静水压作用下Nb3Sn多晶体超导临界温度退化的耦合模型

Nb3Sn超导材料主要用于强磁场超导磁体的制造。力学变形诱导的其超导临界性能退化给强磁场超导磁体装置的电磁性能指标和安全运行造成了极其不利的影响。针对静水压作用下,Nb3Sn单晶体和多晶体表现出的不同退化行为,本文基于Maki De Gennes（MDG）关系式,建立了描述Nb3Sn单晶体变形-超导临界温度耦合响应的本构关系,并借助于多晶体有限元方法,对静水压作用下Nb3Sn多晶体超导临界温度退化响应进行了预测,预测结果与实验结果定性吻合。模型实现了从Nb3Sn单晶体到Nb3Sn多晶体变形-超导临界温度退化响应曲线的一致性预测。研究结果有助于提高对Nb3Sn高场超导材料变形-超导电性能耦合行为的认识,为发展描述运行工况下Nb3Sn超导材料力-电磁-热多物理场多尺度耦合行为的建模与数值计算方法提供了一定的基础;同时,相关结果对于特殊工况下高场超导磁体性能的评估和高应变耐受性超导材料的制备也具有一定的指导作用。     

Nb3Sn高场复合超导体临界性能力学变形效应的多尺度模拟

A15型Nb₃Sn超导体是制造高场( > 10 T)超导磁体线圈的主要材料, 被广泛应用于磁约束可控核聚变、高能物理等强磁场超导磁体装备制造领域. 力学变形诱导的Nb₃Sn超导临界性能退化给高场超导磁体装备的电磁性能指标和安全稳定运行造成了极其不利的影响. 鉴于Nb₃Sn超导体具有复杂的多尺度结构特征, 不同尺度下变形与超导电性能耦合行为是相互关联的, 本文建立了考虑微/细/宏观关联的非线性力电磁耦合本构模型, 提出了从原子尺度A15晶体结构到超导体微结构到宏观非均质Nb₃Sn复合超导体的多尺度模拟模型. 基于多晶体有限元方法, 对静水压加载条件下Nb₃Sn多晶体超导临界温度衰退和单轴拉压加载条件下Nb₃Sn复合多晶体临界性能衰退行为进行了模拟预测, 预测结果与实验观测结果定性吻合. 该模型揭示了Nb₃Sn复合超导体变形-超导电性能多尺度耦合机理, 实现对高场超导体力、电、磁、热耦合行为的预测, 有助于提高对A15型金属间化合物高场超导复合材料力、电、磁、热多尺度耦合行为的认识和描述能力, 为强磁场超导磁体的设计与制造提供有力的理论支撑.      

Nb3Sn单晶超导相转变时的弹性性能变化

Nb3Sn超导体失超，是超导磁体装备运行过程中的重要现象。失超，即超导体从超导相转变为正常相的过程；在强磁场超导磁体工程中，由于超高的储能密度，失超伴随着力/热/电等物理参量在瞬时的剧烈变化。失超瞬时，超导相转变的同时伴随着弹性力学性能的突变，研究超导相转变时弹性性能的变化是失超诱发应力跨尺度分析的关键。本文首先采用第一性原理方法计算了弹性常数随温度的变化规律，结果表明由于未考虑A15结构的超导材料在环境温度变化的情况下产生的特殊电子能带结构，基于准静态近似方法的材料弹性常数计算从0K外推至有限温度时，会导致模拟结果与实验观测结果出现定性上的差异；之后，基于晶格自由能函数，给出了描述立方相Nb3Sn单晶弹性性能随温度变化的解析模型，模型预测结果与实验观测结果定性吻合，初步实现了对Nb3Sn单晶超导相转变时弹性性能变化的理论描述和预测。研究结果对于超导体失超应力的跨尺度模拟及超导磁体的安全分析具有一定的理论参考价值。     

超导线圈在强磁场作用下的弹塑性变形分析

根据超导线圈受电磁力、热膨胀、弯曲应力作用的受力机制,首先理论研究了超导线圈在发生弹塑性变形时内部的应力、应变、位移,然后使用两段直线之间由过渡曲线相连接的简化模型作为超导线的应力-应变曲线的近似特性。利用有限元方法,数值模拟了电磁力作用下典型的Nb3Sn超导线材在不同边界条件下的应力、应变、位移分布情况。计算结果定量显示了超导线的弹塑性变形特性同电流密度的关系,初步预测了超导线圈发生塑性变形的区域和扩展以及支撑结构对超导磁体力学行为的影响。     

Nb3Sn超导线圈力学性能精确分析的双向均质化方法

Nb₃Sn超导磁体运行时产生很高磁场, Nb₃Sn超导线圈会受到很强电磁体力的作用, 从而会产生很大的力学应变. 由于Nb₃Sn超导材料的应变敏感性, 会使得Nb₃Sn磁体线圈的临界性能退化, 这对磁体的安全稳定运行造成极大影响, 所以精确计算超导磁体在电磁体力下的力学行为具有重要的科学意义. Nb₃Sn超导磁体主要是由超导线绕制成线圈结构再经过环氧树脂固化而成, Nb₃Sn超导线是主要由多根微米级的超导芯丝、铜形成的复合结构, 所以从超导芯丝到超导磁体其尺寸跨越了几个数量级, 从而给精确分析超导线圈力学变形带来挑战. 本文首先采用代表性单元均质化方法分析了整体线圈的等效力学参数, 通过对比等效均质化模型与线圈真实结构的计算结果, 发现等效均质化模型存在很大的误差. 因此, 提出一种高精度而且计算代价低的双向均质化分析方法, 研究超导线圈内各组分材料(Nb₃Sn芯丝、铜和环氧树脂)应力-应变分布. 该方法不需要进行大规模的数值建模, 并且与真实复合线圈下的结果对比吻合很好, 由此验证了该方法的有效性和准确性. 最后基于提出的双向均质化分析方法, 详细讨论了Nb₃Sn超导线圈各层材料在电磁力作用下应力-应变随匝数和层数的变化规律.      

高温超导带材多场特性测试系统研制进展(Ⅰ)

高温超导带材具有高的临界电流密度,高磁场下优异的载流特性以及良好的成型性在强电领域如高场磁体、超导电缆等方面应用潜力巨大。在其应用过程中,不可避免的低温-大电流-强磁场环境将对超导材料的载流能力产生影响,而加工过程中的残余应力以及洛伦兹力的存在会显著的降低超导材料的临界电流,造成相应超导装置功能性难以达到设计要求、且成为重要的安全隐患。本文介绍一种新型的适用于超导带材的力-磁-电多场耦合测试系统,该系统目前采用浸泡式制冷,可实现的主要功能有:(1)超导材料临界电流密度测试;(2)拉伸应变对超导带材临界电流的影响研究;(3)磁场对超导带材临界电流的影响研究;(4)力磁耦合情形下超导材料临界电流的变化规律;(5)超导材料磁通稳定性测试。该设备的成功研制将为我国先进超导材料研发提供基础测试平台。     

轻质点阵超结构设计及多功能力学性能调控方法

随着先进制造技术、多学科交叉和人工智能科技的飞速发展,高端装备呈现出轻量化、集成化、复合化、功能化、智能化、柔性化和仿生化等发展趋势.传统结构研究存在结构设计和制造相互分离,复杂结构制造效率低、实际制造结构的性能指标和使用可靠性大幅低于设计理论预测、结构多功能一体化程度不足、经济成本过高等问题.此外,先进工业装备对材料、结构的使用性能、使用环境要求越来越高,亟需开展结构的设计、制造、功能、应用一体化研究,为解决我国先进制造“卡脖子”技术难题提供理论依据和技术支持.轻量化多功能点阵超结构具有轻质高强、抗冲击吸能、减振降噪等性能优势,在航空航天、交通运输、国防、生物医疗、能源、机械等工业领域具有巨大的应用潜力.有鉴于此,受多晶体微结构的多尺度力学设计启发,以“点阵超结构力学设计”为主题,开展点阵超结构的节点、杆件组元,胞元类型、双相结构、梯度结构、多层级结构等典型点阵超结构的几何构筑和力学设计,并阐明多晶体多尺度微观结构启发的点阵超结构力学设计基本原理、多功能力学性能调控方法,以及点阵超结构在不同类型载荷下的结构变形和失效物理机理.     

超磁致伸缩材料多场耦合非线性力学行为的理论研究

超磁致伸缩材料由于具有位移大、响应快、驱动简单等性能优势,在智能系统中具有广阔的应用前景。对于其力学行为的研究,在理论上涉及的关键科学问题是多场耦合问题的理论建模与定量模拟,而其应用需求则涉及对超磁致伸缩器件性能的定量预测及优化。目前超磁致伸缩材料在工业上最广泛的应用是作为换能器的核心制动元件,其磁学、力学行为与工况密切相关。应力、外磁场、环境温度都会改变材料的磁化强度和应变状态,在交变磁场作用下磁致伸缩棒截面上产生涡电流,该损耗使材料的磁化和应变曲线出现洄滞。针对这些问题已有很多学者[1]-[4]进行了研究,这些工作揭示了外部条件对超磁致伸缩材料磁学、力学性质的单向联合作用,如图1中虚线所示。然而对于超磁致伸缩材料力学行为的准确刻画还需要考虑更深层次的多物理场耦合关系（图1中实线所示）：由于超磁致伸缩材料被外场磁化而产生磁致应变的同时,被磁化的介质也可以充当一种源而改变其周围的磁场,改变的程度依赖于介质的变形,因此需要考虑介质对周围磁场的反作用;棒截面上的涡电流除了会带来磁滞损耗外还会产生大量的热,改变周围温度,进而因为热膨胀、热磁效应等改变超磁致伸缩棒的磁学、力学输出,所以涡电流的热效应也不可忽略;此外,超磁致伸缩棒在交变磁场下的振动响应使其应力状态发生改变,在建模时不能只考虑所施加的预应力,材料的实时应力状态必须加以考虑。图1中虚线和实线所指向的过程共同构筑了超磁致伸缩材料的多物理场耦合框架,综合考虑这些因素才能准确描述超磁致伸缩材料多场耦合非线性力学行为。本文围绕上述内容逐步深入,针对这一在理论和应用上具有重要意义的问题,开展了理论建模和数值模拟研究。     

固体热-化-力耦合连续介质理论的研究现状与展望

考虑化学作用的固体多场耦合问题涉及开放系统中多组分物质的复杂动力学过程.这些过程不仅具有不同时空尺度下的多重热力学作用机制,还会引起材料性质的不断变化.深入认识热、化学、力学相互作用下物质与能量的传递和转化方式,合理描述化学反应与固体力学行为的相互影响并建立严密的耦合理论体系,不论是对新型智能材料的功能优化设计,还是对传统材料和结构在耦合场中的性能评估与预测都至关重要,也是当代固体力学发展的一个重要方向.本文针对各领域中广泛存在的固体传热、传质、化学反应和力学行为相互耦合的问题,按照传质-变形耦合问题、反应-变形耦合问题及热-化-力完全耦合问题几种主要类型,介绍了相关连续介质理论建模和求解等方面的研究进展,重点对耦合理论建模中常涉及的几类关键问题进行了深入分析和讨论,并对今后固体热-化-力耦合问题的研究进行了展望.     

高温超导带材超导涂层局部脱黏后的电磁力学行为分析

高温超导带材因其高载流z能力、低交流损耗等优点, 在超导领域得到了广泛的关注, 然而在带材的应用中出现的力学问题严重阻碍了其应用. 基于此, 本文分析了受外部磁场激励YBCO高温超导带材在超导层局部脱黏后的电磁力学响应. 基于超导临界态Bean模型和弹性力学平面应变方法, 给出了超导薄膜内正应力与基底界面处切应力相关联的控制方程, 基于数值方法研究了超导薄膜内的正应力及基底界面处的切应力随外部磁场的变化规律. 结果显示: 在脱黏区域附近, 超导薄膜内的正应力和基底$\!-\!$薄膜界面处的切应力急剧增大, 该正应力及切应力极易引起超导层的进一步脱黏. 同时, 剪切应力在结构边缘处出现极值. 基底材料的属性, 特别是杨氏模量对结构内的应力影响显著, 在软基底材料结构中, 超导薄膜内将出现较大的正应力, 而基底材料较硬时, 在基底$\!-\!$薄膜界面处将出现较大的剪切应力, 这些因素均会引起超导涂层结构的力学及电学性能的退化. 本文研究可望为超导带材的加工制备及脱黏的处理提供一定的理论指引.      

Three-dimensional finite element simulations of ferroelectric polycrystals under electrical and mechanical loading

Complex, non-linear, irreversible, hysteretic behavior of polycrystalline ferroelectric materials under a combined electro-mechanical loading is a result of domain wall motion, causing simultaneous expansion and contraction of unlike domains, grain sub-divisions that have distinct spontaneous polarization and strain. In this paper, a 3-dimensional finite element method is used to simulate such a polycrystalline ferroelectric under electrical and mechanical loading. A constitutive law due to Huber et al. [1999. A constitutive model for ferroelectric polycrystals. J. Mech. Phys. Solids 47, 1663-1697] for switching by domain wall motion in multidomain ferroelectric single crystals is employed in our model to represent each grain, and the finite element method is used to solve the governing conditions of mechanical equilibrium and Gauss's law. The results provide the average behavior for the polycrystalline ceramic. We compare the outcomes predicted by this model with the available experimental data for various electromechanical loading conditions. The qualitative features of ferroelectric switching are predicted well, including hysteresis and butterfly loops, the effect on them of mechanical compression, and the response of the polycrystal to non-proportional electrical loading.     

On correct account of finite rotations in finite plasticity theory

The non-uniqueness of the trantition from nonobjective constitutive relations to objective ones with the use of the principle of material frame-indifference (PMFI) is shown. To eliminate it, the concept of finite strain without rotations (FSWR) for a given material type and each strain component (elastic, plastic) is introduced. In FSWR the rotation is excluded with respect to the natural preferred configuration for a given material. Considered are a simple solid, a liquid, a monocrystal, a polycrystal and a composite. The proecedure is proposed for consistent generalization of known infinitesimal relations for finite strains and rotations. The structure of constitutive relations is derived for anisotropic elasto-plastic mono- and polycrystalline materials.     

Electric-magnetic-force characteristics of rare earth barium copper oxide superconductor high-field coils based on screening effect and strain sensitivity

Rare earth barium copper oxide (REBCO) is the most researched and commercialized second-generation high-temperature superconducting material. Due to the anisotropic structure, strong deformation sensitivity, and central field errors caused by screening current effects, it is still a challenge for commercialization applications. In this study, the transversely isotropic constitutive relationship is selected as the mechanical model based on the structural characteristics of REBCO tapes, and suitable microelements are selected to equate the elastic constants using their average stress-strain relationships. Then, a two-dimensional axisymmetric model for coils wound by single-layer tapes is constructed to analyze the dependence of the electric-magnetic-force distribution in the tape on the strain. Finally, the anisotropic approximation of the homogenized bulk method is used to equate large-turn high-field coils, and the electric-magnetic-force distribution characteristics of the coils with/without screening effects and mechanical strain conditions are investigated, respectively. The results reveal that the mechanical strain has a weakening effect on the electromagnetic field distribution of superconducting tapes, but causes a significant enhancement in the force field distribution. In the presence of 0.5% mechanical strain, the maximum weakening of the peak value of the current density and the critical current density inside the high-field coil can reach about 8% and 13%, respectively, with a nearly 5 times increase in the peak stress. The screening current makes the current field distribution inside the coil improve by about 10 times. The screening current induced magnetic field can reach up to 0.8 T, making the relative error of the high-field coil center up to 7.8%.     

A constitutive relation for pseudo-elastic behaviour in shape memory alloys

A constitutive relation to describe pseudo-elastic deformation in shape memory alloys is presented in this paper. It is capable of describing deformation behaviour of polycrystalline materials under triaxial stress state as well as of monocrystalline materials under one-dimensional condition. Total strain rate is supposed to be composed of elastic strain rate and transformation strain rate. Deformation behaviour of Cu−Zn−Sn alloy and Ti−ni alloy is simulated by use of the proposed constitutive relation. it is shown that simulated results are in a good agreement with experimental data. The project supported by National Natural Science Foundation of China.     

Modeling transients in the mechanical response of copper due to strain path changes

When copper is deformed to large strains its texture and microstructure change drastically, leading to plastic anisotropy and extended transients when it is reloaded along a different strain path. For predicting these transients, we develop a constitutive model for polycrystalline metals that incorporates texture and grain microstructure. The directional anisotropy in the single crystals is considered to be induced by variable latent hardening associated with cross-slip, cut-through of planar dislocation walls, and dislocation-based reversal mechanisms. These effects are introduced in a crystallographic hardening model which is, in turn, implemented into a polycrystal model. This approach successfully explains the flow response of OFHC Cu pre-loaded in tension (compression) and reloaded in tension (compression), and the response of OFHC Cu severely strained in shear by equal channel angular extrusion and subsequently compressed in each of the three orthogonal directions. This new theoretical framework applies to arbitrary strain path changes, and is fully anisotropic.     

Time dependent behavior of ferroelectric materials undergoing changes in their material properties with electric field and temperature

This paper presents a time dependent polarization constitutive model suitable for predicting nonlinear polarization and electro-mechanical strain responses of ferroelectric materials subject to various histories of electric fields. The constitutive model is derived based on a single integral form with nonlinear (electric field and temperature dependent) integrand. The total polarization consists of the time-dependent and residual components. The residual component of the polarization is due to polarization switching in the ferroelectric materials. We use an ‘internal clock’ concept to incorporate the effect of electric field on the rate of polarization. The corresponding strain response is determined through the use of third order piezoelectric constant and/or fourth order electrostrictive constant that vary with polarization stage. It is assumed that in absence of polarization, both piezoelectric and electrostrictive constants are zero. To incorporate the effect of temperature on the overall polarization behavior all material parameters in the constitutive model are allowed to change with the ambient temperature. We present numerical studies on the effect of time, temperature, and electric field on the response of ferroelectric material followed by verification of the constitutive model. Experimental data on lead zirconate titanate (PZT) materials available in the literature are used to verify the model.