Configurational Forces on Elastic Line Singularities

Seo, Youjung; Jung, Gyu-Jin; Kim, Inho; Pak, Youngshang

doi:10.1115/1.4038808

Cited by 6 publications

(1 citation statement)

References 13 publications

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“…The M-integral is also applicable for other defect types without obvious singular point, such as voids, inclusions, dislocations, local plastic zones, etc. (Agiasofitou and Lazar, 2017;Baxevanakis and Giannakopoulos, 2015;Chen, 2009a, 2009b;Hui and Chen, 2010;Lazar and Agiasofitou, 2018;Lazar and Kirchner, 2007;Meyer et al, 2017;Seo et al, 2018;Wang and Chen, 2010). For the general multidefects problems, M-integral describes the global damage caused by the defects within the integration contour, and local defects interaction and coalescence contribute to the value of M-integral (Chang and Wu, 2011;Hu et al, 2012;Li et al, 2017;.…”

Section: Introductionmentioning

confidence: 99%

Damage evaluation for the dispersed microdefects with the aid of M-integral

Zhu

2018

International Journal of Damage Mechanics

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A unified method of evaluating the dispersed microdefects’ equivalent damage area/volume is innovatively proposed by using the M-integral. The corresponding damage evolution rate and fatigue driving force is preliminarily studied for the dispersed microdefects. First, the analytical expression of M-integral is deduced by using the Lagrangian energy density function (Λ), and the corresponding physical meaning of the M-integral is elucidated as the change of the total potential energy due to the damage evolution. Second, the actual damage area/volume induced by underlying dispersed microdefects are assumed equivalent to the area/volume of an individual circular/spherical void while the corresponding values of the M-integral for both cases are equal. As examples, the equivalent damage area associated with the M-integral for a series of representative defect(s) configurations is calculated, including the singular defect (void, crack, and ellipse) and the interactive defects (two voids, two cracks, one void, and one crack). The influences of the defects interaction effect and distribution on the damage level are analyzed quantitatively. Finally, the present method of damage evaluation is proposed to predict fatigue problems of the dispersed defects. A unified fatigue damage evolution law for the dispersed microdefects is preliminarily defined, and a protocol to experimentally measure the damage evolution rate is proposed. The present research will be beneficial to the damage tolerance design and lifetime prediction of engineering structures with dispersed microdefects.

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Section: Introductionmentioning

confidence: 99%

Damage evaluation for the dispersed microdefects with the aid of M-integral

Zhu

2018

International Journal of Damage Mechanics

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Energy and volume changes due to the formation of a circular inhomogeneity in a residual deviatoric stress field

2019

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$$\varvec{J}$$-, M- and $$\varvec{L}$$-integrals of line charges and line forces

Lazar

Agiasofitou

2023

Acta Mech

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In this work, the $$\varvec{J}$$ J -, M- and $$\varvec{L}$$ L -integrals of two line charges and two line forces in generalized plane strain are derived in the framework of three-dimensional (3D) electrostatics and three-dimensional compatible linear elasticity, respectively, in order to study the interaction between them. The key point in this derivation is achieved by expressing the $$\varvec{J}$$ J -, M- and $$\varvec{L}$$ L -integrals of point charges and point forces in three dimensions in terms of the corresponding three-dimensional Green functions, that is, the three-dimensional Green function of the Laplace operator and the three-dimensional Green tensor of the Navier operator, respectively. The major mathematical tool used in deriving the $$\varvec{J}$$ J -, M- and $$L_3$$ L 3 -integrals of line charges and line forces from the corresponding $$\varvec{J}$$ J -, M- and $$\varvec{L}$$ L -integrals of point charges and point forces is the method of embedding or method of descent of Green functions to two dimensions (2D) from the corresponding Green functions in 3D. The analytical expressions of $$\varvec{J}$$ J -, M- and $$L_3$$ L 3 -integrals of line charges and line forces in antiplane and plane strain are derived and discussed. The $$\varvec{J}$$ J -integral is the electrostatic part of the Lorentz force (electrostatic interaction force) between two line charges in electrostatics and the Cherepanov force between two line forces in elasticity. The M-integral of two line sources (charges or forces) equals half the electrostatic interaction energy in electrostatics and half the elastic interaction energy in elasticity of these two line sources, respectively. The $$L_3$$ L 3 -integral of two line sources (charges or forces) is the z-component of the configurational vector moment or the rotational moment representing the total torque about the z-axis caused by the interaction of the two line sources. An important outcome is that the $$\varvec{J}$$ J -integral is twice the negative gradient of the M-integral, leading to the result that the $${\varvec{J}}$$ J -integral for line charges and line forces is a conservative force (with the corresponding interaction energy playing the role of the potential energy) and consequently an irrotational vector field. Finally, the obtained $$\varvec{J}$$ J -, M- and $$L_3$$ L 3 -integrals being functions of the distance and of the angle, are able to describe the physical behaviour of the interaction of two line sources (charges and forces), since they represent the fundamental and necessary quantities, that is, the interaction force, interaction energy and total torque produced by the interaction of these two line sources.

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Configurational Forces on Elastic Line Singularities

Cited by 6 publications

References 13 publications

Damage evaluation for the dispersed microdefects with the aid of M-integral

Damage evaluation for the dispersed microdefects with the aid of M-integral

Energy and volume changes due to the formation of a circular inhomogeneity in a residual deviatoric stress field

$$\varvec{J}$$-, M- and $$\varvec{L}$$-integrals of line charges and line forces

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