Mathematical model of thermocracking of anisotropic brittle materials

A mathematical model of the process of laser-co ntrolled thermocracking for thin plates of aniso-tropic elastic materials has been constructed. By means of sequential replacement of the variable scale along one of the orthogonal coordinates, the problem of determination of the potential has been reduced to the Poisson equation. A comparison with the experiment by the example of thermocracking of a single-crystal quartz plate in a circumferential direction has been carried out.     

Crack growth in polyconvex materials

We discuss a model for crack propagation in an elastic body, where the crack path is described a priori. In particular, we develop in the framework of finite-strain elasticity a rate-independent model for crack evolution which is based on the Griffith fracture criterion. Due to the nonuniqueness of minimizing deformations, the energy-release rate is no longer continuous with respect to time and the position of the crack tip. Thus, the model is formulated in terms of the Clarke differential of the energy, generalizing the classical crack evolution models for elasticity with strictly convex energies. We prove the existence of solutions for our model and also the existence of special solutions, where only certain extremal points of the Clarke differential are allowed.     

Acoustic emissioin monitoring of strength in brittle materials

It has been established that for porcelain, ferrite and cement-porcelain mortar the tensile strength, σ_F, during subsequent loading is closely related to the stress σ_O at which during the unloading period of the proof test the acoustic emission (AE) response changes from a continuous activity to a discrete one. The coefficients in the equation σ_F = A + Bσ_O in bending were found to be the same as those for radial compression. For a very homogeneous material with no continuous AE during unloading, σ_F correlates well with the relative change, κ, in pulse amplitude when two proof tests are carried out. The relationships σ_F(σ_O) and σ_F(κ) are independent of the mode and direction of abrasive machining.     

From brittle to ductile fracture in disordered materials

We introduce a lattice model able to describe damage and yielding in heterogeneous materials ranging from brittle to ductile ones. Ductile fracture surfaces, obtained when the system breaks once the strain is completely localized, are shown to correspond to minimum energy surfaces. The similarity of the resulting fracture paths to the limits of brittle fracture or minimum energy surfaces is quantified. The model exhibits a smooth transition from brittleness to ductility. The dynamics of yielding exhibits avalanches with a power-law distribution.     

Conduction degradation in anisotropic multi-cracked materials

The electrical and thermal conduction properties of disordered solids and the possible degradation processes induced by the generation of cracks are central issues in the field of the heterogeneous materials. However, most of the existing theories are unable to consider an arbitrary density of cracks. We obtained an exact result for the fields induced within an elliptic anisotropic inhomogeneity embedded in a different anisotropic (two-dimensional) conductor. Then, we applied it to show that the degradation process strongly depends on the statistical orientational distribution of defects: in particular we theoretically prove that parallel cracks lead to the power law decay log σ ∼ − log N while random oriented cracks lead to the exponential law decay log σ ∼ −N (where σ is the effective conductivity of a region with a large number N of defects), as recently predicted by numerical findings.     

Dislocation motion in anisotropic multilayer materials

Line integral forms for the elastic field of dislocations in anisotropic, multilayer materials are developed and utilized in Parametric Dislocation Dynamics (PDD) computer simulations. Developed equations account for interface image forces on dislocations as a result of elastic modulus mismatch between adjacent layers. The method is applied to study dislocation motion in multilayer thin films. The operation of dislocation sources, dislocation pileups, confined layer slip (CLS), and the loss of layer confinement are demonstrated for a duplex Cu/Ni system. The strength of a thin film of alternating nanolayers is shown to increase with decreasing layer thickness, and that the maximum strength is determined by the Koehler barrier in the absence of coherency strains. For alternating Cu/Ni nanolayers, the dependence of the strength on the duplex layer thickness is found to be consistent with experimental results, down to a layer thickness of ≈10nm.     

Kinetics of brittle fracture of elastic materials

A phenomenological model is proposed for the evolution of microcavities in materials under load based on a study of the kinetics of brittle fracture in a linearly elastic deformable medium containing a microcavity. The basic principle of the model is that, during deformation of a material containing a micropore, fluctuations of its shape occur. The surface tension at the micropore-medium interface stabilizes these fluctuations but if the load exceeds a critical value, these fluctuations may begin to evolve. In so doing, they distort the shape of the microcavity. These fluctuations are none other than cracks. This concept of crack growth and their nature has a close analogy with the evolution of dendrites formed in supercooled melts as a result of the loss of stable crystal shape. An analysis is made of the laws governing the evolution of a microcavity and local loss of shape stability under steady-state pressure for the case of a sphere containing a quasispherical cavity. Fiz. Tverd. Tela (St. Petersburg) 40, 1259–1263 (July 1998)     

Universal scaling relations in strongly anisotropic materials

We consider the critical temperature in strongly anisotropic antiferromagnetic materials, with weak coupling between stacked planes, in order to determine the interplane coupling constant from experimentally measured susceptibilities. We present theoretical arguments for a universal relation between interplane coupling and susceptibility shown numerically by Yasuda et al. [Phys. Rev. Lett. 94, 217201 (2005)10.1103/PhysRevLett.94.217201]. We predict a more general scaling function if the system is close to a quantum critical point, a similar relation for other susceptibilities than considered in Yasuda et al., and the validity of these relations for more general phase transitions.     

Collective penetration of cumulative jets into brittle materials

The group action of cumulative jets on a composite material made of corundum and glass-fiber reinforced plastic is studied. The obtained results show that the collective action of cumulative jets enhances the efficiency of resistance of a brittle material to high-speed penetration at certain geometric and time relations. These specific features manifest themselves under subsonic penetration conditions and support the mechanism of a radial action of a cavity in a high-strength brittle material on a penetrating cumulative jet.     

Laser ceramics with rare-earth-doped anisotropic materials

The fabrication of laser-grade anisotropic ceramics by a conventional sintering process is not possible owing to optical scattering at randomly oriented grain boundaries. In this Letter, we report the first (to our knowledge) realization of transparent anisotropic ceramics by using a new crystal orientation process based on large magnetic anisotropy induced by 4f electrons. By slip casting in a 1.4 T magnetic field and subsequent heat treatments, we could successfully fabricate laser-grade calcium fluorapatite ceramics with a loss coefficient of 1.5 cm(-1).     

Laser picosecond acoustics in isotropic and anisotropic materials

We present experimental results concerning the laser generation of picosecond acoustic pulses and their propagation in isotropic and anisotropic materials. We make use of a conventional reflectance detection technique as well as interferometric detection to probe the real and imaginary changes in reflectance. We also demonstrate the detection of transverse acoustic waves by mode conversion at an interface between an isotropic polycrystalline film and an anisotropic substrate.     

各向异性材料的热扩散率的分析

在理论上分析了各向异性材料的热扩散率，给出了沿表面任意方向的热扩散率与主热扩散率的关系，从而为实验确定材料中任意方向的热扩散率提供了理论依据。     

Characteristics of surface waves in anisotropic left-handed materials

We report the coexistence of TE and TM surface modes in certain same frequency domain at the interface between one isotropic regular medium and another biaxially anistotropic left-handed medium. The conditions for the existence of TE and TM polarized surface waves in biaxially anisotropic left-handed materials are identified, respectively. The Poynting vector and the energy density associated with surface modes are calculated. Depending on the system parameters, either TE or TM surface modes can have the time averaged Poynting vector directed to or opposite to the mode phase velocity. It is seen that the characteristics of surface waves in biaxially anisotropic left-handed media are significantly different from that in isotropic left-handed media.     

Photoelastic effect and mirage deflection in anisotropic materials

The collinear mirage technique is widely used to measure the thermal diffusivity of semi-transparent materials. However, in a recent paper [A. Salazar, M. Gateshki and A. Sánchez-Lavega: Appl. Phys. Lett. 76, 2665 (2000)], it was shown that for isotropic materials, because of the influence of photoelastic effect, the method was sensitive to the polarization state of the probe beam. The present paper extends the previous work to include anisotropic materials. In particular, we focus on the experimental conditions under which the thermal diffusivity of each crystal system can be measured using the phase method. Our theoretical model indicates that while the thermal diffusivity of isotropic materials can be measured using an unpolarized probe beam, for anisotropic materials, even the use of an unpolarized probe beam does not guarantee the validity of the method in all crystal systems. Experimental measurements performed on cubic, hexagonal and monoclinic crystals confirm the validity of the model. Received: 17 March 2001 / Accepted: 17 March 2001 / Published online: 25 July 2001     

Penetration kinetics of a cumulative jet into brittle materials

The experimental results on the penetration of cumulative jets into brittle materials are analyzed to substantiate the assumption that continuous hydrodynamic penetration is violated. The penetration of a cumulative jet into a brittle material has a jumplike character and consists of hydrodynamic penetration, the collapse of the cavity, and secondary penetration into the collapsed material. For a continuous supply of a cumulative jet, this process is repeated at the penetration depth. The necessary conditions of the secondary penetration consist in a high strength of the brittle material and a high fracture rate, which should provide the spallation and collapse of the cavity walls. Jumplike penetration ends when a rarefaction wave passes to the zone of primary penetration.     

Damage and fracture evolution in brittle materials by shape optimization methods

This paper is devoted to a numerical implementation of the Francfort–Marigo model of damage evolution in brittle materials. This quasi-static model is based, at each time step, on the minimization of a total energy which is the sum of an elastic energy and a Griffith-type dissipated energy. Such a minimization is carried over all geometric mixtures of the two, healthy and damaged, elastic phases, respecting an irreversibility constraint. Numerically, we consider a situation where two well-separated phases coexist, and model their interface by a level set function that is transported according to the shape derivative of the minimized total energy. In the context of interface variations (Hadamard method) and using a steepest descent algorithm, we compute local minimizers of this quasi-static damage model. Initially, the damaged zone is nucleated by using the so-called topological derivative. We show that, when the damaged phase is very weak, our numerical method is able to predict crack propagation, including kinking and branching. Several numerical examples in 2d and 3d are discussed.     

激光切割脆性材料的温度场模拟

激光切割脆性材料是一个复杂的光致热过程。在综合考虑材料的热物性参数、初始条件及边界条件的情况下,运用Ansys软件建立了激光切割脆性材料温度场的三维有限元模型。采用APDL语言实现了对热流密度的高斯分布和强制对流换热及移动激光热源的模拟。通过设置不同的激光切割参数,对温度场的变化进行了模拟分析。所建立的温度场模拟系统可以对实际激光切割脆性材料的热过程进行前期预测,并能对激光切割参数的选择进行一定的优化,以减少实际切割的盲目性。     

Effects of energy dissipation on anisotropic materials

A model and its simulations are presented to describe the effects of energy dissipation on anisotropic systems. When the current electromigration is constant, energy dissipation depends on lattice constants, resistivity, and the angles along the longitudinal and transversal directions. It is shown that an orientation variation of the grain can significantly influence the energy dissipation for some anisotropic materials. Based on calculations for the grain model, the mechanism of grain growth and microstructure evolution under electromigration is explained. Theoretical implications about material selection and reliability are derived.