The effect of shear modulus on the stress distribution produced by a planar array of screw dislocations near a bi-metallic interface
✍ Scribed by D.M. Barnett
- Publisher
- Elsevier Science
- Year
- 1967
- Weight
- 478 KB
- Volume
- 15
- Category
- Article
- ISSN
- 0001-6160
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✦ Synopsis
Using the method of continuously distributed dislocations, an exact solution is obtained for the distribution of a planar array (pileup) of screw dislocations near the junction of a bi-metallic medium formed by welding together two elastic half-planes of different shear moduli. The solution presented is valid for 0 < G,/G, < to, where G, and G, denote the respective shear moduli; the dislocation pileup exists in the phase of modulus G,. Closed form expressions for the stresses generated in the second phase (modulus G,) are given, and it is deduced that near the pileup tip the stresses vary as (L/p)"; L is the pileup length, p the distance from the pileup tip, and a is a known function of G,/G?. If G,/Q, 2 1, then 0 < a 5 l/2, and if G,/a, 2 1, then l/2 5 a < 1. The number, N, of dislocations m the pileup is found as a function of L, G,/G,, and applied stress. As G,/C, increases, N decreases. EFFET DU MODULE DE CISAILLEMENT SUR LA DISTRIBUTION DE CONTRAINTES PRODUITE PAR UN ARRANGEMENT PLAN DE DISLOCATIONS VIS A UN INTERFACE BI-METALLIQUE Par la methode de distribution continue de dislocations, on obtient une forme exacte de la distribution tl'un arrangement plan (empilement) de dislocations vis B la jonction d'un milieu bi-m6tallique obtenu en soudant deux demi-plans blastiques de modules de ci-saillement diffbrents. La solution exposbe est valable pour 0 < G,/G, < co oh G, et B, dbsignent les modules de cisaillement respectifs. L'empilement de dislocations se trouve dens la phase de module G,. On donne les expressions rigoureuses des contraintes produites dens la seconde phase (module G,) et on en dbduit, p&s de la t&e de l'empilement, une variation des contraintes en (L/p)'; L est la longueur de l'empilement, p la distance B la t6te de l'empilement a une fonction oonnue de G,/C,. Si G,/cf, 2 1, alors 0 < a < ) et si G,/a, 2 1, 4 5 a < 1. Le nombre N de dislocations dans l'empilement est fonction dr L, G,/C, et de la contrainte appliquhe.
Quand G,/G, croft, N d&o%.