Achieving a uniform stress field in a coated non-elliptical inhomogeneity in the presence of a mode III crack

2018 ◽  
Vol 69 (6) ◽  
Author(s):  
Xu Wang ◽  
Liang Chen ◽  
Peter Schiavone
Keyword(s):  
Stress Field ◽  
Uniform Stress ◽  
Mode Iii ◽  
Mode Iii Crack ◽  
Elliptical Inhomogeneity ◽  
Uniform Stress Field

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 〈111〉 Elliptic Inclusion in an Anisotropic Solid of Cubic Symmetry

1982 ◽  
Vol 49 (2) ◽  
pp. 353-360 ◽  
Author(s):  
H. C. Yang ◽  
Y. T. Chou
Keyword(s):  
Stress Field ◽  
Uniform Stress ◽  
Elliptic Inclusion ◽  
Cubic Symmetry ◽  
Elastic Fields ◽  
Closed Form Solutions ◽  
Strain Transformation ◽  
Anisotropic Solid ◽  
Uniform Stress Field ◽  
Free Strain

This paper deals with a generalized plane problem in which a uniform stress-free strain transformation takes place in the region of an elliptic cyclinder (the inclusion) oriented in the 〈111〉 direction in an anisotropic solid of cubic symmetry. Closed-form solutions for the elastic fields and the strain energies are presented. The perturbation of an otherwise uniform stress field due to a 〈111〉 elliptic inhomogeneity is also treated including two extreme cases, elliptic cavities and rigid inhomogeneities.

Research on Nonlinear Damping Characteristics of Damping Alloy With Uniform Stress Field

Volume 1 ◽  
2004 ◽  
Author(s):  
Hongzhao Liu ◽  
Ziying Wu ◽  
Lilan Liu ◽  
Daning Yuan ◽  
Zhongming Zhang
Keyword(s):  
Stress Field ◽  
Nonlinear Function ◽  
Nonlinear Damping ◽  
Damping Capacity ◽  
Internal Damping ◽  
Uniform Stress ◽  
Nonlinear Relation ◽  
Uniform Stress Field ◽  
Half Power ◽  
Versus Strain

For the high damping metal material like damping alloy, the damping capacity usually changes with the strain amplitude and frequency nonlinearly. First, to extract the pattern of the internal damping versus strain, two time-domain calculation methods are presented in this paper. One is the moving exponent method (MEM for short) based on FFT (MEM+FFT) and the other is the moving autoregressive model method (MARM). The computing accuracy of the two methods has been compared through numerical simulations. The nonlinear relation curve of loss factor versus strain is achieved by the impulse excitation experiment employing uniform stress field. Then, to extract the pattern of the internal damping versus vibrating frequency, the sine sweep-frequency excitation experiment based on the half-power bandwidth method is carried out. The resulting curve indicates that the internal damping is also a nonlinear function of frequency.

Atomic transport via point defects in crystals III. Migration in a stress field

1985 ◽  
Vol 398 (1814) ◽  
pp. 203-208 ◽  
Keyword(s):  
Stress Field ◽  
Point Defects ◽  
Strain Tensor ◽  
Three Dimensional ◽  
Molecular Volume ◽  
Uniform Stress ◽  
Atomic Transport ◽  
Elastic Dipole ◽  
Uniform Stress Field ◽  
Defect Species

The kinetic theory of isothermal atomic transport via point defects that was presented in two previous papers (Franklin, A. D. & Lidiard, A. B. Proc. R. Soc. Lond . A 389, 405–431 (1983) and Franklin, A. D. & Lidiard, A. B. Proc. R. Soc. Lond . A 392, 457–473 (1984)) has been expanded into a three-dimensional formulation to analyse transport in an applied non-uniform stress field. The fluxes of the various defect species take the general form familiar from non-equilibrium thermodynamics, while the contribution to the force on defect species Y arising from the stress σ αβ is confirmed to be v ∇(λ (Y) αβ σ αβ ), where v is the molecular volume of the solid and λ (Y) αβ is the elastic-dipole strain tensor of the defect species Y (summation over repeated Cartesian indices α, β is here assumed). Full details of these calculations are presented in Lidiard, A. B. A. E. R. E. Rep . no R. 11367 (1984).

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.

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