English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Zendy Open

Presents the pdf analysis as premium feature

PDF Analysis

Insights

Presents the summarisation as premium feature

Summarisation

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the zaia usage as premium feature

ZAIA

Zendy Tools

Zendy Plus

Presents the access of premium content as premium feature

Premium Content

The aim of the present work is the unification of incompatible elasticitytheory of dislocations and Eshelbian mechanics leading naturally to Eshelbiandislocation mechanics. In such a unified framework, we explore the utility ofthe $J$-, $M$-, and $L$-integrals. We give the physical interpretation of the$M$-, and $L$-integrals for dislocations, connecting them with establishedquantities in dislocation theory such as the interaction energy and the$J$-integral of dislocations, which is equivalent to the well-knownPeach-Koehler force. The $J$-, $M$-, and $L$-integrals for dislocations havebeen studied in the framework of three-dimensional, incompatible, linearelasticity. First of all, the general formulas of the $J$-, $M$-, and$L$-integrals for dislocations are given. Next, the examined integrals arespecified for straight dislocations. Finally, the explicit formulas of the$J$-, $M$-, and $L$-integrals are calculated for straight (screw and edge)dislocations in isotropic materials. The obtained results reveal the physicalinterpretation and significance of the $M$-, and $L$-integrals for straightdislocations. The $M$-integral between two straight dislocations (per unitdislocation length) is equal to the half of the interaction energy of the twodislocations (per unit dislocation length) depending on the distance and on theangle, plus twice the corresponding pre-logarithmic energy factor. The$L_3$-integral between two straight dislocations is the $z$-component of theconfigurational vector moment or the rotational moment about the $z$-axiscaused by the interaction between the two dislocations. Fundamental relationsbetween the $J$-, $M$-, and $L_3$-integrals are derived showing the inherentconnection between them. The relations connecting directly the $J$-, $M$-, and$L_3$-integrals with the interaction energy are obtained.

Micromechanics of dislocations in solids: $J$-, $M$-, and $L$-integrals and their fundamental relations