The interaction between a screw dislocation and a wedge-shaped crack in one-dimensional hexagonal piezoelectric quasicrystals

Based on the fundamental equations of piezoelasticity of quasicrystal material,we investigated the interaction between a screw dislocation and a wedge-shaped crack in the piezoelectricity of one-dimensional hexagonal quasicrystals.Explicit analytical solutions are obtained for stress and electric displacement intensity factors of the crack,as well as the force on dislocation.The derivation is based on the conformal mapping method and the perturbation technique.The influences of the wedge angle and dislocation location on the image force are also discussed.The results obtained in this paper can be fully reduced to some special cases already available or deriving new ones.     

Exact analytic solutions for an elliptic hole with asymmetric collinear cracks in a one-dimensional hexagonal quasi-crystal

Using the complex variable function method and the technique of conformal mapping, the anti-plane shear problem of an elliptic hole with asymmetric colfinear cracks in a one-dimensional hexagonal quasi-crystal is solved, and the exact analytic solutions of the stress intensity factors （SIFs） for mode Ⅲ problem are obtained. Under the limiting conditions, the present results reduce to the Griffith crack and many new results obtained as well, such as the circular hole with asymmetric collinear cracks, the elliptic hole with a straight crack, the mode T crack, the cross crack and so on. As far as the phonon field is concerned, these results, which play an important role in many practical and theoretical applications, are shown to be in good agreement with the classical results.     

Interaction between infinitely many dislocations and a semi-infinite crack in one-dimensional hexagonal quasicrystal

By means of analytic function theory, the problems of interaction between infinitely many parallel dislocations and a semi-infinite crack in one-dimensional hexagonal quasicrystal are studied. The analytic solutions of stress fields of the interaction between infinitely many parallel dislocations and a semi-infinite crack in one-dimensional hexagonal quasicrystal are obtained. They indicate that the stress concentration occurs at the dislocation source and the tip of the crack, and the value of the stress increases with the number of the dislocations increasing. These results are the development of interaction among the finitely many defects of quasicrystals, which possesses an important reference value for studying the interaction problems of infinitely many defects in fracture mechanics of quasicrystal.     

一维六方准晶非周期平面内的平面应变理论

针对一维六方准晶中一种新平面弹性问题, 即非周期平面内的平面弹性问题, 通过引入应力势函数, 建立了一维六方准晶中非周期平面内的平面应变理论. 作为应用, 求解了一维六方准晶中垂直于准周期方向的椭圆孔口问题, 得到了其弹性应力场的解析解. 在极限情形下, 可给出裂纹问题的解. 关键词： 一维六方准晶 椭圆孔口 广义解析函数     

一维六方准晶中螺形位错与楔形裂纹的相互作用

采用保角映射方法和扰动技巧,研究了一维六方准晶中螺形位错和半无限楔形裂纹的相互作用. 讨论了位错的位置和楔形角对作用在位错上的力的影响,得到了应力强度因子和作用在 位错上的力的解析解.此外,还详细地讨论了位错对裂纹的影响.当楔形角参数λ=1/2时, 半无限楔形裂纹退化成半无限尖裂纹,相应的结果 可以作为特殊情况而直接得到.     

The interaction between a screw dislocation and an interfacial cruciform crack and collinear linear cracks

The interaction between a screw dislocation and an interfacial cruciform crack and collinear linear cracks under loads at infinity was investigated. General solutions of complex potentials to this problem were derived by using complex potential theory. As illustrative examples, the closed form solution for a screw dislocation interacting with an interfacial cruciform crack and a linear crack is obtained. The stress intensity factor and critical stress intensity factor for dislocation emission are also calculated. The results show that the shielding effect increases with the increase of the shear modulus and the distance between the two cracks, but it decreases with the increase of dislocation azimuth and the distance between the dislocation and the cruciform crack tip. The critical loads at infinity for dislocation emission increase with the increment of the emission angle, the distance the two cracks and the vertical length of the cruciform crack.     

Screw dislocations interacting with two asymmetrical interfacial cracks emanating from an elliptical hole

The interaction between screw dislocations and two asymmetrical interfacial cracks emanating from an elliptic hole under loads at infinity is studied. The closed-form solution is derived for complex potentials. The stress intensity factor and the critical applied stress for the dislocation emission are also calculated. In the limiting cases, well-known results can be obtained from the present solutions. Moreover, new exact solutions for a screw dislocation interacting with some complicated cracks are derived. The results show that the shielding effect increases with the increase in the length of the other cracks and the minor semi axis, but decreases with the increase of dislocation azimuth. The repulsion acting on the dislocation from the other phase and the other crack extend in the horizontal direction, which makes the dislocation emission at the crack tip take place more easily, but the minor semi axis of the elliptical hole extending in the vertical direction makes it more difficult.     

Fracture mechanics of propagating 3-D fatigue cracks with parametric dislocations

Abstract

Propagation of 3-D fatigue cracks is analyzed using a discrete dislocation representation of the crack opening displacement. Three dimensional cracks are represented with Volterra dislocation loops in equilibrium with the applied external load. The stress intensity factor (SIF) is calculated using the Peach–Koehler (PK) force acting on the crack tip dislocation loop. Loading mode decomposition of the SIF is achieved by selection of Burgers vector components to correspond to each fracture mode in the PK force calculations. The interaction between 3-D cracks and free surfaces is taken into account through application of the superposition principle. A boundary integral solution of an elasticity problem in a finite domain is superposed onto the elastic field solution of the discrete dislocation method in an infinite medium. The numerical accuracy of the SIF is ascertained by comparison with known analytical solution of a 3-D crack problem in pure mode I, and for mixed-mode loading. Finally, fatigue crack growth simulations are performed with the Paris law, showing that 3-D cracks do not propagate in a self-similar shape, but they re-configure as a result of their interaction with external boundaries. A specific numerical example of fatigue crack growth is presented to demonstrate the utility of the developed method for studies of 3-D crack growth during fatigue.     

On the dynamic interaction between moving dislocations

Received: 25 August 1997/Accepted: 23 October 1997     

Simple one-dimensional interaction systems with superexponential relaxation times

Finite one-dimensional random processes with local interaction are presented which keep some information of a topological nature about their initial conditions during time, the logarithm of whose expectation grows asymptotically at least asM ³, whereM is the size of the setR _M of states of one component. ActuallyR _M is a circle of lengthM. At every moment of the discrete time every component turns into some kind of average of its neighbors, after which it makes a random step along this circle. All these steps are mutually independent and identically distributed. In the present version the absolute values of the steps never exceed a constant. The processes are uniform in space, time, and the set of states. This estimation contributes to our awareness of what kind of stable behavior one can expect from one-dimensional random processes with local interaction.Partially supported by NSF grant #DMS-932 1216.     

Screw dislocation in semi-infinite non-local hexagonal medium

Abstract

Nonlocal stresses of a screw dislocation near a free surface in a semi-infinite hexagonal medium are investigated by a surface dislocation model. The nonlocal image force on the screw dislocation due to the existing free surface is also obtained. All classical singularities for the stress and image force are eliminated. The maxima of the stress and image force are evaluated. A zero point of the stress is found, which predicts that different states of the shear stress exist simultaneously near the dislocation. The appearance of a zero value at the free surface and a maximum of the dislocation image force can be used to explain the existence of the dislocation free zone.     

注氢纯铝中间隙型位错环一维迁移现象的原位观察

核聚变堆材料在高能粒子辐照过程中会产生大量点缺陷,导致辐照脆性和辐照肿胀等现象.因而,研究点缺陷在辐照过程中的演变过程至关重要.点缺陷团簇的一维迁移现象是这种演变过程的主要研究内容之一.本文采用普通低压(200 kV)透射电镜,在室温条件下对注氢纯铝中的间隙型位错环在电子辐照下的一维迁移现象进行了观察和分析.在200 keV电子辐照下,注氢纯铝中的位错环可多个、同时发生一维迁移运动,也可单个、独立进行一维迁移运动.位错环沿柏氏矢量1/3<111>的方向可进行微米尺度的一维长程迁移,沿柏氏矢量1/2<110>的方向一维迁移也可达数百纳米.电子束辐照时产生的间隙原子浓度梯度是引起位错环一维迁移并决定其迁移方向的原因.位错环发生快速一维迁移时,其后会留下一条运动轨迹;位错环一维迁移的速率越快,运动的轨迹则越长,在完成迁移过后的几十秒内这些运动轨迹会逐渐消失.     

Interaction of two edge dislocations in free-space propagation

This paper studies in detail the interaction of two edge dislocations nested in a Gaussian beam propagating in free space. It shows that in free-space propagation the edge dislocations are unstable and vanish, and two noncanonical vortices with opposite topological charge take place when off-axis distances c₁ and c₂ of two edge dislocations are non-zero, and the condition k²w₀⁸+32c₁c₂(w₀²-2c₁c₂)z²>0 is fulfilled (k-wave number, w₀-waist width). A noncanonical vortex appears when one off-axis distance is zero. However, one edge dislocation is stable when two edge dislocations are perpendicular and one off-axis distance is zero. Two perpendicular edge dislocations both with zero off-axis distance are also stable. The analytical results are illustrated by numerical examples.     

一维有机聚合物中极化子的自旋进动

从理论上讨论一维有机聚合物中由门电压导致的极化子自旋的输运动力学,由于自旋-轨道相互作用,当极化子沿着聚合物链运动时,自旋发生周期性进动.     

A model of crack based on dislocations in smectic A liquid crystals

A plastic crack model for smectic A liquid crystals under longitudinal shear is suggested. The solution of the screw dislocation in smectic A is the key to the correct result that we obtained by overcoming a longstanding puzzle. We further use the dislocation pile-up principle and the singular integral equation method to construct the solution of the crack in the phase. From the solution, we can determine the size of the plastic zone at the crack tip and the crack tip opening （tearing） displacement, which are the parameters relevant to the local stability/instability of materials. Our results may be useful for developing soft-matter mechanics.     

On the accommodation of extrinsic dislocations in grain boundaries

The relaxation of the extrinsic grain boundary dislocation (EGBD) stresses, created by interaction of lattice dislocations with grain boundaries (GBs), is a phenomenon which plays an important role in recrystallization and high temperature deformation of materials. The kinetics of this phenomenon, controlled by GB diffusion, are relatively well established. On the contrary, the processes which operate in order the GBs return to equilibrium are still controversed in vicinal and general GBs.The decomposition in discrete products and the rapid motion of the glissile components observed by High Resolution Electron Microscopy (HREM) in symmetrical tilt GBs support the recent incorporation model of EGBD accommodation. But, until now, these observations and this model are restricted to GBs described by the Structural Unit/Grain Boundary Dislocation (SU/GBD) model. Otherwise, the Spreading phenomenon generally observed by Transmission Electron Microscopy (TEM) in vicinal and general GBs is not clearly understood.This paper is an attempt to review the different EGBD accommodation models and to raise up the question of their relevance to account for the stress relaxation in any grain boundary.     

Connection between the immersing and transfer-matrix methods in one-dimensional scattering problems

We show that application of the immersing and transfer-matrix methods to one-dimensional problems of particles scattering leads to the system of two linear equations for the functions F and Φ expressed by means of the transmission and reflection amplitudes. The expressions of these functions are derived. The offered method is illustrated by the finding of transmission and reflection coefficients for the potential barrier with a constant height. The developed method can be applied in solving the quasi-one-dimensional and two-dimensional problems of scattering.     

Topological phase in one-dimensional Rashba wire

We study the possible topological phase in a one-dimensional(1D) quantum wire with an oscillating Rashba spin–orbital coupling in real space. It is shown that there are a pair of particle–hole symmetric gaps forming in the bulk energy band and fractional boundary states residing in the gap when the system has an inversion symmetry. These states are topologically nontrivial and can be characterized by a quantized Berry phase ±π or nonzero Chern number through dimensional extension. When the Rashba spin–orbital coupling varies slowly with time, the system can pump out 2 charges in a pumping cycle because of the spin flip effect. This quantized pumping is protected by topology and is robust against moderate disorders as long as the disorder strength does not exceed the opened energy gap.     

一维有机导体的Peierls相变研究

根据建立在电子-声子相互作用基础上的Peierls 相变理论，利用形变势模型和半经验晶体轨道方法计算的能带结构数据，对一维有机导体tetrathiafulvalene-tetracyanoquinodimethane的Peierls相变温度进行了计算.并对其金属-绝缘体相变机制进行了讨论. 关键词： 电子-声子相互作用 Peierls相变温度 一维有机导体