โ Scribed by Y.T Chou
No coin nor oath required. For personal study only.
Expressions for the elastic energy of a circular dislocation loop lying in the central plane of an isotropic thin plate are formulated. Computed results are given. These results show that, as might be expected, the thickness effect becomes sensible when the plate thiclkness approaches the dimension of the loop. The effect is greater for loops with Burgers vector normal to the plane of the loop than those with Burgers vector parallel to it.
An example which is presented for loops with Burgers vector normal to the plane of the loop shows that for a plate of half-thickness h = 1000 r, (where r, is the inner cut-off length) the loop energy is overestimated by 100,60, 17,0.07 and NO per cent for loop radii of 106, lo*, 10s, lo* and 10 ry, respectively. For loops with Burgers vector parallel to the plane of the loop and Poisson's ratio equal to f. the corresponding percentages are 74, 38, 6, 0.03 and No. L'ENERGIE DES BOUCLES DE DISLOCATIONS CIRCULAIRES DANS LES LAMES MINCES L'auteur a determine les equations de l'energie Blastique d'unc boucle de dislocation circulaire situ&e dans le plan median dune lame mince isotrope. Les rt&ultats montrent que l'effet de l'epaisseur devient sensible lorsqu'elle est de l'ordre de grandeur des dimensions de la boucle. Cet e&t eat plus important pour des boucles dont le veoteur de Burgers est normal au plan de la boucle. L'auteur presente un exemple de boucles dont le veeteur est normal au plan 06 pour une demi-epaisseur de la feuille h = 1000 rO, l%nergie de la boucle est estimee B 100,60, 17, 0.07 et ~0% du rayon de la boucle, soit respectivement 10 6, IO*, 1O5, 10% et lOr,. Pour des boucles dont le vecteur de Burgers est parall&le au plan et le coefficient de Poisson egal a l/3, Ies pourcentagea correspondants sont 74, 38, 6, 0.03 et NO. DIE ENERGIE KREISFCRMTGER VERSETZUNGSSCHLEIFEN IN DUNNEN PLATTEN Ftir die elastische Energie einer kreisfiirmigen Versetzungsscbleife, die in der Mittelebene einer isotropen diinnen Platte liegt, werden Formeln angegeben. Die Ergebnisse von Berechnungen werden mitgeteilt. Wie zu erwarten, zeigen dicse Ergebnisse, da6 der EinfluB der Dicke merklich wird, wenn sich die Plattendicke dem Schleifendurchmesser nahert. Bei Schleifen, deren Burgersvektor senkrecht zur Schleifenebene steht, ist der Einflu6 groaer, aks wenn der Burgersvektor parallel dazu liegt. Das B&spiel von Sebleifen mit dem Burgersvektor senkrecht zur Schleifenebene zeigt, da3 bei einer Platte mit der Halbdicke h, = 1000 rg (P@ ist der innere Abso~eideradi~) bei Schleifenr~en von 105, lo*, 105, 10% und lOr, die Schle~enener~e um 100, 60, 17, 0.07 bezw. -0 Prozent iiberschfitzt wird. Liegt der Bmgersvektor parallel ZUP Ebene, so smd bei &em Poisson-Verh~ltnis l/3 die entsprechenden Prozentsiitze 74, 38, 6, 0.03 und -0.
๐ SIMILAR VOLUMES
than are actually observed. In addition the model requires that reflections of the type (OO..!} should remain sharp and reflections of the type (hk.0) should become broadened.
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