Longitudinal Shear Problem for an Elastic Body With Two Fixed Edges

1986 ◽  
Vol 53 (4) ◽  
pp. 814-818 ◽  
Author(s):  
N. Hasebe ◽  
T. Sugimoto ◽  
T. Nakamura
Keyword(s):  
Stress Intensity Factor ◽  
Elastic Body ◽  
Arbitrary Shape ◽  
Mapping Function ◽  
Longitudinal Shear ◽  
Complex Stress ◽  
Shear Load ◽  
Elastic Bodies ◽  
Stress Functions ◽  
Shear Problem

A semi-infinite elastic body with an arbitrary shape and an infinite one with a hole under uniform longitudinal shear load are investigated. These bodies have a boundary with two fixed parts. The respective complex stress functions are obtained in closed form by using a conformal mapping function. Doubly connected elastic bodies with symmetry can also be treated. Examples of the stress distribution and expressions for the stress intensity factor are shown.

Compressibility of Two-Dimensional Cavities of Various Shapes

1986 ◽  
Vol 53 (3) ◽  
pp. 500-504 ◽  
Author(s):  
R. W. Zimmerman
Keyword(s):  
Closed Form Solution ◽  
Mapping Function ◽  
Complex Stress ◽  
Form Solution ◽  
Hydrostatic Compression ◽  
Biaxial Compression ◽  
Cavity Surface ◽  
Uniform Pressure ◽  
Two Dimensional ◽  
Stress Functions

Muskhelishvili-Kolosov complex stress functions are used to find the stresses and displacements around two-dimensional cavities under plane strain or plane stress. The boundary conditions considered are either uniform pressure at the cavity surface with vanishing stresses at infinity, or a traction-free cavity surface with uniform biaxial compression at infinity. A closed-form solution is obtained for the case where the mapping function from the interior of the unit circle to the region outside of the cavity has a finite number of terms. The area change of the cavity due to hydrostatic compression at infinity is examined for a variety of shapes, and is found to correlate closely with the square of the perimeter of the hole.

Stress Concentration Factors at an Elliptical Hole on the Interface Between Bonded Dissimilar Half-Planes Under Bending Moment

1996 ◽  
Vol 63 (1) ◽  
pp. 7-14 ◽  
Author(s):  
Mohamed Salama ◽  
Norio Hasebe
Keyword(s):  
Stress Concentration ◽  
Elliptical Hole ◽  
Bending Moment ◽  
Mapping Function ◽  
Complex Stress ◽  
Function Technique ◽  
Rational Mapping ◽  
Stress Functions ◽  
Stress Concentration Factors ◽  
Thin Plate Bending

The problem of thin plate bending of two bonded half-planes with an elliptical hole on the interface and interface cracks on its both sides is presented. A uniformly distributed bending moment applied at the remote ends of the interface is considered. The complex stress functions approach together with the rational mapping function technique are used in the analysis. The solution is obtained in closed form. Distributions of bending and torsional moments, the stress concentration factor as well as the stress intensity factor, are given for all possible dimensions of the elliptical hole, various material constants, and rigidity ratios.

Interaction between a Screw Dislocation Located in Strained Reinforcement Layer and a Lip-Shaped Crack

2012 ◽  
Vol 182-183 ◽  
pp. 1549-1553
Author(s):  
Min Yu ◽  
You Wen Liu
Keyword(s):  
Stress Intensity Factor ◽  
Screw Dislocation ◽  
Complex Function ◽  
Great Influence ◽  
Image Force ◽  
Longitudinal Shear ◽  
Shear Load ◽  
The Matrix ◽  
In Series ◽  
Shaped Crack

The paper is aim to investigate the interaction of a screw dislocation in strained reinforcement with a lip-shaped crack under remote longitudinal shear load using complex variable method of Elasticity. The exact solution of complex function of the matrix and the renforcement layer are obtain in series form; then, the expressions of stress field, image force and stress intensity factor of crack tip can be derived; finally, numerical disccusions are pesented and the results shows that the lip-shaped crack in reinforcement layer has interference effect on the interaction of dislocation and reinforcement layer, and the eigenstrain in x-direction has little effect on image force; however, the eigenstrain in y-direction has great influence on image force.

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.

Defects Mechanics; Three-Body Problem of Defects Interaction among Crack, Dislocations and Twin Boundary in Magnesium

2016 ◽  
Vol 258 ◽  
pp. 11-16 ◽  
Author(s):  
Yoji Shibutani ◽  
Daisuke Matsunaka
Keyword(s):  
Molecular Dynamics ◽  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Intensity Factor ◽  
Stress Field ◽  
Elastic Stress ◽  
Crack Tip ◽  
Complex Stress ◽  
Shielding Effect ◽  
Stress Functions

Dynamics and statics of defects interaction among crack, dislocations and twin boundary (TB) observed in magnesium were investigated using molecular dynamics and elasticity with the complex stress functions to clarify the effect of long-range elastic stress field. An atomic model containing a crack parallel to (10-11) TB was gradually elongated under KI-mode tension by molecular dynamics simulations. Changing the distance between the crack and the TB, four kinds of crack propagation manners were observed, one of which showed the path transition from the crack to the TB itself by shielding effect of piled-up dislocations around the crack tip. The stress intensity factor of the nanosized crack in bulk is 0.28 MPam1/2, which is smaller than that of crack on the TB. The shielding effect due to the piled-up dislocations drastically decreases stress concentration around the crack tip and the stress intensity factor diminishes down to the 0.22, and thus the crack nucleated from the void nucleation and coalescence on the TB was propagated instead. The elastic stress distributions obtained by the superposition of some complex stress functions suggest that the stress field around the crack tip is disturbed by the localized stress due to the TB in the case of crack closest to TB and also by the back stress due to the piled-up dislocations in the case of crack far from TB.

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.

Forces on a Circular Hole Located in Functionally Graded Material

2011 ◽  
Vol 704-705 ◽  
pp. 631-635
Author(s):  
Xian Feng Wang ◽  
Feng Xing ◽  
Norio Hasebe
Keyword(s):  
Circular Hole ◽  
Constant Term ◽  
Complex Stress ◽  
Functionally Graded ◽  
Homogeneous Material ◽  
Dimensional Problem ◽  
Stress Components ◽  
Graded Material ◽  
Stress Functions ◽  
Stress Function Method

The complex stress function method is used in this study to formulate the 2-dimensional problem for nonhomogeneous materials. The Young’s modulus E varies linearly with the coordinate x and the Poisson’s ratio of the material is assumed constant and. The stress components and the boundary conditions are expressed in terms of two complex stress functions in explicit forms. It is noted that the constant term in stress functions has an influence on the stress components, which is different from the homogeneous material case. Subsequently, the problem of a nonhomogeneous plane containing a circular hole subjected to a uniform internal pressure is studied.

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