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In this paper, the elastic wave band gap characteristics of two-dimensional hard-magnetic soft material phononic crystals (HmSM-PnCs) under the applied magnetic field are studied. Firstly, the relevant material parameters of hard-magnetic soft materials (HmSMs) are obtained by the experimental measurement. Then the finite element model of the programmable HmSM-PnCs is established to calculate its band structure under the applied magnetic field. The effects of some factors such as magnetic field, structure thickness, structure porosity, and magnetic anisotropy encoding mode on the band gap are given. The results show that the start and stop frequencies and band gap width can be tunable by changing the magnetic field. The magnetic anisotropy encoding mode has a remarkable effect on the number of band gaps and the critical magnetic field of band gaps. In addition, the effect of geometric size on PnC structure is also discussed. With the increase of the structure thickness, the start and stop frequencies of the band gap increase.

High-temperature superconductor (Re)Ba2Cu3O x (ReBCO) conductor on round core cable (CORC®) has a large current carrying capacity for high field magnets. Lorentz forces acting on CORC conductors, cause a reduction of the critical current, or even permanent degradation of their performance when exceeding critical values. Transverse compressive stress is one of the principal mechanical stresses when CORC cables are bundled to cable-in-conduit conductors (CICC) conductors capable of operating at currents up to 100 kA in magnetic fields of up to 20 T. In this research, a mechanical-electromagnetic model is developed to study the effect of transverse compressive loads on the electromagnetic performance of CORC cables. A mechanical transverse load on the cable is implemented to simulate the electromagnetic force. A comparison of numerical simulations with experiments for a three-layer CORC cable is first performed to validate the model’s reliability, with particular attention to critical current reduction during the transverse compression process. A novel feature of this paper is that the model developed can analyze both mechanical response under transverse compressive loads and electromagnetic performance under applied AC magnetic fields with low amplitudes. On this basis, the model investigates the effects of winding parameters on the axial strain and critical current reduction of the ReBCO layer in a single-layer CORC cable. The numerical analysis shows that increasing the winding angle can reduce the axial strain and critical current reduction of the ReBCO layer in the contact area. Subsequently, a detailed comparative study is carried out studying the axial strain of the ReBCO layer in the non-contact area with and without taking the winding core into account. In addition, a sudden increase in the magnetization loss is explained when the transverse compressive load reaches a certain level. Finally, a six-layer CORC cable’s electromagnetic analysis is performed, and each tape layer’s critical current reduction is investigated and discussed. The comparison of magnetization loss and current density between six- and single-layer CORC cables in the no-strain case is also given. This finite element model can guide optimizing a cable design for specific application conditions.

In this paper, a novel type of cross‐like holes phononic crystal with excellent band gap characteristics, machinability and stability is optimized and designed based on genetic algorithm. The impro...

The elastic wave propagation properties of phononic crystals (PnCs) composed of an elastic matrix embedded in magnetorheological and electrorheological elastomers are studied in this paper. The tunable band gaps and transmission spectra of these materials are calculated using the finite element method and supercell technology. The variations in the band gap characteristics with changes in the electric/magnetic fields are given. The numerical results show that the electric and magnetic fields can be used in combination to adjust the band gaps effectively. The start and stop frequencies of the band gap are obviously affected by the electric field, and the band gap width is regulated more significantly by the magnetic field. The widest and highest band gap can be obtained by combined application of the electric and magnetic fields. In addition, the band gaps can be moved to the low-frequency region by drilling holes in the PnC, which can also open or close new band gaps. These results indicate the possibility of multi-physical field regulation and design optimization of the elastic wave properties of intelligent PnCs.

Superconducting Nb3Sn Rutherford cables can be used in the accelerator magnets above 10 T regions that cannot be reached with NbTi. These cables are composed of superconducting multifilamentary strands, interstitial epoxy, and insulation materials. To properly design the magnets made from these cables, it is essential to analyze their mechanical behavior. The prerequisite for this is the knowledge of the mechanical performance of Rutherford cables. In large magnets, these cables cannot be modeled with all details but effective properties and homogenization are typically required. In this work, an analytical model and numerical approach for predicting the effective mechanical properties of Rutherford cables are developed. The analytical model is established on a two-step homogenization and mechanical analysis for composite. The effective mechanical properties of the filament area and the transverse Young's modulus of the strand are first determined by means of utilizing the mechanical theory of the unit cell approach. The composite effective mechanical properties of the strand and interstitial epoxy are homogenized in the first step. The second step homogenization derives the effective mechanical properties of the strands epoxy composite and insulation layers. The numerical approach to determine the effective mechanical properties is based on the finite-element analysis. The developed methodologies are used to obtain the effective mechanical properties of two Nb3Sn Rutherford cables. The influence of the insulation thickness and modulus, the strand's modulus, is studied.

The Conductor on Round Core (CORC) wire coming under the category of High-Temperature Superconducting (HTS) wires is the promising type used in next-generation magnet-based applications, such as fusion, particle accelerator, magnetic resonance imaging (MRI). However, mechanical deformation due to cabling, winding, and operation of the magnets will degrade the performance of the HTS wires, which might cause severe problems in several aspects. The study of contact characteristics inside the superconducting wire is of considerable significance since they are essential parameters for the understanding of mechanical and electrical responses, indicators for optimizing the cable structure. It also contributes to the safe operation and feasibility of HTS magnets. In this paper, dynamic finite element simulations are applied to obtain the mechanical response of stretched CORC wires. The deformation and the contact stress of the inner tapes are presented. Engineering optimization is done by analyzing the results. © 2002-2011 IEEE.

Pressure drop of cable-in-conduit conductors (CICCs) cooled by a flow of liquid or supercritical helium is one of the key parameters for the design of large superconducting magnet systems, which determines the heat removal capability and the thermal stability. In this article, an analytical model for predicting the pressure drop in CICCs is developed based on an analogy to porous media with the equivalent geometry configuration. This new prediction model indicates that the pressure drop in CICCs is affected by the geometry parameters of cable and the physical properties of the liquid helium, such as void fraction, tortuosity, pore-throat ratio, hydraulic diameter, density, and viscosity of the liquid helium. To verify the validity of the pressure drop model proposed in this article, the predictions are compared with the experimental data, the results show that the predictions are in good agreement with the experimental data. Then, an analytical expression for predicting the friction factor is derived, the obtained expression is in good agreement with experimental data and is superior to the Katheder correlation at large Reynolds number. In addition, the effects of the major geometric parameters on pressure drop are analyzed, the results explain why the Katheder correlation can be used to predict the pressure drop of CICCs.

Assessment of the pressure drop that occurs in cable-in-conduit conductors (CICCs) requires a reliable predictive model. In this paper, a fractal model to predict the pressure drop of helium flows in CICCs is proposed based on the porous media analogy and fractal theory. A fractal friction factor correlation is also derived using the proposed pressure drop model. The good agreement between the predictions and the experimental data for conductors with [Formula: see text] verifies the validity of both the fractal pressure drop model and the friction factor correlation for such configuration conductors. The fractal correlation indicates that the friction factor of the cable bundle in a CICC is related not only to the void fraction but also to the average hydraulic diameter, the tortuosity of the fluid flow paths, the maximum pore size and the fractal dimension of the cable cross-section. This theoretical correlation does not contain any fitting constants and each parameter has a clear physical meaning.

Topological insulators (TIs) are a new type of quantum state materials. Due to their novel physical properties, such as topological protection defect immunity to edge states, TIs have become the focus of attention in condensed matter and material physics. At present, the research on TIs has been gradually extended to classical wave fields such as electromagnetic waves, acoustic waves, and elastic waves, and has aroused extensive research interest. However, for elastic wave systems, most TIs cannot actively control topological interface states due to the limitation of fixed structure, which hinders their application in practical situations. Here, we propose a kind of tunable three-dimensional (3D) valley Hall insulator composed of magnetoelastic materials. First, the topological phase transition can be induced by the asymmetric geometry. Then, the working frequency of topological interface states can be changed by using static magnetic fields. Second, topological phase transformation can also be induced by independently tuning the distribution of static magnetic fields or pre-stress in each unit. Based on this, reconfigurable propagation routes of interface states with arbitrary shapes can be realized by tuning the distribution of static magnetic fields or pre-stress in each unit. Finally, considering the sandwich structure composed of different magnetic fields or pre-stress distribution modes, the waveguide with tunable width and route is designed by coupling edge and bulk states, which is convenient for application and better energy transfer. This study provides a reference for the design of a tunable intelligent elastic waveguide.

Thermoelectric cooling is an attractive technology to achieve active thermal management of electronic devices, integrated circuits and micro-motor mechanism. Time-varying and excessive thermal stress may cause failure in thermoelectric coolers (TECs). Nevertheless, thermal–mechanical response of such devices to the electrical input is not thoroughly analyzed yet. In this paper, a three-dimensional numerical model of TEC is established by finite element method, and effects of structural parameters on its cooling performance and mechanical reliability are discussed. Steady-state experiments are conducted to verify the correctness and rationality of the numerical model. The results show that, under optimal current conditions, the minimum temperature of the cold end of the TEC can be obtained by optimal height and width of thermoelectric legs. Moreover, optimal structural parameters of the TEC providing better cooling performance and reliability are presented; so that, the cold end temperature and von Mises equivalent stress of the optimized TEC could reduce 8.3 K and 22.6% respectively. The cooling performance and mechanical reliability of the TEC are further studied under continuous pulse currents. Influences of the pulse period, amplitude and form of the pulse currents on performances of the TEC are discussed. The results show that, increasing the pulse current form parameter reduces the stress level in the TEC. For the optimized TEC, pulse amplitude of 4 is optimal values to obtain minimum temperature on the cold end. The results of this study are expected to provide useful guideline for design and practical applications of TECs under transient cooling currents.

In this paper, the thermoelectric performance and mechanical reliability of a segmented annular thermoelectric generator under steady state and transient conditions are investigated. The influence of structural parameter on the performance of segmented annular thermoelectric generators is discussed, the optimized design with high thermoelectric performance and reliability is obtained. These results present that with the increase of the structural parameter, the output power of segmented annular thermoelectric generators increases first and then decreases, and the max von Mises stresses in the hot-segment and cold-segment will always achieve an optimal value when the temperature in the hot end is larger than 300 °C. In addition, compared with the single-Skutterudite annular thermoelectric device, the output power of segmented annular thermoelectric generators can improve 18.3%, the max von Mises stress in the hot-segment is decreased by 12.5%. Finally, the thermoelectric performance and reliability of segmented annular thermoelectric generators operating in a sinusoidal heat source are investigated. The results show that the smaller the period and amplitude of the heat source, the better the overall performance of the segmented annular thermoelectric generator. These obtained results may provide some useful guidance for the application of segmented annular thermoelectric generators in the waste heat recovery.

It is well known that the interaction between defect-induced strain field and vortex lattice (VL) gives rise to vortex pinning behaviors. Likewise, magneto-elastic (ME) interaction is caused by the difference between specific volumes of normal phase and superconducting (SC) phase. Acting as inhomogeneous strain sources, the normal-state vortex cores produce local deformation in the surrounding SC matter and thus affect VL energy. ME interaction belongs to the fundamental physics of interdependences between vortex matter and crystal lattice. The review starts with the effects of ME interaction on magnetization, vortex morphology and intervortex interaction. In Sect. 2, theoretical descriptions of ME interaction are classified in terms of different simplifications. The core ideas and outstanding results of these theories are given. It is followed by Sect. 3, where the correlation and difference between ME and pinning interaction are outlined. Although pinning differs from ME interaction in their formation mechanisms, the pinning interaction is established upon the vortex-induced strain field from Ginzburg-Landau (GL) viewpoint. Section 4 goes further with the GL treatment for solving ME and pinning problem; the general thoughts and steps can be found in this section. The last section gives some outlooks which involve pressure dependence of Tc and anisotropy.

Seeking a geometry that can withstand greater transverse loads based on the electromechanical material properties of high-temperature superconducting (HTS) tape is an effective way of improving the transport performance of HTS cables. The cabling method requires the determination of the optimum twist angle of the HTS tape for withstanding transverse loads. This paper investigates the critical current characteristics of HTS tapes under combined deformation. The limit range of the twist angle under the combined deformation is measured and the optimum twist angle of the HTS tape is determined. The results show that the twisting chirality configuration obviously affects the bending strength of the HTS tape. In the elastic range, increasing the pre-twist angle increases the bending strength of the HTS tape, thereby improving the transport performance. In addition, a numerical model is built to further investigate the effect of the twisting chirality configuration on the electromechanical properties of the HTS tape, and the experimental results are explained. The experimental and simulation results generally agree well, and calculations show that there is always a sharp change in stress at the interface of different materials. These findings explain the mechanism of the effect of the twisting chirality configuration on the mechanical behavior and critical current of the HTS tape. They also provide a reference for cabling methodologies for the HTS cable configuration.

We established a three-dimensional (3D) multifilament finite element model for Bi-2212 round wire under axial load and analyzed its mechanical behavior. The model considered the initial thermal residual stress and damage of Bi-2212 superconducting filaments. The proposed model accurately predicted the axial mechanical behavior of strands. In addition, the characteristics of hysteresis loops in the stress–strain curves of Bi-2212 high-temperature superconducting (HTS) round wire under axial cyclic load were also obtained, agreeing well with experimental data. We constructed a 3D multifilament finite element model and 3D homogenized finite element model of a Bi-2212 HTS triplet. Both the results predicted by multifilament finite element model and homogenized model are close to the experimental data. The former gave more accurate stress distribution characteristics of strands than the latter. However, the homogenized model maybe more suitable for modeling of higher-level cables than the triplet model because of its lower computational cost.

A nonlinear magneto-mechanical-thermo-electric coupling finite element model is established for the Terfenol-D/PZT and Ni/PZT laminates structure respectively, based on Maxwell electromagnetic equations and nonlinear constitutive equations of giant magnetostrictive materials. The magnetoelectric (ME) coefficients of the two laminates with considering the coupling stress or without considering the coupling stress are calculated respectively. The results indicate that the predicted values of ME coefficient of our model are very well in agreement with the experimental datas both in the low, intermediate and high magnetic field for the two kinds of materials structures at different temperatures (most of previous theoretical models just give the well comparison in low and intermediate field). The coupling stress has a significant effect on the ME coefficient for the Terfenol-D/PZT laminate, but little effect for the Ni/PZT laminate. The ME coefficient with considering coupling stress is smaller than that without considering coupling stress. Besides, the magnetic flux density, displacement and voltage distribution characteristics of ME laminates at different temperatures and pre-stresses are also detailed investigated. It has been shown a noteworthy phenomenon that the sensitivity of ME effect on temperature and/or pre-stress can be tuned by the pre-stress and/or temperature, respectively. Adjusting pre-stress can reduce the sensitivity of ME effect on temperature, which may promote the stability of ME devices operating in complex environments.

In the process of the HTS cable structure cabling, the HTS tape is subjected to the combined deformation caused by tension, bending, and torsion. The electro-mechanical behaviors and the degradation mechanism of HTS cable are remain elusive. In the present paper, a numerical model is built in ABAQUS software to analyze the winding mechanical behavior of the CORC cable. Then, the critical current degradation is calculated and the effects of the tape width, substrate thickness, pre-stress, winding pitch and helix angle are investigated. The results show that it should be avoid selecting a roller with a much small radius to produce a large strain. The critical current degradation of the cable is minimal when the helix angle equals to 45°, which is the best choice to winding the tape to form the CORC cable. A smaller winding radius can be choose when the thickness of the substrate is in the small strain region of 10–20 µm. This study helps understand the deformation of the HTS tape during the winding process and provides a winding optimization for the CORC cable.

With the growing popularity of flexible micro-electronics and health-monitoring sensors, wearable flexible thermoelectric generators (TEGs) are receiving attention due to their ability to convert body heat into electricity. In this study, a three-dimensional model of wearable TEGs encapsulated in the PDMS material is established based on the nonlinearly coupled thermoelectric transport constitutive law, large deformation of materials, and the 3-parameter Mooney-Rivlin nonlinear hyperelastic constitutive law of polydimethylsiloxane (PDMS) material. The thermoelectric performance and mechanical reliability of the wearable TEG are investigated under the bending load by employing finite element method. A comparison between numerical results and experimental data is conducted for validation of the model. Effects of the leg shape, filling factor and height of the legs are examined on the thermoelectric performance and mechanical reliability of the wearable TEGs. The optimized dimensions of wearable thermoelectric generators are obtained and analyzed. The results show that, thermoelectric performance and flexibility of the wearable TEG can be enhanced by increasing the number of thermocouples in the TEG. The results of this paper provide useful suggestions for the structural design and practical application of wearable TEGs encapsulated in PDMS materials.

We studied the propagation of elastic waves in a two-dimensional (2D) magnetorheological elastomers phononic crystals (MREs-PnCs) plate with a double-sided stubbed that can be tunable by an external magnetic field. The dispersion relations and the transmission properties of the perfect MREs-PnCs and defect MREs-PnCs are numerically calculated by the using finite element method under different magnetic fields. Good agreement was also observed in the experiment results. The results shown that with the increase of the applied magnetic field, the complete band gap of the MREs-PnCs plate gradually widens and moves to the high-order frequency region. In addition, with the introduction of defect modes, defect bands appear in the dispersion relation, and the elastic waves with specific frequencies are located at the point or line defects. This work makes up for the insufficiency of experimental research in related fields and provides a good design basis for MRE-PnCs structures in the future.

Second-generation high-temperature superconducting (2G HTS) tape is used in magnets and cables because of its outstanding electromagnetic characteristics. However, with the development of winding technology, thinner tapes are required in the construction of magnets. The effect of using thinner substrates on the resulting mechanical and electrical properties of 2G HTS tapes must thus be urgently understood. The interfacial adhesive strength is an important index used to characterize the mechanical strength of 2G HTS tape. Previous experimental studies have shown that thermal stress is one of the major factors in the delamination of the component tape used for magnet winding or cable assembly. In this study, the effect of substrate thickness on the interfacial adhesive strength of 2G HTS tape was investigated using peel test modeling. The thermal residual stresses accumulated during tape synthesis and caused by altered temperature during tape preparation and application at 77 K were also considered. To address the geometrical, physical, and boundary nonlinear problem, the finite element method was used. The simulation results indicate that interfacial stress caused by thermal shrinkage may separate the tape near the superconductor layer at the outer edge; however, no significant effect was observed for the central part. When the thermal residual stress was considered, the peel strength was reduced by approximately 20%. The substrate thickness also played an important role in the magnitude of thermal residual stress, which resulted in an increase of the peel strength with decreasing substrate thickness.

The investigation of hysteresis induced self-biased magnetoelectric (ME) coupling in multiferroic nanostructured films is significant for self-biased nano-devices. In this paper, we propose a quasistatic hysteresis model for ME effect in multiferroic nanostructured films based on surface stress model and multi-field coupled hysteretic constitutive model. For an asymmetric structure consisting of different magnetostrictive phases, the flexural strain is considered in the theoretical model. It is revealed that ME coupling in ME composites with nano-scale thickness is significantly size-dependent below critical size, which is enhanced by surface effect. Self-biased ME hysteretic behavior can be observed by considering the hysteretic effect of magnetostrictive materials, resulting in a large ME voltage coefficient in absence of bias magnetic field. The self-biased ME voltage coefficient is affected by pre-stress and thermal variation due to the complex magneto-elastic-thermal coupling characteristics of constituent materials. The proposed model provides a method to analyze and evaluate the nonlinear ME coupling characteristics of self-biased nano-devices operating under extreme stress or temperature conditions.

Protecting the magnets in case of a quench is a challenge for the 16 T superconducting dipole magnets presently designed for the 100 TeV: Future Circular Collider (FCC). These magnets are driven to the foreseen technological limits in terms of critical current, mechanical strength and quench protection. The magnets are protected with CLIQ (Coupling-Loss Induced Quench) system, which is a recently developed quench protection method based on discharging a capacitor bank across part of the winding. The oscillation of the magnet currents and the dissipation of the high stored energy into the windings cause electrodynamic forces and thermal stresses, which may need to be considered in the magnet mechanical design. This paper focuses on mechanical stress analysis during a quench of the 16 T cos-θ and block type dipole magnets. A finite element model allowed studying the stress due to the non-uniform temperature and current distribution in the superconducting coils. Two different CLIQ configurations were considered for the cos-θ design and one for the block type magnet. The analyses of the mechanical behavior of two magnets during a quench without or with hot spot turn were separately carried out. The simulation results show that the stress related to a quench should be considered when designing a high field magnet.

Contact resistance is key for stable operation of electrical contact equipment, and can also be extensively applied. For Tokomak devices in fusion reactors, contact resistance of the superconductor magnet system strongly relates to the alternating current (AC) loss of the cable, the cable is assembled using a certain number of contacting superconducting tapes coated with copper layers on both sides. The contact resistance of a metal solid surface is affected by many factors. In this work, the contact resistance of copper surface samples was studied experimentally under variable normal cyclic load, temperature and number of contact surfaces. This is consistent with real-world working conditions, as the structure of superconducting cables can be changed, and such cables are used under cyclic electromagnetic forces in temperatures which range from room to working temperature. Experimental results showed that contact resistance decreased rapidly with an increase of load. Further, when temperature was varied from 77 to 373 K, the load&ndash, unload contact resistance lag decreased. When the number of contact surfaces was increased, contact resistance increased. Finally, a fitted formula describing the relationship between contact resistance and cyclic times, temperature and number of contact interfaces was determined. This formula can be used to predict variation trends of contact resistance in complex environments and provide more accurate contact resistance parameters for calculating the AC loss of superconducting cables.

The performance of a multi-layer composite superconducting tape depends on operating conditions, such as the applied field, temperature and stress. Therefore, accurate analysis of the electromagnetic-thermo-mechanical coupling behaviors of the high-temperature superconducting (HTS) cable is important to understanding the mechanism of interaction among different physical fields and the success of optimizing the design of the HTS cable structure. This paper develops a three-dimensional finite element model based on the twisted-stack slotted-core HTS cable structure for electro-thermo-mechanical analysis. Critical currents of a single multi-layer composite superconducting tape and the whole HTS cable structure are calculated. Profiles of the magnetic field, current density, temperature and stress are also obtained. It is found that the selection of tapes having higher critical current enhances the transport performance of the cable. Current densities are nonuniformly distributed in the stack. From the bottom to the top of the stack, the current density first increases and then decreases, in inverse relation to the magnetic field. Cooling with liquid helium improves the cable transport capacity. The temperature of the superconducting tapes is slightly higher than that of the aluminum core, but the stress in the aluminum core is greater than that in the superconducting tapes. The results imply that the transport capacity of the cable can be improved by selecting superconducting tapes with high critical current density and arranging them in stacks in a manner consistent with the electromagnetic field distribution. The model also explains the mechanism of interaction between different physical fields. It is a useful tool that clarifies the multiphysics coupling behaviors of an HTS cable with complex structure, and provides a theoretical reference for the design of novel HTS cable structures.

In this paper, a three dimensional finite element model of annular thermoelectric devices is established to optimize the geometric dimensions and the number of thermocouples for the enhancement of the thermoelectric performance and mechanical reliability. The influences of geometric dimensions and the number of the thermocouples on the thermoelectric performance and the mechanical reliability of annular thermoelectric generators are investigated, respectively. The numerical results indicate that with the increasing the angle ratio of the thermoelectric leg, the maximum von Mises stress in the legs of thermocouples decreases first and then increases, and the thermoelectric performance of the annular thermocouple can be significantly improved. In addition, increasing the length of legs of thermocouples would reduce the thermoelectric performance, but improve the mechanical reliability of annular thermocouples. For the whole annular thermoelectric generator, there exists different optimal number of thermocouples to enhance the thermoelectric performance for different external resistance. The number of thermocouples has little influence on the maximum von Mises stress in the legs of annular thermoelectric generators. Finally, the optimal geometric dimensions of the annular thermoelectric generator with high thermoelectric and mechanical performance are also discussed. These results can provide some guidance for the optimization design of annular thermoelectric generators.

High-temperature superconductor (HTS) rare-earth-barium-copper-oxide (REBCO) tapes are very promising for use in high-current cables. The cable geometry and the layout of the superconducting tapes are directly related to the performance of the HTS cable. In this paper, we use numerical methods to perform a comparison study of multiple-stage twisted stacked-tape cable (TSTC) conductors to find better cable structures that can both improve the critical current and minimize the alternating current (AC) losses of the cable. The sub-cable geometry is designed to have a stair-step shape. Three superconducting tape layouts are chosen and their transport performance and AC losses are evaluated. The magnetic field and current density profiles of the cables are obtained. The results show that arrangement of the superconducting tapes from the interior towards the exterior of the cable based on their critical current values in descending order can enhance the cable’s transport capacity while significantly reducing the AC losses. These results imply that cable transport capacity improvements can be achieved by arranging the superconducting tapes in a manner consistent with the electromagnetic field distribution. Through comparison of the critical currents and AC losses of four types of HTS cables, we determine the best structural choice among these cables.

In extreme operating environments, delamination in 2G HTS tapes occurs within and/or near the superconductor layer from high transverse tensile stresses caused by fabrication, Lorentz forces and thermal mismatch, etc. Generally, transverse opening and peeling off are the main delamination modes, and are always studied in anvil and peel tests, respectively. Numerical models of these modes for 2G HTS tape are presented wherein the mixed-mode traction-separation law at the interface of the silver and superconductor layers is considered. Plastic deformations of copper, silver, and Hastelloy® in the HTS tape are taken into account. The results obtained from the transverse opening model show that the maximum average tensile stress is smaller than the delamination tensile strength because delamination is asynchronous in the tape. When a crack appears in the tape, only a small stress ( ≤ 1 MPa) is required to expand the crack to other stress free areas through peeling. Using the peeling model, the dependency of the peel strength on peeling angle is investigated under constant fracture toughness. Peel strength decreases with the peeling angle until the minimum value is reached at 150°, and thereafter increases slightly. Other results indicate that peel strength depends strongly on delamination strength, fracture toughness, and thickness of copper layer. The fracture toughness of the delamination interface, which is difficult to obtain by experiment, can be extracted using the present model.

The energy upgrade of the Large Hadron Collider and Future Circular Collider propose new requirement that the magnetic field of accelerate magnets is up to 16 T. Nb3Sn Rutherford cables are used in magnet design for such high level magnetic field. Rutherford cables must undergo complex stress conditions owing to the extreme magnetic environment and complicated cabling process which often leads to mechanical instability. In this study, a three-dimensional model is established and analyzed to better understand the mechanical behavior of Rutherford cables subjected to different loading conditions during the cabling process. A rapid approach to construct the geometry of a Rutherford cable is first presented, followed by an analysis of its mechanical behavior under axial tension, cyclic tension and transverse compression conditions. Instability behaviors, such as “pop-out” and “cross-over”, are investigated. The results show that the friction coefficient, laying angle and core play important roles in the cable mechanical performance. For better mechanical stability of the strands in Rutherford cables, it is recommended to select a higher friction value among the strands and a laying angle between 74° and 78° for non-cored cable, whereas a larger laying angle is suggested for copper-cored cable.

A volumetric contact theory is developed that is valid for investigating electro-mechanical contact properties between random rough surfaces. The theory includes the contact resistance formula and the elastic and elastoplastic electrical contact models. They do not need to pre-suppose a certain contact pattern, and are not limited to the assumption that the real contact area is much smaller than the nominal contact area. The real contact area between rough surfaces is obtained by calculating the three-dimensional equivalent contact volume, which is a bridge connecting contact resistance and contact deformation. The theory can be used to predict the change of contact resistance with squeezing load in the elastic and plastic ranges. It also shows that the contact volume is the key to the contact problem between random rough surfaces. The models quantify the electrical contact behavior between rough surfaces using the void and real contact volume ratio, which provides a new perspective for understanding the electro-mechanical coupling mechanism between rough surfaces.

The aim of this article is to present a three-dimensional (3D) simulation based on Voronoi tessellation, used to assess the strain dependence of the superconducting critical properties of inhomogeneous polycrystalline Nb3Sn at the microstructural level. To support this objective, we first present a polycrystalline model with equiaxed grains used to analyze the relationship between the polycrystalline structure and the strain response. We analyze the Young's moduli of Nb3Sn at different temperatures with random and preferential polycrystalline orientations, and the relation between the Young's modulus of polycrystalline Nb3Sn and spontaneous tetragonal transformation is discussed. The results indicate that the elastic properties (Young's modulus, stress/strain field) of polycrystalline Nb3Sn are mainly associated with ambient temperature and phase transition and are affected by the grain orientation. Meanwhile, an estimation-based model for the superconducting critical properties of single-crystal Nb3Sn is proposed. This model is based on changes in the electron density of states and phonon frequency induced by strain. The results calculated by the estimation-based model are consistent with the experimental data and the values calculated according to first principles. The change in the strain-induced superconducting properties of polycrystalline Nb3Sn is analyzed by combining the numerically simulated strain field of the polycrystal with the estimation-based model of single-crystal Nb3Sn. Compared to ideal single-crystal Nb3Sn, the superconducting critical temperature of the polycrystalline Nb3Sn superconductor has a higher strain sensitivity, which is related to the non-uniformity of the strain field of the polycrystal.