高温、高压、高应变速率动态过程晶体塑性有限元理论模型及其应用

刘静楠 叶常青 刘桂森 沈耀

刘静楠, 叶常青, 刘桂森, 沈耀. 高温、高压、高应变速率动态过程晶体塑性有限元理论模型及其应用[J]. 高压物理学报, 2020, 34(3): 030102. doi: 10.11858/gywlxb.20190874
引用本文: 刘静楠, 叶常青, 刘桂森, 沈耀. 高温、高压、高应变速率动态过程晶体塑性有限元理论模型及其应用[J]. 高压物理学报, 2020, 34(3): 030102. doi: 10.11858/gywlxb.20190874
LIU Jingnan, YE Changqing, LIU Guisen, SHEN Yao. Crystal Plasticity Finite Element Theoretical Models and Applications for High Temperature, High Pressure and High Strain-Rate Dynamic Process[J]. Chinese Journal of High Pressure Physics, 2020, 34(3): 030102. doi: 10.11858/gywlxb.20190874
Citation: LIU Jingnan, YE Changqing, LIU Guisen, SHEN Yao. Crystal Plasticity Finite Element Theoretical Models and Applications for High Temperature, High Pressure and High Strain-Rate Dynamic Process[J]. Chinese Journal of High Pressure Physics, 2020, 34(3): 030102. doi: 10.11858/gywlxb.20190874

高温、高压、高应变速率动态过程晶体塑性有限元理论模型及其应用

doi: 10.11858/gywlxb.20190874
基金项目: 科学挑战计划(TZ2018001)
详细信息
    作者简介:

    刘静楠(1993-),女,硕士,主要从事动态晶体塑性有限元研究. E-mail:jingnanliu@sjtu.edu.cn

    通讯作者:

    沈 耀(1972-),男,博士,教授,主要从事晶体缺陷行为、力学性能及塑性变形的微观机制研究. E-mail:yaoshen@sjtu.edu.cn

  • 中图分类号: O344.1

Crystal Plasticity Finite Element Theoretical Models and Applications for High Temperature, High Pressure and High Strain-Rate Dynamic Process

  • 摘要: 对于高温、高压、高应变速率加载条件下的材料冲击变形行为,动态晶体塑性模型能够直接反映晶体中塑性滑移的各向异性及其对温度、压力和微观组织结构的依赖性,因而广泛应用于材料的动态冲击力学响应、微观结构演化以及动态损伤破坏的模拟。本文综述了高压冲击下动态晶体塑性有限元的理论模型,主要包括变形运动学、包含状态方程的超弹性本构模型和晶体塑性本构模型,涉及位错滑移、相变、孪生等塑性变形机制,以及层裂、绝热剪切带等动态破坏方式。

     

  • 图  经典的晶体运动学构型

    Figure  1.  Classical configurations of crystal kinematics

    图  引入热膨胀构型的变形梯度分解F = FeFθFp[19]

    Figure  2.  Decomposition of deformation gradient considered thermally-expanded configuration $ {{F}}={{{F}}}^{\rm{e}}{{{{F}}}^{\theta }{{F}}}^{\rm{p}} $ \normalsize[19]

    图  (a)热能协助位错克服势垒(T0 < T1 < T2 < T3)[51],(b)位错在运动过程中遇到的势垒[52]

    Figure  3.  (a) Thermal energy assists dislocations to overcome barriers ( $ {T}_{0}<{T}_{1}<{T}_{2}<{T}_{3} $ \normalsize)[51], and (b) barriers encountered by a dislocation on its course[52]

    图  热软化效应对多晶Ta在32 GPa冲击变形下累积塑性滑移量的影响[29]

    Figure  4.  Influence of thermal softening on accumulated plastic slip of polycrystalline Ta during shock deformation under 32 GPa[29]

    图  α-RDX单晶沿<210>晶向平板撞击变形过程中声子拖曳对(021)<100>滑移系上滑移阻力的影响[26]

    Figure  5.  Influence of phonon drag on slip resistance of (021)<100> slip system, during α-RDX single crystal deformed in plate impact along <210> direction[26]

    图  螺位错滑移的Kink-pair机制[27]

    Figure  6.  Illustration of screw dislocation motion via a Kink-pair mechanism[27]

    图  位错平均运动与热激活运动以及拖曳运动的对比[27]

    Figure  7.  Comparison of the average dislocation velocity with the velocities of thermally-activated and drag-dominated dislocation motions[27]

    图  不同压力加载下位错密度的演化机制[83]

    Figure  8.  Dislocation density evolution mechanisms under different loading pressure[83]

    图  RDX的α相与γ相Gibbs自由能之差与温度、压强的关系[38]

    Figure  9.  Difference between Gibbs free energies of the α and γ RDX polymorphs as a function of pressure and temperature[38]

    图  10  Fe冲击相变的单晶模拟与多晶实验结果[111]

    Figure  10.  Single crystal Fe simulation data and polycrystal experimental data of shock-induced phase transformation[111]

    图  11  冲击变形过程中波的传播及层裂现象(a)、3个时刻的应力波形(b)和3个位置的应力历史(c)[52]

    Figure  11.  Wave propagation and spalling phenomenon (a), stress profiles at three different times (b), as well as stress histories at three different positions (c) during shock deformation[52]

    图  12  铅合金动态晶体塑性有限元模拟结果:(a)层裂形核时的压力,(b)层裂形核时的弹性能密度,(c)经250 m/s冲击加载层裂面附近的等效应力;(d)经350 m/s冲击加载层裂面附近的等效应力[24]

    Figure  12.  Dynamic crystal plasticity finite element simulation results of lead alloy: (a) pressure of spalling nucleation; (b) elastic energy density of spalling nucleation; (c) equivalent stress near the spalling surface under 250 m/s shock loading; (d) equivalent stress near the spalling surface under 350 m/s shock loading[24]

    图  13  多孔晶体的变形梯度分解为弹性部分(Fe)、不可逆偏量部分(Fp)和不可逆体积变形部分(Fd)[134]

    Figure  13.  Decompose deformation gradient of porous crystal into elastic part (Fe) and irreversible volumetric part (Fp) and irreversible volumetric part(Fd)[134]

    图  14  晶粒取向和应力三轴度对孔洞合并的临界状态变量的影响[133]

    Figure  14.  Influence of grain orientation and stress triaxiality on critical state variables for void coalescence[133]

    图  15  经典应力-应变曲线上塑性变形的3个阶段(Stage 1:均匀变形;Stage 2:非均匀变形;Stage 3:宏观热塑性失稳)[51]

    Figure  15.  Three stages of plastic deformation appeared on classical stress-strain curve (Stage1: homogeneous deformation; Stage2: inhomogeneous deformation; Stage3: macroscopic thermoplastic instability)[51]

    图  16  不同累积滑移速率变形$\bar \gamma $=0.05时的温升云图[143]

    Figure  16.  Distribution of temperature increase when $ \bar \gamma = 0.05 $ \normalsize for different accumulated slip rates[143]

    图  17  hcp单晶和多晶样品在105 s–1应变率下的绝热剪切局域化[147]

    Figure  17.  Adiabatic shear localization of hcp single crystal and polycrystalline samples under 105 s–1 strain rate[147]

    图  18  动态冲击载荷下6种织构材料中形成绝热剪切带的临界应变(Vpeak = 20 m/s)[147]

    Figure  18.  Critical strain of adiabatic shear band nucleated in 6 different texture materials under dynamic shock loading ( $ {V_{{\rm{peak}}}} = 20\;{\rm{m}}/{\rm{s}} $ \normalsize) [147]

    A1  运动学符号说明

    A1.   Symbol description of kinematics

    SymbolsDescription
    F(Fe, Fp, Fθ )Deformation gradient including elastic, plastic and thermal components
    L(Le, Lp, Lθ )Velocity gradient including elastic, plastic and thermal components
    ReRotation tensor
    UeRight stretch tensor
    αThermal expansion coefficient tensor
    下载: 导出CSV

    A2  热力学符号说明

    A2.   Symbol description of thermodynamics

    SymbolsDescriptionSymbolsDescription
    DintIntrinsic dissipation of the systemK0Bulk modulus at zero pressure
    ψHelmholtz free energyKPressure derivative of bulk modulus
    sEntropy of the systemTDDebye temperature
    TTemperatureRMolar gas constant
    KTIsothermal bulk modulusMmolMolar mass of the material
    cVHeat capacity at constant volumekBBoltzmann constant
    ΓGrüneisen coefficientXTNVariables related to the lattice thermal vibration
    qnInternal variables for microscopic defects such
    as dislocations in materials
    XTEVariables related to the electron activation
    下载: 导出CSV

    A3  塑性本构符号说明

    A3.   Symbol description of plastic constitution

    SymbolsDescriptionSymbolsDescription
    λ αMean spacing between obstacles${{\,\rho}_{\rm{for}}^{\alpha} }$Forest dislocation density
    ταResolved shear stress ${{t_{\rm r}^{\alpha}}}$The drag-dominated mean transit time between obstacles
    QαActivation energyBViscous drag coefficient
    gαSlip resistance${{\dot{\rho }}_{\rm{nuc}}^{\alpha }}$The nucleation rate
    ${{g}_{\rm{ath}}^{\alpha} }$Athermal slip resistance${{\dot{\rho }}_{\rm{hom}}^{\alpha }}$The homogeneous nucleation rate
    hαβHardening coefficient${ {\dot{\rho }}_{\rm{het}}^{\alpha }}$The heterogeneous nucleation rate
    ραTotal dislocation density${{\dot{\rho }}_{\rm{mult}}^{\alpha }}$The multiplication rate
    ${{\rho}_{\rm{m}}^{\alpha} }$Mobile dislocation density${{\dot{\rho }}_{\rm{trap}}^{\alpha }}$The trapping rate
    ${{\rho}_{\rm{i}}^{\alpha} }$Immobile dislocation density${{\dot{\rho }}_{\rm{ann}}^{\alpha }}$The annihilation rate
    bαBurgers vectordaCapture distance of annihilation
    vαVelocity of mobile dislocations${{t}_{\rm{w}}^{\alpha}}$The thermal activation-dominated waiting time at a barrier
    ${ {\dot{\gamma }}^{\alpha }}$Slip rate on slip system α
    下载: 导出CSV

    A4  超弹性本构符号说明

    A4.   Symbol description of hyper-elastic constitution

    SymbolsDescriptionSymbolsDescription
    ISecond-order unit tensor$\widehat{{{E}}^{\rm{e}}}$Isochoric strain in expanded configuration
    EeElastic Green–Lagrange strain$ \widehat{\widehat{{{E}}^{\rm{e}}}}$Isochoric strain in configuration I
    CeElastic right Cauchy-Green tensor$ \overline {{{{E}}^{\rm{e}}}}$Volumetric strain in configuration I
    $\widehat{{{{F}}}^{\rm{e}}}$Isochoric part of elastic deformationSSecond Piola–Kirchhoff stress
    $\overline {{{{F}}^{\rm{e}}}}$Volumetric expansion
    下载: 导出CSV

    A5  相变、孪晶与动态破坏符号说明

    A5.   Symbol description of phase transformation, twining and damage

    SymbolsDescriptionSymbolsDescription
    FtrDeformation gradient of phase transformation$S_{\rm{tw}}^{\beta}$Twin resistance of twin system
    vpVolume fraction of the parent phaseρdebDislocationdebris density
    vtVolume fraction of the new phase tdmfpDislocation mean free path related to the volume fraction of twin
    vNVolume fraction of all new phases${\varphi}$Void volume fraction
    ftDriving force of phase transformationFdVolumetricpartofplastic deformation gradient in porous crystal plastic model
    f βVolume fraction of twinYrResistance of damage evolution
    γtwCharacteristic shear strain of twining
    下载: 导出CSV
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