Effect of microcracking on electric-field-induced stress intensity factors in dielectric ceramics

This paper gives a quantitative analysis of the effect of near-tip microcracks on electric-field-induced stress intensity factors in isotropic elastic dielectrics. Nucleation of the microcracks is assumed to be governed by the electric-field-induced mean stress or the maximum normal stress. Based on the solutions for the effect of a single microcrack on the local electric field at the main crack, simple formulae are derived for the electric-field-induced stress intensity factors in the presence of the microcracks. It is found that the relative change in the stress intensity factor due to the microcracks for a conducting crack is equal and opposite to that for an insulating crack provided that the distribution of microcrack orientations is random. In particular, the microcracking zone is found to amplify the electric-field-induced stress intensity factor in some cases, especially for stationary insulating cracks, while the microcracking zone wake has an antishielding effect for sufficiently grown conducting cracks. These results are in sharp contrast with the well-known toughening effects of microcracks in elastic media under pure mechanical loads. This is attributed to the fact that the interaction between the microcracks and the main crack in elastic dielectrics under electrical loading is governed essentially by electrostatics, while the shape of the microcracking zone is determined by the electric field induced elastic stress field.     

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 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.     

晶体相场法研究应力状态及晶体取向对微裂纹尖端扩展行为的影响

采用晶体相场模拟研究了单向拉伸作用下初始应力状态、晶体取向角度对单晶材料内部微裂纹尖端扩展行为的影响, 以(111)晶面上的预制中心裂纹为研究对象探讨了微裂纹尖端扩展行为的纳观机理, 结果表明: 微裂纹的扩展行为主要发生在<011>(111)滑移系上, 扩展行为与扩展方向与材料所处的初始应力状态及晶体取向紧密相关. 预拉伸应力状态将首先诱发微裂纹尖端生成滑移位错, 进而导致晶面解理而实现微裂纹尖端沿[011]晶向扩展, 扩展到一定程度后由于位错塞积, 应力集中, 使裂纹扩展方向沿另一滑移方向[101], 并形成锯齿形边缘; 预剪切应力状态下, 微裂纹尖端首先在[101]晶向解理扩展, 并诱发位错产生, 形成空洞聚集型长大的二次裂纹, 形成了明显的剪切带; 预偏变形状态下微裂纹尖端则直接以晶面解理形式[101]在上进行扩展, 直至断裂失效; 微裂纹尖端扩展行为随晶体取向不同而不同, 较小的取向角度会在裂纹尖端形成滑移位错, 诱发空位而形成二次裂纹, 而较大的取向角下的裂纹尖端则以直接解理扩展为主, 扩展方向与拉伸方向几近垂直.     

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.     

Non-local theory solution of two collinear mode-I permeable cracks in a magnetoelectroelastic composite material plane

The non-local theory solution of two collinear mode-I permeable cracks in a magnetoelectroelastic composite material plane was investigated using the generalized Almansi's theorem and the Schmidt method. The problem was formulated through Fourier transform into two pairs of dual integral equations, in which the unknown variables are the jumps in displacements across the crack surfaces. To solve the dual integral equations, the displacement jumps across the crack surfaces were directly expanded as a series of Jacobi polynomials. Numerical examples were provided to show the effects of crack length, the distance between two collinear cracks and the lattice parameter on the stress field, the electric displacement field and the magnetic flux field near the crack tips. Unlike the classical elasticity solutions, it is found that no stress, electric displacement or magnetic flux singularities are present at the crack tips in a magnetoelectroelastic composite material plane. The non-local elastic solutions yield a finite hoop stress at the crack tip, thus allowing us to use the maximum stress as a fracture criterion.     

Crack-stimulated generation of deformation twins in nanocrystalline metals and ceramics

A theoretical model is proposed that describes the generation of deformation twins near brittle cracks of mixed I and II modes in nanocrystalline metals and ceramics. In the framework of the model, a deformation twin nucleates through stress-driven emission of twinning dislocations from a grain boundary distant from the crack tip. The emission is driven by both the external stress concentrated by the pre-existent crack and the stress field of a neighbouring extrinsic grain boundary dislocation. The ranges of the key parameters, the external shear stress, τ, and the crack length, L, are calculated within which the deformation-twin formation near pre-existent cracks is energetically favourable in a typical nanocrystalline metal (Al) and ceramic (3C-SiC). The results of the proposed model account for experimental data on observation of deformation twins in nanocrystalline materials reported in the literature. The deformation-twin formation is treated as a toughening mechanism effectively operating in nanocrystalline metals and ceramics.     

基于准连续介质方法模拟纳米多晶体Ni中裂纹的扩展

通过准连续介质方法模拟了纳米多晶体Ni中裂纹的扩展过程.模拟结果显示:裂纹尖端的应力场可以导致晶界分解、层错和变形孪晶的形成等塑性形变,在距离裂纹尖端越远的位置,变形孪晶越少,在裂纹尖端附近相同距离处,层错要远多于变形孪晶.这反映了局部应力的变化以及广义平面层错能对变形孪晶的影响.计算了裂纹尖端附近区域原子级局部静水应力的分布.计算结果表明:裂纹前端晶界处容易产生细微空洞,这些空洞附近为张应力集中区,并可能促使裂纹沿着晶界扩展.模拟结果定性地反映了纳米多晶体Ni中的裂纹扩展过程,并与相关实验结果符合得很好     

Structure and phonon spectrum of a submonolayer Ni film on the surface of Cu(100)

The equilibrium atomic structure and the phonon spectra of a submonolayer (θ = 0.5 monolayer) Ni film deposited on the surface of Cu(100) are calculated using the potentials obtained by the embedded atom method. We consider atomic relaxation, the vibrational state density distribution on Ni and substrate atoms, and polarization of vibrational modes. Variation of the phonon spectrum upon segregation of Cu atoms on the film surface is considered. It is shown that mixing of vibrations of Ni adatoms with vibrations of substrate atoms occurs in the entire frequency range, leading to a frequency shift of the vibrational modes of the substrate and to the occurrence of new vibrational states atypical of a clean surface. The Cu(100)–c(2 × 2)–Ni structure is dynamically stabler when placed in the subsurface layer of the substrate.     

Specific features of the transformation of local levels into an impurity band of Ag<Subscript>1−<Emphasis Type="Italic">p</Emphasis></Subscript>Al<Subscript><Emphasis Type="Italic">p</Emphasis></Subscript> disordered solid solutions

The phonon densities of states in disordered solid solutions of aluminum in silver are determined using the Jacobi matrix method. The transformation of discrete vibrational levels (local vibrational modes) into an impurity band with increasing concentration of impurity atoms is investigated. The formation of discrete vibrational levels is associated with the presence of individual aluminum impurity atoms in the lattice. It is demonstrated that, at relatively low (approximately 5–15%) aluminum concentrations, the broadening of the main local level is accompanied by the appearance of additional resonance peaks, which contain important information on the interatomic interactions in these solid solutions.     

MOCVD生长的GaN和GaN:Mg薄膜的拉曼散射

通过显微拉曼散射对用金属有机化学气相沉积(MOCVD)法在Al2O3衬底上生长的六方相CaN和掺Mg的P型GaN薄膜进行了研究。在两个样品的拉曼散射谱中同时观察到位于640,660cm^-1附近的两个峰。640cm^-1的峰归因于布里渊区边界(L点)最高声学声子的二倍频,而660cm^-1的峰为布里渊区边界的光学声子支或缺陷诱导的局域振动模。掺Mg的GaN在该处的峰型变宽是Mg诱导的缺陷引起的加宽或Mg的局域模与上述两峰叠加的结果。在掺Mg的样品中还观察到276,376cm^-1几个局域模并给予了解释。同时掺Mg的GaN中出现了应力弛豫的现象,掺Mg引起的失配位错和电子-声子相互作用都有可能对E2模的频率产生影响。     

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.     

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.     

Multiparadigm modeling of dynamical crack propagation in silicon using a reactive force field

We report a study of dynamic cracking in a silicon single crystal in which the ReaxFF reactive force field is used for several thousand atoms near the crack tip, while more than 100,000 atoms are described with a nonreactive force field. ReaxFF is completely derived from quantum mechanical calculations of simple silicon systems without any empirical parameters. Our results reproduce experimental observations of fracture in silicon including changes in crack dynamics for different crack orientations.     

基于涡流脉冲相位热成像的金属材料裂纹检测

涡流热成像可以对金属材料表面、近表面缺陷进行快速准确的检测。采用涡流热成像与脉冲相位分析相结合的方法,针对裂纹附近相位谱的分布规律及温度场对相位谱的影响关系问题,分别对带有上表面裂纹和下表面裂纹的45#钢料进行感应加热仿真和实验分析。结果表明,相位谱分布与温度大小无关,只与温度变化趋势有关,相位谱图对不均匀加热有很好的抑制作用,可以扩大裂纹的检测范围,当频率低于12.5 Hz时能够清晰地识别裂纹。结合实验验证了仿真结论的正确性,为下一步利用相位信息实现缺陷的定量检测提供参考。     

弹性连续介质中氢致裂纹传播理论

弹性连续介质中的氢原子,在裂纹应力场的诱导下发生聚集,形成氢气团,本文计算了气团分布区平均氢浓度,并将该区看作沿裂纹尖端分布的弹性夹杂,确定了夹杂的本征应变,研究了夹杂的应力场P_ij对裂纹位错密度的影响,求得了裂纹尖端总的应力强度因子,认为氢脆机理是氢气团增大了裂纹尖端应力强度因子,最后还讨论了氢致开裂的物理过程及氢致裂纹扩展速率,所得结果与实验符合很好。 关键词：     

Fractoluminescence of poly(phenylene sulfide) and a fiber composite on its basis

The object of investigation is fractoluminescence induced by the blow of a steel striker on plates made of poly(phenylene sulfide) and carbon-iber-einfor ced poly(phenylene sulfide). It is found that fractoluminescence shows up as a series of bursts several tens of microseconds long. Simultaneously, microcracks develop on the surface. It is assumed that the bursts are caused by microcracking. The linear size of the cracks is estimated to vary from 0.2 to 10.0 fum. The crack size distribution obeys a power law. In the composite, the amount of cracks is an order of magnitude smaller than in the poly(phenylene sulfide) and the crack size distribution is somewhat broader because of a larger fraction of large cracks.     

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.     

钛金属应力腐蚀机理电子理论研究

为从理论上揭示钛金属应力腐蚀行为的本质，建立了α钛晶粒及位错塞积形成的微裂纹原子 集团模型，利用递归法(recursion)计算了裂纹及晶粒内的电子结构参量(费米能级、结构能 、表面能、团簇能、环境敏感镶嵌能). 计算结果表明：氢在裂纹处的环境敏感镶嵌能较低 ，易于偏聚在裂纹处，且氢在钛金属裂纹处团簇能为正值不能形成团簇，具有有序化倾向， 趋于形成氢化物. 氢在裂纹处偏聚降低裂纹的表面能，使裂纹容易扩展. 裂纹尖端处费米能 级高于裂纹其他区域，使电子从裂纹尖端流向裂纹其他区域造成电位差，在电解质作用下裂 关键词： 递归法 电子结构 钛 应力腐蚀     

The elastic field of general-shape 3-D cracks

We extend here the Bilby-Eshelby approach of 2-D crack representation with dislocation pileups to treat 3-dimensional cracks of general geometry. Cracks of any specified external bounding 3-D contour under general loading conditions are represented by sets of parametric Somigliana loops that satisfy total (interaction, self, and external) force equilibrium. Loop positions are solved by using a time integration scheme till equilibrium is achieved. The local Burgers vector is suitably adjusted to be proportional to the local applied surface traction on the crack. The developed method is computationally advantageous, since accurate crack stress fields are obtained with very few concentric parametric loops that adjust to the external crack shape and the local force conditions. The method is tested against known elasticity solutions for 3-D cracks and found to be convergent with an increase in the number of pileup dislocation loops. The method is applied to the determination of the stress field around a 3-D Griffith crack under general loading and a grain boundary crack before and after branching.