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.     

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.     

Phonon spectrum and related thermodynamic properties of microcrack in bcc-Fe

The phonon spectrum and the related thermodynamic properties of microcracks in bcc-Fe are studied with the recursion method by using the Finnis--Sinclair (F--S) N-body potential. The initial configuration of the microcracks is established from an anisotropic linear elastic solution and relaxed to an equilibrium by molecular dynamics method. It is shown that the local vibrational density of states of the atoms near a crack tip is considerably different from the bulk phonon spectrum, which is closely associated with the local stress field around the crack tip; meanwhile, the local vibrational energies of atoms near the crack tip are higher than those of atoms in a perfect crystal. These results imply that the crack tip zone is in a complex stress state and closely related to the structure evolution of cracks. It is also found that the phonon excitation is a kind of local effect induced by microcracks. In addition, the microcrack system has a higher vibrational entropy, which reflects the character of phonon spectrum related to the stress field induced by cracks.     

Influence of residual surface stress on the fracture of nanoscale piezoelectric materials with conducting cracks

In this paper,we analyze the stress and electric field intensity factors affected by residual surface stress for conducting cracks in piezoelectric nanomaterials.The problem is reduced to a system of non-linear singular integral equations,whose solution is determined by iteration technique.Numerical results indicate that the residual surface stress can significantly alter the crack tip fields at nanometer length scales.Due to the residual surface stress,281he electric field can produce stress around crack tip.This suggests a strong electromechanical coupling crack tip field for nanoscale piezoelectric materials.Such a finding is considerably different from the classical fracture mechanics results.A transit electric field to stress load ratio is identified,for which influences of residual surface stresses vanish.The research is useful for the applications of nanoscale piezoelectric devices.     

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.     

Elastic behaviour of a wedge sharp crack emanating from a disclination dipole near 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.     

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.     

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.     

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.     

Fracture analysis near the interface crack tip for mode Ⅰ of orthotropic bimaterial

The mechanical behaviors near the interface crack tip for mode Ⅰ of orthotropic bimaterial are researched. With the help of the complex function method and the undetermined coefficient method, non-oscillatory field if the singularity exponent is a real number, and oscillatory field if the singularity exponent is a complex number are discussed, respectively. For each case, the stress functions are constructed which contain twelve undetermined coefficients and an unknown singularity exponent. Based on the boundary conditions, the system of non-homogeneous linear equations is obtained. According to the necessary and sufficient condition for the existence of solution for the system of non-homogeneous linear equations, the singularity exponent is determined under appropriate condition using bimaterial parameters. Both the theoretical formulae of stress intensity factors and analytic solutions of stress or displacement field near the interface crack tip are given. When the two orthotropic materials are the same, the classical results for orthotropic single material are deduced.     

Finite strain stress fields near the tip of an interface crack between a soft incompressible elastic material and a rigid substrate

We present a numerical study of finite strain stress fields near the tip of an interface crack between a rigid substrate and an incompressible hyperelastic solid using the finite element method (FEM). The finite element (FE) simulations make use of a remeshing scheme to overcome mesh distortion. Analyses are carried out by assuming that the crack tip is either pinned, i.e., the elastic material is perfectly bonded (no slip) to the rigid substrate, or the crack lies on a frictionless interface. We focus on a material which hardens exponentially. To explore the effect of geometric constraint on the near tip stress fields, simulations are carried out under plane stress and plane strain conditions. For both the frictionless interface and the pinned crack under plane stress deformation, we found that the true stress field directly ahead of the crack tip is dominated by the normal opening stress and the crack face opens up smoothly. This is also true for an interface crack along a frictionless boundary in plane strain deformation. However, for a pinned interface crack under plane strain deformation, the true opening normal stress is found to be lower than the shear stress and the transverse normal stress. Also, the crack opening profile for a pinned crack under plane strain deformation is completely different from those seen in plane stress and in plane strain (frictionless interface). The crack face flips over and the tip angle is almost tangential to the interface. Our results suggest that interface friction can play a very important role in interfacial fracture of soft materials on hard substrates.     

磁电弹性体中多条位错与Griffith裂纹

根据本征方程，研究磁电弹性体中若干平行螺型位错与Griffith裂纹的相互作用.结合Muskhelishvili方法和算子理论，得到磁电弹性体中由位错和裂纹所诱导的应力场、电场和磁场的解析解.数值算例表明：在裂纹的端点及位错点上仍然存在应力的奇异性，离位错点越远处广义力越小，结论与已有的结果相符，证明了结论的正确性.当位错点与裂纹端点距离越近时，裂纹与位错间的应力场越小，并逐渐趋近于零.     

相干梯度敏感干涉测量技术及在静态断裂力学实验中的应用

介绍了相干梯度敏感(CGS)干涉测量技术的基本原理及其在静态Ⅰ型断裂实验中的应用,验证了该方法对裂纹尖端局部变形场和断裂特性进行定量研究的可行性。给出了代表静态Ⅰ型裂纹尖端奇异场光力学信息的CGS控制方程,模拟并分析了Ⅰ型裂纹尖端的CGS条纹模式,对静态Ⅰ型裂纹尖端变形场和断裂特性进行了三点弯曲的CGS试验,并提取了应力强度因子KⅠ。结果表明,试验结果与理论分析结果相吻合。     

Complex variable method for plane elasticity of icosahedral quasicrystals and elliptic notch problem

The complex variable method for the plane elasticity theory of icosahedral quasi-crystals is developed. Based on the general solution obtained previously, complex representations of stress and displacement components of phonon and phason fields in the quasicrystals are given. With the help of conformal transformation, an analytic solution for the elliptic notch problem of the material is presented. The solution of the Griffith crack problem can be observed as a special case of the results. The stress intensity factor and energy release rate of the crack are also obtained.     

The effect of the boundary conditions on in-plane and out-of-plane stress field in three dimensional plates weakened by free-clamped V-notches

Dealing with the material microstructure an analytical multiscale model has recently been developed by Sih. Physically, the different orders of the stress singularities are related to the different constraints associated with the defect thought as a microscopic V-notch at the tip of the main crack. Irregularities of the material microstructure tend to curl the crack tip being the clamped-free boundary conditions the more realistic and general representation of what occurs on the microscopic V-notch. As a result, mixed mode conditions are always present along the V-notch bisector line.It is known for a long time that at the antisymmetric (mode II) stress distribution ahead of the crack tip generates a coupled out-of-plane singular mode. Recent theoretical and numerical analyses have demonstrated that this out-of-plane mode due to three-dimensional effects occurs also in the case of large V-notches where the mode II stress field is no longer singular. In addition, when the notch opening angle is non-zero, the three-dimensional singular stress state is strongly influenced by the plate thickness.The aim of this paper is to investigate the effect of free-fixed boundary conditions along the notch edges in three dimensional plates weakened by pointed V-notches and quantify the intensity of the out-of-plane singularity occurring under this constraint configuration. For the sake of simplicity a macronotch is considered rather than a micronotch. A synthesis of the magnitude of the stress state through the plate thickness is carried out by using the mean value of the strain energy density over a given control volume embracing the notch tip. The capability of the strain energy density to capture all the combined effects due to the out-of-plane mode make it a powerful parameter at every scale levels.     

Evolution of Crack Tip Constraint in a Mode II Elastic-Plastic Crack Problem

Numerous studies have shown that crack tip constraint has an important effect on the level of conservatism when crack extension is investigated in elastic-plastic fracture mechanics. Constraint effect has been explored extensively in the past but mainly for pure mode I problems. Very few researchers have dealt with the effects of crack tip constraint on mode II or mixed mode I/II fracture in metallic materials. In this paper, the evolution of mode II constraint parameter Q in terms of applied external load is determined numerically for a test specimen under pure mode II loading. The finite element method is utilized to model the specimen and to study the range of validity of mode II constraint parameter determined from a Q—T diagram. The parameter Q calculated from the finite element simulation (or from the full field solution) is compared with the values of Q determined from the Q—T diagram. For low levels of load, the results of full field solution are shown to be consistent well with the results obtained from the Q—T diagram. However, when the external load increases significantly, the results of Q—T diagram are no longer accurate and mode II constraint parameter Q should be calculated directly from finite element results.     

Antiplane analysis for an elliptical inclusion in 1D hexagonal piezoelectric quasicrystal composites

An elliptical inclusion embedded in an infinite 1D hexagonal piezoelectric quasicrystal matrix is analysed in the framework of linear piezoelasticity of quasicrystals. Using the technique of conformal mapping, the closed-form solutions of the complex potentials, all the field quantities in the matrix and the inclusion are obtained under far-field antiplane mechanical loads of the phonon and phason fields and an inplane electrical load. Several special cases, such as a homogeneous material, a soft and permeable inclusion, an impermeable inclusion, a line inclusion, a rigid inclusion and a crack are reduced by the present results. Some numerical examples are provided to shows the variations of the stresses of the phonon and phason fields and the electric field with the shape of hole/inclusion, the dielectric permittivity and the distance from the hole/inclusion.