Circular Rigid Punch With One Smooth and Another Sharp Ends on a Half-Plane With Edge Crack

1997 ◽  
Vol 64 (1) ◽  
pp. 73-79 ◽  
Author(s):  
Norio Hasebe ◽  
Jun Qian
Keyword(s):  
Half Plane ◽  
Hilbert Problem ◽  
Contact Region ◽  
Mapping Function ◽  
Contact Length ◽  
Stress Distributions ◽  
Sharp Corner ◽  
Rigid Punch ◽  
Rational Mapping ◽  
Frictional Coefficients

A circular rigid punch with friction is assumed to contact with a half-plane with one end sliding on the half-plane and another end with a sharp corner. The contact length is determined by satisfying the finite stress condition at the sliding end of the punch. The crack is initiated near the end with a sharp corner where infinite stresses exist. Coulomb’s frictional force is supposed to act on the contact region. The cracked half-plane is mapped into a unit circle by using a rational mapping function, and the problem is transformed into a standard Riemann-Hilbert problem, which is solved by introducing a Plemelj function. The contact length, the stress intensity factors of the crack, and the resultant moment about the origin of the coordinates on the contact region are calculated for different frictional coefficients, Poisson’s ratios of the half-plane, crack lengths, and distances from the crack to the punch, respectively. The stress distributions on the contact region are also shown.

scholarly journals Stress Intensity of Debonding for A Rigid Inclusion Near An Angle Dislocation

2011 ◽  
Vol 5 (1) ◽  
pp. 190-194
Author(s):  
Xianfeng Wang ◽  
Feng Xing ◽  
Norio Hasebe
Keyword(s):  
Stress Intensity ◽  
Rigid Inclusion ◽  
Stress Function ◽  
Hilbert Problem ◽  
Infinite Plate ◽  
Mapping Function ◽  
Function Technique ◽  
Rational Mapping ◽  
Stress Functions ◽  
Point Dislocation

The study of debonding is of importance in providing a good understanding of the bonded interfaces of dissimilar materials. The problem of debonding of an arbitrarily shaped rigid inclusion in an infinite plate with a point dislocation of thin plate bending is investigated in this paper. Herein, the point dislocation is defined with respect to the difference of the plate deflection angle. An analytical solution is obtained by using the complex stress function approach and the rational mapping function technique. In the derivation, the fundamental solutions of the stress boundary value problem are taken as the principal parts of the corresponding stress functions, and through analytical continuation, the problem of obtaining the complementary stress function is reduced to a Riemann-Hilbert problem. Without loss of generality, numerical results are calculated for a square rigid inclusion with a debonding. It is noted that the stress components are singular at the dislocation point, and a stress concentration can be found in the vicinity of the inclusion corner. We also obtain the stress intensity of a debonding in terms of the stress functions. It can be found that when a debonding starts from a corner of the inclusion and extends to another corner progressively, the stress intensity of the debonding increases monotonously; once the debonding extends over the corner points, the value of the stress intensity of the debonding gradually decreases. The relationships between the stress intensity of the debonding and the direction and position of the dislocation are also presented in this paper.

Green Function of a Point Dislocation in Thin Plate with a Partially Debonded Inclusion

2010 ◽  
Vol 156-157 ◽  
pp. 1684-1687
Author(s):  
Xian Feng Wang ◽  
Feng Xing ◽  
Norio Hasebe
Keyword(s):  
Thin Plate ◽  
Rigid Inclusion ◽  
Stress Function ◽  
Hilbert Problem ◽  
Infinite Plate ◽  
Dissimilar Materials ◽  
Mapping Function ◽  
Function Technique ◽  
Rational Mapping ◽  
Point Dislocation

The study of debonding is of importance in providing a good understanding of the bonded interfaces of dissimilar materials. The problem of debonding of an arbitrarily shaped rigid inclusion in an infinite plate with a point dislocation of thin plate bending is investigated in this paper. Herein, the point dislocation is defined with respect to the difference of the plate deflection angle. An analytical solution is obtained by using the complex stress function approach and the rational mapping function technique. In the derivation, the fundamental solutions of the stress boundary value problem are taken as the principal parts of the corresponding stress functions, and through analytical continuation, the problem of obtaining the complementary stress function is reduced to a Riemann-Hilbert problem. Without loss of generality, numerical results are calculated for a square rigid inclusion with a debonding. It is noted that the stress components are singular at the dislocation point, and a stress concentration can be found in the vicinity of the inclusion corner.

Bonded Bi-material Half-Planes With Semi-elliptical Notch Under Tension Along the Interface

1992 ◽  
Vol 59 (1) ◽  
pp. 77-83 ◽  
Author(s):  
Norio Hasebe ◽  
Mikiya Okumura ◽  
Takuji Nakamura
Keyword(s):  
Stress Concentration ◽  
Elliptical Hole ◽  
Mapping Function ◽  
Approximate Expression ◽  
Complex Stress ◽  
Stress Distributions ◽  
Rational Mapping ◽  
Stress Functions ◽  
Elliptical Holes ◽  
Stress Concentration Factors

A problem of two bonded, dissimilar half-planes containing an elliptical hole on the interface is solved. The external load is uniform tension parallel to the interface. A rational mapping function and complex stress functions are used and an analytical solution is obtained. Stress distributions are shown. Stress concentration factors are also obtained for arbitrary lengths of debonding and for several material constants. In addition, an approximate expression of the stress concentration factor is given for elliptical holes and the accuracy is investigated.

A Point Dislocation Interacting with an Elliptical Hole Located at a Bi-Material Interface

2012 ◽  
Vol 151 ◽  
pp. 75-79 ◽  
Author(s):  
Xian Feng Wang ◽  
Feng Xing ◽  
Norio Hasebe ◽  
P.B.N. Prasad
Keyword(s):  
Conformal Mapping ◽  
Unit Circle ◽  
Half Plane ◽  
Elliptical Hole ◽  
Mapping Function ◽  
Complex Stress ◽  
Complex Variables ◽  
Material Interface ◽  
Rational Mapping ◽  
Point Dislocation

The problem of a point dislocation interacting with an elliptical hole at the interface of two bonded half-planes is studied. Complex stress potentials are obtained by applying the methods of complex variables and conformal mapping. A rational mapping function that maps a half plane with a semi-elliptical notch onto a unit circle is used for mapping the bonded half-planes. The solution derived can serve as Green’s function to study internal cracks interacting with an elliptical interfacial cavity.

Frictionless Contact of Layered Half-Planes, Part II: Numerical Results

1993 ◽  
Vol 60 (3) ◽  
pp. 640-645 ◽  
Author(s):  
M.-J. Pindera ◽  
M. S. Lane
Keyword(s):  
Stress Distribution ◽  
Half Plane ◽  
Contact Stress ◽  
Mixed Boundary ◽  
Contact Region ◽  
Contact Problems ◽  
Contact Length ◽  
Unidirectional Composite ◽  
Frictionless Contact ◽  
Contact Stress Distribution

In Part I of this paper, analytical development of a method was presented for the solution of frictionless contact problems of multilayered half-planes consisting of an arbitrary number of isotropic, orthotropic, or monoclinic layers arranged in any sequence. The local/global stiffness matrix approach similar to the one proposed by Bufler (1971) was employed in formulating the surface mixed boundary condition for the unknown stress in the contact region. This approach naturally facilitates decomposition of the integral equation for the contact stress distribution on the top surface of an arbitrarily laminated half-plane into singular and regular parts that, in turn, can be solved using a numerical collocation technique. In Part II of this paper, a number of numerical examples is presented addressing the effect of off-axis plies on contact stress distribution and load versus contact length in layered half-planes laminated with unidirectionally reinforced composite plies. The results indicate that for the considered unidirectional composite, the load versus contact length response is significantly influenced by the orientation of the surface layer and the underlying half-plane, while the corresponding contact stress profiles are considerably less affected.

Green’s Function of a Bimaterial Problem With a Cavity on the Interface—Part I: Theory

2003 ◽  
Vol 72 (3) ◽  
pp. 389-393 ◽  
Author(s):  
P. B. N. Prasad ◽  
Norio Hasebe ◽  
X. F. Wang ◽  
Y. Shirai
Keyword(s):  
Green’S Function ◽  
Half Plane ◽  
Green's Function ◽  
Elliptical Hole ◽  
Mapping Function ◽  
Complex Variables ◽  
Bimaterial Interface ◽  
Rational Mapping ◽  
Upper Half Plane ◽  
Point Dislocation

The problem of a point dislocation interacting with an elliptical hole located on a bimaterial interface is examined. Analytical solution is obtained by employing the techniques of complex variables and conformal mapping. A rational mapping function is used to map a half-plane with a semielliptical notch onto a unit circle. In the first part of this paper, complex potentials for the bimaterial system with an elliptical hole on the interface is derived when a point dislocation is present in the upper half-plane without loss of generality. The solution derived can be used as Green’s function to study internal cracks interacting with an elliptical interfacial cavity.

Debondings at a Semielliptic Rigid Inclusion on the Rim of a Half Plane

1988 ◽  
Vol 55 (3) ◽  
pp. 574-579 ◽  
Author(s):  
N. Hasebe ◽  
S. Tsutsui ◽  
T. Nakamura
Keyword(s):  
Half Plane ◽  
Rigid Inclusion ◽  
Mixed Boundary ◽  
Mapping Function ◽  
Singular Values ◽  
Complex Stress ◽  
Uniform Compression ◽  
Rational Mapping ◽  
Stress Functions ◽  
Clamped Edge

An elastic half plane with a semielliptic rigid inclusion is analyzed as a mixed boundary value problem with a clamped edge. A rational mapping function of a sum of fractional expressions and the complex stress functions are used for the analysis. The debondings emanated from both ends of the semielliptic inclusion under uniform tension is examined and singular values of the stress at the debonded tips are obtained. By using these values, it is examined for some elliptical shapes how the debonding propagates. The stress values at the base of the semielliptic inclusion are also examined. Even if the loading is uniform compression, the debonding may occur at the base.

Asymptotic analysis of the corner-behaviour of a rigid punch bonded to an elastic substrate

2007 ◽  
Vol 42 (5) ◽  
pp. 415-422
Author(s):  
L Bohórquez ◽  
D. A Hills
Keyword(s):  
Stress Field ◽  
Plastic Zone ◽  
Asymptotic Solution ◽  
Asymptotic Analysis ◽  
Half Plane ◽  
Poisson's Ratio ◽  
Rigid Block ◽  
Rigid Punch ◽  
Oscillatory Behaviour ◽  
Elastic Substrate

The contact between a flat-faced rigid block and an elastic half-plane has been studied, showing that an asymptotic solution correctly captures the stress field adjacent to the contact corners for all values of Poisson's ratio. It is shown that, in practical cases, the plastic zone, which is inevitably present at the contact corners, envelopes the oscillatory behaviour implied locally but is surrounded by an elastic hinterland correctly represented by the asymptote.

scholarly journals A Paradox in Sliding Contact Problems With Friction

2003 ◽  
Vol 72 (3) ◽  
pp. 450-452 ◽  
Author(s):  
G. G. Adams ◽  
J. R. Barber ◽  
M. Ciavarella ◽  
J. R. Rice
Keyword(s):  
Half Plane ◽  
Slip Velocity ◽  
Finite Strain ◽  
Applied Pressure ◽  
Strain Analysis ◽  
Contact Problems ◽  
Rigid Punch ◽  
Flat Punch ◽  
Relative Slip ◽  
Velocity Changes

In problems involving the relative sliding to two bodies, the frictional force is taken to oppose the direction of the local relative slip velocity. For a rigid flat punch sliding over a half-plane at any speed, it is shown that the velocities of the half-plane particles near the edges of the punch seem to grow without limit in the same direction as the punch motion. Thus the local relative slip velocity changes sign. This phenomenon leads to a paradox in friction, in the sense that the assumed direction of sliding used for Coulomb friction is opposite that of the resulting slip velocity in the region sufficiently close to each of the edges of the punch. This paradox is not restricted to the case of a rigid punch, as it is due to the deformations in the half-plane over which the pressure is moving. It would therefore occur for any punch shape and elastic constants (including an elastic wedge) for which the applied pressure, moving along the free surface of the half-plane, is singular. The paradox is resolved by using a finite strain analysis of the kinematics for the rigid punch problem and it is expected that finite strain theory would resolve the paradox for a more general contact problem.

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