Two-layered Elastic Half-space Research Articles

Modeling of reflected ultrasonic fields in composed samples

Ultrasonic nondestructive testing involves the study of propagation, reflection and refraction patterns of elastic waves excited by contact or non-contact piezoelectric transducers in the inspected object. The finite element modeling usually requires high computational costs and additional postprocessing to select individual waves from the total solution. When probing joints of homogeneous materials, such as turbine blades made of heat-resistant monocrystalline alloys, the joint boundary is low-contrast, and the reflected signals are relatively weak. This causes additional difficulties for their separation from the total wave field and correct interpretation of the information they bring. To solve this problem, explicit asymptotic representations for reflected and transmitted waves in a two-layer elastic half-space with a surface source are proposed in the present work, which allow fast parametric analysis. They can be used to analyze ultrasonic probing data, for example, to estimate the state of the junction zone or to determine the mutual orientation of the crystals’ principal axes.

Modeling of Contact-Fatigue Failure of a Two-Layer Elastic Half-Space

Modeling of Contact-Fatigue Failure of a Two-Layer Elastic Half-Space

Theoretical and Experimental Study of Changes in the Structure of the Intermediate Layer during Friction between Contacting Bodies.

Friction is often accompanied by local fracture at the boundary of contacting bodies. The space between contacting bodies usually contains moving particles of a different nature, and a change in the effective friction conditions can be associated with a change in the structure of the contact area. This paper presents a new series of experiments where balls simulated the particles of the intermediate layer interacting with an elastic layer of different thickness. The effects of regularization when the balls approached each other were investigated considering different initial configurations (line and spatial structure). The balls simulated the particles of the intermediate layer interacting with the elastic layer of different thickness. The opposite effects of convergence and separation of the balls were observed in different experiments. A model of mutual effect during the contact of two balls with a two-layered elastic half-space was developed. An analysis of tangential forces due to the mutual effect was performed for different layer thicknesses, its relative compliance, and different distances between the balls. It was found that the input parameters defined the sign of the tangential force, which led to the convergence or the separation of the balls. The results can be used to create structures controlling the motion in the intermediate layer.

3D Contact Problem with Adhesion for Two-Layered Elastic Half-Space

3D Contact Problem with Adhesion for Two-Layered Elastic Half-Space

CONTACT OF MULTI-LEVEL PERIODIC SYSTEM OF INDENTERS WITH COATED ELASTIC HALF-SPACE

The contact of a periodic system of spherical indenters of different heights and radii of curvature with two-layered elastic half-space is considered. Numerical-analytical method is developed to determine contact pressure distribution and internal stresses taking into account mutual effect of contact spots. The results for relatively hard and soft coatings are analyzed for different values of input parameters: nominal pressure, contact density, coating thickness.

Analytical investigation of a two-layered elastic half-space containing a cylindrical elastic inhomogeneity under forced torsional rotation

This paper presents a rigorous investigation for a two-layered linear elastic half-space containing a cylindrical elastic inhomogeneity with length equal to the thickness of the top layer undergoing forced torsional rotation applied on a rigid circular disc with the same radius as the cylinder, which is welded on the top of the cylinder. To investigate this complicated system analytically, a combination of Fourier sine and cosine integral transforms for depth, respectively in the domain of inhomogeneity and its matrix at the top layer, and Hankel integral transforms for radial distance in the lower half-space as the remaining part of the matrix are used, which translate the related boundary value problem to a system of coupled singular integral equations for the non-dimensional shear stresses resulted from the continuity and boundary conditions. The system of coupled singular integral equations is solved for some collocation points with a smoothed variable of distance, which is adapted with the use of a free parameter. The validities of both the analytical procedure and numerical evaluations are verified with its degenerated case for the homogeneous case, which is the Reissner–Sagoci problem. In addition, the degree of singularities of the shear stresses in between different regions are estimated in terms of material properties of the layer, inhomogeneity, and the half-space. Moreover, some new graphical results are presented for more understanding of related engineering behavior.

Interfacial fracture of thin elastic layers due to cyclic load

Fracture of thin surface layers, which are harder or softer than the substrate material, is considered for the case of cyclic sliding contact. The study is based on modeling of multiple and single contact of two-layered elastic half-space, identification of elastic properties of the surface layers from indentation results, theoretical and experimental study of relatively hard coatings delamination due to contact fatigue, which arises at the level of asperities. The parameters of damage accumulation law at the coating-substrate interface for two component oxide coating are estimated. The properties of relatively soft coatings, which arises during friction of aluminium alloys because of soft faze extrusion are obtained from indentation data.

Modeling of frictional interaction of a rough indenter and a two-layer elastic half-space

The paper considers frictional interaction of a rough indenter and a two-layer elastic half-space with resort to a periodic contact problem from which the additional displacement due to microirregularities is determined. The effect of the contact density on contact characteristics and internal stresses is studied for relatively hard and relatively soft coatings.

Modeling of contact-fatigue damage accumulation in a two-layer half-space with incomplete adhesion between the layers

A method is proposed for calculating the stress state and fatigue damage accumulation in a two-layer elastic half-space with a system of defects between the layers under the action of normal and tangential distributed forces. The problem is solved by the boundary element method and the double Fourier transform. The effects of the surface layer thickness, degree of imperfection of the intermediate defective layer, and interlayer friction on the distribution of the maximal tangential stresses are analyzed. An example of studying the damage accumulation kinetics taking into account the change in the layer thickness due to surface fracture.

Modeling of fatigue wear of a two-layered elastic half-space in contact with periodic system of indenters

A sliding contact of a two-layered elastic foundation and a periodic system of dies (which is a rough body model) is considered. To study the process of contact fatigue fracture of the elastic layer, a calculation procedure is developed. The method includes the periodic contact problem solution, internal stress calculations taking into account sliding friction, and construction of the damage accumulation function for the two-layered foundation. The results of calculations show that the following types of upper elastic layer fracture occur: the delamination of thin subsurface layers, the surface fatigue wear, and the layer-substrate delamination. The main features of the fracture process depend on the mechanical properties of the layer and substrate materials, the interface conditions, the geometry of the system, and the friction coefficient.

Surface waves in a periodic two-layered elastic half-space with the boundary normal to the layering

The paper deals with the problem of surface waves in a vertically layered elastic half-space. The transmitting medium is composed of periodically repeated two-constituent laminae, and its boundary is assumed to be normal to the layering. The problem is solved using an approximate model proposed by Woźniak (Int J Eng Sci 25:483–499, 1987) and Matysiak and Woźniak (Int J Eng Sci 25:549–559, 1987), which is referred to as the homogenized model with microlocal parameters. The velocity of the surface wave is obtained as a function of geometric and dynamic properties of the laminae. The variation of the surface wave velocity with respect to composite constituents is illustrated by numerical examples.

Using complex potentials to determine the reaction of a prestressed two-layer elastic half-space to a moving load

Complex potentials in common form for compressible and incompressible elastic bodies are used to formulate and solve the problem of stationary motion of a prestressed two-layer elastic half-space under a moving surface load. The results presented are similar to those obtained earlier using the Fourier transform

Axisymmetric contact problems for a two-layer elastic half-space with an annular or circular crack at the interface of the layers

Exact analytical solutions of three related axisymmetric mixed problems of the theory of elasticity are given. These problems are concerned with the pressure of an annular or circular punch on a two-layer half-space taking into account cohesion and the existence of an annular or circular crack at the interface of the layers. The formulation and solution of these problems are based on a special regularization of the solution of the first fundamental boundary-value problem of the theory of elasticity for a single layer when there are arbitrary normal and shear loads on its boundary planes. The solution is constructed by the Hankel transformation method which ensures that the integrals converge for all stresses and displacements.

Surface waves in a periodic two-layered elastic half-space

The paper deals with surface waves propagating through a periodic two-layered elastic half-space. The analysis is performed on the basis of a homogenized model with microlocal parameters. The velocity of the surface wave is obtained as a function of geometric and dynamic properties of the subsequent layers. The numerical examples illustrating the variations of the surface wave velocity are presented.

Steady-state harmonic antiplane vibrations of a two-layer elastic half-space with a cylindrical cavity

Steady-state harmonic antiplane vibrations of a two-layer elastic half-space with a cylindrical cavity

The behaviour of axially and laterally loaded single piles embedded in nonhomogeneous soils

An approximate elastic analysis is made of the working load responses of single piles embedded in a soil of linearly increasing modulus with depth. The formulation employs, within a boundary element algorithm, the fundamental solution for point loads acting at the interface of a two-layer elastic half-space. This analysis is of comparable generality and computational efficiency to earlier elastic solutions of the corresponding homogeneous problem and has distinct advantages in practical applications over the simpler homogeneous soil model, namely, improved predictions of the response due to lateral loads and the rationalization of the selection of soil moduli. These advantages are highlighted in the comparisons made between reported observations on the behaviour of single piles from model and full scale field tests and those predicted by the theory. Comprehensive plots of the results of a parametric study are presented in non-dimensional form. Une analyse élastique approximative est faite à partir des réponses de pieux isolés charges et enfoncés dans un sol ayant un module croissant linéairement avec la profondeur. L'étude emploie, à l'intérieur d'un algorithme d'élément limite, la solution fondamentale pour des charges ponctuelles agissant sur la frontière d'un espace semi-infini élastique à deux couches. Cette analyse est d'une généralité et d'une possibilité de calcul comparables à celles des solutions élastiques precédentes du problème homogène correspondant et a des avantages distincts dans les applications pratiques sur le modèle de sol homogène plus simple, à savoir des prévisions améliorées de la réponse à des charges latérales et la rationalisation de la sélection des modules de sol. Ces avantages sont mis en lumière dans les comparaisons faites entre des observations rapportées sur le comportement de pieux isolés à partir d'essais de chantier sur modèle et en vraie grandeur, et les prévisions effectuées à l'aide de la théorie. Des tracés compréhensibles des résultats d'une étude paramétrique sont présentés dans une forme non-dimensionnelle.