正则变换下的哈密顿原理

正则变换是相空间中一类变量变换.2n 个正则共轭变量 qi 和 pi 变换成2n 个新变量Q_i=Q_i(q,p,t),P_i=P_i(q,p,t), (1)若在此变换下系统运动方程的正则形式不变,则称此变换为正则变换.设 H(q,p,t)和 H′(Q,P,t)分别是 ...     

轴对称件超塑约束胀形中的摩擦效应

尽管超塑胀形作为一种金属成形方法正日渐受到世界各国的普遍关注，但对超塑约束胀形理论的研究报道却还很少，尤其对胀形过程的有限元模拟研究就更为罕见。针对这种情况，采用大变形刚粘塑性有限元法模拟了轴对称零件向圆筒形凹模内超塑约束胀形的变形过程，着重研究了工具工件之界面摩擦对胀形件厚度分布不均匀性和胀形板料向凹模角部充填性的影响．结果表明，随着摩擦的降低，胀形件的侧向较厚部分能有所减薄，可以改善整个胀形件的厚度均匀性，但当摩擦因子Ａｍ≤０．２（相当于摩擦系数μ≤０．１２）时，胀形件极顶部分的减薄过大；摩擦较小时，胀形板料向凹模角部的充填性较好；在考虑到极点附近厚度适度减薄和胀形板料对凹模角部充填性好的前提下，工艺上应当适当减小摩擦，其最佳状态是μ值约为０．３．为了检验所用刚粘塑性有限元法模拟的可靠性，将计算结果与试验结果作了对比，发现两者相当吻合。     

第Ⅱ类尺寸效应影响下金属薄板液压胀形本构模型研究

尺寸效应是微成形研究中的热点和难点之一。目前采用经典塑性理论仍不能对金属薄板液压胀形中尺寸效应对应力变化现象的影响进行较好的解释。为了深入分析该问题,结合应变梯度塑性理论,建立了第Ⅱ类尺寸效应影响下金属薄板液压胀形本构模型。基于该模型,分析了板料厚度变化以及胀形凹模直径变化对液压胀形过程流动应力变化的影响。研究结果表明应用该本构模型能较好地解释金属薄板液压胀形中尺寸效应对应力变化的影响,验证了该本构模型的正确性。     

材料参数对板材胀形过程综合影响的数值研究

本文将Hosford 与Hill 各向异性屈服函数应用于刚粘塑性有限元方法,分析了圆形薄板液压胀形过程.研究了材料性能参数:硬化指数n、速率敏感指数m、厚向各向异性参数R、屈服函数非多项式指数M 对液压胀形过程的综合影响.并通过数值分析,找出了临界厚向断裂应变-ε_3~(ov·)与材料参数关系的经验方程式.屈服表面形状对极限厚度应变的影响,可以用Barlat 提出的包含了R 和M 影响的p 值表示出来.     

选择性激光熔化316L不锈钢在不同成形策略下的冲击性能研究

采用选择性激光熔化(SLM)成形系统HK M250制备了垂直于Z轴的水平类型和平行于Z轴的垂直类型等多种工况的316L不锈钢冲击试样,并对试样缺口采取了SLM直接成形和机械加工成形两种方式。在室温条件下进行了316L不锈钢冲击实验,使用KEYENCE光学成像系统和扫描电镜观察了试样断口形貌,并用扫描电镜观察了不同成形截面的微观组织。实验结果表明,通过机械加工制作缺口相比于SLM直接成形缺口,其试样冲击性能更好;对于两种缺口制作方式,T(t)类型试样的冲击功明显低于H(h)类型试样,这主要是由于T(t)类型试样承载截面的内部缺陷多于H(h)类型试样,从而降低了其冲击功。     

变形-损伤耦合的起塑性恒压轴对称充模胀形的有限元模拟

采用大变形刚粘塑性有限元法模拟超塑性恒压轴对称充模胀形过程、分析了模具几何参数及材料参数对胀形过程中材料的流变行为、胀形制许厚度分布和成形时间的影响规律。给出了质点的流动轨迹、不同时刻制件的剖面形状及应力、应变分布；基于修正的Gurson粘塑性势推导了内部空洞体积分数累积增大模型并据此进行了变形-损伤耦合计算．     

DISCONTINUOUS AND IMPULSIVE EXCITATION

In this paper,we study the solution of differential equation with Dirac function andHeaviside function.arising from discontinuous and impulsive excitation.Firstly,accordingto the theory of differential equation,we suggest x(t)=x_1(t) x_2(t)H(t-a);then wederive the equation of x_1(t)and x_2(t) by terms of property of distribution,and by solvingx_1(t)and x_2(t)we obtain x(t);finally,we make a thorough investigation about periodicimpulsive parametric excitation.     

KINEMATICAL FORCE-FREE FIELDS OF A MAGNETIC ARCH

I.Introducti0nCosmicmagneticfieldswhichoccurinregionsofhighelectricalconductivityandlowdensitymightoftensatisfytheforce-freeconditioncurlH=a(r,t)H(l.l)whereHdenotesthedensityofthemagneticfleld,and2issomescalarfunctionofpositionandtime,sincethepressuregrad…     

变形—损伤耦合的超塑性恒压轴对称充模胀形的有限元模拟

采用大变形刚粘塑性有限元法模拟超塑性恒压轴对称充模胀形过程，分析了模具几何参数及材料参数对胀形过程中材料的流变行为、胀形制件厚度分布和成形时间的影响规律，给出了质点的流动轨迹，不同时刻制件的剖面形状及应力、应变分布；基于修正的Ｇｕｒｓｏｎ粘塑性势推导了内部空洞体积分数累积增大模型并据此进行了变形－损伤耦合计算。     

金属管爆炸胀形炸药能量传递的几何法

导出了金属管爆炸胀形估算炸药传递到工件表面能量几何法公式，该法以炸药的比能为基础进行计算，避免了能量法对大多数炸药缺少能量常数Ｃ和Ｇ试验数据的困难，因而可扩大各种炸药在金属管爆炸胀形中的应用。为炸药用量的估算提供一简单的方法。     

Forming limit during superplastic deformation of sheet metals

ＦＯＲＭＩＮＧＬＩＭＩＴＤＵＲＩＮＧＳＵＰＥＲＰＬＡＳＴＩＣＤＥＦＯＲＭＡＴＩＯＮＯＦＳＨＥＥＴＭＥＴＡＬＳＤｕＺｈｉｘｉａｏ（杜志孝）;ＬｉＭｉａｏｑｕａｎ（李淼泉）;ＬｉｕＭａｂａｏ（刘马宝）;ＷｕＳｈｉｃｈｕｎ（吴诗惇）（Ｆａｃｕｌｔｙ４０２ｏ...     

A noncontacting system for measuring effective stress-strain curves of ultra-thin X-ray-mask materials

A noncontacting test system has been developed for making measurements of the deformation characteristics of the ultra-thin (≈10μm) membrane structures of X-ray masks using a pneumatic bulge test. These measurements, which include the bulge height and radius-of-curvature at the pole, are then analyzed to provide composite estimates of the effective stress and effective strain of the mask membrane materials.     

Oscillatory flows in straight tubes with an axisymmetric bulge

A laser-Doppler anemometer has been used to study oscillatory flow of a Newtonian viscous fluid in straight circular tube with an axisymmetric bulge of two different sizes. The axial velocities were measured at successive cross-sectional planes for sinusoidal waveforms having Reynolds numbers (based on Stokes layer thickness at the inlet) from 445 to 806 and Womersley numbers ranged from 7.2 to 12.2. The cyclic flow development inside the bulge at different phases within a cycle was determined. Stability analysis obtained by solving the Orr–Sommerfield equation on instantaneous velocity profiles showed instability grows progressively during the acceleration phase and transition to turbulence in the bulge happened shortly after the commencement of the deceleration phase. Depending on the bulge geometry, the turbulent region was initially confined either to the proximal or the distal end of the bulge. This region would spread larger as the deceleration phase furthered and the smaller bulge had a larger spread than the bigger bulge. The differences could be attributed to the vortical structures development inside the bulge. Relaminarisation for the flow appeared in the subsequent acceleration phase. Finally, some comparisons had been made with results obtained from using the physiological waveform.     

Dynamic rupture of polymer–metal bilayer plates

Recent theoretical assessments of metal/polymer bilayers indicate a potentially significant delay in the onset of ductile failure modes, especially under dynamic loading, due to strain hardening of the polymer. The response of copper/polyurethane bilayers under dynamic and quasi-static loadings is investigated via static tensile, static bulge forming and dynamic bulge forming tests. Two polyurethanes PU1 and PU2 were chosen with a significant contrast in stiffness and ductility: PU1 has a glass transition temperature T_g close to ?56 °C and at room temperature it has a low modulus, low strength and a high tensile failure strain. In contrast, PU2 has a T_g of 49 °C and at room temperature it has a high modulus and strength but a much smaller tensile failure strain. In most of the tests, the polymer coatings were approximately twice the thickness of the metal layer. Under static loadings (tensile and bulge forming) the PU2 bilayer outperformed the uncoated metal plate of equal mass while the PU1 bilayer had a performance inferior to the equivalent uncoated plate. We attribute this to the fact that the PU2 retards the necking of the copper layer and thus increases its energy absorption capacity while the PU1 coating provides no such synergistic effect. The dynamic bulge forming tests indicate that on an equal mass basis, the dynamic performance of the PU2 bilayers with a weakly bonded polymer coating were comparable to the uncoated plates but intriguingly, when the PU2 was strongly adhered to the copper plates the performance of these bilayers was inferior to that of the uncoated plates. Thus, the coatings do not provide dynamic performance benefits on an equal mass basis. However, it is shown that increasing the mass of a plate by adding a polyurethane layer can improve the performance for a given total blast impulse. Given the ease of applying polyurethane coatings they may provide a practical solution to enhancing the blast resistance of existing metallic structures.     

Balanced Biaxial Testing of Advanced High Strength Steels in Warm Conditions

The main purpose of the present work is to measure the stress–strain behavior under warm conditions (about 100 °C) of advanced high strength steel (AHSS) sheets up to large strains compared to uniaxial tension. The test equipment consists of two main parts, i.e., a hydraulic bulge tester and a heating device. A mechanical system is attached to the test equipment for measuring the membrane stress and thickness strain at the bulge pole. The stress–strain curves were measured for three kinds of AHSS sheets with the proposed test method for various initial temperatures (10, 50 and 100 °C). The proposed method does not provide isothermal stress–strain curves because the specimen temperature increases during the test due to the effect of deformation-induced heating. A numerical scheme using thermo-mechanical finite element (FE) simulations is suggested to deconvolute the isothermal stress–strain curves.     

Measurement of the shapes of foil bulge-test samples

Accurate measurements of important tensile properties of thin metal foils are often quite difficult to achieve in uniaxial tests because of sample-preparation difficulties and the tensile instability called necking. Consequently, hydraulic bulge tests have been introduced as a successful means of suppressing these problems through the use of a simplified specimen geometry and biaxial rather than uniaxial tensile-stress states. Considerable effort has been made by various investigators to relate such biaxial stress-strain and ductility data to uniaxial data, generally following the assumption that the bulge is shaped like a spherical cap. The present study evaluates this assumption for foils by measuring actual shapes with unprecedented accuracy and detail using the two-source holographic technique and a polynomial-spline computer analysis of the resulting interferograms. These measurements were made on nine specimens of 0.127-mm-thick annealed rolled copper foil which had been deformed into bulges of varying heights up to rupture. A comparison is made between the measured shapes and the spherical-cap shape generally assumed in the interpretation of bulge-test data. The spherical assumption gives results which are reasonably valid for the later stages of deformation. Indeed, the stress-strain curve obtained from bulge testing corresponds closely with the uniaxial tensile curves for this material. The strain at failure (i.e., elongation) was greater in the biaxial bulge test than in the uniaxial test but not nearly as great as the strain expected from a theoretical model proposed by Hill. However, all the specimens measured exhibited localized areas with larger radii of curvature. The presence of these “flats” may be associated with a mode of failure in the bulge test which corresponds to necking instability in the uniaxial test, and thereby account for the limited strain to failure.     

Mathematical modelling of the superplastic forming of a long rectangular sheet

Standard finite element software (ANSYS FEM-code) is used to model the superplastic forming of a superplastic sheet alloy into a rectangular die. As distinct from other known approaches the boundary value problem is stated in the present study in terms of the theory of creep. The results of finite element calculations are found to be in a good agreement with corresponding analytical solutions and experimental data for titanium sheet alloy Ti-6Al-4V. The approach suggested can be used in practice for estimating the current geometry and the thickness of the dome and the time intervals both for the constant gas pressure forming and for the constant strain rate forming.     

动脉瘤内流场以及瘤体尺寸的影响的数值研究

采用计算流体动力学(CFD)数值模拟的方法,在周期性脉动速度入流条件下,建立刚性动脉瘤模型并研究了动脉瘤模型中流场的特征(速度、压力、壁面剪切应力)。得到了脉动入流一个周期内流场特征的变化规律,发现动脉瘤的后端有相当高的压力和壁面剪切应力,而且高压力和壁面剪切应力分布的位置几乎是固定的。探讨了不同动脉瘤尺寸对内部流场的影响,动脉瘤的直径与瘤体长度之比越大,瘤壁承受的剪切应力就越大,动脉瘤破裂的危险性就越高。     

Membrane Curvatures and Stress-strain Full Fields of Axisymmetric Bulge Tests from 3D-DIC Measurements. Theory and Validation on Virtual and Experimental results

The bulge test is mostly used to analyze equibiaxial tensile stress state at the pole of inflated isotropic membranes. Three-dimensional digital image correlation (3D-DIC) technique allows the determination of three-dimensional surface displacements and strain fields. In this paper, a method is proposed to determine also the membrane stress tensor fields for in-plane isotropic materials, independently of any constitutive equation. Stress-strain state is then known at any surface point which enriches greatly experimental data deduced from the axisymmetric bulge tests. Our method consists, first in calculating from the 3D-DIC experimental data the membrane curvature tensor at each surface point of the bulge specimen. Then, curvature tensor fields are used to investigate axisymmetry of the test. Finally in the axisymmetric case, membrane stress tensor fields are determined from meridional and circumferential curvatures combined with the measurement of the inflating pressure. Our method is first validated for virtual 3D-DIC data, obtained by numerical simulation of a bulge test using a hyperelastic material model. Afterward, the method is applied to an experimental bulge test performed using as material a silicone elastomer. The stress-strain fields which are obtained using the proposed method are compared with results of the finite element simulation of this overall bulge test using a neo-Hookean model fitted on uniaxial and equibiaxial tensile tests.     

The analysis of forming the bulge in a spilling water wave

The early stages of a spilling breaking water wave leading to the formation of a bulge on the forward face of the wave are investigated. In this study, simultaneous space-time measurements of the free-surface elevation of a spilling breaking water wave are recorded and analyzed. The analysis, carried out in the frame of reference moving with the crest of the wave, reveals that the formation of the bulge is due to the presence of a shock-like mode. In the previous frame of reference, the shock itself is unsteady but its (spatial) location is time independent and coincides with the “toe” of the bulge. As time increases, the shock undergoes a flip (a reflection symmetry) with respect to the midpoint of our time interval. Such a flip is responsible for an abrupt increase of the wave steepness, which will lead to wave breaking at later times. Following these observations, we present a two-dimensional quantitative model which reproduces both the formation of the bulge and the sudden increase of the wave steepness. Supported by the Foundation of the State Education Commission of China