活性无序合金冲击的释能特性及在毁伤元中应用研究进展

侯先苇; 张先锋; 熊玮; 谈梦婷; 刘闯; 戴兰宏

doi:10.11883/bzycj-2023-0189

活性无序合金冲击的释能特性及在毁伤元中应用研究进展

doi: 10.11883/bzycj-2023-0189

侯先苇^1,,
张先锋^1, ,,
熊玮¹,
谈梦婷¹,
刘闯¹,
戴兰宏^{2, 3}

1.
南京理工大学机械工程学院，江苏南京 210094
2.
中国科学院力学研究所非线性力学国家重点实验室，北京 100190
3.
中国科学院大学工程科学学院，北京 101408

基金项目: 国家自然科学基金(11790292，12141202，12002170)

详细信息

作者简介:
侯先苇（1997—　），女，博士研究生，18260081681@163.com

通讯作者:
张先锋（1978—　），男，博士，教授，lynx@njust.edu.cn

中图分类号: O385
计量
- 文章访问数: 538
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- 被引次数: 6
出版历程
- 收稿日期: 2023-05-24
- 修回日期: 2023-08-28
- 网络出版日期: 2023-08-29
- 刊出日期: 2023-09-11

Research progress on impact energy release characteristics of reactive disordered alloy and its application in kill elements

1.
School of Mechanical Engineering, Nanjing University of Science and Technology, Nanjing, Jiangsu 210094, China
2.
State Key Laboratory of Nonlinear Mechanics, Institute of Mechanics, Chinese Academy of Sciences, Beijing 100190, China
3.
School of Engineering Science, University of Chinese Academy of Sciences, Beijing 101408, China

摘要

摘要: 无序合金是一种新型金属材料，突破了传统的合金设计理念，表现出不同于传统合金的优异力学性能、冲击释能及剪切自锐特性，在高温、高压、高应变率等环境具有良好的应用前景。分析活性无序合金的冲击释能特性对其应用于军事领域有着重要的指导作用，能为弹药战斗部的设计提供参考。本文阐述了静动态力学实验中典型无序合金的反应释能现象；总结了撞击速度与活性无序合金释能超压、释能效率之间的关系；讨论了撞击速度、材料破碎程度及靶标特征等因素对活性无序合金释能机理的影响；归纳了制备工艺及元素类型对活性无序合金释能特性的调控效果。进一步，本文梳理了活性无序合金在破片、穿甲弹芯和聚能装药战斗部三个方向的应用研究进展，分析了活性无序合金毁伤元的侵彻行为和作用机制。最后，针对活性无序合金材料未来的发展趋势和需求进行了展望。
- 无序合金 /
- 活性金属 /
- 冲击释能特性 /
- 高效毁伤
Abstract: Disordered alloy is a new kind of reactive material, which breaks through the design concept of traditional alloy and exhibits excellent mechanical properties, impact energy release characteristics and adiabatic shear sensitivity, showing good application prospects in high temperature, high pressure, high strain rates and other application environments. Analyzing the impact energy release characteristics of reactive disordered alloy has an important guiding role for its development in the military field and can provide the basis for the design and application of warheads for ammunition. In this paper, the impact energy release characteristics of reactive disordered alloys are introduced from four aspects, including the energy release phenomenon of chemical reaction, the energy release law induced by impacting, the energy release mechanism and the regulation of the energy release behaviors. The chemical reaction showing energy release phenomenon in static and dynamic mechanical experiments is described. The relationship between impact velocities and the energy release overpressures or the efficiency of energy release of reactive disordered alloys is obtained. The effect between impact velocities and crushing degree of the reactive disordered alloys or characteristics of the target on the energy release mechanism is discussed. At the same time, the regulation effects of preparation process and the kinds of element on energy release effect of disordered alloy materials are summarized. This kind of alloy own good impact energy release characteristics, presented an ideal energetic structural material. Furthermore, the research progress of reactive disordered alloys applied to warheads in military area is summarized from three directions, including fragment, armor-piercing core and shaped charge liner. The macro and micro penetration behavior and mechanism of warheads of reactive disordered alloys are analyzed under high-speed loading conditions. Via the design of the structure, the good penetration and damage performance benefit from the self-sharpening and energy release characteristics of the material. Finally, the further development trend and demands of reactive disordered alloy are prospected.
- disordered alloy /
- reactive metal /
- impact energy release characteristics /
- high efficiency damage

HTML全文

爆炸焊接是一种特殊的爆炸加工技术，在炸药爆轰压力驱动下复板高速冲击碰撞基板，从而使两种不同金属材料焊接复合在一起^[1]。金属爆炸焊接过程涉及炸药爆轰、金属板材高速碰撞和材料塑性变形等，由于历时非常短，一般几十毫秒，实验测试难以捕捉整个爆炸焊接过程。过去几十年，对金属爆炸焊接机理以及技术工艺研究，已有了大量的数值模拟、理论计算和实验工作^[2-3]。工程中，通常采用经验公式设计爆炸焊接参数，或者利用格尼公式、列契特公式等计算复板的飞行姿态和碰撞速度^[4-5]，虽然可以解决一些工程问题，但要深入研究爆炸机理离不开数值模拟。目前，数值模拟仍然以有限元法为主，而爆炸焊接问题相对复杂，涉及炸药爆轰、复板高速冲击基板和金属塑性变形等，必须考虑接触碰撞算法和有限元网格重新划分，如果网格发生畸变和扭曲会造成计算精度和速度严重下降，甚至计算过程终止，特别是复板与基板的厚度相差较大时，还必须考虑二者网格尺度与空间的协调性。

近些年，为了解决有限元法的缺陷与不足，无网格粒子法在爆炸冲击问题中应用比较多。例如：光滑粒子流体动力学法（smoothed particle hydrodynamics, SPH）模拟爆炸焊接界面波、高速碰撞和材料大变形等动力学^[6]。SPH法主要利用核函数在紧支域内进行搜索计算，虽然具有良好的自适应性和灵活性，但是计算规模受到限制，而且在模拟三维问题时计算效率很低。本文中，针对长7.5 m、宽2.15 m的大板幅304L/Q235B金属爆炸焊接，采用物质点法（material point method, MPM）对整个爆炸焊接过程进行三维数值模拟和分析。由数值计算结果，与有限元法或者SPH法以及其他无网格法相比，MPM法在计算规模、数值精度和计算效率等方面都具有比较大的优势。尤其在炸药滑移爆轰作用下金属爆炸焊接的数值计算中，MPM法不仅可避免有限元法因网格畸变而重新划分网格的难题，还可以为爆炸焊接技术工艺参数设计提供依据。

1. 物质点法

物质点法是将欧拉背景网格与拉格朗日粒子单元相互结合的一种数值计算方法，其算法最初在质点网格法（particle in cell, PIC）和流体隐式粒子法（fluent implicit particle, FLIP）基础上发展而来^[7]。

MPM法最重要的特征就是将拉格朗日法和欧拉法结合在一起，粒子单元的数值计算采用显式积分算法求解。建模与有限元法不同，连续介质或离散介质在背景网格内按空间体积划分为粒子单元集合，每个粒子单元都集中了体积、质量、密度、速度和其他材料力学属性，如图1所示。

图 1 背景网格与粒子单元

Figure 1. Background meshes and particles

下载: 全尺寸图片幻灯片

在每一个积分步计算完毕后，背景网格节点参数全部归零，其形状始终保持不变。背景网格还有一个作用，即作为欧拉网格求解运动方程和更新粒子力学参量的中间媒介。MPM法主要用于材料塑性大变形^[8]、炸药爆轰、高速冲击^[9]、流-固耦合分析^[10]以及材料损伤问题的数值计算^[11]。

对于爆炸冲击动力学问题，MPM法主要采用显式积分算法，基本计算过程如下^[12]：（1）定义求解域和划分背景网格；（2）在背景网格内将材料离散为粒子单元，并初始化粒子材料属性和运动参数；（3）求解粒子单元的控制方程（连续质量方程、动量方程和能量方程），然后再施加各种边界条件，更新粒子的速度梯度、应力与应变等。

MPM法的显式积分计算过程与有限元法等类似，都必须满足连续质量方程和动量方程：

$\frac{{d\rho }}{{dt}} + \rho \nabla \cdot {\boldsymbol{v}} = 0$

(1)

$\rho {\boldsymbol{a}}=\nabla \cdot {\boldsymbol{\sigma}}+\rho \boldsymbol{b}$

(2)

式中：t为时间，ρ为材料密度，b为单位体积力，a为加速度，v为速度矢量， $\boldsymbol{\sigma }$ 为柯西应力张量。在MPM法计算前，材料需要离散为 ${N}_{p}$ 个粒子单元，然后定义粒子单元各项参数 $p$ ( $p=\mathrm{1,2},\cdots ,{N}_{p}$ )，即在 $t$ 时刻的质量 ${M}_{p}$ 、密度 ${\rho }_{p}^{t}$ 、坐标 ${\boldsymbol{x}}_{p}^{t}$ 、速度 ${\boldsymbol{v}}_{p}^{t}$ 、柯西应力张量 ${\boldsymbol{\sigma }}_{p}^{t}$ ，在背景网格的计算域内粒子质量是不变的，自然满足连续质量方程(1)。

假设一个试函数 $\boldsymbol{w}$ （类似于有限元形函数），这样动量方程（2）可以变为^[13]：

$\int_\varOmega {\rho {\boldsymbol{w}} \cdot {\boldsymbol{a}}{\text{d}}\varOmega } = - \int_\varOmega {\rho {{\boldsymbol{\sigma }}^{\text{s}}}:\nabla {\boldsymbol{w}}{\text{d}}\varOmega } + \int_{\partial {\varOmega _{\text{c}}}} {\rho {{\boldsymbol{c}}^{\text{s}}} \cdot {\boldsymbol{w}}{\text{d}}S} + \int_\varOmega {\rho {\boldsymbol{w}} \cdot {\boldsymbol{b}}{\text{d}}\varOmega }$

(3)

式中： $\varOmega$ 为当前构形， $\partial {\varOmega }_{\mathrm{c}}$ 为应力边界， ${\boldsymbol{\sigma }}^{\mathrm{s}}$ 为比应力张量（ ${\boldsymbol{\sigma }}^{\mathrm{s}}=\boldsymbol{\sigma }/\rho$ ）， $\boldsymbol{c}$ 为边界应力，并且 ${\boldsymbol{c}}^{\mathrm{s}}=\boldsymbol{c}/\rho$ ，在位移边界试函数 $\boldsymbol{w}$ 为零。这样，集中质量的离散粒子密度可以变成 $\delta$ 函数形式：

$\rho (\boldsymbol{x},t)={\sum }_{p=1}^{{N}_{p}}{M}_{p}\delta (\boldsymbol{x}-{\boldsymbol{x}}_{p}^{t})$

(4)

那么，动量积分方程（3）就可以变成离散粒子单元求和形式：

$\begin{split}{\sum }_{p=1}^{{N}_{p}}\left({M}_{p}\boldsymbol{w}(\boldsymbol{x}_{p}^{t},t)\cdot \boldsymbol{a}(\boldsymbol{x}_{p}^{t},t)\right)=&-{\sum }_{p=1}^{{N}_{p}}\left({M}_{p}{\boldsymbol{\sigma }}^{{\rm{s}}}(\boldsymbol{x}_{p}^{t},t):{\left.\nabla \boldsymbol{w}(\boldsymbol{x},t)\right|}_{\boldsymbol{x}_{p}^{t}}\right)+\\ &{\sum }_{p=1}^{{N}_{p}}\left({M}_{p}\boldsymbol{w}(\boldsymbol{x}_{p}^{t},t)\cdot {\boldsymbol{c}}^{{\rm{s}}}(\boldsymbol{x}_{p}^{t},t)/h\right)+{\sum }_{p=1}^{{N}_{p}}\left({M}_{p}\boldsymbol{w}(\boldsymbol{x}_{p}^{t},t)\cdot \boldsymbol{b}(\boldsymbol{x}_{p}^{t},t)\right) \end{split}$

(5)

式中： $h$ 为边界层的厚度。粒子单元参量通过形函数按比例映射到背景网格节点上，假设背景网格节点参量为 ${\boldsymbol{r}}_{i}^{t}$ （ $i={1,2},\cdots ,{N}_{n}$ ），分别代表坐标 ${\boldsymbol{x}}_{i}^{t}$ 、位移 ${\boldsymbol{u}}_{i}^{t}$ 、速度 ${\boldsymbol{v}}_{i}^{t}$ 、加速度 ${\boldsymbol{a}}_{i}^{t}$ 和试函数 ${\boldsymbol{w}}_{i}^{t}$ 等参数，则计算公式为：

$\boldsymbol{r}_{p}^{t}={\sum }_{i=1}^{{N}_{n}}{\boldsymbol{r}}_{i}^{t}{N}_{i}\left(\boldsymbol{x}_{p}^{t}\right)$

(6)

然后，将背景网格节点参量值代入式(5)：

${\sum }_{i=1}^{{N}_{n}}{\boldsymbol{w}}_{i}^{t}\cdot {\sum }_{j=1}^{{N}_{n}}{m}_{ij}^{t}{\boldsymbol{a}}_{j}^{t}=-{\sum }_{i=1}^{{N}_{n}}{\boldsymbol{w}}_{i}^{t}\cdot {\sum }_{p=1}^{{N}_{p}}{M}_{p}{\boldsymbol{\sigma }}_{p}^{\mathrm{s},t}\cdot {\left.\nabla {N}_{i}\left(\boldsymbol{x}\right)\right|}_{{\boldsymbol{x}}_{p}^{t}}+{\sum }_{i=1}^{{N}_{n}}{\boldsymbol{w}}_{i}^{t}\cdot ({\boldsymbol{c}}_{i}^{t}+{\boldsymbol{b}}_{i}^{t})$

(7)

${m}_{ij}^{t}={\sum }_{p=1}^{{N}_{p}}{M}_{p}{N}_{i}\left({\boldsymbol{x}}_{p}^{t}\right){N}_{j}\left({\boldsymbol{x}}_{p}^{t}\right)$

(8)

${\boldsymbol{c}}_{i}^{t}={\sum }_{p=1}^{{N}_{p}}{M}_{p}{\boldsymbol{c}}_{p}^{{\rm{s}},{t}}{N}_{i}\left({\boldsymbol{x}}_{p}^{t}\right)/h$

(9)

${\boldsymbol{b}}_{i}^{t}={\sum }_{p=1}^{{N}_{p}}{M}_{p}\boldsymbol{b}({\boldsymbol{x}}_{p}^{t},t){N}_{i}\left({\boldsymbol{x}}_{p}^{t}\right)$

(10)

那么，消掉积分求和式(7)两边的试函数，得到：

${\sum }_{j=1}^{{N}_{n}}{m}_{ij}^{t}{\boldsymbol{a}}_{j}^{t}=({\boldsymbol{f}}_{i}^{t}{)}^{\mathrm{i}\mathrm{n}\mathrm{t}}+({\boldsymbol{f}}_{i}^{t}{)}^{\mathrm{e}\mathrm{x}\mathrm{t}}$

(11)

分别计算内部力和外部力：

$({\boldsymbol{f}}_{i}^{t}{)}^{\mathrm{i}\mathrm{n}\mathrm{t}}=-{\sum }_{p=1}^{{N}_{p}}{M}_{p}{\boldsymbol{\sigma }}_{p}^{\mathrm{s},t}\cdot {\left.\nabla {N}_{i}\right|}_{{\boldsymbol{x}}_{p}^{t}}$

(12)

$({f}_{i}^{t}{)}^{\mathrm{e}\mathrm{x}\mathrm{t}}={b}_{p}^{t}+{c}_{p}^{t}$

(13)

这样，就形成了一个对角质量矩阵，式(8)和(10)变成：

${m}_{i}^{t}={\sum }_{p=1}^{{N}_{p}}{M}_{p}{N}_{i}\left({\boldsymbol{x}}_{p}^{t}\right)$

(14)

${b}_{i}^{t}={m}_{i}^{t}b({\boldsymbol{x}}_{p}^{t},t)$

(15)

式(11)变成：

${m}_{i}^{t}{\boldsymbol{a}}_{i}^{t}=({\boldsymbol{f}}_{i}^{t}{)}^{\mathrm{i}\mathrm{n}\mathrm{t}}+({\boldsymbol{f}}_{i}^{t}{)}^{\mathrm{e}\mathrm{x}\mathrm{t}}$

(16)

最后，通过材料本构模型计算每个粒子单元的应力与应变。应力增量为：

${{\Delta }\boldsymbol{\sigma }}_{p}^{t+\mathrm{\Delta }t}=\boldsymbol{E}:{\mathrm{\Delta }{\boldsymbol{\varepsilon}} }_{p}^{t+{\Delta }t}$

(17)

粒子单元在当前时刻应力为：

${\boldsymbol{\sigma }}_{p}^{t+\mathrm{\Delta }t}={\boldsymbol{\sigma }}_{p}^{t}+\mathrm{\Delta }{\boldsymbol{\sigma }}_{p}^{t+\mathrm{\Delta }t}$

(18)

式中：E为切线刚度张量。

当完成一个时间步长积分计算后，背景网格重构，即网格节点参量归零，然后再重复下一个积分步长计算，直到完成所有时间步长的计算。

2. 计算模型

2.1 前处理建模

在实际爆炸焊接工程中，要实现两块不同金属板材的全面积焊接复合，通常应用炸高（金属支架）将复板与基板保持一定间距平行布置，然后在复板上表面均匀地铺装炸药，装药厚度与爆炸焊接窗口和复板材料属性有关。对于长度大于5 m金属板材的爆炸焊接，一般都采用中心起爆方式，即雷管置于板面中间位置，这样有利于提高爆炸复合质量，如图2所示。

图 2 爆炸焊接布置

Figure 2. Distribution pattern of explosive welding

下载: 全尺寸图片幻灯片

本文中，爆炸焊接模拟源于实际项目。炸药为铵油，装药厚度为30 mm，现场测量该厚度炸药的密度ρ为608 kg/m³，爆速仪测得爆速为2 500 m/s；复板材料为304L不锈钢，密度为7 930 kg/m³，板面尺寸为4 mm×2 150 mm ×7 500 mm；基板为Q235B碳钢板，密度为7 850 kg/m³，板面尺寸为25 mm×2 500 mm ×7 500 mm；基板和复板间在爆炸焊接前需要保持一定的间隙，设计炸高为8 mm。

采用物质点法前处理软件WPM（无极粒子建模软件）对炸药、复板和基板进行粒子单元剖分。背景网格单元数量为100×200×100，背景网格单元大小为4 mm，在每个背景网格单元中布置8个物质点，其中炸药质点的数量为430 560，复板质点数量为53 820，基板质点数量为349 830。计算模型的前处理结果如图3所示。

图 3 爆炸焊接前处理模型

Figure 3. The preprocessing models for explosive welding

下载: 全尺寸图片幻灯片

在构建三维爆炸焊接前处理模型时，需注意炸药和金属板材粒子单元的划分密度，通常每个背景网格内设置8个粒子。虽然增加粒子数量，可以在一定程度上提高计算精度，但也会降低数值计算效率。因此，前处理建模要定义适当的粒子单元数量，这样才能获得较理想的计算结果。

2.2 材料模型

2.2.1 复板与基板金属塑性模型

为了实现爆炸焊接三维数值模拟，先构建炸药爆轰及其传播的计算模型。爆炸焊接一般都使用铵油炸药，铵油属于非标准中低爆速炸药，因此爆轰产物状态方程可以应用JWL状态方程，也可以采用：

$p = (\gamma - 1)\rho e$

(19)

式中：p为爆轰压力，经过爆轰实验测定，铵油炸药的多方指数γ=2.0，铵油的比内能e=3.8 MJ/kg。该爆轰状态方程在计算中低爆速炸药的爆轰问题时经常采用，能比较准确地计算出爆轰压力。

在计算炸药爆轰过程中，为使炸药的化学反应和燃烧过程持续地传播下去，MPM法的数值计算中还要定义炸药化学反应率方程，并与爆轰产物状态方程相结合来计算爆轰压力。一般常用的炸药反应率函数使用Wilkins函数：

${F_{}} = \left\{ \begin{array}{*{20}{l}} {\text{0}}&\quad t \text{＜} {t_{\text{b}}} \\ ({{t - {t_{\text{b}}}}})/{{{{\Delta }}L}} &\quad {t_{\text{b}}} \text{≤} t \text{≤} {t_{\text{b}}} + \Delta L \\ {\text{1}} &\quad t \text{＞} {t_{\text{b}}} + \Delta L \end{array} \right.$

(20)

式中：燃烧函数因子F=0～1.0，为表征炸药已经完成爆轰反应的比例系数；t为当前积分步长的计算时间，t_b为爆轰波到达未起爆炸药粒子的时刻，即炸药粒子开始点燃起爆的时间；ΔL=r_bA_e/(v_dL_e,max)，L_e,max和A_e分别为炸药粒子所在的背景网格单元的最大边长和面积，v_d为炸药爆速，参数r_b=3.0～6.0，用于控制炸药燃烧过程。燃烧函数描述了炸药爆轰3个不同区间，分别是炸药未起爆凝固区、爆轰反应过渡区和爆轰气体产物区。

应用燃烧函数，将未起爆炸药与爆轰产物状态方程结合，获得炸药爆轰方程：

$p = p(\rho ,e)F$

(21)

为了模拟炸药粒子持续的爆轰传播过程，在起爆点附近定义炸药粒子的F为1.0，其他炸药粒子的初始F都为0。当炸药起爆粒子单元被定义和初始化后，接下来就可以应用MPM法对炸药爆轰过程进行三维数值模拟。

2.2.2 复板与基板材料模型

复板材料为304L、基板材料为Q235B，爆炸焊接整个过程历时较短，复板与基板的接触碰撞时间为微秒范围，可以认为是绝热过程，数值计算不考虑材料热传导效应。与有限元法类似，MPM法计算必须定义材料模型。为了描述基板和复板金属材料的塑性变形，材料模型均采用Johnson-Cook塑性模型，该模型能够很好地描述金属应变率效应和塑性大变形过程，普遍用于计算金属锻压、塑性大变形和高速碰撞等。Johnson-Cook材料模型为：

$J = (A + B{(\varepsilon _{\text{e}}^{\text{p}})^n})(1 + C\ln {\dot \varepsilon ^*})$

(22)

式中：J为von Mises流动应力，A为材料屈服强度， $\varepsilon _{\text{e}}^{\text{p}}$ 为等效塑性应变， $B$ 、 $n$ 为与材料应变硬化相关的参数， $C$ 为材料应变率相关系数， ${\dot{\varepsilon }}^{*}={\dot{\varepsilon }}_{\text{e}}^{\text{p}}/{\dot{\varepsilon }}_{0}$ ， $\dot{\mathit{\varepsilon }}$ 为相对等效塑性应变率，当 ${\dot \varepsilon ^*} = 1.0$ 时意味着材料流动应力与塑性应变率无关。复板和基板材料模型参数^[14-15]见表1。

表 1 304L/Q235B材料模型参数^[14-15]

Table 1. Material parameters for 304L/Q235B^[14-15]

材料	ρ/(kg·m⁻³)	E/GPa	v	A/MPa	B/MPa	n	C	$\dot{{\varepsilon }_{0}}$ /s⁻¹
Q235B	7 850	210	0.3	380	275	0.36	0.022	0.001
304L	7 930	200	0.3	270	350	0.65	0.070	0.001

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| 显示表格

3. 三维模拟

爆炸焊接计算模型经过前处理粒子单元划分以及不同部件所定义的材料模型，以施加中间起爆点作为初始条件，不考虑空气以及爆炸复合后与地面的接触碰撞过程，并认为爆炸焊接是在绝热条件下，求解过程不使用能量方程。

将前处理模型输入到MPM法求解器中进行计算，设置积分时间步长为0.001 ms，计算总时间为1.0 ms，计算步长总数为1 000。分别得到爆炸焊接的全过程、等效塑性应变场、复板与基板碰撞速度场等模拟结果。

（1）爆炸焊接全过程模拟是对304L/Q235B爆炸焊接板面中间起爆的炸药滑移爆轰、复板与基板高速碰撞变形和两金属板材复合的整个动态过程进行模拟，如图4所示。

图 4 爆炸焊接全过程的模拟

Figure 4. Simulation of the whole process of explosive welding

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（2）为了评估分析爆炸焊接复合板塑性变形量大小，模拟基板与复板在不同时刻的有效塑性应变结果。关于有效塑性应变场变化，如图5所示。

图 5 金属板材的有效塑性应变

Figure 5. Effective plastic strains of the metal plates

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（3）在双金属爆炸焊接中，复板与基板的碰撞速度直接影响着复合板界面结合强度和爆炸复合率，复板和基板在垂直方向的碰撞速度如图6所示。

图 6 金属板材的碰撞速度

Figure 6. Impact velocities of the metal plates

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4. 讨论分析

在炸药爆轰压力驱动下，复板高速碰撞基板使两种金属界面材料发生微熔和塑性流动，从而形成界面波并焊接复合在一起。由塑性应变和碰撞速度模拟结果（见图5～6），随着爆轰波持续地滑移推进，炸药爆轰压力和爆轰波沿着板面以近似圆形曲面形式向前持续传播与推压；而由爆炸焊接实验后的复合板面表观看，复板与基板的板面在滑移爆轰压力作用下发生比较大的塑性弯曲变形以及板材边缘材料损伤撕裂等现象，如图7～8所示。

图 7 爆炸焊接的304L/Q235B复合板

Figure 7. An explosive-welded 304L/Q235B plate

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图 8 爆炸焊接的304L/Q235B复合板边缘

Figure 8. Edge of the explosive-welded 304L/Q235B plate

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比较爆炸焊接实验后的复合板与数值模拟结果（见图4～6），可见MPM法的数值模拟结果与爆炸焊接实验复合板的板形和边缘破损现象基本符合。

接着，分析爆炸焊接的复板与基板的碰撞速度v_p 。这是一个重要的参数，确定了v_p就可以设计炸药爆速、装药厚度和炸高等。由于爆炸焊接实验测试碰撞速度v_p比较困难，为了验证MPM法的三维数值模拟精度，在MPM法数值模拟结果中选择复合板中间的粒子单元，提取复板在0～8 mm间距范围的碰撞速度v_p，同时采用Richter公式对复板飞行姿态进行计算，得到在垂直方向不同位移下的弯折角。计算公式为^[1]：

$y=\delta (1+\gamma )\frac{{\theta }_{\mathrm{max}}}{R}{\displaystyle {\int }_{0}^{\theta }\frac{\text{sin}\theta }{{\theta }_{\mathrm{max}}-\theta }\text{d}\theta }$

(23)

$x=\delta (1+\gamma )\frac{{\theta }_{\mathrm{max}}}{R}{\displaystyle {\int }_{0}^{\theta }\frac{\text{cos}\theta }{{\theta }_{\mathrm{max}}-\theta }\text{d}\theta }$

(24)

式中： y为复板在垂直方向上的位移，x为水平方向坐标，θ为复板弯折角，θ_max为复板最大弯折角，R为质量比，γ为炸药多方指数，δ 为炸药装药厚度。复板最大弯折角θ_max 和质量比R倒数有线性关系：

$\frac{1}{{{\theta _{\max }}}} = {k_1} + \frac{{{k_2}}}{R}$

(25)

${k_1} = \frac{{\sqrt 3 }}{{4\sqrt {(1 - {{\sqrt {{\gamma ^2} - 1} } \mathord{\left/ {\vphantom {{\sqrt {{\gamma ^2} - 1} } \gamma }} \right. } \gamma })} }}$

(26)

${k_2} = \frac{{\sqrt {3({\gamma ^2} - 1)} }}{{2\gamma \sqrt {1 - {{\sqrt {{\gamma ^2} - 1} } \mathord{\left/ {\vphantom {{\sqrt {{\gamma ^2} - 1} } \gamma }} \right. } \gamma }} }}$

(27)

为了求解Richter公式，采用复化Simpson积分算法获得在复板y方向不同位移的弯折角θ后，通过爆速v_d和弯折角θ得到碰撞速度v_p的理论值：

${v_{\text{p}}} = 2{v_{\text{d}}}\sin({\theta \mathord{\left/ {\vphantom {\theta 2}} \right. } 2})$

(28)

这样，就可以由MPM法的数值计算和Richter公式所得到的数据，得到复板向下飞行速度的变化曲线，如图9所示。

图 9 复板的碰撞速度曲线

Figure 9. Impact velocity curves of the clad plate

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MPM法和Richter公式两种方法，在y方向位移4 mm处的碰撞速度分别为348和399 m/s，在8 mm处分别为401和438 m/s，两者相差30～50 m/s，MPM法的数值偏小一些。这是由于两种计算复板飞行速度的算法不同，Richter公式针对二维理想爆轰条件下复板飞行姿态算，并且不考虑与基板碰撞，而采用显式积分算法的MPM法对炸药爆轰驱动复板碰撞基板的整个过程进行三维数值计算。尽管这两种计算方法得到的曲线有所差别，但还在合理范围，两条数据曲线所描述的复板运动在1~4 mm加速段和4 mm后等速段的变化趋势也一致。

通过金属爆炸焊接304L/Q235B的MPM法模拟与实验后的板形及碰撞速度计算曲线对比可知，MPM法数值计算与实验和理论计算结果基本一致，由此也验证了MPM法的数值模拟具有一定的可靠性和参考性。此外，本文中MPM法数值模拟在绝热条件下计算，并未考虑材料热传导问题。因为金属爆炸焊接在碰撞复合界面的材料会发生塑性流动变形和温度瞬间升高的现象，并形成高速金属微射流和复合界面波。这个过程就需要重新构建爆炸焊接局部细观模型，才能应用MPM法进行温度与微射流的模拟计算。

5. 结　论

在大面积金属板材304L/Q235B爆炸焊接实际生产中，除了重点考虑如何确定炸药、间距、碰撞速度等参数，还需注意爆炸复合板可能产生的缺陷。对于产生缺陷的部位和原因，除了通过实验分析，还需数值模拟进一步研究，结合数值模拟与实验并采取有效的技术措施，这样有利于提高爆炸复合板材生产加工质量。

基于爆炸焊接复合板的变形、塑性应变和碰撞速度等三维数值模拟结果可知，在板面中间位置起爆，初始时刻的炸药爆轰处于不稳定状态，起爆点位置可能出现板材结合强度较低的现象。为了避免这个问题，需保证该处装药密度的均匀性，并在起爆点位置适当增加高爆速炸药，以提高雷管的起爆能量。从爆炸复合板整体变形的数值模拟结果来看，复板周边材料出现了撕裂破损现象，这是由于炸药爆轰波在传播到边界处所形成的稀疏波（拉伸波）导致复板周边材料的断裂破损，尤其在复板前后两个短边和直角位置更明显。为了解决这个问题，可以适当增加复板长度和宽度，使炸药边界尺寸延伸，从而降低炸药爆轰稀疏波的拉伸作用，有效地避免该缺陷的产生。

综上所述，对于大面积金属爆炸焊接过程的三维模拟分析，MPM法是一种有效的数值方法。与有限元等其他计算方法相比，MPM法在求解爆炸冲击动力学问题中表现了比较突出的优势，是一种值得深入开发的无网格粒子法。

图 1 室温下空气中测试的锆基非晶合金试样断裂瞬间^[19]

Figure 1. Moment of fracturing a BAA specimen testedat room temperature in air^[19]

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图 2 摆锤冲击试验装置及空气环境中试验现象^[20]

Figure 2. Pendulum impact test device and test phenomena in air environment^[20]

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图 3 Zr_41.2Ti_13.8Cu_12.5Ni₁₀Be_22.5分子轨道能级谱^[20]

Figure 3. Molecular orbital energy spectrum of Zr_41.2Ti_13.8Cu_12.5Ni₁₀Be_22.5^[20]

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图 4 氮气环境中断裂后断口扫描电镜照片^[20]

Figure 4. Scanning electron microscope photos of fracture surface of the specimen fracturing in nitrogen environment^[20]

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图 5 准密闭容器试验^[25]

Figure 5. Quasi-sealed chamber test^[25]

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图 6 高速摄影图片及容器内超压时程曲线^[26]

Figure 6. Video frames and pressure curves inside the chamber^[26]

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图 7 破片撞击靶板后反应产物形貌与成分^[26]

Figure 7. Morphology and composition of the reaction products of fragment after impacting target^[26]

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图 8 高熵合金破片不同撞击速度下压力峰值^[33]

Figure 8. Peak overpressures at different impact velocities of the high-entropy alloy fragments^[33]

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图 9 多种活性材料的单位质量能量密度^[34]

Figure 9. Specific energy per unit mass of various reactive materials^[34]

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图 10 锆基非晶合金动态压缩高速摄影图像^[37]

Figure 10. High-speed photography of Zr-based amorphous alloy under dynamic compression^[37]

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图 11 锆基非晶合金动态压缩模拟损伤云图^[37]

Figure 11. Simulational damage contours of Zr-based amorphous alloy under dynamic compression^[37]

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图 12 氩气中不同撞击速度下动态破碎锆基非晶合金累积质量分布试验数据^[38]

Figure 12. Experimental data of cumulative mass distribution forZr-based amorphous alloy after dynamic fragmentation atdifferent impact velocities in argon atmosphere^[38]

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图 13 TiZrNbV高熵合金动态压缩背散射电子成像结果^[40]

Figure 13. BSE result of TiZrNbV high entropy alloy after dynamic compression^[40]

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图 14 不同撞击速度下回收试样的断口形貌^[40]

Figure 14. Fracture morphology of recovered specimen at different impact velocities^[40]

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图 15 原位晶化对锆基非晶合金能量释放行为的影响^[45]

Figure 15. Effect of in-situ crystalline phases on the energy release behaviors of Zr-based amorphous alloy^[45]

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图 16 NbZrTiTa高熵合金和HfZrTiTa_0.53合金弹丸在不同速度下撞击靶箱后的碎片^[50]

Figure 16. The fragments of NbZrTiTa high-entropy alloy and HfZrTiTa_0.53 high-entropy alloy projectilesimpacting the target at different velocities^[50]

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图 17 1200 m/s速度下NbZrTiTa高熵合金弹丸碎片的截面背散射电子成像^[50]

Figure 17. Cross-section BSE photos of NbZrTiTa high-entropy alloy projectile at 1200 m/s^[50]

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图 18 0.5 mm厚的盖板下破片不同撞击速度对应的压力-时间的曲线^[60]

Figure 18. Pressure as a function of time for a 0.5 mmcover target thicknesses^[60]

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图 19 不同靶板厚度下不同撞击速度对应的超压-时间曲线^[60]

Figure 19. Overpressure as a function of time for differentcover plate at different impact velocities^[60]

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图 20 超压-反应速率曲线^[60]

Figure 20. Reaction efficiency as a function of shock pressure^[60]

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图 21 冲击温度-反应速率曲线^[60]

Figure 21. Reaction efficiency as a function of shock temperature^[60]

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图 22 Zr₅₅Cu₃₀Ni₅Al₁₀非晶合金破片典型速度撞击间隔靶板高速摄影图片^[71]

Figure 22. High-speed photographs of Zr₅₅Cu₃₀Ni₅Al₁₀ amorphous fragments impacting spacing targets at typical velocity^[71]

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图 23 WFeNiMo高熵合金在不同速度下穿靶燃烧过程的高速摄影^[72]

Figure 23. High-speed video frames of combustion process of WFeNiMo HEA at different speeds^[72]

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图 24 高速撞击后高熵合金回收破片细观结构^[72]

Figure 24. Microstructure of high-entropy alloy fragments after high speed impact^[72]

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图 25 非晶破片毁伤后效仿真结果^[73]

Figure 25. Simulation results of amorphous fragmentation damage aftermath^[73]

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图 26 W/Zr基非晶合金预制破片^[11]

Figure 26. W/Zr-based amorphous alloy fragments^[11]

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图 27 预制破片布置方式^[11]

Figure 27. Arrangement of performed fragments^[11]

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图 28 典型时刻高速摄影图片^[11]

Figure 28. High-speed photographs at typical moments^[11]

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图 29 棉被和油箱毁伤情况^[11]

Figure 29. The damage of quilts and fuel tanks^[11]

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图 30 破片侵彻后油箱^[11]

Figure 30. The oil tank penetrated by fragments^[11]

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图 31 复合材料弹芯的“自锐”和钨合金弹芯的“镦粗”^[77]

Figure 31. “Self-sharpening” of composite core and the “upsetting” of tungsten alloy core^[77]

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图 32 弹芯残体照片^[82]

Figure 32. Pictures of penetrator residual^[82]

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图 33 钨丝/锆基非晶复合材料侵彻深度与着靶动能及长径比的关系曲线^{[80, 86]}

Figure 33. Curves of kinetic energy and penetration depth of Wf/Zr-MG and WHA rods^{[80, 86]}

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图 34 不同直径钨丝/锆基非晶复合材料着靶速度-侵彻深度关系^[86]

Figure 34. Relationship between penetration depth and impact velocities of different Zr-based composite materials^[86]

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图 35 多组分钨丝/锆基非晶合金复合材料杆弹横截面^[86]

Figure 35. The cross section of multi-component Wf/Zr-based amorphous composite rod projectiles^[86]

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图 36 分段式钨丝/锆基非晶合金复合材料杆弹及侵彻结果（单位：mm）^[86]

Figure 36. Segmented Wf/Zr-based amorphous composite rod projectiles and penetration results (unit: mm)^[86]

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图 37 弹体侵彻靶体的高速摄像^[88]

Figure 37. High-speed video photographs of the projectiles penetrating the targets^[88]

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图 38 长杆弹侵彻深度和撞击动能的关系^[88]

Figure 38. Relation between penetration depth and kineticenergy of long rod projectiles^[88]

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图 39 长杆弹弹孔体积和撞击动能的关系曲线^[88]

Figure 39. Relation between total penetration volume and kinetic energy of long rod projectiles^[88]

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图 40 弹体侵彻靶板典型过程^[89]

Figure 40. Typical frames of the projectiles penetrating the targets^[89]

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图 41 弹体侵彻后靶板表面毁伤效果^[89]

Figure 41. The targets damaged surface after the projectiles penetrating^[89]

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图 42 钨丝/锆基非晶合金复合材料自锐剪切失效的 4 种模式^[81]

Figure 42. Four modes of self-sharpening shear failure of Wf/Zr-based amorphous composites material^[81]

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图 43 钨丝增强金属玻璃复合材料弹残余弹体头部及其附近位置 SEM 图像^[79]

Figure 43. SEM images of tungsten wire reinforced metal glass composite residual projectile head and its vicinity^[79]

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图 44 回收弹体TEM测试结果^[90]

Figure 44. Transmission electron microscope (TEM) bright-field images of LRPs after impact^[90]

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图 45 回收弹体TEM明图中的变形孪晶和堆叠断层^[90]

Figure 45. TEM results showging the multiple deformation twins and the stack faults^[90]

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图 46 钨丝/锆基非晶合金复合材料杆弹不同着靶速度下的侵彻断裂模式^[86]

Figure 46. Fracture modes of Wf/Zr-based amorphous composite projectile at different impact velocities^[86]

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图 47 WFeNiMo和93W长杆弹对靶体的侵彻深度与动能关系^[9]

Figure 47. Depth of WFeNiMo rod and 93W rod penetrating targets versus kinetic energy^[9]

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图 48 等截面直管内两相的流动模型^[91]

Figure 48. Model of two-phase flow in a straight pipe with equal cross section^[91]

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图 49 不同初始浓度及密度对硬相浓度演化的影响^[91]

Figure 49. Effect of initial concentration on concentration evolution of hard phase^[91]

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图 50 Zr₅₇Cu_15.4Ni_12.6Al₁₀Nb₅非晶合金射流成型形态^[95]

Figure 50. Shape of Zr₅₇Cu_15.4Ni_12.6Al₁₀Nb₅ jet forming^[95]

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图 51 Zr_41.2Ti_13.8Cu_12.5Ni₁₀Be_22.5非晶合金射流成型形态^[96]

Figure 51. Shape of Zr_41.2Ti_13.8Cu_12.5Ni₁₀Be_22.5 jet forming^[96]

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图 52 塑性和脆性药型罩形成的射流^[98]

Figure 52. Jets by plastic and brittle liner^[98]

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图 53 两种材料杆式射流不同时刻下的成形状态^[99]

Figure 53. Shape of rod jets about two materials at different times^[99]

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图 54 CrMnFeCoNi与紫铜材料流动速度（V₂）与临界压垮角（β_c）关系^[100]

Figure 54. Relationship between flow velocity (V₂) and critical crushing angle (β_c) of CrMnFeCoNi and copper^[100]

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图 55 材料流动速度（V₂）与临界压垮角（β_c）曲线不同取值位置有限元仿真结果^[100]

Figure 55. Finite element simulation results of value positions of flow velocity (V₂) and critical crushing angle (β_c) curve^[100]

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图 56 不同硬化指数k下射流形态对比^[100]

Figure 56. Comparison of jet shape under different hardening index (k)^[100]

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图 57 不同炸高下药型罩侵彻深度^[105]

Figure 57. Penetration depths of liners under different stand off^[105]

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图 58 数值模拟模型及成型射流^[12]

Figure 58. Model and jet structure of numerical simulation^[12]

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图 59 聚能装药结构^[109]

Figure 59. Shaped charge^[109]

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图 60 靶板截面形貌和晶相^[12]

Figure 60. Cross-section profile and crystal phase of target plate^[12]

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图 61 残余射流区的XRD谱^[12]

Figure 61. XRD spectrum of residual zone^[12]

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图 62 残余射流区的EDS谱^[12]

Figure 62. EDS spectrum of residual zone^[12]

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图 63 射流侵彻后靶板的EBSD细观分析：(a)变形区IPF图；(a)中区域b的（b₁、b₂）IPF图和对应的KAM图；(a)中区域c的(c₁, c₂) IPF图和对应的KAM图^[113]

Figure 63. Microstructural analysis of the residual jet after penetration via EBSD: (a) IPF map of deformation zone; (b₁, b₂) IPF map and corresponding KAM map of region b in (a); (c₁, c₂) IPF map and corresponding KAM map of region c in (a)^[113]

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图 64 再结晶区的高倍BSE-SEM图像(a)及线扫描分析(b)：在(a)中显示的两个晶界上进行线扫描，其对应的位置在(b)中用虚线标记^[113]

Figure 64. High-magnification BSE-SEM images (a) and line scan analysis (b) of the recrystallization region: a line scan was conducted across two grain boundaries as displayed in (a), the corresponding locations of which are labeled with dashed lines in (b)^[113]

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图 65 CoCrNi残余射流侵彻后的TEM组织分析：(a) CoCrNi残余射流的TEM照片，其中的白色虚线标记了沿晶界的纳米尺寸沉淀；(b) 降水（图(a)中的红色矩形区域）的HAADF-TEM照片；(c～e) 图(b)中对应的Co、Cr、Ni元素分布；(f) 降水SAED图（区域I(b)），(g) 图(b)中Ⅰ，Ⅱ，Ⅲ，Ⅳ区域Co，Cr，Ni元素含量^[113]

Figure 65. Microstructural analysis of CoCrNi residual jet after penetration by TEM: (a) TEM images of CoCrNi residual jet, where the white dashed line marks the nanosized precipitations along grain boundaries; (b) HAADF-TEM image of the precipitation (red rectangle region in (a)); (c–e) Corresponding element distributions of Co, Cr, and Ni in (b); (f) SAED pattern ofprecipitation (region I in (b)); (g) Element content of Co, Cr, and Ni in region I, II, III, IV in (b)^[113]

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表 1 锆基非晶合金的冲击化学反应行为^[36]

Table 1. Impact-induced chemical reaction behavior of ZrTiNiCuBe^[36]

射击序号	靶板厚度/mm	撞击速度/（m·s⁻¹）	超压峰值/MPa	扩孔半径/mm	挠度/mm
1	3	1450	0.02	7～10	10～15
2	3	1560	0.04	10～15	15～20
3	2	1348	0.05	20～25	20～25
4	2	1218	0.024	8～12	10～15
5	4.5	1630	0.021	7～10	8～10

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1. 董鹏飞，梁增友，邓德志，郝永强，乔炳旭. 管–管板爆炸焊接中圆管膨胀规律. 焊接. 2023(02): 38-43 . 百度学术
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1. 物质点法
2. 计算模型
2.1 前处理建模
2.2 材料模型
3. 三维模拟
4. 讨论分析
5. 结　论

活性无序合金冲击的释能特性及在毁伤元中应用研究进展

doi: 10.11883/bzycj-2023-0189

作者简介: 侯先苇（1997— ），女，博士研究生，18260081681@163.com

通讯作者: 张先锋（1978— ），男，博士，教授，lynx@njust.edu.cn

计量

出版历程

Research progress on impact energy release characteristics of reactive disordered alloy and its application in kill elements

1. 物质点法

2. 计算模型

2.1 前处理建模

2.2 材料模型

2.2.1 复板与基板金属塑性模型

2.2.2 复板与基板材料模型

3. 三维模拟

4. 讨论分析

5. 结 论

期刊类型引用(1)

其他类型引用(5)

计量

出版历程

目录

1. 物质点法

2. 计算模型

2.1 前处理建模

2.2 材料模型

3. 三维模拟

4. 讨论分析

5. 结 论

作者简介:
侯先苇（1997—　），女，博士研究生，18260081681@163.com

通讯作者:
张先锋（1978—　），男，博士，教授，lynx@njust.edu.cn

5. 结　论

5. 结　论