 \left( h - \frac{F}{S} \right) \quad (3)$$

with $h_c$ the contact depth, converted to contact area through the tip area function.

To compare nanoindentation tests to more common uniaxial tensile tests of REBCO tapes found in the literature, hardness was converted into a representative stress $\sigma_r$ corresponding to the flow stress associated with ~ 8% plastic strain. Ker-mouche's definition [21] was used for a Berkovich tip:

$$\sigma_r = \frac{0.085H}{0.235 - 0.784\frac{H}{E}} \quad (4)$$

### C. Micropillar compression

Micropillar compression involves applying a displacement to a flat punch while measuring the load response of the sample. By monitoring the displacement of the punch $u$ and the load $F$, the whole stress-train curve can be extracted directly within one test [22].

Microcompression tests were conducted using an *in situ* displacement-controlled Alemnis ASA nanoindenter installed in a Zeiss Gemini Supra 55VP SEM to target and visualize the pillars. A 5 µm diameter diamond flat punch was used. The tests were performed at a displacement speed of 100 nm/s up to a maximum displacement of approximately one-third of the initial pillar height. To obtain the true displacement of the pillar $u_{\text{pil}}$, the punch displacement $u$ was corrected by subtracting the contributions of the frame stiffness $S_f$ (= 1100 mN/µm determined by a calibration procedure) and the substrate stiffness $S_s$ (= 2$E^*r_{\text{avg}}$ estimated by Sneddon's equation, where $E^*$ is the reduced elastic modulus of the material measured by nanoindentation and $r_{\text{avg}}$ is the initial average radius of the pillar):

$$u_{\text{pil}} = u - \frac{F}{S_{\text{eff}}} , \quad \frac{1}{S_{\text{eff}}} = \frac{1}{S_f} + \frac{1}{S_s} \quad (5)$$

The $F - u_{\text{pil}}$ curves were then converted into $\sigma_{\text{true}} - \varepsilon_{\text{true}}$ curves (true stress-strain) as follows:

$$\varepsilon_{\text{true}} = -\ln\left(\frac{h_{\text{pil}} - u_{\text{pil}}}{h_{\text{pil}}}\right) \quad (6)$$

$$\sigma_{\text{true}} = \frac{F}{A} \quad (7)$$

where $A$ is the current cross-sectional area of the pillar, determined based on the radial expansion of the pillar [22] with a constant Poisson's ratio of 0.3.
### D. Micropillar splitting

Micropillar splitting involves driving a sharp tip into the pillar until it fractures. The critical load $F_c$ at which the pillar splits for the first time allows the determination of the fracture toughness of the material using the following relation [23]:

$$K_c = \gamma \frac{F_c}{r_{\text{avg}}^{3/2}} \quad (8)$$

where $\gamma$ is a coefficient that depends on the elastic-plastic properties of the material ($E/H$ ratio) and the geometry of the indenter. Splitting tests on the REBCO were conducted with the same *in situ* setup used for compression, but with a cube corner tip and a displacement rate of 20 nm/s. The $\gamma$ coefficient was estimated to be 0.76 based on the properties of REBCO obtained through nanoindentation and the geometry of the tip used [23].

## III. RESULTS AND DISCUSSIONS

### A. Elastic-plastic properties of individual layers measured by instrumented nanoindentation

Table II reports the elastic-plastic properties of Hastelloy, Cu, MgO and REBCO layers obtained by nanoindentation. Focusing on the elastic modulus, we observe that the values measured for Hastelloy fall within the range commonly reported in the literature and on manufacturers' data sheets [24], differing by only a few percentage points. Interestingly, the measured elastic modulus for the electroplated copper is relatively at the lower end of the expected range of 80 to 110 GPa. However, similar values have been reported by Ilin et al. [15] where the properties of electroplated copper were indirectly identified from tensile tests on SuperPower® tapes, yielding an elastic modulus of $E = 80$ GPa at room temperature.

These results encouraged the application of this methodology to the REBCO and MgO layers, for which little or no data are currently available in the literature. Indeed, to the

<table><caption>TABLE II
MECHANICAL PROPERTIES OF REBCO TAPE LAYERS MEASURED BY NANOINDENTATION AT 150 NM DEPTH (ELASTIC MODULUS $E$, HARDNESS $H$, REPRESENTATIVE STRESS $\sigma_r$) AND MICROPILLAR SPLITTING (FRACTURE TOUGHNESS $K_c$).</caption><thead><tr><th></th><th>Hastelloy</th><th>Copper</th><th>MgO</th><th>REBCO</th></tr></thead><tbody><tr><td><i>E</i> (GPa)</td><td>197 ± 5</td><td>84 ± 3</td><td>95 ± 4</td><td>155 ± 5</td></tr><tr><td><i>H</i> (GPa)</td><td>4.80 ± 0.17</td><td>1.55 ± 0.10</td><td>2.28 ± 0.15</td><td>8.90 ± 0.47</td></tr><tr><td>σ<sub>r</sub> (GPa)</td><td>1.90 ± 0.06</td><td>0.60 ± 0.04</td><td>0.90 ± 0.06</td><td>4.00 ± 0.19</td></tr><tr><td><i>K</i><sub>c</sub> (MPa·m<sup>1/2</sup>)</td><td>-</td><td>-</td><td>-</td><td>1.34 ± 0.12</td></tr></tbody></table>

best of our knowledge, the elastic properties of REBCO have only been measured on single crystal bulks using methods such as the three-point bending test [16], nano or Vickers indentation [25]–[27], or even techniques based on phonon dispersion curves [28]. For REBCO, reported values range from 149 to 185 GPa, obtained through Vickers indentation, as cited in [26] and [27].

Our measured value for REBCO is $E = 155$ GPa, which falls in the aforementioned range, and it is also remarkably close to the value of 157 GPa [29], often used as reference value by magnet designers. Regarding the MgO layer, we measured an elastic modulus of $E = 95$ GPa, which, to our knowledge, is the first publicly reported measurement for this material.

### B. Plastic flow behavior of metal layers measured by micropillar compression

The true stress-strain curves of Hastelloy and copper layers obtained by micropillar compression are presented in Fig. 3(a). For Hastelloy, the initial yield strength at which the material begins to exhibit plasticity ranges from 1.2 to 1.4 GPa. These values are at the upper end of the range of yield stresses measured in tensile tests on samples extracted from REBCO tapes [15], [30], with measured $R_{p0.2}$ values at room temperature of 891 MPa and 1225 MPa respectively, but are in good

<figure><img src="image_6.png" /><figcaption>Fig. 3. (a) True stress-strain curves of Hastelloy and copper layers obtained by micropillar compression. (b)-(c) SEM images of a representative Hastelloy pillar before and after compression, respectively. (d)-(e) SEM images of a representative copper pillar before and after compression, respectively.</figcaption></figure>
agreement with those measured on bare substrates, as reported
by [31]. Indeed, Radcliff et al. showed that yield strength of
the substrate is affected by the heat cycle it sees during the
REBCO deposition process, decreasing from 1.5 to 1.2 GPa,
as the process temperature increases from 700 to 800 °C.
This suggests that the manufacturing processes adopted by
different manufacturers can significantly influence the yield
strength of the substrate material, leading to some variation in
the measured values depending on the manufacturer.

In the plastic flow regime, we can observe a substantial
scattering between the curves, though the stress levels saturate
in most cases between 1.5 and 1.8 GPa, slightly lower than the
representative stress of 1.9 GPa obtained by nanoindentation.
Regarding copper, the curves are also scattered, but the level of
plastic flow is clearly lower than that of Hastelloy, with little
strain-hardening and a flow stress saturating at ~ 0.6 GPa
on average. This value perfectly matches the representative
stress of 0.6 GPa obtained by nanoindentation and is also
in agreement with other micropillar compression studies on
physical vapor deposited (PVD) copper for microelectronic
applications [32].

To better understand the origin of the scatter in the exper-
imental stress-strain curves as well as to unravel the plastic
deformation mechanisms in each material, Fig. 3(b)-(c) and
Fig. 3(d)-(e) show SEM images of representative Hastelloy and
copper pillars, respectively, before and after compression.

Before compression, the Hastelloy pillar exhibits no visible
defects, while after compression, the pillar is sheared along
well-defined planes. These planes are in fact slip planes
activated during mechanical loading. It is important to note

that Hastelloy grains have a size of 5-10 µm, larger than
the pillar size, meaning we are essentially compressing a
single crystal. The activation of certain slip systems rather
than others depends on the crystal orientation relative to the
loading direction. This explains why the stress-strain curves of
Hastelloy are scattered based on the grain orientation in which
the pillar was machined. It also explains why nanoindentation
gives a higher flow stress value compared to compression,
as the multiaxial stress state generated by the pyramidal tip
penetration activates multiple slip systems, which mutually
hindering each other and overall harden the material.

The copper pillar, on the contrary, has many defects in its
initial microstructure, particularly porosities (cf. Fig. 1(a)) and
cracks (cf. Fig. 3(d)). These defects are stress concentration
sites that drive the plastic deformation process, as observed in
Fig. 3(e) where the top of the pillar has collapsed along the
path of pre-existing conical cracks. The scatter in the copper
stress-strain curves is thus explained by the statistical presence
of defects in each pillar.

*C. Fracture toughness of REBCO layer measured by micropillar splitting*

The true stress-strain curve of a representative compression
test of a REBCO micropillar is shown in Fig. 4(a), with SEM
images of the pillar before compression and after the first
fracture in Fig. 4(b)-(c). It is observed from the stress-strain
curve that the stress level increases almost proportionally
with the strain level up to a stress of ~ 2.5 GPa (strain of
~ 2 %), where the stress drops abruptly. This stress drop is
due to the fracture of the pillar by buckling, as evidenced

<figure><img src="image_7.png" /><figcaption>Fig. 4. (a) True stress-strain curve obtained by compression of a REBCO micropillar. (b)-(c) SEM images of the REBCO pillar before compression and after the first fracture, respectively. (d) Load-displacement curves obtained from splitting REBCO micropillars. (e)-(f) SEM images of a representative REBCO pillar before splitting and after the first fracture, respectively.</figcaption></figure>
by Fig. 4(c), a typical failure mode for brittle materials as previously shown with the compression of carbon fiber pillars [33]. Thus, REBCO appears to behave like a brittle material. The stress level at which fracture occurs confirms this, since the fracture stress of 2.5 GPa obtained by microcompression is lower than the plastic flow stress of 4 GPa measured by nanoindentation. REBCO is therefore brittle in the sense that it fractures within its elastic domain. The fracture toughness of REBCO was determined by micropillar splitting, which is particularly well-suited for brittle materials.

The load-displacement curves obtained from splitting three REBCO micropillars are shown in Fig. 4(d), with SEM images of a representative pillar before splitting and after the first fracture in Fig. 4(e)-(f). The loading curves are very reproducible and lead to a critical load of around 2 mN at which the pillar splits instantly, as observed in Fig. 4(f), giving the fracture toughness of REBCO at $1.34 \pm 0.12 \text{ MPa.m}^{1/2}$ (value reported in Table II). This value is very close to that measured on another type of REBCO using microcantilever beam bending, which range between 0.8 and $1.8 \text{ MPa.m}^{1/2}$ [18]. However, micropillar splitting is an easier and more robust method as it does not depend on the geometry of a notch, which is particularly difficult to machine, resulting in very low dispersion in fracture toughness values.

## IV. CONCLUSION

The accurate knowledge of the elastic-plastic and fracture toughness properties of REBCO CC layers' materials is a fundamental requirement for the faithful stress analyses of superconducting magnet systems. This work demonstrates how the combination of three standard micromechanical experiments can effectively quantify intrinsic mechanical properties at the constituent scale of superconducting tape layers. Nanoinindentation proves efficient for measuring the elastic modulus and yield stress. Micropillar testing provides valuable insights into plastic flow behavior and enables the quantification of stress-strain curves. Micropillar splitting is a promising test for assessing fracture toughness, especially on brittle materials such as the REBCO layer investigated in this paper. The results obtained in this campaign show excellent agreement with literature data. Thanks to its versatility, the utilized methodology can be applied to any architecture of technical superconductors, both Low Temperature Superconductors (LTS) and High Temperature Superconductors (HTS). Although the micromechanical tests in this study were conducted at room temperature, recent advances in cryogenic micromechanical testing suggest that this methodology may soon be adaptable to temperatures closer to real operational conditions.

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