Stresses in a Half Space in the Process of Contact Interaction with a Notched Surface

We propose a mathematical model and the solution of a periodic contact problem of interaction of a notched surface with an elastic half space, study the mutual influence of microasperities in the contact surfaces, and determine the isolines of the maximum level of tangential stresses near the contact zone. This enables us to predict the regions of fracture (wear) for actual tribocouples.     

Modelling Crack Closure for an Interface Crack Under Harmonic Loading

The paper is devoted to a linear crack located between two dissimilar elastic half-spaces under normally incident harmonic tension-compression loading. The system of boundary integral equations for displacements and tractions is derived from the dynamic Somigliana identity. The dynamic stress intensity factors (the opening and the transverse shear modes) are computed as functions of the loading frequency taking the contact interaction of the opposite crack faces into account. The results are compared with those obtained neglecting the crack closure.     

Stresses in a Half Plane Weakened by a Crack and Reinforced with a Patch

We propose a computational model for the analysis of the stress-strain state and limiting equilibrium in the system of a half plane and a patch in the two-dimensional statement of the problem. Numerical calculations are performed for special cases of elastoplastic and brittle fracture.     

The Effect of Frequency in the Problem of Interface Crack Under Harmonic Loading

The breakage of a tiny tail on a head of solid glass just removed from a glass bath and treated by fluoric acid (a “Batavian tear") makes the tear explode into a cloud of dust with the sound like that of a shot. This explosion reminds that of TNT but TNT disintegrates into molecules of the order of 10⁻⁹ m while the glass particles of dust are of the order of 10⁻⁶ m and have the same chemical composition as the solid glass. Rock bursts in deep mines of South Africa and Russia represent another example of the sudden, explosive self-destruction. To explain this phenomenon the theory of self-sustaining fracture waves was suggested earlier by Galin and Cherepanov (1966). This theory was based on the analogy with detonation waves later criticized as insufficiently substantiated. The approach presented below is based only on the conservation laws and does not use any analogies. It proves that the self-sustaining fracture wave can propagate only in compressed structures at the speed of longitudinal elastic waves.     

Contact of the Faces of an Interface Thermally Insulated Crack Under Thermomechanical Loading

Materials Science - We study the thermoelastic behavior of a heterogeneous bimaterial with interface crack whose faces are in contact at the ends under the action of compressive forces and a...     

Stresses Near a Disk-Shaped Sharp Slot with Tangential Contact Interaction Between Its Surfaces

We propose a new statement of the problem of elastic equilibrium of a disk-shaped slot whose surfaces are loaded by an arbitrary normal load vanishing on its front according to a certain law. By the method of discontinuous Weber-Schafheitlin integrals, it is shown that, in this case, there exists a unique state of elastic equilibrium with regular distribution of stresses over the front of the slot. According to the concept of boundary layer, the jump of tangential stresses formed on the surfaces of the slot due to the continuity of the components of the vector of local rigid rotation Ω on its front is continued in the plane of the slot and guarantees the validity of the equilibrium conditions provided that the normal stresses are equal to zero (the effect of boundary layer). The numerical analysis shows that the jump of tangential stresses in the boundary layer outside the slot rapidly decreases with the distance from the front in complete agreement with the Saint-Venant principle. If a jump of tangential stresses on the surfaces of the slot is absent (and exists outside the slot), then these surfaces have a kink in the front of the slot and the volume strains possess a logarithmic singularity. This situation can be regarded as the limiting state corresponding to the onset of plastic deformation or brittle fracture. If the tangential stresses do not have jump in the entire plane of the slot, then the solution of the problem does not exist. __________ Translated from Fizyko-Khimichna Mekhanika Materialiv, Vol. 41, No. 3, pp. 71–84, May–June, 2005.     

Impact Loading of the Surfaces of Coplanar Cracks in a Half Space with Restrained Surface

We study the dynamic interaction of plane cracks in an elastic half space with rigidly restrained surface. The problem is reduced to the solution of a system of two-dimensional boundary integral equations of Helmholtz-potential type for unknown functions of crack opening displacements. As an example, we consider the case of impact fracture loading of the crack surfaces whose time dependence is described by the Heaviside function. The time dependences of the stress intensity factors are established and analyzed.     

Contact Interaction of Crack Faces under Oblique Incidence of a Harmonic Wave

The contact interaction of the opposite faces of a crack under oblique incidence of a harmonic wave is considered. The problem is solved by the method of boundary integral equations using an iterative algorithm. The contact forces and the displacement discontinuity on the crack faces are studied for different values of the friction coefficient.     

Weight Function for a Crack in a Two-dimensional Orthotropic Medium Under Impact Shear Loading

The paper examines the elastodynamic response of an infinite two-dimensional orthotr- opic medium containing a central crack under impact shear loading. Laplace and Fourier integral transforms are employed to reduce the problem to a pair of dual integral equations in the Laplace transformed plane. These equations are reduced to integral differential equations, which have been solved in the low frequency domain by iterations. To determine time dependence, these equations are inverted to yield the dynamic stress intensity factor (SIF) for shear point force loading that corresponds to the weight function for the crack under shear loading. It is used to derive SIF for polynomial loading.     

Breaking of Contact Between an Elastic Half Space and a Rigid Base in a Circular Region Under the Action of a Circular Heat Sink

Materials Science - We study the process of local delamination between an elastic heat-conducting half space and a rigid thermally insulated base in a circular domain under the action of heat sinks...     

Invariant Points on Energy Contours Around a Crack Tip Under Mixed Mode Loading

The locus of points around a crack tip where the strain energy density is set equal to a critical value reveals interesting features. It is seen that, for certain cases, two points on this locus remain invariant with respect to the phase of the applied loads. The existence of these invariant points is examined for different configurations - a crack in a homogeneous isotropic medium, an interface crack and an inclined interface crack. This analysis is extended to the two components of strain energy density – volumetric (VSED) and distortional (DSED). This revised version was published online in August 2006 with corrections to the Cover Date.     

Thermo-elastic Stresses in a Functional Graded Material Under Thermal Loading,Pure Bending and Thermo-mechanical Coupling

Analytical expressions have been derived for the through thickness stresses of a Functional graded materials (FGMs) thin plate subjected to thermal loading, pure bending and thermo-mechanical coupling, respectively. The structure is comprised of a metallic layer, a ceramic layer and a functional graded layer. Continuous gradation of the volume fraction in the FGM layer is modeled in the form of an "m" power polynomial of the coordinate axis in thickness direction of the plate. Numerical scheme of discretizing the continuous FGM layer with different graded distributions such as linear (m=1), quadratic (m=2) and square root (m=0.5) has been developed by the averaging technique of composites. Solutions for the stress distributions have been derived for the system under thermal loading, pure bending and thermo-mechanical coupling, respectively.     

Thermoelastic State of a Half Space Containing a Thermally Active Circular Crack Perpendicular to Its Edge

The problem of stationary thermal conductivity and thermoelasticity is solved by the method of boundary integral equations for a semiinfinite body containing a circular crack perpendicular to its edge provided that temperature (or a heat flow is specified) on the crack surfaces. The boundary of the body is unloaded and either is thermally insulated or its temperature is equal to zero. We study the influence of the depth of location of the circular crack on the stress intensity factor for a constant temperature (or heat flow) specified on the crack surfaces. Under thermal loading (unlike the case of constant force loading), the stress intensity factors attain their maximum values on the side of the half space opposite to its boundary. __________ Translated from Fizyko-Khimichna Mekhanika Materialiv, Vol. 41, No. 2, pp. 16–22, March–April, 2005.     

Circular Disk with Radial Internal Crack Under the Action of Model Contact Loads

Materials Science - We solve the plane problem of the theory of elasticity for a circular disk weakened by an arbitrarily located internal radial crack subjected to the action of a model contact...     

Transient Disturbance in a Half Space Under Thermoelasticity with Two Relaxation Times Due to Moving Internal Heat Source

In this paper transient waves caused by a line heat source moving with a uniform velocity inside isotropic homogeneous thermoelastic half-space are studied under the GL model of generalized thermoelasticity. The problem is reduced to the solution of three differential equations by introducing the elastic vector potential and the thermoelastic scalar potential. Using Laplace and Fourier transforms solutions are obtained in transforms domain. Applying inverse transforms approximate solutions of the displacement at the boundary valid in the small time range are given. Also the approximate region valid for the solutions is given and two special cases, (i) the source is motionless and (ii) the relaxation times vanish, are studied. Numerical evaluations are presented for the medium of copper.