基于箭形累积损伤的裂纹尖端力学:奇异性分级和多尺度分段

在适度的空间和时间尺度组合下,裂纹既可在几个月中蠕变几个纳米,也能在几秒钟内扩展10km.虽然裂纹的尖端没有实际的质量,但是它能通过激活周围的物质而处于高能量状态.依赖于材料的损伤方向,激活质量的减少和增加可发生在尺度转变之前或之后.每个尺度区的分段阈值被假定为与裂纹尖端速度的平方a~2和激活质量密度M的乘积有关:W=M_(↓↑)a_(↑↓)~2和D=M~(↓↑)a_(↑↓)~2.W和D分别被称为直接吸收和自耗散能量密度.正如下标/上标符号所示,激活的质量密度M_(↓↑)和M~(↓↑)与裂纹尖端速度a变化趋势相反,既可增加也可减少.a~2和M的互补效应隐含着常用于宇宙物理学建模的膨胀和/或收缩的物理过程.在用于尺度敏感的裂纹尖端的行为时,激活的质量密度有相同的解释.分段时的多尺度可以由…皮观、纳观、微观和宏观…组成.因此,形象地说,材料损伤过程可以通过裂纹扩展过程中非均匀的总体和局部能量的传递来模拟.疲劳裂纹扩展引起的材料损伤被用来阐释由大到小和由慢到快的尺度/时间序,热力学中的冷→热和有序→无序转换.这一过程正巧与宇宙演化的箭形方向相反,宇宙演化遵循小→大和快→慢,而热力学相反,遵循热→冷和无序→有序.为了表示由损伤萌生所造成的类裂缝型缺陷的不均匀性,提出了一个被称为裂纹尖端力学(crack tip mechanics,CTM)的新模式.涉及的范围是模拟原子列之间的界面裂纹或连续体中分叉的切口.假如需要的话,尺寸和时间的范围可以复盖从皮观到宏观甚至更大.虽然采用疲劳裂纹来说明CTM的基本原理,在宇宙物理学背景中与直接吸收和自耗散相关的膨胀和收缩的情况可以描述裂纹周围激活质量的行为,它们可看为能量的汇或源.奇异性被用来捕获能量的源或汇的特性,物理上,两者作为界面的一部分,从数学上看则是不连续的线的一部分.能量从一种形式变为另一种形式取决于能量吸收或耗散的箭形损伤时间,这之中牵涉到尺度分段和奇异性强度的联合应用.材料组分随时间的劣化是根据指定的设计寿命导出的,从而使材料的响应与加载率的时间历史匹配.2024-T3铝板的皮观/纳观/微观/宏观开裂模型用来说明什么地方可以增加结构的寿命部分.皮观/纳观/微观/宏观/结构系统的性能随时间劣化可以用9个尺度转变物理参数来描述:纳观/微观区有3个(μ_(na/mi)~*,σ_(na/mi)~*,d_(na/mi)~*),微观/宏观区有3个(μ_(mi/ma)~*,σ_(mi/ma)~*,d_(mi/ma)~*),皮观/纳观区有3个(μ_(pi/na)~*,σ_(pi/na)~*,d_(pi/na)~*).下标pi,na,mi,ma和struc分别表示皮观、纳观、微观、宏观和结构.只要知道两个相连的尺度敏感参数,在较低尺度的时间相关的局部物理参数就完成了分析连续体的形式论,虽然它们并不需要用实验来知道.更具体地说,根据皮观→纳观→微观→宏观分别有1.25/1.00/0.75/0.50的λ奇异性强度,皮观裂纹、纳观裂纹、微观裂纹和宏观裂纹的转变特征是从时间箭形的指定的寿命预期来确定的.附加的0.25强度的奇异性可用于结构元件.回想起来,λ=0.5相应于断裂力学中的应力分量与r~(0.5)成反比,r是与宏观裂纹尖端的距离.微观裂纹、纳观裂纹和皮观裂纹分别赋予r~(-0.75),r~(-1.0),r~(-1.25)的奇异性.箭形时间(以年为单位)取决于问题的定义.设备的关键部件可用1.5~±/2.5~±/3.5~±/5.5~±寿命分布和总寿命为13~±年(a)的皮观/纳观/微观/宏观尺度来设计运行.上标±表示多于或少于实际运行的时间.累进损伤被假定为发生在皮观→纳观→微观→宏观方向.同样的方案用于20年总寿命的2024-T3铝板的疲劳损伤,按照1.5~±/2.5~±/3.5~±/5.5~±/7.0~±的方式将它的寿命分布在皮观、纳观、微观、宏观和结构的尺度上,这样的指定只是满足在每个尺度范围内损伤内部材料结构所用的能量匹配,因此可以强制执行在总寿命的跨度内精确的时间相关的材料性能劣化过程.     

Synthesis of Novel Chiral Diol Ligands for the Enantioselective Reactions

The chiral diols ((,(,((,((-Tetraaryl-1,3-dioxolane-4,5-dimethanols) have been used for the formation of cyclic titanates and similar derivatives of Mg, Al and Zr. These complexes of oxophilic metal centers were employed in catalytic and stiochiometric enantioselective reactions such as enantioselective addition reactions of carbon-centered nucleophiles to aldehydes1, [2+2] cycloadditions2, and Diels-Alder reactions3. So far, the two hydrogen atoms of all this type of diols are in trans form…     

The diffraction of elastic waves by an imperfect fusion bond

We consider diffraction by a semi-infinite crack located alonga fusion interface between two differing elastic media. Twotypes of crack, namely open and partially closed cracks, areinvestigated. An open crack is modelled by a stress-free contactboundary condition and a partially closed crack is modelledby a spring contact boundary condition. For the latter, thejump in the stress across the crack is assumed to be proportionalto the jump in the displacement across the crack. This situationarises in, for example, a K-weld where the fine grain of theparent material (for example, ferritic or forged austeniticsteel) is in stark contrast with the coarse-grained weld metal(for example, austenitic weld metal). In the metal weld thedirection of the grain axis varies through the metal. However,diffraction is a local phenomenon and so the austenitic steelis assumed to have a zonal axis so that it may be modelled bya transversely isotropic composite. The ferritic or forged austeniticsteel will be modelled as an isotropic material.     

On the electric current from electrodes in a magnetized semiconductor film

The problem on the electric current from electrodes in a magnetizedsemiconductor film is reduced to the skew derivative problemfor the Laplace equation outside cuts in a plane. The problemfor the Laplace equation is studied under different conditionsat infinity, which have a certain physical meaning. With thehelp of potential theory, the skew derivative problem is reducedto a Fredholm integral equation of the second kind, which isuniquely solvable. The Neumann problem for the Laplace equationin the exterior of cuts in a plane is a particular case of ourproblem.     

Synthesis and luminescence properties of Cr(III) complexes with cyclam-type ligands having pendant chromophores, trans-[Cr(L)Cl(2)]Cl

The synthesis and spectroscopic properties of new cyclam-type ligands 5,7-dimethyl-6-R-1,4,8,11-tetraazacyclotetradecane (L), where R is a pendant chromophore such as an anthracene derivative, are reported. These ligands were prepared according to a nickel(II) template procedure, and the X-ray crystal structures of several Ni(II) intermediates are described. Reaction of the free base ligands L with CrCl(3)x3THF resulted in facile formation of trans-[Cr(L)Cl(2)]Cl complexes, and the structures and spectroscopic characterizations of these complexes are also described. Examination of the photophysical properties of trans-[Cr(L)Cl(2)]Cl solutions at 77 K demonstrated the emission spectra to be dominated by phosphorescence from the ligand field doublet of the chromium(III) center. This also applies to the Cr(III) complex trans-[Cr(mac)Cl(2)]Cl, where mac is the anthracene derivative 5,7-dimethyl-6-anthracenylcyclam. Excitation into the pi-pi(*) states of the anthracene leads to marked quenching of the fluorescence from this chromophore and sensitized phosphorescence from the metal-centered doublet state.     

Metal-insulator crossover in high T c cuprates: A gauge field approach

A metal-insulator crossover appears in the experimental data for in-plane resistivity of underdoped cuprates and a range of superconducting cuprates in the presence of a strong magnetic field suppressing superconductivity. We propose an explanation for this phenomenon based on a gauge field theory approach to the t-J model. In this approach, based on a formal spin-charge separation, the low energy effective action describes gapful spinons (with a theoretically derived doping dependence of the gap m _s ² ∼ δ| ln δ|) and holons with finite Fermi surface (ɛF ∼ tδ) interacting via a gauge field whose basic effect on the spinons is to bind them into overdamped spin waves, shifting their gap by a damping term linear in T, which causes the metal-insulator crossover. The presence of a magnetic field perpendicular to the plane acts by increasing the damping, in turn producing a big positive transverse in-plane magnetoresistance at low T, as experimentally observed.     

Zinc dissolution and passivation in buffered phosphate solutions: Part I. A comparative study with sodium hydroxide solutions

Zn dissolution and passivation in buffered phosphate electrolyte in the pH range between 7 and 13.5 has been studied under a wide variety of experimental conditions. The electrode rest potential shows three regions depending on pH. Between pH 7 and 10 a constant value was found while a slope of 60 mV is obtained from a plot of E_r vs. pH. In the pH range 10–11.5 a mixed potential could be established due to the minimum buffer capacity of the system. The necessary charge for passivation was found to be 1.5 mC cm^?2 and this was attributed to a monolayer film. From l.s.v. and RDE results a change on Zn dissolution mechanism from a dissolution precipitation to a solid phase process with pH can be postulated. Time and potential effects on product reduction would show that there are chemical transformations on the electrode surface as a second step on the electrode poassivation. From experimental kinetic parameters an empirical rate equation for Zn dissolution is found asi_a=2k_aFc_OH^?c_{(PO4^3?)t^0.5}exp[(3/2)EF/RT)]Accordingly a reaction mechanism is postulated where PO₄^3? ions act as dissolution promoters, while HPO₄^2?, through the formation of NaZnPO₄·H₂O glass, would act as a dissolution inhibitor.     

A new approach to reduction of the Neumann problem in acoustic scattering to a non-hypersingular integral equation

The Neumann problem for the propagative Helmholtz equation inthe exterior of several bodies (obstacles) is studied in twoand three dimensions by a special modification of the boundaryintegral equation method. This modification can be called the'method of interior boundaries', because additional boundariesare introduced inside scattering bodies. The solution of theproblem is obtained in the form of a single layer potentialon the whole boundary. The density in the potential satisfiesthe uniquely solvable Fredholm equation of the second kind andcan be computed by standard codes. In fact our method holdsfor any positive wave numbers.