Hyung Jip Choi

The problem for bonded half-planes containing a crack at an arbitrary angle to the graded interfacial zone

The plane problem for bonded elastic half-planes containing a crack at an arbitrary angle to the graded interfacial zone is considered in this paper. The interfacial zone is treated as a nonhomogeneous interlayer with its elastic modulus varying continuously in thickness direction. Based on the use of the Fourier integral transform method and with the aid of the stiffness matrix approach, the crack problem is formulated as a system of singular integral equations for arbitrary crack surface tractions. The main results presented are the variations of mixed-mode stress intensity factors as a function of the crack orientation angle for various combinations of material and geometric parameters of bonded media in conjunction with the nonhomogeneity in the graded interlayer. The probable cleavage angles for the crack growth direction are also evaluated under the remote biaxial loading, together with the corresponding values of effective tensile mode stress intensity factors.

Bonded dissimilar strips with a crack perpendicular to the functionally graded interface

The mode I crack problem for two dissimilar infinite strips bonded through a functionally graded interfacial zone is investigated within the framework of plane elasticity. The graded interfacial zone is treated as a nonhomogeneous continuum, having the continuously varying elastic modulus between the dissimilar homogeneous strips. A crack is assumed to be embedded in one of the strips perpendicular to the nominal interface. With the aid of the stiffness matrix approach, a set of homogeneous conditions relevant to the proposed crack problem is readily satisfied. Subsequent application of the mixed conditions on the cracked plane then leads to a singular integral equation of the first kind which is solved numerically. In consequence, the variations of stress intensity factors are provided as functions of geometric and material parameters of the bonded structure. The effect of the material nonhomogeneity in the interfacial zone is further addressed by measuring the degree of correspondence with the results that are obtained based on the use of the homogenized interfacial elastic property.

An analysis of cracking in a layered medium with a functionally graded nonhomogeneous interface

The plane elasticity solution is presented in this paper for the crack problem of a layered medium. A functionally graded interfacial region is assumed to exist as a distinct nonhomogeneous transitional layer with the exponentially varying elastic property between the dissimilar homogeneous surface layer and the substrate. The substrate is considered to be semi-infinite containing a crack perpendicular to the nominal interface. The stiffness matrix approach is employed as an efficient method offormulating the proposed crack problem. A Cauchy-type singular integral equation is then derived. The main results presented are the variations of stress intensity factors as functions of geometric and material parameters of the layered medium. Specifically, the influences of the crack size and location and the layer thickness are addressed for various material combinations.

Interfacial cracking in a graded coating/substrate system loaded by a frictional sliding flat punch

An analysis of a coupled plane elasticity problem of crack/contact mechanics for a coating/substrate system with functionally graded properties is performed, where the rigid flat punch slides over the surface of the coated system that contains a crack. The graded material is treated as a non-homogeneous interlayer between dissimilar, homogeneous phases of the coated medium and the crack is assumed to exist along the interface between the interlayer and the substrate. Based on the Fourier integral transform method and the transfer matrix approach, formulation of the current coupled mixed boundary value problem lends itself to the derivation of a set of three simultaneous Cauchy-type singular integral equations. In the numerical results, the emphasis is placed on the investigation of interactions between the contact stress field and the crack-tip behaviour for various combinations of material, geometric and loading parameters of the coated system. Specifically, effects of interfacial cracking on the distributions of the contact pressure and the in-plane stress component along the coating surface are examined and the mixed-mode stress intensity factors evaluated from the crack-tip stress field with the square-root singularity are provided as a function of punch location. Further addressed is the quantification of the singular character of contact pressure distributions at the trailing and leading edges of the flat punch in terms of the punch-edge stress intensity factors. Implicit in this particular analysis of the coupled crack/contact problem presented henceforth is that the crack closure behaviour under the compressive contact stress field is not taken into account, ignoring the influence of crack-face contact and friction.

Stress Analysis of Multilayered Anisotropic Elastic Media

The stress analysis of media subjected to applied surface tractions is performed. The solutions are obtained based on the Fouier transfrom technique together with the aid of he stiffness matrix approach. It can be uniformly applied to media with transversely isotropic, orthotropic, and monoclinic layers

Effects of graded layering on the tip behavior of a vertical crack in a substrate under frictional Hertzian contact

Abstract An analysis of a crack in a substrate overlaid with a functionally graded material subjected to frictional contact loading is performed, within the linear plane elasticity framework. The graded material exists as an interlayer between the dissimilar phases of the coating/substrate system or as a graded coating deposited on the substrate. The crack in the underlying substrate is oriented perpendicular to the boundary of the coated medium. The contact pressure is assumed to be Hertzian and the resulting normal and friction-induced tangential tractions acting on the boundary of the medium give rise to the mixed-mode behavior at the crack tips. Formulation of the problem is reduced to solving a set of singular integral equations. In the numerical results, the emphasis is given to the effects of material, geometric, and loading parameters on the values of the stress intensity factors. Further addressed are the correlations of such parameters to the crack growth mechanisms in terms of the probable cleavage angles at the crack tips, the effective tensile mode stress intensity factors, and the ranges of stress intensity factors. In the present analysis, the contact between the crack faces is not taken into account so that the influence of crack-face friction is neglected.

THERMOELASTIC PROBLEM OF STEADY-STATE HEAT FLOW DISTURBED BY A CRACK PERPENDICULAR TO THE GRADED INTERFACIAL ZONE IN BONDED MATERIALS

The plane thermoelasticity equations are used to investigate the steady-state nonisothermal crack problem for bonded materials with a graded interfacial zone. The interfacial zone is modeled as a nonhomogeneous interlayer having continuously varying thermoelastic moduli in the exponential form between the dissimilar, homogeneous half-planes. A crack is assumed to exist in one of the half-planes oriented perpendicular to the nominal interface, disturbing a uniform heat flow. Based on the method of Fourier integral transform, formulation of the crack problem is reduced to solving two sets of Cauchy-type singular integral equations for temperature and thermal stress fields. The heat-flux intensity factors and the thermally induced mode II stress intensity factors are defined in order to characterize the singular behavior of temperature gradients and thermal stresses, respectively, in the vicinity of the crack tips. In the numerical results, the values of heat-flux and thermal-stress intensity factors are pre...The plane thermoelasticity equations are used to investigate the steady-state nonisothermal crack problem for bonded materials with a graded interfacial zone. The interfacial zone is modeled as a nonhomogeneous interlayer having continuously varying thermoelastic moduli in the exponential form between the dissimilar, homogeneous half-planes. A crack is assumed to exist in one of the half-planes oriented perpendicular to the nominal interface, disturbing a uniform heat flow. Based on the method of Fourier integral transform, formulation of the crack problem is reduced to solving two sets of Cauchy-type singular integral equations for temperature and thermal stress fields. The heat-flux intensity factors and the thermally induced mode II stress intensity factors are defined in order to characterize the singular behavior of temperature gradients and thermal stresses, respectively, in the vicinity of the crack tips. In the numerical results, the values of heat-flux and thermal-stress intensity factors are presented for various combinations of material and geometric parameters of the dissimilar media bonded through a thermoelastically graded interfacial zone. The influence of crack-surface partial conductance on the near-tip temperature and thermal stress fields is also addressed.

Elastodynamic Response of a Crack Perpendicular to the Graded Interfacial Zone in Bonded Dissimilar Materials Under Antiplane Shear Impact

A solution is given for the elastodynamic problem of a crack perpendicular to the graded interfacial zone in bonded materials under the action of antiplane shear impact. The interfacial zone is modeled as a nonhomogeneous interlayer with the power-law variations of its shear modulus and mass density between the two dissimilar, homogeneous half-planes. Laplace and Fourier integral transforms are employed to reduce the transient problem to the solution of a Cauchy-type singular integral equation in the Laplace transform domain. Via the numerical inversion of the Laplace transforms, the values of the dynamic stress intensity factors are obtained as a function of time. As a result, the influences of material and geometric parameters of the bonded media on the overshoot characteristics of the dynamic stress intensities are discussed. A comparison is also made with the corresponding elastostatic solutions, addressing the inertia effect on the dynamic load transfer to the crack tips for various combinations of the physical properties.

Anti-plane shear behavior of an arbitrarily oriented crack in bonded materials with a nonhomogeneous interfacial zone

The anti-plane shear problem of bonded elastic materials containing a crack at an arbitrary angle to the graded interfacial zone is investigated in this paper. The interfacial zone is modeled as a nonhomogeneous interlayer of finite thickness with the continuously varying shear modulus between the two dissimilar, homogeneous half-planes. Formulation of the crack problem is based upon the use of the Fourier integral transform method and the coordinate transformations of basic field variables. The resulting Cauchy-type singular integral equation is solved numerically to provide the values of modeIII stress intensity factors. A comprehensive parametric study is then presented of the influence of crack obliquity on the stress intensity factors for different crack size and locations and for different material combinations, in conjunction with the material nonhomogeneity within the graded interfacial zone.

TRANSIENT THERMAL STRESSES IN A CLADDED SEMI-INFINITE MEDIUM CONTAINING AN UNDERCLAD CRACK

The transient thermal stress problem for a cladded medium containing an underclad crack is studied within the two-dimensional framework of uncoupled, quasi-static thermoelasticity. The cladded medium is modeled such that a thin cladding is bonded to a substrate via a transitional layer. The cladding and the transitional layer are represented as homogeneous strips, while the substrate is regarded as a half-plane having a crack oriented normal to its surface. The transient thermal loading is prescribed in the form of a gradual or sudden cooldown applied at the medium bounding surface. The flexibility / stiffness matrix approach is introduced as an efficient means of formulating the proposed crack problem. Subject to equivalent transient thermal tractions acting on the location of the crack, a Cauchy-type singular integral equation is derived and solved numerically. Transient thermal stress intensity factors are then evaulated to demonstrate the response of the underclad crack as functions of various geometr...