Effect of transverse compressive stress applied at room temperature on Nb₃Sn Rutherford cables

The cross section of the double stack specimen is reported in figure 1 and a 3D representation of the impregnated specimen and the cables without impregnation are presented in figure 2. The cable was produced at CERN with a planetary Rutherford cabling machine, wrapped then reacted, and finally impregnated with CTD-101 K epoxy resin. It is composed of forty RRP^® 108/127 wires, each of 0.7 mm diameter. The parameters of the cable and the wire are summarized in tables 1 and 2. The specimen has a double stack non-inverted configuration, represented in figures 2(b) and 3(b). After impregnation, it has a rectangular cross-section imposed by the impregnation mold. The final block specimen is represented in figure 2(a).

Table 2. Cable parameters.

Parameter	Value
ID	H15OC0220B
Number of strands	40
Transposition pitch	100 mm
Keystone	0.808∘
Mid-thickness	1.25 mm
Width	14.7 mm
Insulation	S-2 glass
	C-shaped MICA
	0.9 mm gap
Core	316 l
	$(25\,\mu\textrm{m} \times 12\,\textrm{mm})$
Impregnation	CTD-101 K

The two 1.8 m long Rutherford cables are wrapped with C-shape MICA foils, then individually covered by braided S-2 Glass and finally wrapped again with S-2 glass that holds them together (structure visible in figure 3(b)). The specimen is reacted with the following heat treatment: a ramp of $25\,^{\circ}\textrm{C}\,\textrm{h}^{-1}$ to $210\,^{\circ}\textrm{C}$, 48 h at $210\,^{\circ}\textrm{C}$, ramp of $50\,^{\circ}\textrm{C}\,\textrm{h}^{-1}$ to $400\,^{\circ}\textrm{C}$, 50 h at $400\,^{\circ}\textrm{C}$ and final ramp at $50\,^{\circ}\textrm{C}\,\textrm{h}^{-1}$ to $650\,^{\circ}\textrm{C}$ held for 50 h. After reaction, it is vacuum impregnated with epoxy resin in a purpose-designed impregnation mold.

The schematic layout for the test in FReSCa of the 1.8 m long specimen is presented in figure 4. At one end, the specimen is connected to the current leads via Nb-Ti cables soldered with Sn-Ag after the heat treatment and the impregnation process. At the other end, the two cables of the specimen are soldered together via a copper strip placed between them, along 200 mm, prior to the reaction process. This joint is realized by copper diffusion bonding which occurs during the heat treatment of the specimen. Voltage taps monitor the voltage across each cable. They consist of thin copper strips placed on the cable, across the width, after the fiberglass wrapping. A length space without voltage taps, located in the middle of the specimen, is used for applying the pressure.

The dimensions of one cable in the double stack are 14.7 mm width and 1.25 mm mid-thickness. The dimensions of the double stack after insulation and impregnation are 15.7 mm width and 3.8 mm thickness. The dimensions of the cable are taken from the cabling report from CERN [27] and the dimensions of the double-stack are measured optically with a microscope after metallographic preparation as detailed in section 2.4.

The conductor, cable, heat treatment and insulation are all representative for the 11 T dipole magnets of HL-LHC.

The transverse stress is applied using the test setup developed at CERN and described in detail in [1, 2, 22]. Picture and schematic views are reported in figures 5 and 6. The compressive load is transmitted to the stack specimen by a hydraulic press using a dedicated die 44 mm long and 17 mm wide. The specimen is allowed to expand longitudinally, along its length, and transversally, across its width. An arrangement of Polyimide films and pre-scale films are placed between the die and the sample to respectively assure a better homogeneity of the applied pressure and measure the stress distribution on the surface of the specimen. Four calibrated load cells, distributed on the pressing tool, are used to control the load. The stress evaluated from the pre-scale films is quantified to be within 12.5% of the average stress derived by the load cells [22]. The observation of the pre-scale films indicates a higher pressure in the central part of the specimen. The transverse pressure reported in the following sections is the average pressure measured by the load cells.

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The 1.8 m long double-stack specimen used for critical current measurements is installed in the hydraulic press with dedicated supports to avoid bending. The pressure is applied at room temperature in the central area where there are not voltage taps (area 1 in figure 4). The load is maintained for 2 min as recommended for the use of pre-scale films [28]. A cumulative load, which covers the range from 130 MPa to 190 MPa with a step increase of 10 MPa, is first applied. Between each stress level, the specimen is unloaded to 0 MPa and an electrical measurement is performed as described in section 2.3. This loading sequence is followed by 20 cycles to 190 MPa with unloads at 0 MPa. The test procedure is reported in figure 7(a).

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For the samples cut after the electrical measurements from the non-damaged areas (areas 2 and 3 in figure 4—describe in section 2.4), the same mechanical setup is used, but the samples are duplicated and subjected to monotonic or cumulative loads. The samples subjected to monotonic loads are loaded to the target pressure and then unloaded to 0 MPa. The samples subjected to cumulative loads are loaded to the target pressure in the same way than for the area used for I_c measurements (see above). This area (area 1 in figure 4) was indeed submitted only to cumulative loading since it was loaded to increasing stress levels applied all to the same area. For both cumulative and monotonic loadings, the load is maintained for 2 min. Four stress levels are applied: 140 MPa, 160 MPa, 170 MPa and 180 MPa. The loadings for the monotonic and cumulative 160 MPa stress levels are presented in figure 7(b) as example.

Critical current measurements of the 1.8 m long double-stack specimen are performed in the FReSCa test station at 4.3 K and in external magnetic fields B_app from 7 T to 9.6 T. The applied field is parallel to the width and perpendicular to the thickness of the specimen. The resulting direction of the Lorentz force F_L is reported in figure 8. The loaded area (area 1 in figure 4) is located in the homogeneous field region of the FReSCa test station. The specimen is not restricted in its width but to avoid movements during the test, the specimen is pre-loaded to 50 MPa via a plate, compressed onto the specimen, with bolts every 40 mm, as represented in figure 8. This measurement, performed before application of the transverse pressure at room temperature, defines the baseline performance of the specimen. It is referred to as virgin sample hereafter.

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The critical current tests are done at different B_app and with ramp rates of 300 A s⁻¹, 200 A s⁻¹, 100 A s⁻¹ and 50 A s⁻¹. For each background magnetic field, the critical current measurement is repeated at least eight times.

After the transport measurements in FReSCa, several samples are cut from three different areas of the 1.8 m long specimen to perform the metallographic analysis. The cut areas are detailed in figure 4. The cuts are done with a diamond wire saw to minimize the impact on the mechanical state of the samples. The area 1 of the specimen, represented in figure 4, is the area used during the electrical tests. This sample is located approximately in the middle of the long specimen and was exposed to the high field region in the FReSCa test station. It is cut to evaluate its damage state after being submitted to the cumulative loadings followed by 20 cycles at 190 MPa and the successive cooling-down and warming-up associated to the electrical measurements (see section 2.3). This sample is called hereafter 190 MPa cycled sample. Additionally, samples are cut from the specimen near the position of the so-called 190 MPa cycled sample, i.e. from area 2 in figure 4. The samples are analyzed to check that no damage was induced during the transport measurements campaign. These samples are used as reference samples for the rest of the study to guarantee that no damage is generated from the metallographic preparation. They are prepared together with the loaded samples and they undergo the same procedure. Representative observations of the reference samples are presented figure 9. The leftover length of the specimen (area 3 in figure 4) is cut in seven 60 mm long samples without voltage tap. These samples were loaded to the target pressure with monotonic or cumulative loadings following the description in section 2.2 and are used to compare the metallographic analysis with the electrical measurements in section 3.2.

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The samples were embedded in circular shape epoxy resin to protect them during metallographic preparation. The impregnation was performed at room temperature. The samples were mechanically grinded with SiC pads with decreasing grit sizes of P320, P600 and P1200. They were then polished with water-based diamond solutions of decreasing particle sizes of 9 µm, 3 µm and 1 µm. The grinding and polishing steps were performed using an automatic polishing machine with a load on the sample of 10 N for the grinding and 0.5 N for the polishing steps. A final vibro-polishing step was performed during 6 h with a colloidal silica suspension of 0.02 µm particle size. Between each step, the samples were gently cleaned with metallographic soap on a soft cloth and dried.

Transverse and longitudinal cross sections were analyzed. Figure 10 defines the different polishing planes used to analyze the damage state of the samples. The transverse cross-section (plane X–Y in figure 10) gives polished sample as represented in figure 10(b). It allows to have an overview of the complete specimen and to look for any damage in the cross-section. Two longitudinal polishing directions are used—side and top. The side longitudinal direction (plane Y–Z in figure 10), gives polished sample as represented in figure 10(d). It allows to observe the strands located at the edge of the cable, the kink (see figure 1), which are heavily deformed from the cabling process. The top longitudinal cross-section (plane X–Z in figure 10), gives polished sample as represented in figure 10(c). It allows to observe a large area of the sample and to identify transversal cracks in a sub-element. These types of cracks, presented in figure 11, can cut transversally the sub-elements across the entire A15 phase, preventing the current to flow. They were observed in strands loaded with bending and reported to be the main source of degradation in the CICC in [9–14].

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For each sample, the analysis was performed with an optical microscope Olympus BX51. A Zeiss EVO10 scanning electron microscope (SEM) was used to perform observations of the samples subjected to 140 MPa cumulated stress, 160 MPa monotonic stress and 190 MPa cycled stresses. The analysis of the observations was performed using FIJI-ImageJ [29] and manual analysis.

An overview of the damage state and an evaluation of the pattern and distribution of cracks are summarized in one figure for each analyzed sample in figure 15. The authors chose to represent the damage state by coloring the identified cracked sub-elements with a color indicating the number of cracks identified via optical microscopy. The color scheme adopted is the following: yellow for sub-elements with one crack, orange for sub-elements with two cracks, red for sub-elements with three cracks, and finally dark red when four or more cracks appear. This representation report on the frequency and not on the size of the cracks. Observations and analysis are discussed in section 3.2.

Representative V–I curves of the critical current measurements in a background field of 7.5 T after application of the 140 MPa and 190 MPa cumulative stress levels are presented in figure 12. The evaluation of the critical current (I_c ) and the n-value (n) is done with the electrical field (E) criterion of ${E_c = {0.1}\,\mu\textrm{V}\,\textrm{cm}^{-1}}$. The data are treated with a moving average window smoothing. The non-linear fitting takes into account the offset (E₀) of the measurement, the residual resistive slope ($m*I$) and the power law ($E_c*(I/I_c)^n$) according to:

$$\begin{eqnarray} &&E = E_0+m*I+E_c*\left(\frac{I}{I_c}\right)^n \end{eqnarray} \tag{ 1 }$$

where E is the electrical field across the sample and I is the transferred current.

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Figure 13 reports the results of the I_c measurements after application of the successive stress levels. In figure 13(a), the critical current of the two cables is plotted for background magnetic fields of 7 T and 9.6 T. We can observe an increase of the critical current until 140 MPa and then a decrease for increasing stress levels. The increase (up to ≈5%) is due to a change in the strain state of Nb₃Sn. The superconducting phase is in a compressive state after the heat treatment. The application of a load on the specimen induces a release of the strain with a consequent I_c increase [30]. In figure 13(b), we can observe the I_c field dependence of one of the two cable at different stress levels. The self-field contribution of the cable is taken into account in the analysis: a self-field value corresponding to 79 mT kA⁻¹, calculated via a finite element simulation, is added to the applied background field (B_background) to obtain the total magnetic field (B_total) in the cable. The measured critical currents of the cable are compared with the values derived from the single wire measurements [31]. These calculated values represent an upper and a lower I_c boundary. The values are estimated using the established formula [31]:

$$\begin{align} I = n_{\textrm{wire}}*\frac{C}{B_{\textrm{total}}}*\left(\frac{B_{\textrm{total}}}{B_{c2}^*}\right)^{0.5}*\left(1-\frac{B_{\textrm{total}}}{B_{c2}^*}\right)^2 \end{align} \tag{ 2 }$$

with the number of wire $n_{\textrm{wire}} = 40$, $B_{c2} = 24.4\,\textrm{T}$, the lower boundary $C_{\textrm{min}} = {30.331}\,\textrm{kAT}\,\textrm{wire}^{-1}$ and the upper boundary $C_{\textrm{max}} = {37.471}\,\textrm{kAT}\,\textrm{wire}^{-1}$.

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For the specimen before loading and for cumulative loading up to 170 MPa, the critical current is found to be in the expected range. After application of 180 MPa, the critical current is below the expected value from single wire measurement.

Figure 14 presents for each of the two cables the evolution of the critical current, normalized to the critical current of the virgin sample (figure 14(a)), and of the n-value (figure 14(b)) for the applied cumulative stresses and in background fields of 7 T and 9.6 T. At 140 MPa, the critical current reaches a maximum and the n-value does not change. From 140 MPa to 170 MPa, the critical current decreases but is still above the virgin value. The n-value starts decreasing for stresses higher than 160 MPa. After application of 180 MPa, the critical current is lower than the virgin sample by 2% and than its maximum value by 6%. After application of 190 MPa, the critical current is lower than the virgin sample by 6% and than its maximum by 10%. The n-value also decreases from about 90 to less than 50. After mechanical cycling, I_c further degrades: a degradation of 16% from the virgin sample has been measured, with no significant change of the n-value.

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Figure 15 presents the analysis of the crack distribution of the metallographic samples loaded at 140 MPa, 160 MPa and 170 MPa and the 190 MPa cycled sample accordingly to the stress scenarios presented in section 2.2. Cracks are already visible at a pressure of 140 MPa, as visible in figure 15(a). The monotonic loading generates a crack density lower than the cumulated one. Damage is localized mainly in the middle of the cable and the thin edge is less damaged than the thick one. This observation is in line with what is measured by the pre-scale film used during the transverse compression, as discussed in section 2.2, and is attributed to the non-inverted configuration. The non-inverted configuration implies a thickness of impregnation higher at the thin edge and a stress concentration higher at the thick edge.

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For the 160 MPa, 170 MPa, 180 MPa and 190 MPa cycled samples, cracks in the sub-elements are mainly localized, in the transverse cross-section, in planes oriented 45^∘ with respect to the loading direction, as visible on the analysis in figure 15. The X-shaped damaged area is represented figure 16 by the red line on single strands with random hexagonal orientation. It was already observed in strands transversally loaded in [2, 18, 32]. The sub-elements are twisted and arranged following a hexagonal pattern in a strand. It is thus important to note that the 45^∘ planes in which the damaged sub-elements are concentrated do not seems to be impacted by the orientation of the hexagonal structure as represented figure 16. As visible in figure 15 for the different stress levels, the X-shaped area is always oriented the same for all the strands, which have different orientation of hexagonal pattern. This area can be divided into four affected zones, represented in figure 16. In strands with approximately 1 to 10 sub-elements affected, cracks are localized in zone A, B and C. As the crack density increases, zone C seems more affected. In heavily damaged strands, cracks are observed in zone D with a localized high crack density in zone C and D compared to surrounding sub-elements. At the sub-element scale, most of the cracks are oriented parallel or with a small angle to the transverse loading direction. This direction corresponds to the Y-direction of the double-stack in the present configuration. Cracks oriented in the X-direction, also called horizontal cracks, were observed in severely damaged strands and localized in zone C.

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Figure 17 presents representative observations of cracked sub-elements in the 190 MPa cycled sample (area 1 in figure 4). At the sub-element scale, cracks are mainly oriented radially as in figure 17(a). Cracks oriented in the Y-direction, i.e. parallel cracks, not radial and visible in transverse cross-section, were also observed as shown figure 17(b). In the longitudinal cross-section, few cracks were observed in the strands located at the edge of the cable—called kink, see figure 1. They are mainly oriented in the longitudinal direction of the sub-element, named longitudinal cracks in figure 17(c) and in [1, 2], or straight cracks in [21]. Other cracks oriented with wave shape around the porosity in the core of the sub-elements are also visible, named wavy cracks in figure 17(c) and in [21]. Among the dozens of samples analyzed, only one sub-element showed a crack across the entire A15 phase, named transverse cracks in enlarged view of figure 17(c). On the other hand, several longitudinal cracks were identified in strands not located at the edge of the cable, as shown in figure 17(d). These cracks, up to about 0.1 mm to 0.2 mm long and largely opened as shown in figures 17(d) and (e), are propagating from the core of the sub-element to its external surface. These cracks can thus prevent the flow of the current since they cut radially the sub-element.

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For stress levels equal or higher than the 160 MPa level, cracks seem to initiate from porosities in the core of the sub-element or from the phase's interfaces (Nb/Nb₃Sn and Nb₃Sn/Cu-Sn core), as shown in figure 18 for the 160 MPa cumulated sample and in figures 17(a) and (b) for the 190 MPa cycled sample. The observed cracks do not seem to initiate in the restack porosities. No cracks were observed in the unreacted Nb barrier. At a stress level of 140 MPa, all cracks observed initiated from the core (Nb₃Sn/Cu-Sn core or Nb₃Sn/porosity).

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