scholarly journals Consideration of wear in plane contact of rectangular punch and elastic half-plane

2019 ◽  
pp. 138-141
Author(s):  
V. M. Onyshkevych ◽  
G. T. Sulym
Keyword(s):  
Half Plane ◽  
Integral Transformation ◽  
Initial Approximation ◽  
Vertical Displacement ◽  
Fourier Integral ◽  
Mean Value ◽  
Theory Of Elasticity ◽  
Contact Stresses ◽  
Dual Integral Equations ◽  
Plane Contact

The plane contact problem on wear of elastic half-plane by a rigid punch has been considered. The punch moves with constant velocity. Arising thermal effects are neglected because the problem is investigated in stationary statement. In this case the crumpling of the nonhomogeneities of the surfaces and abrasion of half-plane take place. Out of the punch the surface of half-plane is free of load. The solution for problem of theory of elasticity is constructed by means of Fourier integral transformation. Contact stresses are found in Fourier series which coefficients satisfy the dual integral equations. It leads to the system of nonlinear algebraical equations for unknown coefficients by a method of collocations. This system is reduced to linear system in the partial most interesting cases for computing of maximum and minimum wear. The iterative scheme is considered for investigation of other nonlinear cases, for initial approximation the mean value of boundary cases is used. The evolutions of contact stresses, wear and abrasion in the time are given. For both last cases increase or invariable of vertical displacement correspondently is obtained. In the boundary cases coincidence of results with known is obtained.

scholarly journals Contact Problem for an Elastic Layer on an Elastic Half Plane Loaded by Means of Three Rigid Flat Punches

2013 ◽  
Vol 2013 ◽  
pp. 1-14 ◽  
Author(s):  
T. S. Ozsahin ◽  
O. Taskıner
Keyword(s):  
Contact Problem ◽  
Half Plane ◽  
Elastic Layer ◽  
Integral Transformation ◽  
Vertical Displacement ◽  
Theory Of Elasticity ◽  
Load Factor ◽  
Initial Separation ◽  
Compressive Loads ◽  
Contact Stress Distribution

The frictionless contact problem for an elastic layer resting on an elastic half plane is considered. The problem is solved by using the theory of elasticity and integral transformation technique. The compressive loadsPandQ(per unit thickness in direction) are applied to the layer through three rigid flat punches. The elastic layer is also subjected to uniform vertical body force due to effect of gravity. The contact along the interface between elastic layer and half plane is continuous, if the value of the load factor,λ, is less than a critical value, . In this case, initial separation loads, and initial separation points, are determined. Also the required distance between the punches to avoid any separation between the punches and the elastic layer is studied and the limit distance between punches that ends interaction of punches is investigated for various dimensionless quantities. However, if tensile tractions are not allowed on the interface, for the layer separates from the interface along a certain finite region. Numerical results for distance determining the separation area, vertical displacement in the separation zone, contact stress distribution along the interface between elastic layer and half plane are given for this discontinuous contact case.

scholarly journals Conditions of cracking of a stringer

2005 ◽  
Vol 2005 (3) ◽  
pp. 377-389 ◽  
Author(s):  
D. I. Bardzokas ◽  
G. I. Sfyris
Keyword(s):  
Contact Problem ◽  
Brittle Failure ◽  
Integral Transformation ◽  
Infinite Plate ◽  
Fourier Integral ◽  
Contact Stresses ◽  
Accurate Solution ◽  
Theory And Practice ◽  
External Loading ◽  
Distributed Forces

In the limits of brittle failure of materials, we investigate the problem of possible cracking of an infinite stringer on the boundary of an elastic half-infinite plate. The plate is exposed to tensioning by uniformly distributed forces, and also to contact stresses due to application of forces on the stringer. The accurate solution of a contact problem of interaction of an infinitely continuous stringer is constructed. With the help of this solution, we formulate the condition of cracking of a stringer and the necessary restrictions for external loading, which provide the contacts of a broken stringer with a plate without propagation of a crack inside the stringer. The problem considered here is of interest for theory and practice. We firstly formulate the modified problem of E. Melan and with the help of Fourier integral transformation, we construct its acoustic solution and then formulate the condition of cracking of an infinite stringer. After that, reveal the necessary restrictions on external loadings, which provide the contact of the failed stringer with a plate without propagation of the crack inside the plate.

Dynamical (harmonic) interface stress field in the half-plane covered by the prestretched layer under a strip load

2005 ◽  
Vol 40 (3) ◽  
pp. 225-234 ◽  
Author(s):  
S D Akbarov ◽  
C Guler
Keyword(s):  
Stress Distribution ◽  
Half Plane ◽  
Integral Transformation ◽  
Three Dimensional ◽  
Engineering Application ◽  
Fourier Integral ◽  
Dynamical Problem ◽  
Harmonic Load ◽  
Normal Stress Distribution ◽  
Application Fields

Within the framework of the piecewise homogeneous body model, by employing the three-dimensional linearized theory of elastic waves in initially stressed bodies the dynamical problem of the stress distribution in a half-plane covered with a prestretched layer is investigated. It is assumed that the free face plane of the covered layer is subjected to a uniformly distributed harmonic load acting on a strip extending to infinity in the x3 direction, which is perpendicular to the x1-x2 plane and is of width 2a in the x1 direction. The plane-strain state in the x1-x2 plane is analysed. The corresponding boundary-value problems are investigated by employing the exponential Fourier integral transformation. The numerical results regarding the interface normal stress distribution are presented. The influences of the problem parameters and pre-stretching of the covered layer on this distribution are analysed. Practical engineering application fields of the results are suggested.

scholarly journals Sliding Contact Between a Cylindrical Punch and a Graded Half-Plane With an Arbitrary Gradient Direction

2015 ◽  
Vol 82 (4) ◽  
Author(s):  
Chen Peijian ◽  
Chen Shaohua ◽  
Peng Juan
Keyword(s):  
Half Plane ◽  
Integral Transformation ◽  
Contact Region ◽  
Fourier Integral ◽  
Graded Materials ◽  
Special Cases ◽  
Cylindrical Punch ◽  
The Moment ◽  
Gradient Variation ◽  
Stable Sliding

Contact behavior of a rigid cylindrical punch sliding on an elastically graded half-plane with shear modulus gradient variation in an arbitrary direction is investigated. The governing partial differential equations and the boundary conditions are achieved with the help of Fourier integral transformation. As a result, the present problem is reduced to a singular integral equation of the second kind, which can be solved numerically. Furthermore, the presently general model can be well degraded to special cases of a lateral gradient half-plane and a homogeneous one. Normal stress in the contact region is predicted with different material parameters, which is usually used to estimate the possibility of surface crack initiation. The moment that is needed to ensure stable sliding of the cylindrical punch on the contact surface is further predicted. The result in the present paper should be helpful for the design of novel graded materials with surfaces of strong abrasion resistance.

scholarly journals Half-plane contacts subject to remote tension

2021 ◽  
pp. 030932472098844
Author(s):  
Nils Cwiekala ◽  
David A Hills
Keyword(s):  
Contact Problem ◽  
Half Plane ◽  
Asymptotic Form ◽  
Fretting Fatigue ◽  
The State ◽  
Partial Slip ◽  
Practical Relevance ◽  
Plane Contact ◽  
State Of Stress ◽  
Plane Contact Problem

The state of stress present in an elastic half-plane contact problem, where one or both bodies is subject to remote tension has been investigated, both for conditions of full stick and partial slip. The state of stress present near the contact edges is studied for different loading scenarios in an asymptotic form. This is of practical relevance to the study of contacts experiencing fretting fatigue, and enables the environment in which cracks nucleate to be specified.

scholarly journals RELATIVE PORE VOLUME UNDER INDENTATION OF POROUS MATERIALS

2021 ◽  
Vol 83 (4) ◽  
pp. 462-470
Author(s):  
V.B. Zelentsov ◽  
A.D. Zagrebneva ◽  
P.A. Lapina ◽  
S.M. Aizikovich ◽  
Wang Yun-Che
Keyword(s):  
Porous Material ◽  
Contact Problem ◽  
Porous Layer ◽  
Pore Volume ◽  
Lower Boundary ◽  
Contact Stresses ◽  
Plane Contact ◽  
Plane Contact Problem ◽  
Static Contact ◽  
Rigidity Modulus

Investigation of the function of the relative volume of pores under the load action is carried out on the base of the solution of the static contact problem of the indentation of a layer made of a material with voids or unfilled pores. A rigid strip indenter with a flat base is pressed into a porous layer that is adhered to a non-deformable base along the lower boundary. The formulated 3D problem of the indentation of a porous layer is reduced to solving the plane contact problem of the indentation of a porous strip. The plane contact problem is reduced to solving an integral equation for unknown contact stresses, the solution of which is constructed by the method of successive approximations in the form of an asymptotic expansion in the dimensionless parameter of the problem. The obtained contact stresses and the force acting on the indenter made it possible to study the influence of the nonclassical moduli of the layer porous material (the connectivity modulus and pore rigidity modulus) on the main contact characteristics and on the distribution of the function of the relative pore volume. The connectivity modulus increase leads to an increase in the compliance of the layer porous material, the pore rigidity modulus increase leads to an increase in the rigidity of the layer porous material. The maximum value of the distribution function of the relative pore volume in the porous material of the layer is achieved under the indenter base centre, regardless of the change in the porous material non-classical moduli.

Partial slip contact analysis for a monoclinic half plane

2020 ◽  
pp. 108128652096283
Author(s):  
İ Çömez ◽  
Y Alinia ◽  
MA Güler ◽  
S El-Borgi
Keyword(s):  
Integral Equations ◽  
Half Plane ◽  
Singular Integral ◽  
Integral Transform ◽  
Mixed Boundary ◽  
Normal Load ◽  
Fibrous Composite ◽  
Singular Integral Equations ◽  
Contact Stresses ◽  
Partial Slip

In this paper, the nonlinear partial slip contact problem between a monoclinic half plane and a rigid punch of an arbitrary profile subjected to a normal load is considered. Applying Fourier integral transform and the appropriate boundary conditions, the mixed-boundary value problem is reduced to a set of two coupled singular integral equations, with the unknowns being the contact stresses under the punch in addition to the stick zone size. The Gauss–Chebyshev discretization method is used to convert the singular integral equations into a set of nonlinear algebraic equations, which are solved with a suitable iterative algorithm to yield the lengths of the stick zone in addition to the contact pressures. Following a validation section, an extensive parametric study is performed to illustrate the effects of material anisotropy on the contact stresses and length of the stick zone for typical monoclinic fibrous composite materials.

Behavior of a Horizontal Fluid Filled Crack Under Moving Hertzian Load

2005 ◽  
Author(s):  
X. Jin ◽  
L. M. Keer ◽  
E. L. Chez
Keyword(s):  
Half Plane ◽  
Continuous Distribution ◽  
Contact Stresses ◽  
Hertzian Contact ◽  
Subsurface Crack ◽  
Intensity Factors ◽  
Crack Volume ◽  
Rolling Body ◽  
Soft Inclusion ◽  
Edge Dislocations

Numerical analysis is presented for a fluid filled subsurface crack in an elastic half plane loaded by Hertzian contact stresses. The opening volume of the horizontal Griffith crack is fully occupied by an incompressible fluid. In the presence of friction, a moving Hertzian line contact load is applied at the surface of the half plane. The stress intensity factors at the tips of the fluid filled crack are analyzed on condition that the change of the opening crack volume vanishes due to the fluid incompressibility. The method used is that of replacing the crack by a continuous distribution of edge dislocations. As a cycle of rolling can be viewed as shifting the Hertzian contact stresses across the surface of the half plane, the results of this analysis may prove useful in the prediction of rolling fatigue of an elastic rolling body containing a soft inclusion.

Thermoplastic Instability for the Transient Contact Problem of Two Sliding Half-Planes

1986 ◽  
Vol 53 (3) ◽  
pp. 565-572 ◽  
Author(s):  
A. Azarkhin ◽  
J. R. Barber
Keyword(s):  
Steady State ◽  
Pressure Distribution ◽  
Half Plane ◽  
Initial Pressure ◽  
Approximate Solutions ◽  
Steady State Solution ◽  
Fourier Integral ◽  
Numerical Results ◽  
Initial Size ◽  
Transient Contact

We study the time dependent problem of a nonconducting half-plane sliding on the surface of a conductor with heat generation at the interface due to friction. The conducting half-plane is slightly rounded to give a Hertzian initial pressure distribution. Relationships are established for temperature and thermoelastic displacements due to a heat input of cosine type through the surface, and then these are used to obtain the solution in the form of a double Fourier integral. Numerical results show that, if the ratio of the initial size of the area of contact to that in the steady state is less than some critical value, the area of contact and the pressure distribution change smoothly toward the steady state solution. Otherwise the area of contact goes through bifurcation. The bifurcation accelerates the process. Numerical results are compared with previous approximate solutions.

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