| Nb3Sn superconducting wire is widely used in large-scale strong magnetic field because of its high current-carrying density and high critical magnetic field strength.For example,the TF（Toroidal Field coil）and CS（Central Solenoid）coils of TOKAMAK,which is planned by the International Thermonuclear Experimental Reactor（ITER）,are made of Nb3Sn superconducting strands.The diameter of Nb3Sn strand is about 0.81mm,and there are thousands of Nb3Sn superconducting wires with a diameter of about 2～3 μm in it.The complicated micro-geometric structure brings great difficulties and workload to the research of mechanical behavior of Nb3Sn strand.In addition,the preparation temperature of Nb3Sn strands is as high as 1000K,and it enters the superconducting state under the working condition of liquid helium（4.2K）.The huge temperature difference from the preparation temperature to the working temperature will produce temperature stress,which will cause the initial damage of Nb3Sn fibers which are extremely sensitive to strain before they bear mechanical load,resulting in the degradation of the mechanical properties of superconducting strands.Therefore,the establishment of a numerical model that can consider the effects of material plasticity,fiber fracture damage and temperature stress is helpful to the analysis of mechanical behavior and engineering application of Nb3Sn strand.The main research of this paper is as follows:Firstly,according to the multi-scale geometric characteristics of the strands,three-level layering and two-level equivalent treatment were carried out,and the layered multi-scale analysis model of EAS-Nb3Sn strands was established.The equivalent elastic parameters and equivalent thermal expansion coefficients of representative units at each level of strands were calculated numerically.Considering the temperature difference of about 900K from the preparation temperature to the working temperature,the equivalent parameters of EAS-Nb3Sn strands with different layers in the temperature range of 4K-923K and the macroscopic stress-strain relationship of the strands considering the plasticity of the copper protective layer are numerically analyzed.The numerical results show that the lower the temperature is,the larger the equivalent elastic modulus（Young’s modulus and shear modulus）of each layer of the strands are,while the smaller the equivalent thermal expansion coefficient is.The numerical simulation results of homogenized EAS-Nb3Sn strands under small deformation are in good agreement with the experimental results,which shows that the equivalent model obtained by homogenizing EAS-Nb3Sn strands in this paper can be used to study the mechanical properties of composite strands simply and efficiently.Secondly,considering the strain sensitivity of Nb3Sn compound,Nb3Sn fiber in the strand is easy to break under slight strain.Based on Curtin-Zhou model,the damage theory of fiber reinforced composites considering temperature stress is put forward.The influence of initial temperature damage caused by temperature stress on the constitutive relation of Nb3Sn fiber was numerically studied,and the phenomenological characterization models of initial temperature damage of Nb3Sn fiber at different working temperatures were given.In order to analyze the elastic-plastic behavior of strands at all levels considering fiber damage,a new calculation method considering matrix plasticity in micromechanical homogenization model is proposed according to the definition of secant modulus of plastic materials.Based on the layered multi-scale model of EAS-Nb3Sn strand considering fiber fracture damage,the elastic-plastic mechanical behavior of each layer of strand under uniaxial tensile load is numerically analyzed.The elastic-plastic numerical simulation results of EAS-Nb3Sn strands considering fiber damage at different working temperatures are in good agreement with the experimental results,which indicates that the new calculation method considering matrix plasticity proposed in this paper is feasible and effective. |
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