Average Eshelby tensor and elastic field for helical inclusion problems

Abstract

Elastic field of helical inclusion and average Eshelby tensor for helix, <Sh>, with various different helical parameters (p: pitch, d: core diameter, D: outer diameter, L: longitudinal length, n: number of turns) were predicted by two types of Green's function method, Eshelby inclusion method (EIM) and boundary integral equation method (BIE). Helical inclusion model revealed that the effects of helical pitch was found to have the most significant influence on 〈Sh〉, and resultant stress obtained by average Eshelby tensor model for helix (AETM) through EIM was comparable to that of spherical inclusion at the increased number of helical turn and aspect ratio, α = L/D. Local stress analysis by EIM and BIE under a given dilatational eigenstrain proved that the stress profile of helical cross-section shows large stress gradient in angular and radial stress components, and their equivalent stress on helical cross-section are largely different from the stress of entire helical volume computed by AETM, which reflect the influence of the rotational stress symmetry of helical inclusion on average stress. Finally, thermal residual stress of Fe0.7Pd0.3 nano-helix embedded in alumina template was predicted by equivalent inclusion method using AETM for nano-helix.