scholarly journals Uniformity of stresses inside a non-elliptical inhomogeneity interacting with a mode III crack

2018 ◽  
Vol 474 (2218) ◽  
pp. 20180304 ◽  
Author(s):  
Xu Wang ◽  
Liang Chen ◽  
Peter Schiavone
Keyword(s):  
Stress Field ◽  
Singular Integral Equations ◽  
Infinite Matrix ◽  
Mode Iii ◽  
Mode Iii Crack ◽  
Elliptical Inhomogeneity ◽  
Internal Stress Field ◽  
Uniform Stress Field ◽  
Cauchy Singular Integral ◽  
Mapping Techniques

Using conformal mapping techniques and the theory of Cauchy singular integral equations, we prove that it is possible to maintain a uniform internal stress field inside a non-elliptical elastic inhomogeneity embedded in an infinite matrix subjected to uniform remote stress despite the fact that the inhomogeneity interacts with a finite mode III crack. The crack can be modelled either as a Griffith crack or as a Zener–Stroh crack. Our analysis further indicates that the existence of the crack plays a key role in influencing the shape of the corresponding inhomogeneity but not the internal uniform stress field inside the inhomogeneity. Numerical examples are presented to demonstrate the solution.

Uniform Stresses Inside an Elliptical Inhomogeneity With an Imperfect Interface in Plane Elasticity

2008 ◽  
Vol 75 (5) ◽  
Author(s):  
X. Wang ◽  
E. Pan ◽  
L. J. Sudak
Keyword(s):  
Stress Field ◽  
Imperfect Interface ◽  
Plane Elasticity ◽  
Uniform Stress ◽  
Uniform Loading ◽  
Elliptical Inhomogeneity ◽  
Interface Function ◽  
Internal Stress Field ◽  
Uniform Stress Field ◽  
Tangential Directions

We consider an elliptical inhomogeneity embedded in an infinite isotropic elastic matrix subjected to in-plane deformations under the assumption of remote uniform loading. The inhomogeneity-matrix interface is assumed to be imperfect, which is simulated by the spring-layer model with vanishing thickness. Its behavior is based on the assumption that tractions are continuous but displacements are discontinuous across the interface. We further assume that the same degree of imperfection on the interface is realized in both the normal and tangential directions. We find a form of interface function, which leads to uniform stress field within the elliptical inhomogeneity. The explicit expressions for the uniform stress field within the elliptical inhomogeneity are derived. The obtained results are verified by comparison with existing solutions. The condition under which the internal stress field is not only uniform but also hydrostatic is also presented.

The Mode III Crack Problem in Bonded Materials With a Nonhomogeneous Interfacial Zone

1991 ◽  
Vol 58 (2) ◽  
pp. 419-427 ◽  
Author(s):  
F. Erdogan ◽  
A. C. Kaya ◽  
P. F. Joseph
Keyword(s):  
Stress Field ◽  
Subcritical Crack Growth ◽  
Crack Problem ◽  
Homogeneous Medium ◽  
Interfacial Region ◽  
Interfacial Zone ◽  
Mode Iii ◽  
Mode Iii Crack ◽  
Bonded Materials ◽  
Square Root Singularity

In this paper the mode III crack problem for two bonded homogeneous half planes is considered. The interfacial zone is modeled by a nonhomogeneous strip in such a way that the shear modulus is a continuous function throughout the composite medium and has discontinuous derivatives along the boundaries of the interfacial zone. The problem is formulated for cracks perpendicular to the nominal interface and is solved for various crack locations in and around the interfacial region. The asymptotic stress field near the tip of a crack terminating at an interface is examined and it is shown that, unlike the corresponding stress field in piecewise homogeneous materials, in this case the stresses have the standard square root singularity and their variation is identical to that of a crack in a homogeneous medium. With application to the subcritical crack growth process in mind, the results given include mostly the stress intensity factors for some typical crack geometries and various material combinations.

Elastic cloaking for a periodic distribution of parallel finite cracks

2021 ◽  
Vol 477 (2249) ◽  
pp. 20200997
Author(s):  
Ping Yang ◽  
Xu Wang ◽  
Peter Schiavone
Keyword(s):  
Half Plane ◽  
Singular Integral ◽  
Singular Integral Equations ◽  
Mode Iii ◽  
Original Design ◽  
Periodic Distribution ◽  
Wavy Interface ◽  
Cauchy Singular Integral ◽  
Periodic Cracks ◽  
The Right

We achieve elastic cloaking for a periodic distribution of an infinite number of parallel finite mode III cracks by means of the complex variable method and the theory of Cauchy singular integral equations. The cloaking bimaterial structure is composed of an undisturbed uniformly stressed left half-plane perfectly bonded via a wavy interface to the right half-plane which contains periodic cracks. The original design of the wavy interface and the positions of the periodic cracks are ultimately reduced to the solution of a Cauchy singular integral equation which can be solved numerically.

A hole of irregular shape interacting with a non-parabolic open inhomogeneity with internal uniform anti-plane stresses

2020 ◽  
pp. 108128652097024
Author(s):  
Xu Wang ◽  
Ping Yang ◽  
Peter Schiavone
Keyword(s):  
Free Boundary ◽  
Stress Field ◽  
Conformal Mapping ◽  
Analytic Continuation ◽  
Uniform Stress ◽  
Surrounding Matrix ◽  
Parabolic Shape ◽  
Uniform Stress Field ◽  
Elastic Inhomogeneity ◽  
Mapping Techniques

We use conformal mapping techniques together with analytic continuation to show that a non-parabolic open elastic inhomogeneity continues to admit a state of uniform internal stress when a hole with closed curvilinear traction-free boundary is placed in its vicinity and the surrounding matrix is subjected to uniform remote anti-plane stresses. The internal uniform stress field inside the inhomogeneity is found to be independent of the existence of the nearby hole and the specific non-parabolic shape of the inhomogeneity. In contrast, the non-parabolic shape of the inhomogeneity is influenced solely by the existence of the nearby hole.

A circular Eshelby inclusion interacting with a non-parabolic open inhomogeneity with internal uniform anti-plane stresses

2019 ◽  
Vol 25 (3) ◽  
pp. 573-581 ◽  
Author(s):  
Xu Wang ◽  
Ping Yang ◽  
Peter Schiavone
Keyword(s):  
Stress Field ◽  
Conformal Mapping ◽  
Stress Distributions ◽  
Uniform Stress ◽  
Elastic Deformations ◽  
Surrounding Matrix ◽  
Eshelby Inclusion ◽  
The Matrix ◽  
Uniform Stress Field ◽  
Mapping Techniques

Using conformal mapping techniques and analytic continuation, we prove that when subjected to anti-plane elastic deformations, a non-parabolic open inhomogeneity continues to admit an internal uniform stress field when a circular Eshelby inclusion is placed in its vicinity and the surrounding matrix is subjected to uniform remote stresses. Explicit expressions for the non-uniform stress distributions in the matrix and in the circular Eshelby inclusion are obtained. The internal uniform stress field is independent of the shape of the inhomogeneity and the presence of the circular Eshelby inclusion, whereas the existence of the circular Eshelby inclusion exerts a significant influence on the shape of the non-parabolic open inhomogeneity as well as on the non-uniform stress distributions in the matrix and in the circular Eshelby inclusion itself.

Effects of finite chain extensibility on the stress fields near the tip of a mode III crack

2011 ◽  
Vol 467 (2135) ◽  
pp. 3170-3187 ◽  
Author(s):  
Rong Long ◽  
Chung-Yuen Hui
Keyword(s):  
Stress Field ◽  
Crack Tip ◽  
Stress Fields ◽  
Small Scale ◽  
Finite Chain ◽  
Mode Iii ◽  
Mode Iii Crack ◽  
Scale Yielding ◽  
Stress And Deformation ◽  
Crack Tip Stress

We carried out a detailed analysis of the asymptotic stress and deformation fields at the tip of a mode III crack in a hyperelastic solid described by Gent's model. This model accounts for finite chain extensibility so that the deformation everywhere in the solid, including the crack tip, is bounded. We also present an exact solution for the ‘small-scale yielding’ problem where the region of large deformation is small compared with specimen dimensions. Our result shows that the crack tip stress field is non-separable. In addition, an infinite number of parameters are needed to completely specify the angular variation of crack tip stress field.

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