Icosahedral quasicrystals solids with an elliptic hole under uniform heat flow

The complex variable method for solving the two-dimensional thermal stress problem of icosahedral quasicrystals is stated. The closed-form solutions for icosahedral quasicrystals containing an elliptical hole subjected to a remote uniform heat flow are obtained. When the hole degenerates into a crack, the explicit solutions for the stress intensity factors is presented.     

Elastic analysis of an elliptic notch in quasicrystals of point group 10 subjected to shear loading

Based on the stress potential and complex variable function method, this paper makes an elastic analysis of an elliptic notch subjected to uniform shear stress at infinity in quasicrystals with point group 10. With the aid of conformal transformation, an exact solution for the elliptic notch of the quasicrystals is obtained. The solution of the mode {\rm II} Griffith crack as a special case is constructed. The stress intensity factor and energy release rate have been also obtained as a direct result of the crack solution.     

Finite size specimens with cracks of icosahedral Al Pd Mn quasicrystals

Icosahedral quasicrystals are the most important and thermodynamically stable in all about 200 kinds of quasicrystals currently observed. Beyond the scope of classical elasticity, apart from a phonon displacement field, there is a phason displacement field in the elasticity of the quasicrystal, which induces an important effect on the mechanical properties of the material and makes an analytical solution difficult to obtain. In this paper, a finite element algorithm for the static elasticity of icosahedral quasicrystals is developed by transforming the elastic boundary value problem of the icosahedral quasicrystals into an equivalent variational problem. Analytical and numerical solutions for an icosahedral Al–Pd–Mn quasicrystal cuboid subjected to a uniaxial tension with different phonon–phason coupling parameters are given to verify the validity of the numerical approach. A comparison between the analytical and numerical solutions of the specimen demonstrates the accuracy and efficiency of the present algorithm. Finally, in order to reveal the fracture behavior of the icosahedral Al–Pd–Mn quasicrystal, a cracked specimen with a finite size of matter is investigated, both with and without phonon–phason coupling. Meanwhile, the geometry factors are calculated, including the stress intensity factor and the crack opening displacement for the finite-size specimen. Computational results reveal the importance of phonon–phason coupling effect on the icosahedral Al–Pd–Mn quasicrystal. Furthermore, the finite element procedure can be used to solve more complicated boundary value problems.     

Finite size specimens with cracks of icosahedral AI-Pd-Mn quasicrystals

Icosahedral quasicrystals are the most important and thermodynamically stable in all about 200 kinds of quasicrystals currently observed. Beyond the scope of classical elasticity, apart from a phonon displacement field, there is a phason displacement field in the elasticity of the quasicrystal, which induces an important effect on the mechanical properties of the material and makes an analytical solution difficult to obtain. In this paper, a finite element algorithm for the static elasticity of icosahedral quasicrystals is developed by transforming the elastic boundary value problem of the icosahedral quasicrystals into an equivalent variational problem. Analytical and numerical solutions for an icosahedral A1-Pd-Mn quasicrystal cuboid subjected to a uniaxial tension with different phonon-phason coupling parameters are given to verify the validity of the numerical approach. A comparison between the analytical and numerical solutions of the specimen demonstrates the accuracy and efficiency of the present algorithm. Finally, in order to reveal the fracture behavior of the icosahedral A1-Pd-Mn quasicrystal, a cracked specimen with a finite size of matter is investigated, both with and without phonon-phason coupling. Meanwhile, the geometry factors are calculated, including the stress intensity factor and the crack opening displacement for the finite-size specimen. Computational results reveal the importance of pbonon-phason coupling effect on the icosahedral A1-Pd-Mn quasicrystal. Furthermore, the finite element procedure can be used to solve more complicated boundary value problems.     

Shielding effect and emission criterion of a screw dislocation near an interfacial blunt crack

Shielding effect and emission criterion of a screw dislocation near an interfacial blunt crack are dealt with in this paper. Utilizing the conformal mapping technique, the closed-form solutions are derived for complex potentials and stress fields due to a screw dislocation located near the interfacial blunt crack. The stress intensity factor on the crack tips and the critical stress intensity factor for dislocation emission are also calculated. The influence of the orientation of the dislocation and the morphology of the blunt crack as well as the material elastic dissimilarity on the shielding effect and the emission criterion is discussed in detail. The results show that positive screw dislocations can reduce the stress intensity factor of the interfacial blunt crack tip (shielding effect). The shielding effect increases with the increase of the shear modulus of the lower half-plane, but it decreases with the increase of the dislocation azimuth angle. The critical loads at infinity for dislocation emission increases with the increase of emission angle and curvature radius of blunt crack tip, and the most probable angle for screw dislocation emission is zero. The present solutions contain previous results as special cases.     

Shielding Effect and Emission Criterion of a Screw Dislocation Near an Interfacial

Shielding effect and emission criterion of a screw dislocation near an interracial crisscross crack are dealt with in this paper. Utilizing the conformal mapping technique, the closed-form solutions are derived for complex potentials and stress fields due to a screw dislocation located near the interracial crisscross crack. The stress intensity factor on the crack tips and the critical stress intensity factor for dislocation emission are also calculated. The influence of the orientation of the dislocation and the morphology of the crisscross crack as well as the material elastic dissimilarity on the shielding effect and the emission criterion is discussed in detail. The results show that positive screw dislocations can reduce the stress intensity factor of the interracial crisscross crack tip （shielding effect）. The shielding effect increases with the increase of the shear modulus of the lower half-plane, but it decreases with the increase of the dislocation azimuth angle and the distance between the dislocation and the crack tip. The critical loads at infinity for dislocation emission increases with the increase of emission angle and the vertical length of the crisscross crack, and the most probable angle for screw dislocation emission is zero. The present solutions contain previous results as special cases.     

Elastic analysis of a mode Ⅱ crack in an icosahedral quasicrystal

Based on the displacement potential functions, the elastic analysis of a mode II crack in an icosahedral quasicrystal is performed by using the Fourier transform and dual integral equation theory. By the solution, the analytic expressions for the displacement field and stress field are obtained. The asymptotic behaviours of the phonon and phason stress fields around the crack tip indicate that the stresses near the crack tip exhibit a square root singularity. The most important physical quantities of fracture theory, crack stress intensity factor and energy release rate, are evaluated in an explicit version.     

Dynamic behaviour of the icosahedral Al——Pd——Mn quasicrystal with a Griffith crack

The dynamic response of an icosahedral Al--Pd--Mn quasicrystal with a Griffith crack to impact loading is investigated in this paper. The elastohydrodynamic model for the wave propagation and diffusion together with their interaction is adopted. Numerical results of stress, displacement and dynamic stress intensity factors are obtained by using the finite difference method. The effects of wave propagation, diffusion and phonon--phason coupling on the quasicrystal in the dynamic process are discussed in detail, where the phason dynamics is explored particularly.     

Plastic analysis of the crack problem in two-dimensional decagonal Al-Ni-Co quasicrystalline materials of point group 10,10

The fundamental plastic nature of the quasicrystalline materials remains an open problem due to its essential complicacy. By developing the proposed generalized cohesive force model, the plastic deformation of crack in point group 10, 10 decagonal quasicrystals is analysed strictly and systematically. The crack tip opening displacement （CTOD） and the size of the plastic zone around the crack tip are determined exactly. The quantity of the crack tip opening displacement can be used as a parameter of nonlinear fracture mechanics of quasicrystalline material. In addition, the present work may provide a way for the plastic analysis of quasicrystals.     

Plastic analysis of the crack problem in two-dimensional decagonal Al-Ni-Co quasicrystalline materials of point group 10,■

The fundamental plastic nature of the quasicrystalline materials remains an open problem due to its essential complicacy.By developing the proposed generalized cohesive force model,the plastic deformation of crack in point group 10,10 decagonal quasicrystals is analysed strictly and systematically.The crack tip opening displacement(CTOD) and the size of the plastic zone around the crack tip are determined exactly.The quantity of the crack tip opening displacement can be used as a parameter of nonlinear fracture mechanics of quasicrystalline material.In addition,the present work may provide a way for the plastic analysis of quasicrystals.     

Realization of Tip Tilting By 8-Step Line Tilting

By direct calculation of rotation matrices of SO（3）, we show how certain specific sequence of eight consecutive rotations of digital angles can yield a tilting of a facet mirror. We also design a detailed program specifically to tilt an array of mirrors from planar orientation to the required focusing orientation. We describe how to use the 8-step to realize the focusing of the mirror array. We have found, in our designed program, an important feature of row-sharing during the rotations for the columns and similarly the column-sharing during the rotations for the row. This feature can save a lot of operating time during the actual realization of the mechanical movements.     

Characterizing a proton beam with two different methods in beam halo experiments

In beam halo experiments, it is very important to correctly characterize the RFQ output proton beam. In order to simulate the beam dynamics properly, we must first know the correct initial beam parameters. We have used two different methods, quadrupole scans and multi-wire scanners to determine the transverse phase-space properties of the proton beam. The experimental data were analyzed by fitting to the 3-D nonlinear simulation code IMPACT. For the quadrupole scan method, we found that the RMS beam radius and the measured beam-core profiles agreed very well with the simulations. For the multi-wire scanner method, we choose the case of a matched beam. By fitting the IMPACT simulation results to the measured data, we obtained the Courant-Snyder parameters and the emittance of the beam. The difference between the two methods is about eight percent, which is acceptable in our experiments.     

Fracture of solids in aggressive gases

An interrelation between the surface energy of a material and the work of plastic deformation at a crack tip is analyzed. Theoretical relationships for the limiting stress intensity factors of a crack tip in a medium of aggressive gases and in vacuum are derived. The results of the calculations are compared with the experimental data.     

Elastic analysis of a mode II crack in a decagonal quasi—crystal

The elastic analysis of a mode II Griffith crack penetrating through a decagonal quasi-crystal along the periodic axis is made within the context of the continuum theory. By using a general solution obtained previously, the problem in the case of uniform shear stress at infinity is solved, and the analytical expressions for the entire stress field disturbed by an internal crack are derived in an explicit form. The asymptotic fields of the displacement and stress around a crack tip in both phonon and phason fields indicate that the stresses near a crack tip exhibit the square-root singularity. The formula for evaluating the energy release rate is also given. If imposing that the phason field is absent, the well-known results of a mode II crack in a conventional material are recovered from the present results.     

Statistical properties of the photoelectron energy spectrum generated by an intense laser pulse and a continuous X-ray

This study shows that the photoelectron energy spectrum generated by an intense laser pulse in the presence of a continuous X-ray has interesting and useful statistical properties. The total photoionization production is linearly propor- tional to the time duration of the laser pulse and the square of the beam size. The spectral double energy-integration is an intrinsic value of the laser-assisted X-ray photoionization, which linearly depends on the laser intensity and which quantita- tively reflects the strengths of the laser-field modulation and the quantum interference between photoelectrons. The spectral energy width also linearly depends on the laser intensity. These linear relationships suggest new methods for the in-situ measurement of laser intensity and pulse duration with high precision.     

Effect of electric current on the migration of hydrogen interstitial atoms in the region of a crack tip in a crystal

The effect of a constant electric current on the migration of interstitial atoms dissolved in a crystal in the region of a tensile crack tip is estimated. The calculation takes into account plastic deformation that is produced in the vicinity of the crack tip in the loaded sample by dislocation motion in active slip planes of the crystal under the action of mechanically and electrically induced shear stresses, Joule heat release, the Thomson effect, and ponderomotive forces and allows for the effect of gas exchange near the crack edges on the evolution of the distribution of interstitial impurity atoms. The time dependence of the stress intensity factor is found for both the cases of the presence and absence of a constant electric current near the crack tip. Numerical calculations are performed for an α-Fe crystal.     

Elastic behaviour of an edge dislocation near a sharp crack emanating from a semi-elliptical blunt crack

The interaction between an edge dislocation and a crack emanating from a semi-elliptic hole is dealt with. Utilizing the complex variable method, closed form solutions are derived for complex potentials and stress fields. The stress intensity factor at the tip of the crack and the image force acting on the edge dislocation are also calculated. The influence of the morphology of the blunt crack and the position of the edge dislocation on the shielding effect to the crack and the image force is examined in detail. The results indicate that the shielding or anti-shielding effect to the stress intensity factor increases acutely when the dislocation approaches the tip of the crack. The effect of the morphology of the blunt crack on the stress intensity factor of the crack and the image force is very significant.     

Elastic behaviour of a wedge disclination dipole near a sharp crack emanating from a semi-elliptical blunt crack

The interaction between a wedge disclination dipole and a crack emanating from a semi-elliptic hole is investigated. Utilising the complex variable method, the closed form solutions are derived for complex potentials and stress fields. The stress intensity factor at the tip of the crack and the image force acting on the disclination dipole center are also calculated. The influence of the morphology of the blunt crack and the position of the disclination dipole on the shielding effect to the crack and the image force is examined in detail. The results indicate that the shielding or anti-shielding effect to the stress intensity factor increases when the wedge disclination dipole approaches the tip of the crack. The effects of the morphology of the blunt crack on the stress intensity factor of the crack and the image force are very significant.     

碳纤维布补强梁裂尖奇异性的光学焦散线实验研究

通过光学焦散线方法对碳纤维布加固含裂纹梁进行三点弯荷载下的静荷载和冲击实验,研究了其断裂特性。在静态实验研究中,记录了不同载荷状态下裂纹的焦散斑光学图像,计算了与之对应的裂纹尖端的应力强度因子,分析了试件在粘贴加固不同长度的碳纤维布情况下焦散斑和应力强度因子演化规律。在动态实验中,记录了裂纹扩展的过程和在此过程中不同时刻的焦散斑和裂纹扩展的路线。通过各瞬间的焦散斑图像,分析裂纹的扩展长度及速度,并得到各时刻的动态应力强度因子。