By V. L. Indenbom
This quantity goals to supply an intensive remedy of the phenomena of elastic anisostropy and a dialogue on dislocation mobilities. The publication offers a large remedy of those themes, and comprises descriptions of exact theoretical types to explain dislocations and cracks, and relocating dislocations. an summary is given of the actual behaviour caused by dislocation mobility in fabrics, reminiscent of flow and climb, interactions with element defects and the behaviour of dislocations lower than radiation resembling creep and swelling
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Additional info for Elastic Strain Fields and Dislocation Mobility
When we divide the displacement in eq. (60) into two parts, b u[(P) = -f+Vl(P), (61) 4π where Ω is the solid angle under which the loop is seen from point P, then V\(P) is a potential (without a curl) field which can be expressed in the form Ki(P) = ^ ( b ^ ) ( P , P / ) d x i , (60') j with any stress function tensor φ\/. Using eq. (55) and transforming the contour integral in eq. , the /cth component of the displacement at point P is equal to the work done by stresses afj due to the unit force applied at point P in the direction k on the discontinuities in displacements bj9 arising due to the formation of a dislocation.
At the point with normal n to the interface, the equilibrium conditions, ιι·[σ]=0, (101) and the compatibility conditions, n x [5σ] xn = -nx [#°] x w, (102) should be fulfilled. Here, SG is used as a short notation for the matrix with (/-element Sijklakl. These conditions coincide with the corresponding equations of the one-dimensional problem with stresses σ and the intrinsic deformations i° replaced by the jumps in these quantities, [σ] and \_S°~\. 2). This may be readily verified by substituting eq.
L. Indenbom 54 where integration is carried out in the plane normal to the dislocation line over a ring of an internal radius r0 of the order of the lattice parameter and an external radius R of the order of the crystal size. Such a cut-off of the integral is associated with the divergence in eq. (166) at small and large distances from the dislocation and is caused, on one hand, by the inapplicability of the continuum description in the vicinity of the dislocation core, and, on the other hand, by the slow decrease of the elastic field with the distance from the dislocation line.