Effective spring stiffness for a planar periodic array of collinear cracks at an interface between two dissimilar isotropic materials

Explicit analytical expressions are obtained for the longitudinal and transverse effective spring stiffnesses of a planar periodic array of collinear cracks at the interface between two dissimilar isotropic materials; they are shown to be identical in a general case of elastic dissimilarity (the well-known open interface crack model is employed for the solution). Since the interfacial spring stiffness can be experimentally determined from ultrasound reflection and transmission analysis, the proposed expressions can be useful in estimating the percentage of disbond area between two dissimilar materials, which is directly related to the residual strength of the interface. The effects of elastic dissimilarity, crack density and crack interaction on the effective spring stiffness are clearly represented in the solution. It is shown that in general the crack interaction weakly depends on material dissimilarity and, for most practical cases, the crack interaction is nearly the same as that for crack arrays between identical solids. This allows approximate factorization of the effective spring stiffness for an array of cracks between dissimilar materials in terms of an elastic dissimilarity factor and two factors obtained for cracks in a homogeneous material: the effective spring stiffness for non-interacting (independent) cracks and the crack interaction factor. In order to avoid the effect of the crack surface interpenetration zones on the effective spring stiffness, the range of the tensile to transverse load ratios is obtained under the assumption of small-scale contact conditions. Since real cracks are often slightly open (due to prior loading history and plastic deformation), it is demonstrated that for ultrasound applications the results obtained are valid for most practical cases of small interfacial cracks as long as the mid-crack opening normalized by the crack length is at least in the order of 10⁻⁵.     

Periodic array of staggered planar cracks in an anisotropic elastic medium

The problem of determining the elastic displacements and stresses in an infinite anisotropic medium containing a periodic array of staggered planar cracks is considered. It is reduced to a system of Hadamard finite-part singular (hypersingular) integral equations with the crack-opening displacements as unknown functions. The integral equations may be solved numerically by a collocation technique. Numerical results for specific cases involving isotropic and transversely isotropic materials are obtained.     

A periodic array of cracks in functional graded materials subjected to thermo-mechanical loading

A periodic array of cracks in an infinite functionally graded material under mechanical and/or thermal loading is investigated. Due to non-uniform heating or cooling, compressive stresses occur causing the crack surfaces to come into contact at a certain contact length. The mixed boundary value problem is reduced to a singular integral equation with the crack contact length as an additional unknown variable. Numerical results for stress intensity factors and the crack contact length are obtained as a function of crack spacing. Effect of the material non-homogeneity on the crack tip intensity factors is discussed. Some suggestions are made for the design of thermal resistive functionally graded materials.     

Plane problems of an arbitrary array of cracks emanating from the edge of an elliptical hole

This paper presents a unified analysis of interaction problems of an elliptical hole and an arbitrary array of internal cracks as well as edge cracks including kinked cracks and branched cracks. The analysis is based on the body force method, in which new expressions of the body force densities and resultant force boundary conditions are introduced in order to improve the accuracy and applicability. Numerical calculations are performed for various problems of practical imoportance, and the stress intensity factors are given in dimensionless forms. The analysis also covers the problems of a semi-infinite plate containing an arbitrary array of cracks just by assuming a large aspect ratio of the elliptical hole.     

相控阵超声绝对声时法测量底面开口裂纹

针对工件内表面开口裂纹单面单侧定量检测困难的问题,采用相控阵超声绝对声时法(Absolute Arrival Time Technique,AATT)从单面单侧对不同厚度试块中的底面人工开口裂纹自身高度测量进行了数值仿真和实验,并对焊缝中的自然裂纹进行了AATT测量。对比AATT测量结果与常规衍射时差法超声检测(Time of Flight Diffraction,TOFD)测量结果并分析,发现AATT从单面单侧对底面开口裂纹进行定量测量可以达到与常规TOFD同样的测量精度。AATT操作简便,可单面单侧定量测量2 mm以上底面开口裂纹的自身高度。     

Semi-infinite array of cracks in a uniform stress field

The collinear semi-infinite array of periodically distributed cracks in a loaded infinite plane is considered. The formulation is based on consideration of the complex stress potentials. The numerical procedure allows one to obtain the resulting stress field or stress intensity factors with any prior specified accuracy. The formulation can be extended to any geometry of collinear crack interacting with semi-infinite crack array. The results demonstrate a significant edge effect in reducing local stress intensity factors.     

The torsion of a circular cylinder containing a symmetric array of edge cracks

In this paper the authors make use of a recent advance in the theory of Mellin transforms to find the stress intensity factors and crack energy of a symmetric array of edge cracks in a circular cylinder under torsion. Two special cases are considered in detail and the results are given in graphical form.     

Numerical analysis of doubly periodic array of cracks/rigid-line inclusions in an infinite isotropic medium using the boundary integral equation method

In this paper, the boundary integral equation approaches are used to study the doubly periodic array of cracks/rigid-line inclusions in an infinite isotropic plane medium. For the doubly periodic rigid-line inclusion problems, the special integral equation containing the axial and shear forces within the rigid-line inclusion is used. The doubly periodic crack problems are dealt with using the displacement discontinuous integral equation approach. Stress intensity factors, effective elastic properties for doubly periodic array of cracks/rigid-line inclusions are calculated and compared with the available numerical solutions.     

Failure of a plate with a circular hole resulting from an array of surface cracks

The problem of brittle failure of an isotropic homogeneous plate perforated by a circular hole as a result of the development of an array of small equal surface cracks was investigated. The plate was loaded by a uniform uniaxial stress at an arbitrary inclination with respect to the system of the cracks. From the study the critical value of the applied stress for failure of the plate by propagation of the most vulnerable crack was determined. Useful results governing the dependence of the critical stress on the number of cracks, the inclination of the applied stress, the length of the cracks and the Poisson's ratio of the plate were derived.     

基于水平分置线性双阵列的超声全聚焦成像方法在粗晶材料检测中的应用

针对粗晶材料超声检测信噪比低的问题,提出了一种水平分置线性双阵列超声成像方法。将两个线阵超声换能器沿直线水平分置在待检区域表面两侧,用收发分离的信号采集模式,一侧激发,另一侧记录各通道数据,进行聚焦成像。相比单阵列和同位置双线阵检测,文中的方法有效地减少了背向散射信号对缺陷信号的干扰,提高了成像信噪比。在粗晶铜质试块上的成像实验结果表明,当缺陷距离阵列较近时,文中的方法优于单阵列和同位置双线阵方法,成像信噪比提高约5～10 dB;当缺陷距离阵列较远时,单阵列模式和同位置双线阵检测方法失效,但文中的方法依然可以识别缺陷。文中的研究为粗晶材料的超声检测提供了一种可行的方案。     

The linear steady thermoelastic problem for a strip with a collinear array of Griffith cracks parallel to its edges

The problem of determining the thermal stresses when a uniform heat flow in a thermoelastic strip is disturbed by a collinear array of cracks is discussed. The solution of the Duhamel-Neumann equations is posed in terms of harmonic functions, which leads to dual series relations whose solutions are known. Numerical results for the stress intensity factors at the crack tips are displayed in graphical form.     

Fabrication of a one-dimensional array of nanopores horizontally aligned on a Si substrate

A one-dimensional array of nanopores horizontally aligned on a silicon substrate was successfully fabricated by anodic aluminum oxidation (AAO) using a modified two-step procedure. SEM pictures show clear nanostructures of well-aligned one-dimensional nanopore arrays without cracks at the interfaces of the sandwiched structures. The processes are compatible with the planar silicon integrated circuit processing technology, promising for applications in nanoelectronics. The formation mechanism of a single nanopore array on Si substrates was also discussed.     

A study of two-dimensional array transducers for limited diffraction beams

The newly developed limited diffraction beams such as the Bessel beams and X waves have a large depth of field and approximate depth-independent property. They have possible applications in medical imaging, color Doppler imaging, tissue characterization, and nondestructive evaluation of materials, and in other wave related physical branches such as electromagnetics and optics. However, limited diffraction beams are currently produced with an annular array transducer that has to be steered mechanically. In this paper, we study the feasibility of steering these beams with a two-dimensional array, and show that there will be almost no distortion of beams if the effective aperture reduction of the array is properly compensated so that the beams have a constant transverse profile as they are steered. In addition, methods for reducing the complexity of the electronic multiplexing of the array elements are proposed. We also investigate the influences of the interelement distance and the size of array elements on the sidelobes and grating lobes of limited diffraction beams as the beams are steered. They are similar to those previously reported for conventional beams.     

Cu@C composite nanotube array and its application as an enzyme-free glucose sensor

We report a novel hydrothermal method for the synthesis of a Cu@C nanotube array on a centimeter-scale substrate for the first time. In this hydrothermal reaction process, employing the carbon coated ZnO nanorod array as an inexpensive and partially sacrificial template, along with the ZnO dissolving in the alkaline atmosphere, the formed Cu particles deposit and grow on the carbon surface gradually. Importantly, the carbon shell of the template is not only essential to the preservation of the array configuration, but also makes a significant contribution to the final nanostructure. Such a method provides a morphology-reservation transformation when various shaped carbon-containing templates are adopted. Moreover, this designed Cu@C array has been demonstrated as an excellent electrode material for an enzyme-free glucose sensor in terms of sensitivity (1200 μA mM( - 1) cm( - 2)) and significantly lower applied potential (-0.2 V). Our results present the first preparation of the Cu@C composite nanotube array and may open up an opportunity for rational design of advanced electrode materials for enzyme-free glucose sensors.     

Static stresses in a periodically layered anisotropic elastic composite containing a periodic array of planar cracks

Summary The problem of calculating the static elastic stresses in a periodically layered anisotropic composite containing a periodic array of planar cracks is considered. We formulate the problem in terms of a system of simultaneous finite-part singular integral equations which can be solved numerically using collocation techniques. The solution of the integral equations enables relevant quantities such as the stress intensity factors to be computed. Numerical results are obtained for specific cases of the problem.     

Multifunctional probe array for nano patterning and imaging

This letter reports the design, fabrication, and testing of a multifunctional scanning probe array for nanoscale imaging and patterning. The probe array consists of multiple cantilever probes, with each probe being able to perform a dedicated function such as scanning probe lithography (e.g., dip pen nanolithography and scanning probe contact printing) or scanning probe microscopy (e.g., atomic force microscopy and lateral force microscopy). The bending states of each probe can be controlled by using an integrated thermal electric actuator so that it is possible to engage any individual probe(s) independently for writing or imaging purposes. The multifunctional probe array is therefore capable of performing a rich variety of operations with minimal chemical crosstalk and high registration accuracy. It will eliminate the need for probe chip exchanges and increase the operational efficiency. The probe tips in a given array may be made of different materials. Further, the tip and cantilever may be made of different materials for a given probe. In this work, we focus on the development of a probe array consisting of dip pen nanolithography probes, scanning probe contact printing probes (of various tip sizes), and scanning probe microscopy probes.     

On the solution of doubly periodic array of cracks

We present a correct procedure for the determination of the stress intensity factor at the tip of a crack in a doubly periodic array contained in an infinite elastic solid. It is based on the use of weight functions for an infinite row of periodic cracks, thus avoiding the use of divergent double infinite summations.     

In-plane problem for wave propagation through elastic solids with a periodic array of cracks

Summary In the context of wave propagation in damaged (elastic) solids, an analytical method previously introduced for scalar problems, is now applied to study the (vector) problem for normal penetration of a longitudinal plane wave into a periodic array of collinear cracks. Reduced the problem to an integral equation holding over the openings, an approximation of one-mode type leads to analytical solutions and then to explicit representations for the wave fields and the scattering parameters. Some graphs will finally compare our results with the numerical ones by other authors.     

Temperature distribution in an array of moving cracks acting as heat sinks

The temperature distribution in a periodic array of parallel cracks acting as heat sinks is studied for the case of stationary crack motion by use of the Wiener–Hopf method. The problem arises in the investigation of cracks propagating into solid material, where the stresses driving crack motion are caused by heat transfer from the solid through the crack surfaces. The solution is given in terms of Fourier integrals involving infinite products. The heat-flux distribution in the vicinity of the crack tips is computed analytically from the high wavenumber asymptotics. Numerical solutions of the temperature distribution are presented for several values of the Biot and Péclet number, and the effect of varying these parameters is discussed qualitatively.     

An eigenfunction expansion-variational method based on a unit cell in analysis of a generally doubly periodic array of cracks

A new variational functional for a unit cell of a heterogeneous solid with periodic microstructures is constructed by incorporating the quasi-periodicity of the displacement field and the periodicity of the stress and strain fields into the strain energy functional. The functional can accommodate a broad class of periodic structures including the case where symmetry or antisymmetry properties of the unit cell may not exist. Then the functional is applied to deal with a doubly periodic array of cracks under plane and anti-plane loading. By combining with the eigenfunction expansions of the complex potentials satisfying the traction-free condition on the crack surfaces, an eigenfunction expansion-variational method based on a unit cell is developed. Numerical examples are presented and compared with existing results to demonstrate the high accuracy and efficiency, and wide application scope of the present method. Some interesting phenomena of multi-crack interaction, which do not occur in the case of symmetrical arrays of cracks, are revealed and discussed.