Mutual influence of the faces contact area and the pre-fracture zone near the tip of the interfacial crack

2020 ◽  
Vol 13 (3) ◽  
pp. 143-161
Author(s):  
M.V. Dudyk
Keyword(s):  
Contact Area ◽  
Fracture Zone ◽  
Mutual Influence ◽  
Interfacial Crack ◽  
Normal Displacement ◽  
Crack Model ◽  
Hopf Equation ◽  
Resistant Material ◽  
Order Of Magnitude ◽  
Crack Faces

BACKGROUND: Under plane strain conditions, a crack model was developed on a plane interface between two different materials, which assumes the existence near its tip of the faces contact area and a narrow lateral pre-fracture zone in a less crack-resistant material of the composite compound. The pre-fracture zone is modeled by the line of normal displacement rupture, on which the normal stress is equal to the tensile strength of the material. Assuming that the dimensions of the pre-fracture zone and the contact zone have the same order of magnitude and are significantly smaller than the crack length, the problem is reduced to the vector Wiener–Hopf equation. METHODS: An approximate method for solving the vector Wiener–Hopf equation was developed, which was used to obtain the equations for determining the sizes of the pre-fracture zone and the contact faces area. The pre-fracture zone orientation was determined from the condition of the potential energy maximum accumulated in the zone. Numerical calculations of the indicated parameters and analysis of their dependences on the configuration and module of external load are executed. RESULTS: A significant mutual influence of the pre-fracture zone and crack faces contact on their sizes and orientation of the zone was revealed.

A Crack Model of a Bone Cement Interface

1984 ◽  
Vol 106 (3) ◽  
pp. 235-243 ◽  
Author(s):  
J. P. Clech ◽  
L. M. Keer ◽  
J. L. Lewis
Keyword(s):  
Bone Cement ◽  
Cohesive Zone ◽  
Edge Crack ◽  
Crack Problem ◽  
Bimaterial Interface ◽  
Fracture Mechanisms ◽  
Homogeneous Material ◽  
Crack Model ◽  
Cement Interface ◽  
Crack Faces

This paper is concerned with the fracture mechanics of a bone-cement interface that includes a cohesive zone effect on the crack faces. This accounts for the experimentally observed strengthening mechanism due to the mechanical interlock between the crack faces. Edge crack models are developed where the cohesive zone is simulated by a continuous or a discrete distribution of linear or nonlinear springs. It is shown that the solution obtained by assuming a homogeneous material is fairly close to the exact solution for the bimaterial interface edge crack problem. On the basis of that approximation, the analysis is conducted for the problem of two interacting edge cracks, one at the interface, and the other one in the cement. The small crack that was observed to initiate in the cement, close to the bone-cement interface, does not affect much the mode I stress-intensity factor at the tip of the interface crack. However it may grow, leading to a catastrophic breakdown of the cement. The analysis and following discussion point out an interdependency between bone-cement interface strength and cement strength not previously appreciated. The suggested crack models provide a framework for quantifying the fracture mechanisms at the bone-cement interface.

Elliptical Contact Area Between Elastic Bodies Bounded by High Order Surfaces

2005 ◽  
Author(s):  
Emanuel N. Diaconescu
Keyword(s):  
Analytical Solution ◽  
Pressure Distribution ◽  
Fourth Order ◽  
Contact Area ◽  
High Order ◽  
Normal Displacement ◽  
Hertz Theory ◽  
Elastic Bodies ◽  
Surface Normal ◽  
Elliptical Contact

Hertz theory fails when contacting surfaces are expressed by a sum of even polynomials of higher powers than two. An alternative analytical solution implies the knowledge of contact area. In the case of elliptical domains, there are some published proposals for the correlation between pressure distribution and surface normal displacement. This paper identifies the class of high order surfaces which lead to elliptical contact domains and solves a contact between fourth order surfaces.

scholarly journals Relative contact area in metal-polymer joints

2018 ◽  
Vol 224 ◽  
pp. 02051 ◽  
Author(s):  
Peter Ogar ◽  
Yurij Alpatov ◽  
Denis Gorokhov
Keyword(s):  
Contact Area ◽  
Mutual Influence ◽  
Theoretical Studies ◽  
Relative Area ◽  
Empirical Dependence ◽  
Roughness Model ◽  
Wide Range ◽  
Metal Polymer

The paper is devoted to the specification of the parameters of Bartenev-Lavrentiev’s empirical dependence for the relative area of contact with taking into account the mutual influence of asperities. The relative contact area is determined using a discrete roughness model for a wide range of distributions of the peaks of the asperities in the rough layer. It is shown that when determining the relative contact area, the distribution of the asperities in height practically does not affect the final result, since the obtained dependences coincide. This fact allowed us to determine the parameters of engineering dependence, which coincides with the results of theoretical studies.

Some aspects of forces and fields in atomic models of crack tips

1991 ◽  
Vol 6 (12) ◽  
pp. 2565-2577 ◽  
Author(s):  
R.G. Hoagland ◽  
M.S. Daw ◽  
J.P. Hirth
Keyword(s):  
Crack Tip ◽  
Lattice Parameter ◽  
Crack Model ◽  
Dislocation Emission ◽  
Linear Elastic ◽  
Partial Dislocations ◽  
Atomistic Models ◽  
Crack Tips ◽  
Eam Potential ◽  
Crack Faces

This paper examines the stresses and displacement gradients in atomistic models of cracks based on an EAM potential devised for aluminum. Methods for computing these quantities are described. Results are presented for two models differing in terms of the orientations of the crack relative to the crystal, a [100] (010) orientation that behaves in a brittle fashion and a [111] (110) orientation that emits partial dislocations prior to extending. Both models display lattice trapping. The stresses in the brittle crack model are compared with the linear elastic prediction and found to be in remarkably good agreement to within distances of about one lattice parameter of the crack tip and at the free surface where contributions from sources other than strain energy (e.g., surface tension) influence the results. Similar results are observed for the ductile model until dislocation emission occurs. The largest stresses that develop just prior to crack extension or dislocation emission are used to estimate the ratio of theoretical tensile strength to shear strength in this material. Eshelby's conservation integrals, F and M, are also computed. F is found to be essentially contour independent and in agreement with the linear elastic prediction in both models until dislocation emission occurs, at which point a large screening contribution arises from the emitted partials. The contour size dependence of M reveals some interesting features of the crack tip including a slight wobble of the crack tip inside its potential well with changing applied K and the existence of forces acting to move the crack faces apart as blunting occurs.

The impact of a rigid circular cylinder on an elastic solid

1962 ◽  
Vol 255 (1053) ◽  
pp. 153-191 ◽  
Keyword(s):  
Laplace Transform ◽  
Elastic Body ◽  
Contact Area ◽  
Elastic Solid ◽  
Coupled System ◽  
Poisson's Ratio ◽  
Normal Displacement ◽  
Plane Boundary ◽  
The Laplace Transform ◽  
Perfect Adherence

A method is described for approximating to any degree of accuracy the solution of the following problem: An elastic body which is bounded by a plane on one side, but extends to infinity otherwise, is hit by a circular disk of given mass, radius, and initial speed perpendicular to the plane boundary. The whole surface of the disk enters into contact with the elastic body at the same time and stays in contact at all its points from then on. The disk is assumed to be rigid, i.e. it does not allow the particles of the elastic body in the contact area to move relative to each other in a direction perpendicular to the plane boundary. For the relative motion of these particles parallel to the face of the disk several conditions are considered, representing perfect lubrication, various degrees of viscous friction and perfect adherence. With the help of various Mellin transformations a method is indicated which leads to an expansion of the motion in powers of the Laplace transform variable. The case of perfect adherence needs some special consideration, and a simple approximation for the static problem is found. The case of perfect lubrication is then treated in more detail by a different method which replaces the condition of constant normal displacement in the contact area by an equivalent number of requirements for certain averages over the normal displacement in the contact area. The condition of rigidity for the disk is not exactly satisfied, but it is possible to judge the accuracy of the approximation (with the help of asymptotic expansions in the Laplace transform variable) at the initial time, when discrepancies are largest. The concept of ‘mode of vibration’ is introduced. Any transient in the coupled system of elastic body and rigid disk can be described as superposition of modes, each of which is an exponentially damped harmonic oscillation of the coupled system with a frequency and damping constant independent of the particular transient. The motion of the impinging disk is then seen to be dominated mostly by the lowest mode, provided the mass of the disk is not too small. The displacement perpendicular to the boundary outside of the contact area has been calculated. This calculation is not more difficult than the corresponding one in the case of a point-like source at the plane boundary of an elastic solid. Numerical computations were carried out for the case of perfect lubrication with the help of the Elecom digital computer in order to determine the first two modes and their contributions to the motion of the disk. As long as Poisson’s ratio for the elastic solid exceeds 1/4, the results do not depend strongly on the value of Poisson’s ratio. The ratio of the areal mass densities of the disk to the elastic solid is the main parameter of the theory. The shear wave velocity of the elastic solid determines the time scale of the motion.

On the Tangential Displacement of a Surface Point Due to a Cuboid of Uniform Plastic Strain in a Half-Space

2008 ◽  
Author(s):  
B. Fulleringer ◽  
V. Boucly ◽  
D. Ne´lias
Keyword(s):  
Plastic Strain ◽  
Yield Stress ◽  
Half Space ◽  
Normal Displacement ◽  
Tangential Displacement ◽  
Surface Point ◽  
Stick Slip ◽  
Uniform Shear ◽  
Influence Coefficients ◽  
Order Of Magnitude

The elastic solution of a tangentially loaded contact is known as the Cerruti’s solution. Since the contact surfaces could be easily discretized in small rectangles of uniform shear stress the elastic problem is usually numerically solved by summation of well known integral solution. For soft metallic materials, metals at high temperature, rough surfaces or dry contacts with high friction coefficient, the yield stress within the material could be easily exceeded. This paper presents the effect of a cuboid of uniform plastic strain in a half-space on the tangential displacement of a surface point. It is found that the influence coefficients are of the same order of magnitude as the ones describing the normal displacement. This result is of great importance for stick-slip contact problem when coupling the normal and tangential behavior in the elastic-plastic regime, and also for metals and alloys with low or moderate yield stress.

Failure Analysis of Reinforced Concrete Bridge Column Using Cohesive and Adhesive Interfaces

2006 ◽  
Vol 321-323 ◽  
pp. 716-719 ◽  
Author(s):  
In Kyu Rhee ◽  
Hee Up Lee ◽  
Jun S. Lee ◽  
Woo Kim
Keyword(s):  
Reinforced Concrete ◽  
Failure Analysis ◽  
Interfacial Crack ◽  
Concrete Columns ◽  
Crack Model ◽  
Concrete Bridge ◽  
Reinforced Concrete Columns ◽  
Reinforced Concrete Bridge ◽  
Bridge Column ◽  
The University

This study examines the performance of adhesive and cohesive interfacial crack model in assessing the brittle shear behavior of reinforced concrete bridge columns. The quarter-scale reinforced concrete columns tested at the University of California at San Diego by Xiao et al. (1993) to explore the ductility of reinforced concrete columns under cyclic loading. The three columns R-1, R-3 and R-5 with different transverse reinforcement are considered for finite element failure analysis.

scholarly journals Inverse problem for cracked inhomogeneous Kirchhoff–Love plate with two hinged rigid inclusions

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Nyurgun Lazarev
Keyword(s):  
Inverse Problem ◽  
Interfacial Crack ◽  
Variational Problems ◽  
Elastic Media ◽  
Displacement Boundary ◽  
Joint Point ◽  
The Family ◽  
Crack Faces ◽  
Inequality Type ◽  
Passage To The Limit

AbstractWe consider a family of variational problems on the equilibrium of a composite Kirchhoff–Love plate containing two flat rectilinear rigid inclusions, which are connected in a hinged manner. It is assumed that both inclusions are delaminated from an elastic matrix, thus forming an interfacial crack between the inclusions and the surrounding elastic media. Displacement boundary conditions of an inequality type are set on the crack faces that ensure a mutual nonpenetration of opposite crack faces. The problems of the family depend on a parameter specifying the coordinate of a connection point of the inclusions. For the considered family of problems, we formulate a new inverse problem of finding unknown coordinates of a hinge joint point. The continuity of solutions of the problems on this parameter is proved. The solvability of this inverse problem has been established. Using a passage to the limit, a qualitative connection between the problems for plates with flat and bulk hinged inclusions is shown.

scholarly journals Analysis of Multiple Fatigue Cracks—Part II: Results

1992 ◽  
Vol 114 (3) ◽  
pp. 462-468 ◽  
Author(s):  
M. C. Dubourg ◽  
M. Godet ◽  
B. Villechaise
Keyword(s):  
Load Transfer ◽  
Fatigue Cracks ◽  
Interfacial Crack ◽  
Frictional Resistance ◽  
Mode I ◽  
Crack Interaction ◽  
Intensity Factors ◽  
Linear Elastic ◽  
Elastic Fracture ◽  
Crack Faces

A semianalytical model of multiple fatigue crack analysis in sliding contact is developed. Linear elastic fracture mechanics is applied. Frictional resistance between crack faces is taken into account. Five crack interaction mechanisms have been identified. Load transfer between cracks can cause both significant increases and drops in stress intensity factors both in mode I and II. The interaction depends on the distance between cracks, their relative position with respect to the loading zone, and the interfacial crack coefficient of friction.

scholarly journals Numerical Investigation on Hydraulic Properties of Artificial-Splitting Granite Fractures during Normal and Shear Deformations

Geofluids ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-16 ◽  
Author(s):  
Feng Xiong ◽  
Qinghui Jiang ◽  
Mingxi Chen
Keyword(s):  
Contact Area ◽  
Hydraulic Properties ◽  
Numerical Results ◽  
Normal Displacement ◽  
Rock Fractures ◽  
Fracture Permeability ◽  
Normal Loading ◽  
New Model ◽  
Hydraulic Aperture ◽  
Mechanical Aperture

This study explores the effects of normal loading and shearing on hydraulic properties in roughness-walled rock fractures. The geometries of five fractures were measured by the 3D scanning technology. The flow simulation was performed for rough rock fractures with large displacements during normal loading and shearing by finite volume method (FVM). The results demonstrate that the deformation of fracture with increasing normal stress and shear causes nonuniform changes in void space geometry and further influences fracture permeability. Associated with normal displacement are an increase in contact area and a decrease in mechanical aperture. The transmissivity is decreasing by 3 orders of magnitude response to applied normal displacement values of 0.0 mm to 1.8 mm. In contrast, an increase in mechanical aperture and contact ratio that occurs with increasing shear displacement values of 0.0 mm to 4.0 mm is associated with decreasing distinctly transmissivity by 1.5–2 orders of magnitude. Based on the numerical results, an empirical equation is proposed to evaluate the effects of contact area and roughness of fracture on the hydraulic aperture. The good agreement between numerical results and the predicted results by the new model indicates that the proposed model is capable of estimating the hydraulic aperture of rock fractures through parametric analyses, compared with other published models from available literature. In addition, the new model succeeds in predicting the transmissivity in Develi and Babadagli (2014) water flow experiments.

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