Deformation rates effects in softwoods: Crack dynamics with lattice fracture modelling

Present study contributes towards understanding crack toughness against the intrinsic deformation rate sensitivity. A methodology for characterizing fracture dependence in softwoods through experimental and numerical analysis has been developed. Time-dependence was found to be the characterising parameter. Image analysis of fracture data acquired with high-speed camera showed that the crack speed histories are stochastic and erratic. In the higher rate range, crack dynamics is characterized as episodic and locally heterogeneous, with irregular jumps and arrests. Critical crack propagation speed at the highest rate tested of 200 mm/min was found to be between 0.7 m/s and 4 m/s (14.3 km/h). Fracture toughness decreased at both slow static and high loading rates, with the mean maximum at 1 mm/min, which is a static deformation rate specific to short-term standard tests. At 200 mm/min deformation rate, inertial effects suggested dynamic fracture response. Explanations of loading rates effects relate to the micro-processes in the fracture process zone (FPZ) and fracture mechanisms, which are simulated with discrete lattice fracture model (LFM). The model included viscous bi-linear stress relaxation into the softening relation and random stochastic finite element properties. Novel characterisation of softwoods is crucial for sensible numerical modeling in seismic structural situations.     

Collective mode dynamics of the vortex lattice in a highT c superconductor

Dispersion relations have been obtained numerically for the collective modes of the flux line lattice of a highT _c superconductor in the London limit and the effect of pinning forces is included. It is found that the waves propagating along the magnetic field the dispersion consists of two branches and that the low frequency branch may interact with other low-frequency excitations in the lattice.     

Crack in a lattice waveguide

We consider some structures where the harmonic ‘feeding’ wave localized at the crack faces can force the crack to grow. First, we present some results related to a lattice with a high-contrast layer, where the wave speed is larger than in the ambient matrix. The analytical solution obtained for the steady-state regime, where the crack speed is independent of the wave amplitude, is used to determine the energy relations and the wave-amplitude-dependent position of the crack front relative to the feeding wave. The corresponding numerical simulations confirmed the existence of the steady-state regime within a range of the wave amplitude. For lager amplitudes the simulations revealed a set of ordered crack-speed oscillation regimes, where the average crack speed is characterized by a stepwise dependence on the wave amplitude. We show that the related cluster-type wave representation allows the average crack speeds to be determined analytically. We also show the connection between the cluster representation and the ‘local’ crack-speeds within the cluster. As an example of a continuous system, where the crack can uniformly grow under the localized harmonic wave, an elastic flexural plate is considered. Both symmetric and antisymmetric fracture modes are examined.     

Crack dynamics and explosive burn via generalized coordinates

The growth of cracks and their role in the formation of hot spots in explosives are addressed in a three-part discussion. First the method of generalized coordinates is used to represent crack dynamics with two ordinary differential equations for crack opening and growth. These account for both stable and unstable behavior. Second, the behavior of burning cracks is addressed by coupling those differential equations to a burn model to show that burning cracks can exhibit either mild or violently unstable behavior. Finally, in the third part, it is shown that the burning crack algorithm in combination with SCRAM (which deals with Statistical CRAck Mechanics) can account for the reactive behavior of a plastic-bonded explosive (PBX 9501) subjected to multiple shocks. SCRAM allows for representation of brittle behavior in a variety of explosives, propellants, ceramics and geological materials. This revised version was published online in June 2006 with corrections to the Cover Date.     

Thermo-mechanical Deformation in Magneto-micropolar Elastic Medium

The present investigation is concerned with a two-dimensional problem in electromagnetic micropolar elasticity for a half-space whose surface is subjected to distributed (concentrated or continuous) thermo-mechanical sources in the presence of a transverse magnetic field. As an application of the approach, the sources are taken as uniformly or linearly distributed. Laplace and Fourier transform techniques are used to solve the problem. The integral transforms have been inverted by using a numerical technique to obtain the components of normal strain, normal stress, tangential couple stress, and temperature distribution in the physical domain. Magnetic effects on the components of normal strain, normal stress, tangential couple stress, and temperature distribution have been depicted graphically for two different theories of generalized thermoelasticity, Lord and Shulman (L–S) theory and Green and Lindsay (G–L) theory. A particular case of interest is also deduced from the present investigation.     

Crack path selection in piezoelectric bimaterials

The problem of crack path selection in piezoelectric bimaterials is considered in this paper. Based on the Stroh formulation for anisotropic material and Green’s functions for piezoelectric bimaterials, the crack problem is expressed in terms of coupled singular integral equations at first, and then the equations are used to solve for stress and electric displacement fields numerically. A crack impinging an interface joining two dissimilar materials may arrest or may advance by either penetrating the interface or deflecting into it. The competition between deflection and penetration is investigated using the maximum energy release rate criterion. Numerical results are presented to study the role of remote electroelastic loads on the path selection of crack extension.     

Electroelastic response of a flat annular crack in a piezoelectric fiber surrounded by an elastic medium

Following the theory of linear piezoelectricity, the electroelastic problem of a flat annular crack in a piezoelectric fiber embedded in an elastic medium is considered. Fourier and Hankel transform techniques are employed to formulate the mixed-boundary-value problem as a singular integral equation. The stress-intensity factor, energy-release rate and energy-density factor are computed for some piezoelectric composites, and the influence of applied electric fields on the normalized values is displayed graphically.     

二维非线性单原子正方晶格色散摄动分析

声子晶体的色散关系决定弹性波在其中的传播方式。从二维无限周期结构的波动方程出发,提出了一种分析非线性离散型声子晶体的色散关系的一阶近似摄动法。通过引入Bloch理论与小参数摄动展开法,得到了一阶近似的色散关系与频散曲线,以分析不同方向上的阻抗配置与非线性系数对频散及群速度的影响。以二维单原子正方晶格为例,得到了其一阶频散曲线。色散结果显示带隙及传播方向与波幅相关。最后模拟了晶格对点谐波激励的响应,以验证摄动分析有效性。     

Control of lattice spacing in a triangular lattice of feeble magnetic particles formed by induced magnetic dipole interactions

We studied methods of controlling the spacing between particles in the triangular lattice formed by feeble magnetic particles through induced magnetic dipole interaction. Formation of a triangular lattice is described by the balance between the magnetic force and the interaction of induced magnetic dipoles. The intensity of the magnetic force is proportional to the volume of particles V and the difference in the magnetic susceptibilities between the particles and the surrounding medium Δχ. On the other hand, the intensity of the induced magnetic dipole interaction depends on the square of V and Δχ. Therefore, altering the magnetic susceptibility difference by changing the susceptibility of the surrounding medium, volume of the particles, and intensity and spatial distribution of the applied magnetic field effectively controls the distance between the particles. In this study, these three methods were evaluated through experiment and molecular dynamics simulations. The distance between the particles, i.e. the lattice constant of the triangular lattice, was varied from 1.7 to 4.0 in units of the particle diameter. Formation of self-organized triangular lattice through the induced magnetic dipole interaction is based on magnetism, a physical property that all materials have. Therefore, this phenomenon is applicable to any materials of any size. Consequently, structure formation through induced magnetic dipole interaction is a potential way of fabricating materials with ordered structures.     

Control of lattice spacing in a triangular lattice of feeble magnetic particles formed by induced magnetic dipole interactions

Abstract

We studied methods of controlling the spacing between particles in the triangular lattice formed by feeble magnetic particles through induced magnetic dipole interaction. Formation of a triangular lattice is described by the balance between the magnetic force and the interaction of induced magnetic dipoles. The intensity of the magnetic force is proportional to the volume of particles V and the difference in the magnetic susceptibilities between the particles and the surrounding medium Δχ. On the other hand, the intensity of the induced magnetic dipole interaction depends on the square of V and Δχ. Therefore, altering the magnetic susceptibility difference by changing the susceptibility of the surrounding medium, volume of the particles, and intensity and spatial distribution of the applied magnetic field effectively controls the distance between the particles. In this study, these three methods were evaluated through experiment and molecular dynamics simulations. The distance between the particles, i.e. the lattice constant of the triangular lattice, was varied from 1.7 to 4.0 in units of the particle diameter. Formation of self-organized triangular lattice through the induced magnetic dipole interaction is based on magnetism, a physical property that all materials have. Therefore, this phenomenon is applicable to any materials of any size. Consequently, structure formation through induced magnetic dipole interaction is a potential way of fabricating materials with ordered structures.     

FEM Modeling of Crack Propagation in a Model Multiphase Alloy

In this paper, several widely applied fracture criteria were first numerically examined and the crack-tip-region Jntegral criterion was confirmed to be more applicable to predict fracture angle in an elastic-plastic multiphase material. Then, the crack propagation in an idealized an elastic-plastic finite element method. The variation dendritic two-phase AI-7%Si alloy was modeled using of crack growth driving force with crack extension was also demonstrated. It is found that the crack path is significantly influenced by the presence of α-phase near the crack tip, and the crack growth driving force varies drastically from place to place. Lastly, the simulated fracture path in the two-phase model alloy was compared with the experimentally observed fracture path.     

Numerical investigation of crack growth in concrete subjected to compression by the generalized beam lattice model

The beam lattice-type models, such as the Euler–Bernoulli (or Timoshenko) beam lattice and the generalized beam (GB) lattice, have been proved very effective in simulating failure processes in concrete and rock due to its simplicity and easy implementation. However, these existing lattice models only take into account tensile failures, so it may be not applicable to simulation of failure behaviors under compressive states. The main aim in this paper is to incorporate Mohr–Coulomb failure criterion, which is widely used in many kinds of materials, into the GB lattice procedure. The improved GB lattice procedure has the capability of modeling both element failures and contact/separation of cracked elements. The numerical examples show its effectiveness in simulating compressive failures. Furthermore, the influences of lateral confinement, friction angle, stiffness of loading platen, inclusion of aggregates on failure processes are respectively analyzed in detail.     

Crack initiation strength of an interface between a submicron-thick film and a substrate

The focus of this study was to evaluate the fracture initiation criteria of the interface between a thin film and a substrate by Bogy’s, Kitamura’s and Griffth’s methods. The critical stress intensity parameter K_ijC in Bogy’s method and the concentrated stress parameter σ_ijC in Kitamura’s method were calculated based on the singular stress field near the interface edge. The work of separation per unit area Γ_ο in Griffth’s method was calculated based on the work of fracture process. The results obtained show that in comparison among interface strengths, the fracture toughness K_θθC and the concentrated stress parameter σ_θθC were respectively applied to material combinations with specific edge geometry and with weak stress singularity, while the work of separation per unit area Γ_ο was applied in all cases.     

Crack paths in composite materials

Composites are often exposed to harsh loading conditions. This may lead to crack formation and propagation. In this paper, an algorithm is described to predict the path of pre-existing cracks in homogeneous materials, based on an incremental approach. The approach is shown to also deal with the highly heterogeneous behaviour of periodically distributed composites.     

Modulated structure and superconductivity in 2D electron-hole lattice system

The close relationship between modulated structures and superconductivity in high-T_c oxide superconductors is explained by using a two-dimensional (2D) electron-hole lattice. The 2D electron-hole lattice is constructed on the crystal surface or between adjacent layers by neutralizing polarization charges caused by a local polarization along thec-axis. The local polarization in the oxide superconductors is often accompanied by a modulated structure, with the modulation period corresponding to the length of one side of the 2D electron-hole lattice,D. Assuming that the Cooper pairs can be formed through the exchange of the phonons of the 2D electron-hole lattice oscillation, we show that both the optimum carrier density and the peak value of the transition temperature are approximately proportional toD ^–3/2 andD ^–2, respectively, and that for a typical value ofD 15 Å, they are estimated to be on the order of 10¹⁴/cm² and 100 K, respectively.     

Numerical integration of lattice rotation in polycrystal plasticity

A numerical algorithm to calculate the lattice rotation in polycrystal plasticity models, that is based on the analytical integration of the lattice rotation update equation, is presented. Implicit and explicit implementations perform equally well and are superior to the currently used numerical integration schemes. Copyright © 2001 John Wiley & Sons, Ltd.     

Crack identification in rotating shafts by coupled response measurements

In this paper a new method is applied in rotating cracked shafts to identify the depth and the location of a transverse surface crack. A local compliance matrix of different degrees of freedom is used to model the transverse crack in a shaft of circular cross section, based on available expressions of the stress intensity factors and the associated expressions for the strain energy release rates. It is known that when a crack exists in a structure, such as a beam, then the excitation in one-direction causes coupled vibrations in other directions. This property is used here to identify the crack. The shaft is modeled as a rotating Timoshenko beam including the gyroscopic effect and the axial vibration due to coupling. The method used here is based on the measurements of the axial vibration response due to different excitation frequencies and shaft revolutions. The figures presented are used to identify the crack.     

General solution for arc crack problem in thermoelastic medium

A problem of a circular arc-shaped crack in an infinite plate under the thermal loading is solved by using the complex variable function and the integral equation method. General solution for arbitrary heat flux along the crack face is obtained. For some particular cases, for example, the constant heat flux case and remote heat flux case, a closed form solution is obtained. The solution technique is effective in derivation and compact in form.     

Local lattice instability and ionic transport in high-temperature superconductors

Ionic transport, a characteristic feature of superionic conductors, is analyzed microscopically for the RBa₂Cu₃O{7-Σ} (R = rare earth) high-temperature superconductors. The electronic correlation effects are considered to be responsible for the formation of a local double-well potential for apical oxygen, which in its turn results in a decrease of the activation energy for interstitial chain oxygen defects. The behavior of the double well upon reduction of the oxygen content is discussed and its possible manifestation in the low-frequency dynamical response is considered.