高速冲击表面处理对金属材料力学性能和组织结构的影响

高玉魁; 陶雪菲

doi:10.11883/bzycj-2020-0342

高速冲击表面处理对金属材料力学性能和组织结构的影响

doi: 10.11883/bzycj-2020-0342

高玉魁^{1, 2,},
陶雪菲³

1.
同济大学材料科学与工程学院，上海 201804
2.
上海市金属功能材料开发应用重点实验室，上海 201804
3.
同济大学航空航天与力学学院，上海 200092

详细信息

作者简介:
高玉魁（1973－　），男，博士，教授，ykgao12088@126.com

中图分类号: O347.3; TB31
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- 被引次数: 3
出版历程
- 收稿日期: 2020-09-22
- 修回日期: 2020-11-21
- 网络出版日期: 2021-03-18
- 刊出日期: 2021-04-14

A review on the influences of high speed impact surface treatments on mechanical properties and microstructures of metallic materials

GAO Yukui^{1, 2
,},
TAO Xuefei³

1.
School of Materials Science and Engineering, Tongji University, Shanghai 201804, China
2.
Shanghai Key Laboratory od R&D for Metallic Function Materials, Shanghai 201804, China
3.
School of Aerospace Engineering and Applied Mechanics, Tongji University, Shanghai 200092, China

摘要

摘要: 高速冲击表面处理过程中的应变率对金属材料的宏观力学性能和微观组织结构都具有重要影响。根据当前应变率效应的研究成果，从宏观与微观相结合的角度出发，综述了高速冲击表面处理过程中应变率对金属材料强度和塑性的影响规律，并重点阐述了不同应变率下金属材料内部微观组织结构的演变规律，主要包括晶粒结构、绝热剪切带、相变、位错组态和析出相以及变形孪晶等。此外，还分析了组织结构随应变率的演化和微观变形机制的转变对材料力学性能的强化和弱化机理。最后，对高速冲击表面处理梯度组织的变形特点进行了总结。提出了不同组织结构对材料性能影响的综合效应模型，以期为应变率效应的深入研究奠定基础。
- 高速冲击表面处理 /
- 金属材料 /
- 应变率效应 /
- 力学性能 /
- 微观组织结构
Abstract: The strain rate during the process of high speed impact surface treatments has a significant effect on the mechanical properties as well as the microstructures of metallic materials. In this paper, the effects of strain rate during the process of high speed impact surface treatments on the variation of both strength and ductility of metallic materials are reviewed from macroscopic and microscopic prospective based on the current research achievements. The emphases are concentrated on the microstructural evolution under various strain rates, including grain structures, adiabatic shear bands, phases, dislocation structures, precipitates and deformation twins. At relatively low strain rates, grains tend to be elongated with respect to the loading direction, and they may be refined when the strain increases to a certain extent. In comparison, with the increment of strain rates, the free path of dislocation motion is remarkably reduced so that grains can be further refined to consume the impact energy and dislocations are multiplied significantly. However, the relatively high strain rates may also bring about adiabatic temperature rise and frictional heat, which may give rise to dynamic recovery and recrystallization in some materials so that the dislocation density would in turn be reduced. Moreover, precipitates can be formed and they may interact with dislocations owing to the combined effects of high strain rates and temperature rise. When the strain rates increase to the extremely high level, the movement of dislocations may be inhibited and deformation twins can be triggered to coordinate the deformation. As a result, the strain rate effects are complicated phenomena which comprehensively affect the microstructural strengthening and softening effects. Based on these, the influences of both microstructural evolution and the transition of microscopic deformation mechanisms with strain rates on the enhancement and deterioration of mechanical properties are analyzed. Finally, the characteristics of deformation mechanisms of the gradient microstructures derived from high velocity impact surface treatments are concluded. Furthermore, a comprehensive model embodying the influences of different microstructures is proposed, which can provide a foundation for the further researches of strain rate effects.
- high speed impact surface treatment /
- metallic materials /
- strain rate effects /
- mechanical properties /
- microstructures

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利用超空泡现象可以大幅度减小水下运动物体的摩擦阻力，从而大大提高其航行速度。基于超空泡原理的高速射弹，利用其弹道末端的剩余动能可拦截鱼雷、击毁水雷和破除水下障碍等。20世纪末，在美国，机载快速灭雷系统(RAMICS)已经装备部队，超空泡射弹水下速度超过1 000 m/s。Y.D.Vlasenko^[1]、Y.N.Savchenko^[2]、I.N.Kirschner^[3]开展的超空泡射弹实验水下运动速度分别达到1 300、1 350和1 549 m/s，已超过了水中声速1 450 m/s。目前，超空泡射弹还在进一步向高速方向发展^[4-6]。在不考虑流体的压缩性效应时，Y.S.Chou^[7]、S.S.Kulkarni等^[8]、K.Ohtani等^[9]对射弹超空泡流动和弹体运动特性进行了计算。由于射弹高速冲击导致的流体压缩性效应不容忽视，A.N.Varghese等^[10]、A.D.Vasin^[11-13]、V.V.Serebryakov等^[4-6]基于细长体理论和渐近匹配展开法对超空泡形态影响的可压缩效应进行了理论研究，张志宏等^[14-15]进一步拓展得到了亚、超声速条件下细长锥形射弹的超空泡形态二阶近似解，金永刚等^[16]、张志宏等^[17]建立了高速射弹超空泡流场的数值计算方法。

超声速超空泡射弹发射后在水下依靠惯性无动力飞行，其速度从超声速逐渐减至亚声速，期间需要经历压缩性效应显著的跨声速阶段。另外，超空泡射弹还需在变水深条件下运动，水深变化引起的重力效应(环境压力和空泡数的变化)也不容忽视。因而，需要综合分析流体压缩性和重力效应对高速射弹超空泡形态和流体动力特性的影响。文献[14-17]仅能反映流体压缩性效应对超空泡形态和流场的影响，没有反映流体的重力效应。本文中，针对高速细长锥形超空泡射弹的实际应用背景，综合计及流体的重力和压缩性效应影响，统一建立亚、超声速条件下超空泡流动的理论模型和数值计算方法，系统完整地解决高速射弹的超空泡形态、射弹表面压力分布和压差阻力系数等计算问题，拟为下一步超空泡射弹的弹型优化设计和水下弹道预报提供理论基础。

1. 数学问题

在细长锥形射弹底部建立柱坐标系(x, r)，如图 1所示。设射弹绕流为理想可压缩流体无旋运动，来流速度为U_∞。根据亚、超声速流动特点，假定亚声速时超空泡尾部采用Riabouchinsky闭合方式，超声速时则不需提供闭合方式。考虑重力对超空泡流动的影响，假定重力加速度g指向x轴负方向，当射弹沿x轴负方向运动时，对应于流体重力势能减小即垂直入水方向，反之为垂直出水方向。由于入水开空泡通大气的复杂性，本文中只考虑射弹在液体中的水平、垂直向下和向上的运动，不考虑气水交界面上的入水问题。射弹半径r=r₁(x)=ε(x+l)预先给定，超空泡半径r=R(x)和长度L则需通过计算确定，其中l和R_n分别为射弹长度和底部半径，取小参数ε=R_n/l。

图 1 细长锥形射弹及超空泡坐标系

Figure 1. Coordinate system on slender conical projectile and supercavity

下载: 全尺寸图片幻灯片

设高速射弹引起的流场扰动速度势为φ，则描述亚、超声速超空泡流动的数学问题是：

$\left( {1 - Ma_\infty ^2} \right)\frac{{{\partial ^2}\varphi }}{{\partial {x^2}}} + \frac{{{\partial ^2}\varphi }}{{\partial {r^2}}} + \frac{{\partial \varphi }}{{r\partial r}} = 0\quad M{a_\infty } < 1\;{\rm{ or }}\;M{a_\infty } > 1$

(1)

$\frac{{\partial \varphi }}{{\partial r}} = \left( {{U_\infty } + \frac{{\partial \varphi }}{{\partial x}}} \right)\frac{{{\rm{d}}r}}{{{\rm{d}}x}}\quad r = {r_1}(x),r = R(x)$

(2)

$\nabla \varphi \to 0\quad \quad \quad (x,r) \to \infty$

(3)

${r_1} = R,\frac{{{\rm{d}}{r_1}}}{{{\rm{d}}x}} = \frac{{{\rm{d}}R}}{{{\rm{d}}x}}\quad \quad \quad \quad x = 0$

(4)

式中：Ma_∞=U_∞/a_∞为无穷远处来流马赫数，a_∞为无穷远处来流声速。

流体压力与密度关系采用Tait状态方程描述，即:

$\frac{{p + B}}{{{p_\infty } + B}} = {\left( {\frac{\rho }{{{\rho _\infty }}}} \right)^n}$

(5)

式中：p_∞、ρ_∞为无穷远处来流压力和密度；p、ρ为流场中某点压力和密度；n=7.15；B=298 MPa。

计及重力效应的伯努利方程为：

$\frac{n}{{n - 1}}\frac{{p + B}}{\rho } + \frac{{{U^2}}}{2} + gx = \frac{n}{{n - 1}}\frac{{{p_\infty } + B}}{{{\rho _\infty }}} + \frac{{U_\infty ^2}}{2} + g{x_\infty }$

(6)

式中：x_∞为重力场参考平面坐标，取x_∞=0时对应于射弹底面的中心位置。

对细长锥形射弹，流场压力系数可导出：

${C_p} = \frac{{p - {p_\infty }}}{{0.5{\rho _\infty }U_\infty ^2}} = \frac{2}{{nMa_\infty ^2}}\left( {{{\left( {1 - \frac{{n - 1}}{2}Ma_\infty ^2\left( {\frac{{2{\varphi _x}}}{{{U_\infty }}} + \frac{{\varphi _r^2}}{{U_\infty ^2}} + \frac{{2\left( {x - {x_\infty }} \right)}}{{F{r^2}{R_n}}}} \right)} \right)}^{\frac{n}{{n - 1}}}} - 1} \right)$

(7)

式中：傅鲁德数 $F r=U_{\infty} / \sqrt{g R_{n}}$ 。

定义空化数为 $\sigma=\frac{p_{\infty}-p_{\mathrm{v}}}{0.5 \rho_{\infty} U_{\infty}^{2}}$ ，其中p_∞=p_a+ρgh，p_a为当地大气压，p_v为水的饱和蒸汽压，ρ为水的密度，h为水面距射弹底面中心的高度。在空泡边界0≤x≤L－l上，有C_p=－σ。

2. 积分-微分方程

根据亚、超声速流动特点，流场扰动速度势可分别写为：

$\varphi (x,r) = - \int_{ - l}^L {\frac{{q(\xi ){\rm{d}}\xi }}{{4\pi \sqrt {{{(x - \xi )}^2} + {{(mr)}^2}} }}} \quad M{a_\infty } < 1$

(8)

$\varphi (x,r) = - \int_{ - l}^{x - mr} {\frac{{q(\xi ){\rm{d}}\xi }}{{2{\rm{ \mathsf{ π} }}\sqrt {{{(x - \xi )}^2} - {{(mr)}^2}} }}} \quad M{a_\infty } > 1$

(9)

式中： $m=\sqrt{\left|1-M a_{\infty}^{2}\right|} ; q(\xi)=U_{\infty}\left.\frac{\mathrm{d} S}{\mathrm{d} x}\right|_{x=\xi}$ ；S=πr²，为细长射弹及超空泡横截面面积。

利用式(2)和式(4)，将式(8)、式(9)分别代入式(7)，得到描述亚、超声速细长锥形射弹超空泡形态(0≤x≤L－l)的非线性积分-微分方程分别为：

$\begin{array}{*{20}{c}} {\int_0^{L - l} {{{\left. {\frac{{{{\rm{d}}^2}\zeta }}{{{\rm{d}}{x^2}}}} \right|}_{x = \xi }}} \frac{{{\rm{d}}\xi }}{{\sqrt {{{(x - \xi )}^2} + {m^2}\zeta } }} = - 2{\sigma _m} + \frac{{4\left( {x - {x_\infty }} \right)}}{{F{r^2}{R_n}}} + \frac{1}{{2\zeta }}{{\left( {\frac{{{\rm{d}}\zeta }}{{{\rm{d}}x}}} \right)}^2} - }\\ {2{\varepsilon ^2}\ln \frac{{\left( {x + l + \sqrt {{{(x + l)}^2} + {m^2}\zeta } } \right)\left( {x - L + l + \sqrt {{{(x - L + l)}^2} + {m^2}\zeta } } \right)}}{{\left( {x + \sqrt {{x^2} + {m^2}\zeta } } \right)\left( {x - L + \sqrt {{{(x - L)}^2} + {m^2}\zeta } } \right)}}\quad M{a_\infty } < 1} \end{array}$

(10)

$\begin{array}{*{20}{c}} {\int_0^{x - mR} {{{\left. {\frac{{{d^2}\zeta }}{{d{x^2}}}} \right|}_{x = \hat \xi }}} \frac{1}{{{{\left( {{{(x - \xi )}^2} - {m^2}\zeta } \right)}^{1/2}}}}{\rm{d}}\xi = }\\ { - {\sigma _m} + \frac{{2\left( {x - {x_\infty }} \right)}}{{F{r^2}{R_n}}} + \frac{1}{{4\zeta }}{{\left( {\frac{{{\rm{d}}\zeta }}{{{\rm{d}}x}}} \right)}^2} - 2{\varepsilon ^2}\ln \frac{{x + l + \sqrt {{{(x + l)}^2} - {m^2}\zeta } }}{{x + \sqrt {{x^2} - {m^2}\zeta } }}\quad M{a_\infty } > 1} \end{array}$

(11)

式中： $\zeta=R^{2}, \sigma_{m}=\frac{2}{(n-1) M a_{\infty}^{2}}\left(1-\left(1-\frac{n M a_{\infty}^{2}}{2} \sigma\right)^{\frac{n-1}{n}}\right)$ 。

3. 离散及迭代方法

求解超空泡形态，可将超空泡沿长度方向均匀分成N段，有N+1个节点，且x₁=0，x_N+1=L－l。设ζ在每段的相邻两节点之间按x(x_i≤x≤x_i+1)的二次多项式变化，即：

$\zeta = {\zeta _i} + {a_i}\left( {x - {x_i}} \right) + {b_i}{\left( {x - {x_i}} \right)^2}\quad i = 1,2, \cdots ,N$

(12)

式中：a_i和b_i是待定系数。

利用式(4)及dζ/dx在各节点处连续的条件，得a₁=2εR_n以及a_i+1的递推公式为：

${a_{i + 1}} = {a_i} + 2{b_i}\left( {{x_{i + 1}} - {x_i}} \right)\quad i = 1,2, \cdots ,N$

(13)

利用式(12)，可得计算各节点x_k处超空泡ζ_k的累加表达式为：

${\zeta _k} = {\zeta _1} + \sum\limits_{i = 1}^{k - 1} {\left( {{a_i}\left( {{x_{i + 1}} - {x_i}} \right) + {b_i}{{\left( {{x_{i + 1}} - {x_i}} \right)}^2}} \right)} \quad k = 2,3, \cdots ,N + 1$

(14)

系数b_i(i=1, 2, …, N)的确定成为超空泡形态计算的关键。在亚、超声速条件下，将式(12)分别代入式(10)和式(11)，得到求解b_i的线性代数方程组和递推公式分别为：

$\begin{array}{l} \sum\limits_{i = 1}^N {{b_i}} \ln \frac{{{x_k} - {x_{i + 1}} + \sqrt {{{\left( {{x_k} - {x_{i + 1}}} \right)}^2} + {m^2}{\zeta _k}} }}{{{x_k} - {x_i} + \sqrt {{{\left( {{x_k} - {x_i}} \right)}^2} + {m^2}{\zeta _k}} }} = {\sigma _m} - \frac{{2\left( {{x_k} - {x_\infty }} \right)}}{{F{r^2}{R_n}}} - \frac{1}{{4{\zeta _k}}}{\left( {{{\left. {\frac{{{\rm{d}}\zeta }}{{{\rm{d}}x}}} \right|}_{x = {x_k}}}} \right)^2} + \\ \;\;\;\;{\varepsilon ^2}\ln \frac{{\left( {{x_k} + l + \sqrt {{{\left( {{x_k} + l} \right)}^2} + {m^2}{\zeta _k}} } \right)\left( {{x_k} - L + l + \sqrt {{{\left( {{x_k} - L + l} \right)}^2} + {m^2}{\zeta _k}} } \right)}}{{\left( {{x_k} + \sqrt {x_k^2 + {m^2}{\zeta _k}} } \right)\left( {{x_k} - L + \sqrt {{{\left( {x_k^2 - L} \right)}^2} + {m^2}{\zeta _k}} } \right)}}\\ \;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;k = 1,2, \cdots ,N,M{a_\infty } < 1 \end{array}$

(15)

$\begin{array}{*{20}{c}} {{b_i}\ln \frac{{{m^2}{\zeta _{i + 1}}}}{{{{\left( {{x_{i + 1}} - {x_i} + \sqrt {{{\left( {{x_{i + 1}} - {x_i}} \right)}^2} - {m^2}{\zeta _{i + 1}}} } \right)}^2}}} = {\sigma _m} - \frac{{2\left( {{x_{i + 1}} - {x_\infty }} \right)}}{{F{r^2}{R_n}}} - \frac{1}{{4{\zeta _{i + 1}}}}{{\left( {{{\left. {\frac{{d\zeta }}{{dx}}} \right|}_{x = {x_{i + 1}}}}} \right)}^2} + }\\ {2{\varepsilon ^2}\ln \frac{{{x_{i + 1}} + l + \sqrt {{{\left( {{x_{i + 1}} + l} \right)}^2} - {m^2}{\zeta _{i + 1}}} }}{{{x_{i + 1}} + \sqrt {x_{i + 1}^2 - {m^2}{\zeta _{i + 1}}} }} - }\\ {2{\mathop{\rm sgn}} (i - 1)\sum\limits_{j = 1}^{i - 1} {{b_j}} \ln \frac{{{x_{i + 1}} - {x_{j + 1}} + \sqrt {{{\left( {{x_{i + 1}} - {x_{j + 1}}} \right)}^2} - {m^2}{\zeta _{i + 1}}} }}{{{x_{i + 1}} - {x_j} + \sqrt {{{\left( {{x_{i + 1}} - {x_j}} \right)}^2} - {m^2}{\zeta _{i + 1}}} }}\quad i = 1,2, \cdots ,N,M{a_\infty } > 1} \end{array}$

(16)

式中：ζ_k=R_k²，ζ_i+1=R_i+1²。

在已知射弹几何参数和运动参数条件下，采用超空泡形态的一阶近似解^[13-15]作为初解，可以加快计算的收敛速度。超空泡最终长度及外形由 $\left.\zeta\right|_{x=L-l}=R_{n}^{2}$ 确定^[16-17]。根据计算得到的超空泡形态，利用式(8)或式(9)以及式(7)，可以计算得到超空泡流动的速度场和压力场。而亚、超声速条件下细长锥形射弹表面上(－l≤x≤0)的压力系数分别为：

$\begin{array}{l} {C_p} = \frac{2}{{nMa_\infty ^2}}\left( {\left( {1 - \frac{{n - 1}}{2}Ma_\infty ^2\left( {\sum\limits_{i = 1}^N {{b_i}} \ln \frac{{x - {x_{i + 1}} + \sqrt {{{\left( {x - {x_{i + 1}}} \right)}^2} + {m^2}{\zeta _b}} }}{{x - {x_i} + \sqrt {{{\left( {x - {x_i}} \right)}^2} + {m^2}{\zeta _b}} }} + } \right.} \right.} \right.\\ \left. {{{\left. {\left. {{\varepsilon ^2}\ln \frac{{{\rm{e}}\left( {x + \sqrt {{x^2} + {m^2}{\zeta _b}} } \right)\left( {x - L + \sqrt {{{(x - L)}^2} + {m^2}{\zeta _b}} } \right)}}{{\left( {x + l + \sqrt {{{(x + l)}^2} + {m^2}{\zeta _b}} } \right)\left( {x - L + l + \sqrt {{{(x - L + l)}^2} + {m^2}{\zeta _b}} } \right)}} + \frac{{2\left( {x - {x_\infty }} \right)}}{{F{r^2}{R_n}}}} \right)} \right)}^{\frac{n}{{n - 1}}}} - 1} \right)\\ \;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;M{a_\infty } < 1 \end{array}$

(17)

${C_p} = \frac{2}{{nMa_\infty ^2}}\left( {{{\left( {1 - \frac{{n - 1}}{2}Ma_\infty ^2\left( {{\varepsilon ^2}\ln \frac{{{\mathop{\rm e}\nolimits} {m^2}{\varepsilon ^2}}}{{{{\left( {1 + \sqrt {1 - {m^2}{\varepsilon ^2}} } \right)}^2}}} + \frac{{2\left( {x - {x_\infty }} \right)}}{{F{r^2}{R_n}}}} \right)} \right)}^{\frac{n}{{n - 1}}}} - 1} \right)\quad M{a_\infty } > 1$

(18)

式中：ζ_b=r₁²=ε²(x+l)²。

通过积分，可以进一步得到以πR_n²为特征面积的细长锥形射弹压差阻力系数为^{[7, 10]}：

${C_D} = \frac{D}{{0.5{\rho _\infty }U_\infty ^2{\rm{ \mathsf{ π} }}R_n^2}} = \frac{2}{{{l^2}}}\int_{ - l}^0 {(x + l)} {C_p}{\rm{d}}x + \sigma$

(19)

式中：D为射弹的压差阻力。

4. 结果与分析

取射弹几何参数为：l=120 mm，R_n=6 mm，ε=0.05。由文献[4-6]，超空泡长细比λ的渐近解为：

$\sigma = \frac{2}{{{\lambda ^2}}}\ln \frac{\lambda }{{m\sqrt {\rm{e}} }}$

(20)

在已知射弹运动速度时，可以计算来流马赫数Ma_∞和空化数σ，通过式(10)或式(11)和式(14)，可以计算亚声速或超声速条件下细长锥形射弹的超空泡形态，并进一步得到超空泡长细比与马赫数的变化关系。不同深度射弹水平运动时超空泡长细比的渐近解与数值解结果比较如图 2所示，两者整体上符合较好，验证了本文理论模型和数值解法的正确性。在大部分情况下，λ随Ma_∞基本呈线性变化，即随Ma_∞增加超空泡形态将变得更加细长。但在跨声速(0.8 < Ma_∞ < 1.2)时，曲线将会出现一个窄的尖峰，此时λ随Ma_∞呈非线性变化。在Ma_∞相同时，不计重力效应的超空泡长细比最大(这里可视为水深为零)，随着水深增加(如h=20, 40 m)，λ将逐渐减小，说明水深增加将使超空泡向短粗方向发展。

图 2 超空泡长细比的数值解与渐近解

Figure 2. Supercavity aspect ratio between numericaland asymptotic solution

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在射弹深度和速度恒定(如h=20 m，Ma_∞=0.7, 1.2)时，计算射弹水平及出、入水运动的超空泡形态。当射弹水平运动(对应于Fr→∞)时，计算得到的超空泡形态在亚声速时前后对称，在超声速时前后稍微不对称，主要原因是：亚声速时扰动可向流场四周传播，而超声速时扰动仅在马赫锥内向下游传播。在射弹垂直入水(对应于Fr²>0)或垂直出水(因射弹运动方向与重力加速度g方向相反，对应于Fr² < 0)时，由于重力效应的影响，推迟或加速了超空泡尾部的封闭，使超空泡的长度拉长或缩短，如图 3所示。射弹出入水时重力效应主要影响超空泡的尾部形态，并使超空泡前后呈现不对称。

图 3 运动方式对超空泡形态的影响

Figure 3. Effect of movement modeon supercavity profile

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另外，重力效应并不完全体现在Fr数的大小上，由式(10)和式(11)可以看出，它同时还与超空泡的尺度坐标x有关。计算分析表明，当射弹沿水平方向或沿垂直出水方向运动时，超空泡尾部可以自然封闭，因而可以得到超空泡形态的收敛解。当射弹沿垂直入水方向运动时，由于超空泡长度随Ma_∞增加而增加，当Ma_∞过大导致超空泡长度过长而入水深度不足时，由于超空泡来不及封闭，则无法满足超空泡尾部的闭合准则，理论计算将得不到收敛的超空泡形态数值解。

重力效应对超空泡尺度的影响还与水深大小有关，如图 4所示。图中纵坐标L_u/L_h、R_u/R_h分别为射弹出水和水平运动的超空泡长度和最大半径之比。在水深较小(如水深为零)时，超空泡尺度受重力效应的影响较大，且随Ma_∞的增加而增加。相对于射弹水平运动的超空泡尺度，射弹出水时超空泡长度比半径减小得更快，即在同样的Ma_∞下，L_u/L_h偏离1的位置比R_u/R_h大。当水深增加(如h=20 m)时，L_u/L_h和R_u/R_h偏离1的位置减小。说明水深较大时，射弹出水时的超空泡尺度受重力效应的影响相对减小，即更加接近于射弹水平运动时的超空泡尺度。因此，水深越大，无论射弹是水平运动还是垂向运动，他们的超空泡尺度大小就越接近，重力效应对射弹不同运动方式形成的超空泡尺度的影响就越小。

图 4 出水与水平运动超空泡长度和最大半径之比

Figure 4. Ratio of supercavity length to maximum radiusfor upward to horizontal movement

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在射弹速度恒定时，进一步计算水深变化对射弹出水超空泡形态的影响。当射弹沿垂直方向(垂直向下或垂直向上)运动时，其超空泡在垂向将遭受不同的重力作用。图 5为射弹以速度Ma_∞=0.7垂直出水的超空泡形态，水深h分别为10、20、30、40 m。可见，随着水深增加，超空泡长度和半径将依次缩小，但缩小的趋势逐渐减缓。

图 5 深度对出水超空泡尺度的影响

Figure 5. Effect of depth on supercavity scalefor upward movement

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当射弹沿水平方向运动时，由于不同深度条件下空化数不同，也将导致所形成的超空泡尺度不同。当射弹以亚声速Ma_∞=0.8和超声速Ma_∞=1.2作水平运动时，深度增加将使超空泡长度和最大半径相应缩小。水深小时减小得快，水深大时减小得慢，如图 6所示。说明水深较小时，超空泡尺度对深度变化比较敏感，而水深较大时，深度变化对超空泡尺度的影响较小。

图 6 深度对超空泡长度和半径的影响

Figure 6. Effect of depth on supercavity length and radius

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考虑重力和压缩性效应, 计算射弹表面压力分布和压差阻力系数随马赫数的变化关系。在水深一定(如h=20 m)时，Ma_∞的变化对射弹表面压力分布有较大影响，射弹表面的压力系数在锥尖处为驻点压力，亚声速时由锥尖至锥底逐渐减小，在锥底处压力系数减小为各自水深和速度下的负空化数，如图 7所示。当Ma_∞由0.3增加至0.7时，压力系数增加较慢，当Ma_∞由0.7增加至0.9时，压力系数增加较快，而当Ma_∞由0.9增加至0.99时，压力系数则急剧增加。Ma_∞的变化反映了流体压缩性效应的影响。

图 7 不同马赫数下的压力系数分布

Figure 7. Pressure coefficients for different Mach number

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超声速条件下，由式(18)可知，相同速度时射弹表面压力系数与水深无关。由于超声速时Fr很大，而射弹尺度又很小，因此无论射弹是水平运动还是出水或入水运动，射弹表面的压力系数将基本保持不变，且近似为常数。

射弹的压差阻力系数与其表面的压力系数和空化数的大小有关。通过射弹表面的压力系数分布，可以定性反映射弹运动的压差阻力系数大小。在亚声速时，压差阻力系数随水深增加有明显增加，主要是由水深变化导致的空化数增加而引起的，如图 8所示。在超声速时，由于射弹速度大，水深增加引起的空化数变化小，不同水深、相同速度时射弹表面的压力系数分布基本保持不变，因而压差阻力系数与水深变化关系不大。因此，在亚声速时流体重力效应对压差阻力系数的影响较大，而在超声速时则影响较小。

图 8 不同深度时压差阻力系数与马赫数的关系

Figure 8. Base drag coefficient vs. Mach numberat different depths

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在0.8 < Ma_∞ < 1.2时，压差阻力系数增加迅速，主要是流体的压缩性效应导致射弹表面压力系数迅速增加造成的。此外，流体的压缩性效应还体现在对超空泡尺度的改变上。图 9为射弹在3种深度(h=0, 20, 40 m)水平运动时的可压与不可压超空泡流动的参数之比，其中L/L₀、R/R₀、C_D/C_D0分别为超空泡长度之比、超空泡最大半径之比、射弹压差阻力系数之比。当Ma_∞→1时，有L/L₀>1.7、R/R₀>1.4、C_D/C_D0>1.8，说明流体压缩性效应在跨声速范围内影响明显。当Ma_∞ < 0.3和Ma_∞→2时，可压与不可压超空泡流动的参数之比趋于1，说明此时流体的压缩性效应较小。对Ma_∞>2的高超声速情况，流体压缩性效应将随Ma_∞增加而增加。因此可知，射弹运动速度范围不同，导致的流体压缩性效应影响也不同，如果在理论模型中不考虑流体的压缩性效应，计算结果将会引起较大误差。

图 9 可压缩与不可压缩流动参数之比

Figure 9. Flow parameter ratio of compressibilityto incompressibility

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5. 结论

建立的亚、超声速细长锥形射弹超空泡流动的理论模型和计算方法，考虑了流体的压缩性特别是重力效应，可以计算细长锥形射弹运动方式、深度、速度的变化对超空泡形态和流体动力系数的影响。对细长锥形射弹垂直出入水运动，流体重力效应主要体现在沿深度方向空泡周围的压力改变上。对细长锥形射弹水平运动，流体重力效应主要体现在水深变化导致的空泡数改变上。亚声速时，流体重力效应对细长锥形射弹压差阻力系数有明显影响，而超声速时影响较小。流体压缩性效应对超空泡形态、细长锥形射弹表面压力分布和射弹压差阻力系数的影响主要体现在跨临界速度和高超声速范围内。由于理论模型中未计及跨声速时的非线性效应影响，因而在跨声速范围时计算结果只能定性反映超空泡射弹的流动特性变化。

图 1 材料性能的影响因素示意图^[3]

Figure 1. Schematic diagram of the influencing factors of mechanical properties^[3]

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图 2 根据应变率的加载模式分类^[7]

Figure 2. Classifications of loads with reference to strain rate^[7]

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图 3 不同材料高速冲击表面处理前后力学性能变化^{[21, 23]}

Figure 3. Mechanical properties of different materials processed by various high velocity impact surface treatments^{[21, 23]}

FSW: Friction stir welding; LW: laser-welded; HAZ: heat affected zone; FZ: fusion zone

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图 4 不同材料经高速冲击表面处理后的塑性变化^[24-26]

Figure 4. The plastic changes of different materials processed by high velocity impact surface treatments^[24-26]

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图 5 不同材料经高速冲击表面处理后的拉伸断口^[27-28]

Figure 5. Tensile fracture morphologies of different materials after high speed impact surface treatment^[27-28]

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图 6 不同梯度材料的应力应变曲线^[30-31]

Figure 6. The stress-strain curves of different gradient materials^[30-31]

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图 7 低应变率表面处理后的晶粒形貌^[34-35]

Figure 7. Grain structure of materials processed by low-strain-rate surface treatments^[34-35]

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图 8 表面形变处理横截面梯度形貌^[37-39]

Figure 8. The cross section morphologies of the specimen processed by surface mechanical treatment^[37-39]

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图 9 AA2060铝锂合金喷丸过程中的动态回复再结晶^[46]

Figure 9. Dynamic recovery and recrystallization of AA2060 Al-Li alloy induced by shot peening^[46]

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图 10 AA2060铝锂合金喷丸前后晶粒取向图^[46]

Figure 10. Grain orientation map of AA2060 Al-Li alloy before and after shot peening^[46]

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图 11 304奥氏体不锈钢的冲击相变^[57]

Figure 11. Phase transformation of 304 austenite stainless steel by impact deformation^[57]

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图 12 不同材料在不同高速冲击表面处理下的形变诱发相变^[60-62]

Figure 12. Deformation induced phase transformation of different materials under different high velocity impact surface treatments^[60-62]

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图 13 位错组态随应变量和应变率的演变规律示意图^[66-67]

Figure 13. Proposed diagram of dislocation evolution with the increment of plastic strain and strain rates^[66-67]

(LGs: large grains; DLs: dislocation lines; DWs: dislocation walls; DTs: dislocation tangles; UFGs: ultrafine-grains; NGs: nano-grains)

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图 14 高速冲击表面处理后不同深度处的位错组态^[68-70]

Figure 14. Dislocations at different depths after high velocity impact surface treatments^[68-70]

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图 15 不同材料在不同高速冲击表面处理变形时析出相变化^[72-74]

Figure 15. The variation of precipitates of different materials deformed under different high velocity impact surface treatments^[72-74]

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图 16 位错运动通过强化相方式^[77]

Figure 16. The ways of dislocation moving through strengthening phases^[77]

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图 17 应变率对位错与析出相之间相互作用的影响^[77]

Figure 17. Effects of strain rate on the interaction of dislocations and precipitates^[77]

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图 18 位错到变形孪晶的演变规律示意图^[68]

Figure 18. Schematic diagram of the transformation from dislocations to deformation twins with the increment of plastic strain and strain rates^[68]

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图 19 高应变率下变形孪晶^[85-86]

Figure 19. Deformation twins occurred under high strain rates^[85-86]

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图 20 纳米晶铝TEM图像^[41]

Figure 20. TEM micrographs of nanocrystalline aluminum deformed by manually grinding^[41]

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图 21 Thompson双四面体与纳米孪晶片层的相对位向关系^[89]

Figure 21. A schematics showing the relative orientation between a double Thompson tetrahedra and twin lamellae^[89]

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图 22 试样变形示意图

Figure 22. Schematic diagram of sample deformation

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1. 数学问题
2. 积分-微分方程
3. 离散及迭代方法
4. 结果与分析
5. 结论

高速冲击表面处理对金属材料力学性能和组织结构的影响

doi: 10.11883/bzycj-2020-0342

作者简介: 高玉魁（1973－ ），男，博士，教授，ykgao12088@126.com

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