超高速碰撞闪光强度与碰撞角度关系

为了测量超高速碰撞过程中产生的闪光现象,进而研究相近碰撞速度、不同入射角度(弹道与靶板平面的夹角)条件下超高速碰撞产生闪光在整个物理过程的闪光强度随时间的变化规律,设计了适用于瞬态闪光测量的光学高温计测量系统。通过二级轻气炮加载LY12球形铝弹丸,运用设计的瞬态高温计测量系统分别进行了入射角度为30°,45°,60°和90°相近碰撞速度条件下碰撞LY12铝靶产生闪光现象的测量。获得了平均碰撞闪光强度峰值与碰撞角度的关系,平均碰撞闪光强度峰值随碰撞角度的减小而增大,碰撞角度为30°时表现更为明显。     

JB-9001钝感炸药冲击Hugoniot关系测试

 利用“压力对比法”实验技术，通过锰铜压力计测试待测炸药样品和LY12铝样品在LY12铝飞片的同时撞击下的界面压力p_exp和p_Al，从冲击波关系式和正交回归直线拟合分析，确定了JB-9001钝感炸药的冲击Hugoniot关系。     

JB9014钝感炸药冲击绝热线测量

 利用压力对比法,采用锰铜计测量待测炸药样品和LY12铝标准样品在LY12铝飞片同时撞击下的界面压力,运用冲击波关系式和正交回归直线拟合分析,确定了JB9014钝感炸药冲击绝热线关系式。     

激光辐照超音速气流下TA15钛合金和LY12铝合金的热响应

利用超音速气流环境模拟装置,开展了自然对流和马赫数为3切向气流下,1064nm连续激光辐照TA15钛合金和LY12铝合金热响应实验研究,得到了材料在两种条件下的温升曲线及熔穿时间。结果表明:在激光辐照材料未使得其表面发生熔化前,气流对材料激光辐照过程中的冷却效应较为明显,在表面发生熔化时,熔化的液态物质在气流切向力剥蚀作用下被吹离材料表面,使得激光继续作用在材料上,熔化→剥离→熔化→剥离如此反复,可加速熔穿过程;此外,切向气流将影响钛合金这类热扩散系数较低材料的温度场分布,使得气流下游处的温度高于上游,而对铝合金这类热扩散系数较高的材料而言,影响不明显。     

40GPa压力范围内铜和铝的准等熵压缩线

 基于自行研制的磁驱动准等熵压缩加载实验装置CQ-1.5,利用全光纤位移干涉仪（Doppler Pins System, DPS）、激光速度干涉计（Velocity Interferometer System for Any Reflectors, VISAR）两种测试手段,以及反积分数据处理方法,实验测量了40 GPa压力范围内T1铜、LY12硬铝和L1纯铝3种材料的准等熵压缩线,将实验准等熵压缩线与基于Grüneisen状态方程的理论等熵压缩线和冲击Hugoniot线进行了比较。结果表明,在该压力范围内,实验准等熵压缩线与理论等熵压缩线相一致,两者偏差小于3%;实验准等熵压缩线靠近冲击Hugoniot线,位于其下方,与国外文献发表的结果相同,进一步表明,实验测量结果正确可靠。     

冲击波作用下铝的等效剪切模量

提出了冲击波作用下通过测量沿着准弹性卸载过程纵波波速与体波波速得到等效剪切模量的方法,应用该方法对LY12铝在20—70 GPa冲击压力下的等效剪切模量进行了测量.实验结果表明,等效剪切模量随应力线性减少直至反向屈服时为零,而初始卸载时的等效剪切模量可以由修正的Steinberg-Cochran-Guinan模型进行描述.应用得到的等效剪切模量进行了初步数值模拟,计算结果与实验测量的粒子速度剖面符合很好,重现了准弹性卸载到塑性卸载的光滑过渡. 关键词： 等效剪切模量 波速 准弹性卸载 冲击波 铝     

PROFILES OF INFLATED SURFACES

We study the shape of inflated surfaces introduced in [3] and [12]. More precisely, we analyze profiles of surfaces obtained by inflating a convex polyhedron, or more generally an almost everywhere flat surface, with a symmetry plane. We show that such profiles are in a one-parameter family of curves which we describe explicitly as the solutions of a certain differential equation.     

高应变率压缩加载下LY12铝圆管的剪切断裂研究

 通过回收破片的断口观察和金相分析研究了LY12铝圆管在高应变率压缩过程中的剪切断裂现象；回收破片具有典型的剪切断裂特征，断口与径向近似成45°夹角，断口观察发现断口面经历过径向摩擦；破片金相分析表明，绝热剪切带和裂纹首先在圆管内壁附近产生，然后沿最大剪应力线向外壁扩展。利用数值计算给出了圆管在内爆压缩加载下管壁内微元的应力、应变历史，为分析LY12铝圆管的剪切断裂提供了参考。     

Rocking Curves of X-Ray Asymmetric Bragg Diffraction with Two-Dimensional Curvature of Wave Front

The X-ray asymmetric Bragg diffraction in a perfect semi-infinite crystal with plane entrance surface is considered taking into account the two-dimensional curvature of the wave front of an incident wave. An expression for reflection coefficient using the Green function is obtained in the approximation of locally plane wave and the rocking curves are investigated as functions of angular departure from the selected exact Bragg direction in the diffraction plane and in the direction perpendicular to the diffraction plane. The shape, position and dimensions of total reflection region of rocking curves are studied depending on the degree of asymmetry of diffraction geometry. The requirements to the spatial and temporal coherence for obtaining the rocking curves are estimated.     

Rocking Curves of X-ray Asymmetrical Laue Diffraction with Two-Dimensional Curvature of Wave Front

X-ray asymmetrical Laue diffraction in a perfect crystal with plane front surface was considered taking into account the two-dimensional curvature of a wave incident on the crystal. Using an appropriate Green function the dependences of rocking curves on deviation angles from selected exact Bragg direction were examined in the diffraction plane and in the direction perpendicular to the diffraction plane in locally plane wave approximation. The dependence of rocking curves on the degree of asymmetry of diffraction geometry was investigated. Analytical expressions for half widths of rocking curves in the diffraction plane and in the direction perpendicular to the diffraction plane are obtained. Some requirements to spatial and temporal coherence are estimated.     

LY12-M铝中冲击波衰减机理的实验研究

 应用锰铜压阻计测量了峰压为4.92 GPa的平面冲击波在LY12-M铝中的衰减规律，对试样进行了正电子寿命谱探测和维氏显微硬度测试，分析了位错等缺陷对冲击波非流体动力学衰减的影响，同时还对LY12-M铝的冲击硬化效应进行了探讨。     

Scatter of fatigue data owing to material microscopic effects

A common phenomenon of fatigue test data reported in the open literature such as S-N curves exhibits the scatter of points for a group of same specimens under the same loading condition.The reason is well known that the microstructure is different from specimen to specimen even in the same group.Specifically,a fatigue failure process is a multi-scale problem so that a fatigue failure model should have the ability to take the microscopic effect into account.A physically-based trans-scale crack model is established and the analytical solution is obtained by coupling the micro-and macro-scale.Obtained is the trans-scale stress intensity factor as well as the trans-scale strain energy density(SED)factor.By taking this trans-scale SEDF as a key controlling parameter for the fatigue crack propagation from micro-to macro-scale,a trans-scale fatigue crack growth model is proposed in this work which can reflect the microscopic effect and scale transition in a fatigue process.The fatigue test data of aluminum alloy LY12 plate specimens is chosen to check the model.Two S-N experimental curves for cyclic stress ratio R=0.02 and R=0.6 are selected.The scattering test data points and two S-N curves for both R=0.02 and R=0.6 are exactly re-produced by application of the proposed model.It is demonstrated that the proposed model is able to reflect the multiscaling effect in a fatigue process.The result also shows that the microscopic effect has a pronounced influence on the fatigue life of specimens.     

Shear modulus of shock-compressed LY12 aluminium up to melting point

Asymmetric plate impact experiments are conducted on LY12 aluminium alloy in a pressure range of 85-131 GPa. The longitudinal sound speeds axe obtained from the time-resolved particle speed profiles of the specimen measured with Velocity Interferometer System for Any Reflector （VISAR） technique, and they are shown to be good agreement with our previously reported data of this alloy in a pressure range of 20-70 GPa, and also with those of 2024 aluminium reported by McQueen. Using all of the longitudinal speeds and the corresponding bulk speeds calculated from the Gruneisen equation of state （EOS）, shear moduli of LY12 aluminium alloy are obtained. A comparison of the shear moduli in the solid phase region with those estimated from the Steinberg model demonstrate that the latter are systematically lower than the measurements. By re-analysing the pressure effect on the shear modulus, a modified equation is proposed, in which the pressure term of P/η^1/3 in the Steinberg model is replaced by a linear term. Good agreement between experiments and the modified equation is obtained, which implies that the shear modulus of LY12 aluminium varies linearly both with pressure and with temperature throughout the whole solid phase region. On the other hand, shear modulus of aluminium in a solid-liquid mixed phrase region decreases gradually and smoothly, a feature that is very different from the drastic dropping at the melting point under static conditions.     

Shear modulus of shock-compressed LY12 aluminium up to melting point

Asymmetric plate impact experiments are conducted on LY12 aluminium alloy in a pressure range of 85--131\,GPa. The longitudinal sound speeds are obtained from the time-resolved particle speed profiles of the specimen measured with Velocity Interferometer System for Any Reflector (VISAR) technique, and they are shown to be good agreement with our previously reported data of this alloy in a pressure range of 20--70\,GPa, and also with those of 2024 aluminium reported by McQueen. Using all of the longitudinal speeds and the corresponding bulk speeds calculated from the Gruneisen equation of state (EOS), shear moduli of LY12 aluminium alloy are obtained. A comparison of the shear moduli in the solid phase region with those estimated from the Steinberg model demonstrate that the latter are systematically lower than the measurements. By re-analysing the pressure effect on the shear modulus, a modified equation is proposed, in which the pressure term of $P/\eta^{1/3}$ in the Steinberg model is replaced by a linear term. Good agreement between experiments and the modified equation is obtained, which implies that the shear modulus of LY12 aluminium varies linearly both with pressure and with temperature throughout the whole solid phase region. On the other hand, shear modulus of aluminium in a solid-liquid mixed phrase region decreases gradually and smoothly, a feature that is very different from the drastic dropping at the melting point under static conditions.     

Fatigue damage rule of LY12CZ aluminium alloy under sequential biaxial loading

A series of biaxial two-level variable amplitude loading tests are conducted on smooth tubular specimens of LY12CZ aluminium alloy.The loading paths of 90°out-of-phase,45°out-of-phase and 45°in-phase are utilized.The fatigue damage cumulative rules under two-level step loading of three loading paths are analyzed.By introducing a parameter which is a function of the phase lag angle between the axial and the torsional loading,a new multiaxial nonlinear fatigue damage cumulative model is proposed.The proposed model is evaluated by the experimental data for two-level loading,multi-level loading of LY12CZ aluminium alloy,and multi-level loading of 45 steel.Fatigue lives predicted are within a factor of 2 scatter band.     

The Threshold Absolute Value of a Relay Control Bringing a Satellite to a Gravitationally Stable Position in Optimal Time

The properties of the solution to the well-known problem of the optimal orientation of a satellite in the plane of a circular orbit and its steering to a gravitationally stable angular position, which was posed and considered earlier by Vladimir V. Beletskij, have been refined. The constraint on the control torque module is considered as the main parameter of the problem. It turned out that, even in the case when the admissible control torque exceeds the gravitational moment in magnitude, in the phase plane the existence of additional switching curves corresponding to relay control with two switchings is possible. As a result, a simple numerical algorithm is proposed, and with its help the threshold absolute control value is found at which the indicated switching curves are infinitesimal, and their coordinates in the phase plane are found.     

无氧铜等熵卸载路径的实验研究

 采用化爆加载,以黄铜为飞片、无氧铜为靶板,测量了以抗氢钢（HR2）、重玻璃（SiO₂）、铝合金（LY12/LF6）、镁铝合金（MB2）、有机玻璃（PMMA）和空气（Air）为垫块（Anvil）材料中的冲击波速度（上述材料的Hugoniot状态参数C₀、λ均为已知）,由此确定了无氧铜的等熵卸载路径。结果表明：在冲击态（即初始卸载态）高达219 GPa的压力范围内,无氧铜的等熵卸载过程可用Grüneisen状态方程在ργ=ρ₀γ₀近似下作很好的描述;各条卸载路径到一个大气压的终态粒子速度U_S与镜像反演的粒子速度2u的偏差(U_S-2u)/(2u),随冲击波压力的增加而增大。     

Integrable System and Motion of Curves in Projective and Similarity Geometries

Based on the natural frame in the projective geometry, motions of curves in projective geometry are studied. It is shown that several integrable equations including Sawada-Kotera and KK equations arise from motion of plane curves in projective geometries. Motion of space curves described by acceleration field and governed by endowing an extra space variable in similarity geometry P³ is also studied.     

超高速碰撞LY12铝靶产生闪光辐射的速度及角度效应

为了研究超高速碰撞产生闪光辐射的速度及角度效应,利用建立的瞬态光纤高温计测量系统结合二级轻气炮加载系统,进行了6种实验条件下的超高速碰撞实验。每组实验使用一组光纤探头,基于实验所获原始数据结合标定,通过Matlab编程处理得到了给定实验条件及光纤探头安装条件下,超高速碰撞LY12铝靶产生的闪光辐射与碰撞速度和弹丸入射角度的关系。实验结果表明,超高速碰撞LY12铝靶产生的闪光辐射在温度峰值出现前近似与碰撞速度和弹丸入射角度(弹道与靶板平面的夹角)正弦乘积的平方成正比;碰撞闪光辐射在温度峰值出现后近似与碰撞速度和弹丸入射角度正弦乘积的0.75次幂成正比,与理论推导结果基本吻合。     

Euler elasticae in the plane and the Whitney-Graustein theorem

In this paper, we study normal forms of plane curves and knots. We investigate the Euler functional E (the integral of the square of the curvature along the given curve) for closed plane curves, and introduce a closely related functional A, defined for polygonal curves in the plane ?² and its modified version A _R , defined for polygonal knots in Euclidean space ?³. For closed plane curves, we find the critical points of E and, among them, distinguish the minima of E, which give us the normal forms of plane curves. The minimization of the functional A for plane curves, implemented in a computer animation, gives a very visual approximation of the process of gradient descent along the Euler functional E and, thereby, illustrates the homotopy in the proof of the classical Whitney-Graustein theorem. In ?³, the minimization of A _R (implemented in a 3D animation) shows how classical knots (or more precisely thin knotted solid tori, which model resilient closed wire curves in space) are isotoped to normal forms.