The stress driven instability in elastic crystals: Mathematical models and physical manifestations

Summary Equilibrium equations and stability conditions for the simple deformable elastic body are derived by means of considering a minimum of the static energy principle. The energy is supposed to be sum of the volume (elastic) and the surface terms. The ability to change relative positions of different material particles is taken into account, and appropriate natural definitions of the first and second variations of the energy are introduced and calculated explicitly. Considering the case of negligible magnitude of the surface tension, we establish that an equilibrium state of a nonhydrostatically stressed simple elastic body (of any physically reasonable elastic energy potential and of any symmetry) possessing any small smooth part of free surface is always unstable with respect to relative transfer of the material particles along the surface. Surface tension suppresses the mentioned instability with respect to sufficiently short disturbances of the boundary surface and thus can probably provide local smoothness of the equilibrium shape of the crystal. We derive explicit formulas for critical wavelength for the simplest models of the internal and surface energies and for the simplest equilibrium configurations. We also formulate the simplest problem of mathematical physics, revealing peculiarities and difficulties of the problem of equilibrium shape of elastic crystals, and discuss possible manifestations of the above-mentioned instability in the problems of crystal growth, materials science, fracture, physical chemistry, and low-temperature physics.     

聚丙烯/POE共混组成对材料断裂行为的影响

采用基本断裂功(EWF)方法对聚丙烯(PP)/聚烯烃弹性体(POE)共混物的注射双边缺口拉伸试样的断裂行为进行了研究,比较了不同POE含量对共混物各断裂参数的影响.结果表明,PP和用量为5phr POE的共混物都可完全满足EWF方法的要求,共混物的断裂韧性-比基本断裂功we,较PP有显著提高;POE用量为10phr以上的共混物则出现明显的成颈现象而限制了EWF方法的应用;PP和各种POE用量的共混物都得到了其屈服所需要的比基本断裂功we,y和比塑性功β′wp,y.     

Hydraulic conductivity of rock fractures

The flow of a single-phase fluid through a rough-walled rock fracture is discussed within the context of fluid mechanics. The derivation of the cubic law is given as the solution to the Navier-Stokes equations for flow between smooth, parallel plates - the only fracture geometry that is amenable to exact treatment. The various geometric and kinematic conditions that are necessary in order for the Navier-Stokes equations to be replaced by the more tractable lubrication or Hele-Shaw equations are studied and quantified. In general, this requires a sufficiently low flow rate, and some restrictions on the spatial rate of change of the aperture profile. Various analytical and numerical results are reviewed pertaining to the problem of relating the effective hydraulic aperture to the statistics of the aperture distribution. These studies all lead to the conclusion that the effective hydraulic aperture is less than the mean aperture, by a factor that depends on the ratio of the mean value of the aperture to its standard deviation. The tortuosity effect caused by regions where the rock walls are in contact with each other is studied using the Hele-Shaw equations, leading to a simple correction factor that depends on the area fraction occupied by the contact regions. Finally, the predicted hydraulic apertures are compared to measured values for eight data sets from the literature for which aperture and conductivity data were available on the same fracture. It is found that reasonably accurate predictions of hydraulic conductivity can be made based solely on the first two moments of the aperture distribution function, and the proportion of contact area.     

磁场对含稀土铝锂合金断裂特征的影响

以含铈铝锂合金为研究对象，研究了磁场对含稀土铝锂合金时效过程的影响，从断裂特征及微观组织两方面分析了磁场作用规律。实验结果表明：未加磁场时，合金的断裂特征以理断裂为主；扁平晶粒厚度不匀，在磁场作用下，此合金的断裂特征与微观组织发生明显改观，随磁感应强度增强，合金主断裂面上准解理断裂特征减弱，同时二次裂纹增多，分层比较升高；扁平晶粒厚度变薄，尺寸趋于均匀。用少体物理理论，探讨了磁场对含稀土合金原子扩散过程的影响，为进一步研究稀土元素在磁场中的行为及其局域效应提供了一定的实验依据。     

CePO_4/Ce-ZrO_2可加工陶瓷性能与断裂机制研究

以Ce ZrO2为基体,通过复合不同加入量的第二相CePO4颗粒,研究了陶瓷材料力学性能的变化,并借助加载能谱仪(EDS)的扫描电子显微镜(SEM)对材料弯曲断口及压痕裂纹扩展方式进行分析。当CePO4加入量为25%时,虽然材料力学性能有一定下降,但已经能用WC刀具进行加工。材料的弯曲断口显示,CePO4在两相体系中的断裂呈层片状形式;加入CePO4后,由于两相之间弱结合界面的存在,压痕裂纹扩展形式发生明显变化,由连续扩展机制过渡为不连续扩展。由这两种机制形成的材料断裂过程是阶段性的,在实际中可以用作材料最终破坏前的预报。     

原子吸收光谱法测定拉伸断口铬镍钼钛钢样品中主成分

研究了毫克级铬镍钼风样品中主成分镍的火焰原子吸收光谱法（FAAS法）和铬、钼、钒、钛、铝的塞曼恒温平台石墨炉原子吸收光谱法（ZSTPF－AAS法）。采用了微波溶样技术作为防污染样品预处理技术，采用石墨管硅涂层改进技术提高了仪器的测试精度。其中铬、镍、钼、钒、钛、铝的相对标准偏差分别为2.7%,0.97%,8.6%,7.3%,1.7%,7.3%。其加标回收率分别为96.5%,97%,96.7%,93%,98%,91%。通过分析，发现在较低温度下铬镍钼钛钢断面上有轻微的钼偏析现象，可能是拉伸断裂的主要化学影响因素。     

EPR study of free radicals in a main chain thermotropic polymer

Free radicals were generated in a rigid rod-like copolymer via mechanical route and by gamma radiation. The (EPR) method was used for studying free radicals formed at 123 K. The spectra of free radicals observed and the influence of molecular motions on the transport of radical centers in the fracture surface layer are discussed.     

冲击压缩下玻璃等脆性材料中失效波的研究进展

失效波的研究始于Rasorenov和Kanel发现K1 9玻璃样品后自由表面速度时程曲线上有反常再压缩信号。失效波是二十世纪九十年代冲击动力学研究领域的一个重要发现 ,它是指在一维平面应变冲击压缩下 ,在玻璃等脆性材料中由冲击波引起的一种独特的失效或破坏现象。较为系统地回顾近年来对失效波的研究工作 ,评述了研究现状、最新结果、发展趋势、研究方法和实验手段 ,对尚存的问题进行了分析讨论 ,并介绍了玻璃材料的基本特性。最后简单汇报了作者在这方面的研究工作和取得的阶段性结果。     

Propagation of a pre-existing turbulent fluid fracture

The propagation of rough and smooth wall pre-existing turbulent fluid fractures is investigated. The laminar fluid fracture is included as a special case for comparison. Lubrication theory is assumed to apply in the fracture and turbulence is introduced through the wall shear stress. The Perkins–Kern–Nordgren approximation is made in which the fluid pressure is proportional to the half-width of the fracture. The fracture half-width satisfies a non-linear diffusion equation. By using a linear combination of the Lie point symmetries of the non-linear diffusion equation a group invariant solution for the fracture length, volume and half-width is derived. The evolution of the length, half-width and mean flow velocity is analysed for a range of working conditions at the fracture entry. It is found that the mean flow velocity increases approximately linearly along the fracture.     

Determination of crack growth kinetics in non-reinforced semi-crystalline thermoplastics using the linear elastic fracture mechanics (LEFM) approach

The aim of this study was to find a satisfactory method to characterize the fatigue crack growth behavior of non-reinforced, semi-crystalline thermoplastic polymers using linear elastic fracture mechanics (LEFM). For this, crack growth curves (crack length versus cycle number) as well as crack growth kinetics curves (crack growth rate da/dN versus amplitude stress intensity factor ΔK) had to be generated. As methods suggested by ISO 15850 and ASTM E 647-11 failed to provide satisfactory results for the crack growth curves, a more advanced method was searched for and finally found in the literature. Regarding the crack growth kinetics curve, the idea of the calculation was based on methods recommended in ISO 15850 and ASTM E 647-11. However, these methods had to be considerably modified and improved in order to get accurate results with little scatter. The whole methodology was developed and verified with fatigue crack growth tests on two semi-crystalline thermoplastics (polyoxymethylene POM and polyetheretherketone PEEK).