Evaluation of the Eshelby solution for the ellipsoidal inclusion and heterogeneity

Meng, Chunfang; Heltsley, Will; Pollard, David D.

doi:10.1016/j.cageo.2011.07.008

Cited by 55 publications

(35 citation statements)

References 12 publications

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“…Several researchers have adopted the exterior Eshelby tensor to compute stresses outside of an inclusion. Their results include determination of the effective elastoplastic behavior of metal matrix composites; the elastic field outside of an elliptic cylindrical inclusion; and the development of general purpose numerical codes to determine the exterior stresses for an ellipsoidal heterogeneity . As shown in the following sections, we will adopt this process to determine stresses near pores in the otherwise homogeneous elastic material.…”

Section: Introductionmentioning

confidence: 99%

Application of critical distances to fatigue at pores

Sobotka

Enright

McClung

2019

Fatigue Fract Eng Mat Struct

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This work applies Taylor's theory of critical distance to quantify the effect of defects on fatigue initiation in an additively manufactured metal. We focus on hollow pores that are ideal spherical, prolate, and oblate spheroids isolated in an otherwise homogeneous linear‐elastic material. These conditions support the development of exact solutions using the exterior Eshelby tensor for a pore in a remote, arbitrary stress field. For spheres, this solution process admits simple closed‐form solutions for principal stresses disturbed by the pore. For prolate and oblate spheroids, we present the solutions as graphical curves showing stress variations under uniaxial tension. This report then extends the analysis to determine the effect of defects on a parametric, power‐law stress range vs fatigue life model. By propagating the distributed stress fields through this model, this study demonstrates the effect of pore size, pore shape, stress, and parametric fatigue properties on the life reduction due to porosity. These results suggest several approaches to increasing fatigue lives in porous materials, eg, reducing the pore size, promoting spherical pores, and increasing the microstructural parameter (comparable to the El Haddad parameter). Results presented in this work may be useful to inform trends of fatigue strength and fatigue initiation lives in metallic alloys with limited porosity, eg, additively manufactured materials that have been HIP'ed.

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Section: Introductionmentioning

confidence: 99%

Application of critical distances to fatigue at pores

Sobotka

Enright

McClung

2019

Fatigue Fract Eng Mat Struct

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“…In a number of geophysical applications, our code presented in Meng et al (2012Meng et al ( , https://doi.org/10.1016Meng et al ( /j.cageo.2011.008) is adopted. Among those, people sometimes use the code to fit surface deformation/strain data.…”

Section: Plain Language Summarymentioning

confidence: 99%

“…Meng et al () modify (Mura, , 11.30) to obtain the displacement field

u_{i} false(boldx false) = \frac{1}{8 π false(1 - ν false)} ((), ψ_{, j l i} ϵ_{j l}^{*} - 2 ν {ϵ_{m m}^{*} ϕ}_{, i} - 4 false(1 - ν false) {ϵ_{i l}^{*} ϕ}_{, l}),

where ν is Poisson's ratio and ϕ and ψ are given by integrals

\begin{matrix} right ϕ (x) = & left \int_{normalΩ} | x - {boldx}^{'} | d {boldx}^{'}, & right \\ right ψ (x) = & left \int_{normalΩ} \frac{1}{| x - {boldx}^{'} |} d {boldx}^{'}, \end{matrix}

where Ω is the inclusion region. The subscript (·), i denotes spatial gradient in i th dimension.…”

Section: Introductionmentioning

confidence: 99%

“…Reches () and Healy () present closed form solution with computer codes, where two of the ellipsoid's semiaxes are equal. A computer code that evaluates the true triaxial Eshelby solution has not appeared in public domain until Meng et al () present their code Esh3D (originally in Matlab™) and make it open source.…”

Section: Introductionmentioning

confidence: 99%

“…For the interior stress, the inelastic strain needs to be subtracted from the total strain. Meng et al (2012) modify (Mura, 1987, 11.30) to obtain the displacement field…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Esh3D, an Analytical and Numerical Hybrid Code for Full Space and Half‐Space Eshelby's Inclusion Problems

Meng

2019

Earth and Space Science

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I present an open source code Esh3D that evaluates the quasi‐static elastic displacement and stress fields perturbed by ellipsoidal inclusions, known as the Eshelby solution. The improvement over my previous work includes obtaining solutions in half‐space by numerically canceling the traction to stage a free surface. The discrete numerical domain allows nonplanar surface. I first briefly introduce the ellipsoidal inclusion problem and solution evaluation. Then, I describe the traction cancellation method in forming the half‐space solutions. Next, I emulate a planar fault with a low aspect ratio ellipsoid and compare the half‐space solution against the well‐known Okada solution for flat and topographic surfaces. Finally, I provide comparisons between the full space and half‐space solutions to illustrate the free surface effects on the displacement and stress fields.

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