微尺度压痕实验的数值模拟及相关问题研究

目前国际上占主导地位的纳米压痕技术是由Oliver与Pharr提出并发展,目前的纳米压痕可以给出整个加、卸载过程的载荷—位移曲线以及硬度与弹性模量随压痕深度变化的曲线,从而提供了丰富的、比较精确的信息,为利用它探索材料比较完整的力学特性提供了可能.为达到该目的,就必须对压痕实验的加、卸过程进行较为深入的研究.作为主要的研究工具,有限元方法模拟微压痕过程在探讨通过实验数据得到更多、更准确的材料表层力学性能参数以及解释实验现象等方面发挥着重要作用.基于计算机速度与容量的原因,较早进行微压痕过程有限元模拟的BhattacharyaandNix、LaursenandSino都使用圆锥压头模拟维氏显微硬度标准正四棱锥Vicker压头与纳米压痕仪标准正三棱锥Berkovich压头,因为圆锥压头具有旋转对称性,可用二维旋转对称单元(二维实体单元)进行计算从而降低计算规模.即便如此,以当时大型计算机的水平,对规模为400~2000个四节点矩形单元的有限元模型进行一次完整的加、卸载过程也需要1~2天.到目前为止,微尺度压痕实验的数值模拟沿用二维模型.事实上,由于加工工艺的限制,微尺度压痕仪的压头如Berkovich与Vicker压头均不个旋转对称性;就微观尺度而言,实际的表层材料都是非均匀的.这些特征均不能由二维模拟体现,所以该文首先建立三维有限元模型,模拟带滑动接触的微尺度压痕加、卸载过程.在此基础上重点讨论了压头几何效应的问题,如二维模拟与三维模拟的关系、显微硬度与纳米的压痕硬度的关系、不同压头下材料的应力应变场、压痕间距与压痕边界的效应等,最后针对微尺度压痕实验中出现的压痕硬度随压痕深度减小而升高的现象,讨论了影响不同压痕深度硬度值的因素.

若干流体力学问题的数学性质研究

该文利用高智的扩散抛物化方程组理论及流体力学基本方程组的特征次特征理论,流体大小尺度（LSS）方程组理论以及摄动有限差分（PFD）方法,研究若干流体力学问题的数学性质.该文得到的主要结论有：1.利用湍流大小尺度（LSS）方程组推导出湍流大小尺度涡量（LSSV）方程组,并证明两个关于湍流大小尺度涡量的命题,从而得到湍流封闭大小尺度涡量（CLSSV）方程组,并对已有的近程相互作用命题进行推广.2.根据扩散抛物化方程组理论和流体力学层次结构方程组的特征和次特征方法,研究了抛物化稳定性方程组（PSE）的特征和次特征以及消除PSE的剩余椭圆特性的问题.3.利用摄动有限差分（PFD）方法得到对流扩散反应方程的变步长摄动有限差分格式,是等步长摄动有限差分格式的推广.

肝脏中生物流体流动的多重介质渗流模型和数值模拟

本文采用生物渗流理论，建立了肝脏内不同生物流体流动的多重介质渗流模型，采用有限元法求解这种特殊的渗流问题，根据数值计算结果揭示了肝内血液、组织液以及胆汁等的流动规律，并探讨了肝脏血流动力学的一些问题。论文将肝脏内部与生物代谢功能有关的肝血窦和窦周间隙当作两重并存的多孔介质，血液在肝血窦中，以及组织液在窦周间隙中的流动均当作渗流处理，通过Starling公式考虑了两重介质之间的流量交换，从而建立了肝血窦-窦周间隙的双重介质模型。针对肝脏胆汁分泌功能，将肝脏内密布的毛血肝管网当作多孔介质，以受静压及渗透压驱动的流体跨壁流动表示肝汁从肝细胞向毛细肝管的分泌，肝汁在毛细胆管网中的流动作为渗流处理，从而建立了肝汁分泌与输运的双重介质模型。采用有限元法求解了生物流体的双重介质渗流问题，针对非牛顿渗流和两重介质的相互作用，本文发展了一种嵌套迭代方法，即采用直接迭代求解血液在肝血窦中的非线性渗流，采用交替迭代解决双重介质渗流中由跨壁流支引起的相互流体交换，直接迭代嵌套于交替迭代中。这种算法比较有效的解决了包含非牛顿渗流的双重介质渗流问题。根据生物多孔介质中微细管系统的构筑方式以及不同微细管系统之间的联系方式，论文提出将生物多孔介质划分为分级多孔介质和多重多孔介质两种主要类型。基于多相混合物的平均化的理论，论文推导了双重多孔介质中的动量守恒方程、质量守恒方程以及相应的渗流方程，建立了双重多孔介质渗流的平均化模型。基于分级多孔介质渗流的理论，论文将脏器中的血管树按管径分为不同级别的多孔介质，各级血管中和血液流动均作为渗流处理，从而提出了计算脏器整体血流的一种渗流方法。采用这种方法，在论文提出的肝血窦 - 窦周间隙双重介质渗流流模型的基础之上，初步研究了肝脏门静脉系统的血液动力学规律。采用本文提出的肝血窦 - 窦周间隙双重介质模型和胆汁分泌 - 流动的双重介质模型，得到了血液、组织液和胆汁在肝小叶中的压力分布和速度分布，并分析了肝血窦壁的跨壁流动模式，胆汁流量的影响因素，以及窦周间隙中组织液流量与肝血窦中血液流动及肝血窦壁渗透系数等因素的关系，揭示了肝脏内血液、组织液及胆汁等生物流体流动的一般规律。

脉冲激光离散重熔热物理及组织性能研究

利用OM及FEM研究了铁基合金Nd:YAG脉冲激光熔凝区的几何形态及其变化规律、以及熔凝的热物理过程；利用OM、SEM、TEM、X-射线衍射仪及磨损实验机，研究了两种铁基热模具材料脉冲激光熔凝组织及其时效组织结构，以及熔凝区规则离散分布规律对材料抗磨损性能的影响。在10~5～10~7W/cm~2的脉冲激光平均功率密度范围内，可得到热传导型和深熔型两类强化区，当临界平均功率密度大于5 * 10~5W/cm~2，同时临界激光作用时间大于2ms时，热传导型强休区向深熔型强休区转变。熔化过程中，在熔池中形成上部以对流传热为主，底部以导热为主的传热模式，流场、温度场和压力场均随脉冲激光作用时间变化，最大流速、压力和温度梯度分别可达100m/s、数个大气压和10~(8-9) ℃C/m量级。凝固过程中，固液界面上的最大温度梯度、凝固速率和冷却速度时间和空间位置变化，分别可达10~(8-9) ℃/m量级、10~(-1)m/s量级和10~(7-8) ℃/s量级，其中冷却速度得到实验验证。亚共晶合金铸铁脉冲激光熔凝组织为δ-铁素体与M_3C的层片状共晶组织，还含有部分γ-奥氏体和少量的高碳孪晶马氏体组织，δ-铁素体和γ-奥氏体中均存在高密度位错亚结构。5CrMnMo钢脉冲激光熔凝组织由板条马氏体及少量的孪晶马氏体构成，马氏体中也存在高密度位错亚结构。上述两种组织经高温时效后，仍保持较细的晶粒，并有大量细小均匀弥散分布的碳化物析出，其中铸铁熔凝组织析出M_(23)C_6碳化物，M_(23)C_6可在M_3C/γ-奥氏体相界面或M_3C内部原位形核，亦可在δ-铁素体中弥散析出。两种材料的熔凝组织及其时效组织的显微硬度均明显高于相应的原始组织，也高于激光连续扫描熔凝的结果。脉冲激光规则离散熔凝加工在材料表面形成软硬相间的“原位”功能层，能显著降低裂纹形成的敏感性，提高材料表层的抗磨粒磨损性能，时效后仍具有较好的抗磨损性能。以熔凝强化区直径作为中心间距进行规则离散熔凝处理可使材料表面获得最佳抗磨损性能。

微裂纹细观损伤理论

材料的宏细观破坏理论是当前固体力学和材料科学研究的一个重要课题。本文在对连续损伤理论和细观损伤理论进行评述的基础上，着重研究了脆性材料中微裂纹细观损伤问题。本文建立了一套完整的细观损伤理论来分析二维多裂纹体问题。该理论的基本方法是基本解叠加法，此方法直接考虑了微裂纹之间的相互作用以及有限边界的影响。通过叠加原理，使在裂纹面和外边界满足边界条件，用边界配置法化控制方程组为线性方程组，进行数值求解。本文以裂纹密度为参量，针对微裂纹随机分布和平行分布两种情况，计算了无限大体中代表性体元（VRVE）和多裂纹有限体的有效弹性模量。数值计算结果表明，本文所用方法具有统一与直能的优点，采用此法所得模量与试验结果吻合，在处理多裂纹体问题时计算效率高、精度好，对求解多裂纹问题非常有效。此外，通过建立微裂纹晶内扩展准则和穿晶扩展准则，分析了微裂纹扩展连接直至裂纹形成、扩展这一全过程的细观力学行为，对微裂纹的损伤演化过程进行了直接模拟，计算了含微裂纹矩形板的宏观应国变关系曲线。本文进一步提出了三维微裂纹相互作用的数学分析方法 — 扁球坐标和位移函数法，并采用边界配置法或裂纹面面力平均化方法进行求解。数值结果表明，扁球坐标和位移函数法分析三维微裂纹的相互作用问题是有效可行的。最后，本文提出了埋入基体的镶嵌体胞模型，建立了计算非均质体有效弹性模量的解析表达式。该式从理论上讲是严格的，且具有形式简单、内涵丰富及有效弹性模量能显式表达等优点。针对球体含球形夹杂、裂纹及旋转扁球体含球形夹杂、裂纹等不同体胞结构计算了其有效弹性模量，并与其他细观力学方法所得结果进行了比较。本文还将埋入基体的镶嵌体胞模型进行了发展，研究了二相颗粒复合材料的弹塑性本构关系（基体为弹性而颗粒为塑性材料），计算了球体含球形颗粒用旋转扁球体含扁球状颗粒两种体胞结构的宏观应力 - 应变曲线。

COLOR-HOLOGRAPHY USING THE ANGULAR SELECTIVITY OF VOLUME RECORDING MEDIA

A display hologram of an object can be recorded and reconstructed in three primary colors if the angular selectivity of volume recording media is exploited. Three holograms are recorded in the same medium, each at a different primary color. These three holograms are reconstructed by simultaneous illumination of the hologram with the original reference beams. By proper choice of the angles that the reference beams make to the hologram, it is possible to suppress strongly cross talk between the different reconstructions (e.g., the red object reconstruction in green light). The technique exhibits high resolution, high diffraction efficiency, and vivid colors. Through the addition of three holographically recorded volume gratings it is possible to reconstruct the hologram with a beam of white light. The saturation and brightness of each primary color in the reconstruction can be adjusted by selection of an appropriate thickness for the corresponding grating.

Space-resolved spectral diagnosis of line-shaped laser-produced magnesium plasmas

Space-resolved spectra of line-shaped laser-produced magnesium plasmas in the normal direction of the target have been obtained using a pinhole crystal spectrograph. These spectra are treated by a spectrum analyzing code for obtaining the true spectra and fine structures of overlapped lines. The spatial distributions of electron temperature and density along the normal direction of the target surface have been obtained with different spectral diagnostic techniques. Especially, the electron density plateaus beyond the critical surface in line-shaped magnesium plasmas have been obtained with a fitting technique applied to the Stark-broadened Ly-alpha wings of hydrogenic ions. The difference of plasma parameters between those obtained by different diagnostic techniques is discussed. Other phenomena, such as plasma satellites, population inversion, etc., which are observed in magnesium plasmas, are also presented.

Attosecond pulse extreme-ultraviolet photoionization in a two-color laser field

Attosecond-pulse extreme-ultraviolet (XUV) photoionization in a two-color laser field is investigated. Attosecond pulse trains with different numbers of pulses are examined, and their strong dependence on photoelectronic spectra is found. Single-color driving-laser-field-assisted attosecond XUV photoionization cannot determine the number of attosecond pulses from the photoelectronic energy spectrum that are detected orthogonally to the beam direction and the electric field vector of the linearly polarized laser field. A two-color-field-assisted XUV photoionization scheme is proposed for directly determining the number of attosecond pulses from a spectrum detected orthogonally. (C) 2005 Optical Society of America.

Single attosecond pulse generation using two-color polarized time-gating technique

It is proposed that single attosecond pulses be generated via high-order harmonic generation by using a two-color pump pulse with time dependent ellipticity. The two-color pump pulse is created by the fundamental field and its second harmonic: the fundamental field is left-circularly polarized and the second harmonic is right-circularly polarized. Numerical simulations show that single attosecond pulses can be produced in the cut-off region by using the synthesis of 20 fs left-hand and right-hand circularly polarized pulses with a pulse delay of 20 fs. The attosecond pulses produced this way are much stronger than that produced by a few-cycle linear polarized pulse of comparable intensity. (c) 2005 Optical Society of America

Optimization of multi-cycle two-color laser fields for the generation of an isolated attosecond pulse

The effect of the mixing of pulsed two color fields on the generation of an isolated attosecond pulse has been systematically investigated. One main color is 800 nm and the other color (or secondary color) is varied from 1.2 to 2.4 mu m. This work shows that the continuum length behaves in a similar way to the behavior of the difference in the square of the amplitude of the strongest and next strongest cycle. As the mixing ratio is increased, the optimal wavelength for the extended continuum shifts toward shorter wavelength side. There is a certain mixing ratio of intensities at which the continuum length bifurcates, i.e., the existence of two optimal wavelengths. As the mixing ratio is further increased, each branch bifurcates again into two sub-branches. This 2D map analysis of the mixing ratio and the wavelength of the secondary field easily allows one to select a proper wavelength and the mixing ratio for a given pulse duration of the primary field. The study shows that an isolated sub-100 attosecond pulse can be generated mixing an 11 fs full-width-half-maximum (FWHM), 800 laser pulse with an 1840 nm FWHM pulse. Furthermore the result reveals that a 33 fs FWHM, 800 nm pulse can produce an isolated pulse below 200 as, when properly mixed. (c) 2008 Optical Society of America.

Enhancement and broadening of extreme-ultraviolet supercontinuum in a relative phase controlled two-color laser field

We experimentally demonstrate the generation of an extreme-ultraviolet (XUV) supercontinuum in argon with a two-color laser field consisting of an intense 7 fs pulse at 800 nm and a relatively weak 37 fs pulse at 400 nm. By controlling the relative time delay between the two laser pulses, we observe enhanced high-order harmonic generation as well as spectral broadening of the supercontinuum. A method to produce isolated attosecond pulses with variable width and intensity is proposed. (C) 2008 Optical Society of America.

Reduced deep-tissue image degradation in three-dimensional multiphoton microscopy with concentric two-color two-photon fluorescence excitation

We theoretically demonstrate that enhanced penetration depth in three-dimensional multiphoton microscopy can be achieved using concentric two-color two-photon (C2C2P) fluorescence excitation in which the two excitation beams are separated in space before reaching their common focal spot. Monte Carlo simulation shows that, in comparison with the one-color two-photon excitation scheme, the C2C2P fluorescence microscopy provides a significantly greater penetration depth for imaging into a highly scattering medium. (C) 2008 Optical Society of America.

Theoretical investigation of single attosecond pulse generation in an orthogonally polarized two-color laser field

We theoretically demonstrate the generation of extreme ultraviolet supercontinua in an orthogonally polarized two-color few-cycle laser field. We show that the ionized electrons can be driven back to their parent ion after traveling along curved trajectories in a plane perpendicular to the beam propagation direction, giving rise to a train of attosecond pulses at different polarization angles. A single isolated attosecond pulse can be obtained by blocking the low-order high harmonics, which contribute to the formation of the satellite pulses. (C) 2008 Optical Society of America.

Two-color two-photon excitation of indole using a femtosecond laser regenerative amplifier

The fluorescence emission from indole resulting from two-color two-photon (2C2P) excitation with 400 and 800 nm wavelengths is observed, using the second harmonic and fundamental wavelength of a 800 nm 40 fs pulsed Ti:Sapphire femtosecond (fs) regenerative amplifier operating at a repetition rate of 1 kHz. By delaying one fs laser pulse relative to the other, the cross correlation of fluorescence is observed, which indicates the generation of 2C2P fluorescence signal in the experiment. The strongest 2C2P fluorescence emission characterized by the peak of cross correlation curve suggests optimal temporal overlap of the two fs laser pulses. The 2C2P fluorescence signal is linearly dependent on the total excitation intensity. The fluorescence signals with 400 nm and 800 nm irradiation alone are also demonstrated and discussed in this paper. (C) 2008 Elsevier B.V. All rights reserved.