On crack path stability in a layered material

Crack paths in an elastic layer on top of a substrate are considered. Crack growth is initiated from an edge crack in the layer. The plane of the initially straight crack forms an angle to the free surface. The load consists of a pair of forces applied at the crack mouth and parallel to the interface. Crack paths are calculated using a boundary element method. Crack growth is assumed to proceed along a path for which the mode II stress intensity factor vanishes. The inclination and the length of the initial crack are varied. The effect of two different substrates on the crack path evolution is demonstrated. A crack path initially leading perpendicularly to the interface is shown to be directionally unstable for a rigid substrate. Irrespective of its initial angle, the crack does not reach the interface, but reaches the free surface if the layer is infinitely long. At finite layer length the crack reaches the upper free surface if the initial crack inclination to the surface is small enough. For an inextendable flexible substrate, on the other hand, the crack reaches the interface if its initial inclination is large enough. For the flexible substrate an unstable path parallel with the sides of an infinitely long layer is identified. The results are compared with experimental results and discussed in view of characterisation of directionally unstable crack paths. The energy release rate for an inclined edge crack is determined analytically.

Shell correction and pairing energies in the dinuclear system model

We investigate the dependences of the potential energy surfaces (PES) and the fusion probabilities for some cold fusion reactions leading to super-heavy elements on the nuclear shell effect and pairing energy. It is found that the shell effect plays an important role in the fusion of the super-heavy element while pairing energy's contribution is insignificant. The fusion probabilities and evaporation residue cross sections as functions of the Ge-isotope projectile bombarding Pb-208 are also investigated. It is found that evaporation residue cross sections do not always increase with the increasing neutron number of Ge-isotope

Ordered magnetic core-manganese oxide shell nanostructures and their application in water treatment

In this paper, we have reported a facile method for the synthesis of ordered magnetic core-manganese oxide shell nanostructures. The process included two steps. First, manganese ferrite nanoparticles were obtained through a solvothermal method. Then, the manganese ferrite nanoparticles were mixed directly with KMnO4 solution without any additional modified procedures of the magnetic cores. It has been found that Mn element in the core can react with KMnO4 to form manganese oxide which acts as a seed for the in-situ growth of manganese oxide shells. This is significant for the controllable fabrication of symmetrical ordered manganese oxide shell structures. The shell thickness can be easily controlled through the reaction time. Transmission electron microscopy, scanning electron microscopy, X-ray photoelectron spectroscopy, X-ray powder diffraction and energy-dispersive X-ray spectroscopy have been employed to characterize the products at different reaction time.

扬子地区上奥陶－下志留统黑色岩系形成机理

The black rock series of the Upper Ordovician - Lower Silurian in Yangtze area are important source rocks and have exceptional characteristics of sediment, biology, element geochemistry, carbon and oxygen isotope, organic geochemistry and etc. These characteristics are the reflection of important geology events. Due to scarce system research, many problems that relate to the development mechanism of source rocks are not solved. And this restricts the exploration of Oil and gas in South China. In this paper, author studied the palaeo-climate, palaeo-structure and palaeo-environment of the Upper Ordovician - Lower Silurian in Yangtze area by sedimentology, palaeobiology and geochemistry, especially the element geochemistry and isotope geochemistry. The environment model of source rocks is established and some conclusions are drawn. The Upper Ordovician - Lower Silurian sediment types in Yangtze area are mostly black shales, next, mudstone, shell limestone and siltystone. During the Late Ordovician and Earily Silurian periods, a series of big upheaval and depressed are distributed in Yangtze area, and the strata pattern of interphase upheaval and depressed led to Yangtze palaeosea isolated with outside sea. So the stagnant and anoxic environment that are the favorable factor of rich organic black shales sediment is formed in Yangtze area. That Chemical Index of Alteration (CIA) values of the lower Wufeng formation and Longmaxi formation exhibits moderate chemistry weathering suggests they were deposited under the circumstances of the warm and humid climate. However, the large difference of the CIA values of N.extraordinarius-N.ojsuensis biozone suggests that climate is changeful. Therefore, there were two different kinds of climates in the course of the deposition of the Wufeng formation and Longmaxi formation. During the Late Ordovician - Earily Silurian periods, in Yangtze palaeosea, the surface water which is full of rich nutriment and abundant bacterium - algae has high palaeo-productivity that is obvious difference in the different space – time. The content of sulphate changes gradually from the surface water columns to the deep water columns. That is, salinity in the surface water columns is serious low and the salinity in deep water columns is normal. Salinity delamination is favor of the forming of deep anoxic environment. During Wufeng period, the oxidated and low sulfate environment exists in the upper Yangtze palaeosea, while the anoxic and normal salinity environment occurs in the lower Yangtze palaeosea. During the Late Wufeng and Guanyinqiao periods, the steady anoxic environment is replaced by oxidated environment. During the Longmaxi period, layered and anoxic environment recur. In Yangtze area, studies of δ13C of sedimentary organic carbon show a positive δ13C excursion up to 4‰ in the Guanyinqiao stage and then, acute negative excursion in the earily Longmaxi stage. These organic carbon isotopes curve are not only efficient measure of carving up strata borderline, but also reflected the change of originality productivity. These organic carbon isotopes curves showed the process of the enhanced embedding of the global organic carbon. Anoxic event is the main factor of increasing organic carbon embedding speed. And the reduced organic carbon embedding in Hirnantian stage is due to the water column with abundant oxygen. The δ34S values are gradually positive excursion from P.pacificus biozone to N.extraordinarius biozone, and reach the maximum in the Upper Hirnantian stage. Then, the δ34S values are negative excursion. The excursions of δ13C and δ34S reflect the acute change of environment. The formation of source rocks is largely dependent on the nature of organisms from which kerogen is derived and the preservation conditions of organic matter, which are fundamentally dependent on a favourable combination of various elements in which organisms live and are subsequently buried. These elements include palaeoclimate, palaeostructure and palaeoenvironmental conditions. Based on above mentioned circumstance, the coupling connection of source rock and the palaeoclimate, and of palaeostructure and palaeoenvironmental conditions are confirmed, and the “anoxic-marginal depression-photosynthesis” environemental model is established. It is indicated that anoxic played important role in production of organic matter. The produced organic matter was accumulated in marginal depression of the Yangtze area. The photosynthesis is favor of the high productivity. Source rocks have a good perspective, like that of “hot shale” deposited in North Africa.

Effect of Rock Mass Structure and Block Size on the Slope Stability-Physical Modeling and Discrete Element Simulation

This paper studies the stability of jointed rock slopes by using our improved three-dimensional discrete element methods (DEM) and physical modeling. Results show that the DEM can simulate all failure modes of rock slopes with different joint configurations. The stress in each rock block is not homogeneous and blocks rotate in failure development. Failure modes depend on the configuration of joints. Toppling failure is observed for the slope with straight joints and sliding failure is observed for the slope with staged joints. The DEM results are also compared with those of limit equilibrium method (LEM). Without considering the joints in rock masses, the LEM predicts much higher factor of safety than physical modeling and DEM. The failure mode and factor of safety predicted by the DEM are in good agreement with laboratory tests for any jointed rock slope.

三峡永久船闸高边坡开挖三维离散元数值模拟:3-D Simulation of the Excavation of High Steep Slope of Three-Gorges Permanent Lock by Distinct Element Method

采用面一面接触的三维离散元刚性块体模型,从实测节理面中取出其中的三组,按照其倾向、倾角和节理间距将三峡永久船闸未开挖的区域划分为10~5个离散单元,通过施加力边界条件,给出了与实测初始地应力场接近的数值模拟结果；然后,分4步模拟了永久船闸的开挖过程。计算结果表明：开挖过程会引起节理面出现张开趋势,个别岩体还会沿着节理面滑移。岩体位移的不对称现象较为自然地说明了由节理引起的岩体各向异性特征。

A Numerical Study of Indentation Using Indenters of Different Geometry

Finite element simulation of the Berkovich, Vickers, Knoop, and cone indenters was carried out for the indentation of elastic-plastic material. To fix the semiapex angle of the cone, several rules of equivalence were used and examined. Despite the asymmetry and differences in the stress and strain fields, it was established that for the Berkovich and Vickers indenters, the load-displacement relation can closely be simulated by a single cone indenter having a semiapex angle equal to 70.3degrees in accordance with the rule of the volume equivalence. On the other hand, none of the rules is applicable to the Knoop indenter owing to its great asymmetry. The finite element method developed here is also applicable to layered or gradient materials with slight modifications.

Determination of Proper Processing Conditions of Material Surface Heat Treatment Through Finite Element Method

A two-dimensional model has been developed based on the experimental results of stainless steel remelting with the laminar plasma technology to investigate the transient thermo-physical characteristics of the melt pool liquids. The influence of the temperature field, temperature gradient, solidification rate and cooling rate on the processing conditions has been investigated numerically. Not only have the appropriate processing conditions been determined according to the calculations, but also they have been predicted with a criterion established based on the concept of equivalent temperature area density (ETAD) that is actually a function of the processing parameters and material properties. The comparison between the resulting conditions shows that the ETAD method can better predict the optimum condition.

Elastic Waves in a Hybrid Multilayered Piezoelectric Plate

An analytical-numerical method is presented for analyzing dispersion and characteristic surface of waves in a hybrid multilayered piezoelectric plate. In this method, the multilayered piezoelectric plate is divided into a number of layered elements with three-nodal-lines in the wall thickness, the coupling between the elastic field and the electric field is considered in each element. The associated frequency dispersion equation is developed and the phase velocity and slowness, as well as the group velocity and slowness are established in terms of the Rayleigh quotient. Six characteristic wave surfaces are introduced to visualize the effects of anisotropy and piezoelectricity on wave propagation. Examples provide a full understanding for the complex phenomena of elastic waves in hybrid multilayered piezoelectric media.

A New Finite Element Method for Strain Gradient Theories and Applications to Fracture Analyses

A new compatible finite element method for strain gradient theories is presented. In the new finite element method, pure displacement derivatives are taken as the fundamental variables. The new numerical method is successfully used to analyze the simple strain gradient problems – the fundamental fracture problems. Through comparing the numerical solutions with the existed exact solutions, the effectiveness of the new finite element method is tested and confirmed. Additionally, an application of the Zienkiewicz–Taylor C1 finite element method to the strain gradient problem is discussed. By using the new finite element method, plane-strain mode I and mode II crack tip fields are calculated based on a constitutive law which is a simple generalization of the conventional J2 deformation plasticity theory to include strain gradient effects. Three new constitutive parameters enter to characterize the scale over which strain gradient effects become important. During the analysis the general compressible version of Fleck–Hutchinson strain gradient plasticity is adopted. Crack tip solutions, the traction distributions along the plane ahead of the crack tip are calculated. The solutions display the considerable elevation of traction within the zone near the crack tip.

Distinct Element Analysis on Propagation Characteristics of P-Wave in Rock Pillar with Finite length

以节理岩体等效刚度的概念为基础,讨论了离散元刚性块体模型中节理刚度的选取问题。采用面-面接触模型模拟了纵波在一维岩体中的传播,给出了纵波波形；研究了阻尼比、软弱夹层以及节理间是否可拉对波传播规律的影响。

A finite element method for cracked components of structures

In this paper, a method is developed for determining the effective stiffness of the cracked component. The stiffness matrix of the cracked component is integrated into the global stiffness matrix of the finite element model of the global platform for the FE calculation of the structure in any environmental conditions. The stiffness matrix equation of the cracked component is derived by use of the finite variation principle and fracture mechanics. The equivalent parameters defining the element that simulates the cracked component are mathematically presented, and can be easily used for the FE calculation of large scale cracked structures together with any finite element program. The theories developed are validated by both lab tests and numerical calculations, and applied to the evaluation of crack effect on the strength of a fixed platform and a self-elevating drilling rig.

Iterative method using consistent mass matrix in axisymmetrical finite element analysis of hypervelocity impact

We present in this paper an iterative method using consistent mass matrix in axisymmetrical finite element analysis of hypervelocity impact. To retain the advantage of integration on an element-by-element basis which is at the heart of modern hydrocodes, we suggest that the first step should be to solve for accelerations at an advanced time step by using the lumped mass approach, then iterate using a consistent mass matrix to improve the estimate. Examples are given to show the improved resolution with the new method.

Finite Element Analysis of Deformed Legs of Offshore Platform Structures

The element stiffness matrix of the equivalent beam or pipe element of the deformed leg of the platform is derived by the finite element method. The stresses and displacements of some damaged components are calculated, and the numeri-cal solutions agree well with those obtained by the fine mesh finite element method. Finally, as an application of this method, the stresses of some platform structures are calculated and analyzed.