title: Ð ÐµÐ»Ð°ÐºÑÐ°ÑÐ¸Ñ Ð¾ÑÑÐ°ÑÐ¾ÑÐ½ÑÑ Ð½Ð°Ð¿ÑÑÐ¶ÐµÐ½Ð¸Ð¹ Ð² ÐºÐ¾Ð¼Ð¿Ð¾Ð·Ð¸ÑÐ½Ð¾Ð¹ Ð½Ð°Ð½Ð¾Ð¿ÑÐ¾Ð²Ð¾Ð»Ð¾ÐºÐµ Ñ ÑÐ´ÑÐ¾Ð¼ Ð² Ð²Ð¸Ð´Ðµ Ð¿ÑÑÐ¼Ð¾Ð¹ Ð¿ÑÑÐ¸ÑÐ³Ð¾Ð»ÑÐ½Ð¾Ð¹ Ð¿ÑÐ¸Ð·Ð¼Ñ
title: Ð²ÑÐ¿ÑÑÐºÐ½Ð°Ñ ÐºÐ²Ð°Ð»Ð¸ÑÐ¸ÐºÐ°ÑÐ¸Ð¾Ð½Ð½Ð°Ñ ÑÐ°Ð±Ð¾ÑÐ° Ð¼Ð°Ð³Ð¸ÑÑÑÐ°
titleType: Subtitle
title: Relaxation of residual stresses in a composite nanowire with a core in the form of a straight pentagonal prism
Creators: name: ÐÑÐ±Ð½Ð¾Ð²Ð°, ÐÐ°ÑÐ¸Ñ
Publisher: name: Ð¡Ð°Ð½ÐºÑ-ÐÐµÑÐµÑÐ±ÑÑÐ³ÑÐºÐ¸Ð¹ Ð¿Ð¾Ð»Ð¸ÑÐµÑÐ½Ð¸ÑÐµÑÐºÐ¸Ð¹ ÑÐ½Ð¸Ð²ÐµÑÑÐ¸ÑÐµÑ ÐÐµÑÑÐ° ÐÐµÐ»Ð¸ÐºÐ¾Ð³Ð¾
Year: 2020
Subjects: ÐÐ°Ð¿ÑÑÐ¶ÐµÐ½Ð¸Ñ (Ð¼ÐµÑ .)
ÐÐ°Ð½Ð¾ÑÑÑÑÐºÑÑÑÐ½ÑÐµ Ð¼Ð°ÑÐµÑÐ¸Ð°Ð»Ñ
ÐÑÐ¾Ð²Ð¾Ð»Ð¾ÐºÐ°
ÐÐ¾Ð¼Ð¿Ð¾Ð·Ð¸ÑÐ¸Ð¾Ð½Ð½ÑÐµ Ð¼Ð°ÑÐµÑÐ¸Ð°Ð»Ñ
Ð´Ð¸ÑÐ»Ð¾ÐºÐ°ÑÐ¸Ñ Ð½ÐµÑÐ¾Ð¾ÑÐ²ÐµÑÑÑÐ²Ð¸Ñ
Ð²ÐºÐ»ÑÑÐµÐ½Ð¸Ðµ Ð² Ð²Ð¸Ð´Ðµ Ð¼Ð½Ð¾Ð³Ð¾ÑÐ³Ð¾Ð»ÑÐ½Ð¾Ð¹ Ð¿ÑÐ¸Ð·Ð¼Ñ
mismatch dislocation
inclusion as a polygonal prism

description: ÐÐ¸ÑÑÐµÑÑÐ°ÑÐ¸Ñ ÑÐ¾Ð´ÐµÑÐ¶Ð¸Ñ 49 ÑÑÑÐ°Ð½Ð¸Ñ, 29 ÑÐ¸ÑÑÐ½ÐºÐ¾Ð², 20 ÑÐ¾ÑÐ¼ÑÐ» Ð¸ 81 Ð¸ÑÑÐ¾ÑÐ½Ð¸ÐºÐ° Ð»Ð¸ÑÐµÑÐ°ÑÑÑÑ. ÐÐ»ÑÑÐµÐ²ÑÐµ ÑÐ»Ð¾Ð²Ð°: Ð½Ð°Ð½Ð¾Ð¿ÑÐ¾Ð²Ð¾Ð»Ð¾ÐºÐ°; Ð½Ð°Ð¿ÑÑÐ¶ÐµÐ½Ð¸Ñ Ð½ÐµÑÐ¾Ð¾ÑÐ²ÐµÑÑÑÐ²Ð¸Ñ; ÑÐµÐ»Ð°ÐºÑÐ°ÑÐ¸Ñ Ð½Ð°Ð¿ÑÑÐ¶ÐµÐ½Ð¸Ð¹; ÐºÐ¾Ð¼Ð¿Ð¾Ð·Ð¸ÑÐ½Ð°Ñ Ð½Ð°Ð½Ð¾Ð¿ÑÐ¾Ð²Ð¾Ð»Ð¾ÐºÐ° ÑÐ¸Ð¿Ð° Â«ÑÐ´ÑÐ¾-Ð¾Ð±Ð¾Ð»Ð¾ÑÐºÐ°Â»; Ð´Ð¸ÑÐ»Ð¾ÐºÐ°ÑÐ¸Ñ Ð½ÐµÑÐ¾Ð¾ÑÐ²ÐµÑÑÑÐ²Ð¸Ñ; Ð²ÐºÐ»ÑÑÐµÐ½Ð¸Ðµ Ð² Ð²Ð¸Ð´Ðµ Ð¼Ð½Ð¾Ð³Ð¾ÑÐ³Ð¾Ð»ÑÐ½Ð¾Ð¹ Ð¿ÑÐ¸Ð·Ð¼Ñ. ÐÐ±ÑÐµÐºÑ Ð¸ÑÑÐ»ÐµÐ´Ð¾Ð²Ð°Ð½Ð¸Ñ: ÑÐµÐ»Ð°ÐºÑÐ°ÑÐ¸Ñ Ð¾ÑÑÐ°ÑÐ¾ÑÐ½ÑÑ Ð½Ð°Ð¿ÑÑÐ¶ÐµÐ½Ð¸Ð¹ Ð² Ð¿ÐµÐ½ÑÐ°Ð³Ð¾Ð½Ð°Ð»ÑÐ½ÑÑ Ð½Ð°Ð½Ð¾Ð¿ÑÐ¾Ð²Ð¾Ð»Ð¾ÐºÐ°Ñ Ð·Ð° ÑÑÐµÑ Ð·Ð°ÑÐ¾Ð¶Ð´ÐµÐ½Ð¸Ñ Ð¿ÐµÐ½ÑÐ°Ð³Ð¾Ð½Ð°Ð»ÑÐ½Ð¾Ð³Ð¾ Ð²ÐºÐ»ÑÑÐµÐ½Ð¸Ñ. Ð¦ÐµÐ»Ñ Ð¸ÑÑÐ»ÐµÐ´Ð¾Ð²Ð°Ð½Ð¸Ñ: ÑÐ°Ð·ÑÐ°Ð±Ð¾ÑÐºÐ° ÑÐµÐ¾ÑÐµÑÐ¸ÑÐµÑÐºÐ¾Ð¹ Ð¼Ð¾Ð´ÐµÐ»Ð¸ ÑÐµÐ»Ð°ÐºÑÐ°ÑÐ¸Ð¸ Ð¾ÑÑÐ°ÑÐ¾ÑÐ½ÑÑ Ð½Ð°Ð¿ÑÑÐ¶ÐµÐ½Ð¸Ð¹ Ð² Ð¿ÐµÐ½ÑÐ°Ð³Ð¾Ð½Ð°Ð»ÑÐ½ÑÑ Ð½Ð°Ð½Ð¾Ð¿ÑÐ¾Ð²Ð¾Ð»Ð¾ÐºÐ°Ñ Ð·Ð° ÑÑÐµÑ Ð·Ð°ÑÐ¾Ð¶Ð´ÐµÐ½Ð¸Ñ Ð²ÐºÐ»ÑÑÐµÐ½Ð¸Ñ Ñ ÑÑÐµÑÐ¾Ð¼ ÑÐ°ÐºÐ¾Ð¹ Ð¾ÑÐ¾Ð±ÐµÐ½Ð½Ð¾ÑÑÐ¸ ÑÑÑÑÐºÑÑÑÑ ÐºÐ°Ðº ÑÐµÐ°Ð»ÑÐ½Ð°Ñ Ð¾Ð³ÑÐ°Ð½ÐºÐ° Ð²ÐºÐ»ÑÑÐµÐ½Ð¸Ñ. Ð ÐµÐ·ÑÐ»ÑÑÐ°ÑÑ Ð¸ÑÑÐ»ÐµÐ´Ð¾Ð²Ð°Ð½Ð¸Ñ: ÐÑÐµÐ´Ð»Ð¾Ð¶ÐµÐ½Ð° ÑÐµÐ¾ÑÐµÑÐ¸ÑÐµÑÐºÐ°Ñ Ð¼Ð¾Ð´ÐµÐ»Ñ, Ð¾Ð¿Ð¸ÑÑÐ²Ð°ÑÑÐ°Ñ ÑÐµÐ»Ð°ÐºÑÐ°ÑÐ¸Ñ Ð¾ÑÑÐ°ÑÐ¾ÑÐ½ÑÑ Ð½Ð°Ð¿ÑÑÐ¶ÐµÐ½Ð¸Ð¹ Ð² Ð¿ÐµÐ½ÑÐ°Ð³Ð¾Ð½Ð°Ð»ÑÐ½Ð¾Ð¹ Ð½Ð°Ð½Ð¾Ð¿ÑÐ¾Ð²Ð¾Ð»Ð¾ÐºÐµ Ð·Ð° ÑÑÐµÑ Ð·Ð°ÑÐ¾Ð¶Ð´ÐµÐ½Ð¸Ñ ÑÐ¾Ð¾ÑÐ½Ð¾Ð³Ð¾ Ð´Ð¸Ð»Ð°ÑÐ°ÑÐ¸Ð¾Ð½Ð½Ð¾Ð³Ð¾ Ð²ÐºÐ»ÑÑÐµÐ½Ð¸Ñ, Ð¸Ð¼ÐµÑÑÐµÐ³Ð¾ Ð¾Ð³ÑÐ°Ð½ÐºÑ Ð² Ð²Ð¸Ð´Ðµ Ð¿ÑÐ°Ð²Ð¸Ð»ÑÐ½Ð¾Ð¹ Ð¿ÑÑÐ¸ÑÐ³Ð¾Ð»ÑÐ½Ð¾Ð¹ Ð¿ÑÐ¸Ð·Ð¼Ñ, Ð¾Ð¿ÑÐµÐ´ÐµÐ»ÐµÐ½Ñ ÑÐ½ÐµÑÐ³Ð¸Ñ Ð²Ð·Ð°Ð¸Ð¼Ð¾Ð´ÐµÐ¹ÑÑÐ²Ð¸Ñ n-ÑÐ³Ð¾Ð»ÑÐ½Ð¾Ð³Ð¾ Ð²ÐºÐ»ÑÑÐµÐ½Ð¸Ñ Ñ Ð¿Ð¾Ð»ÐµÐ¼ ÐºÐ»Ð¸Ð½Ð¾Ð²Ð¾Ð¹ Ð´Ð¸ÑÐºÐ»Ð¸Ð½Ð°ÑÐ¸Ð¸ Ð² ÑÐ¸Ð»Ð¸Ð½Ð´ÑÐµ (Ð°Ð½Ð°Ð»Ð¸ÑÐ¸ÑÐµÑÐºÐ¸) Ð¸ ÑÐ¿ÑÑÐ³Ð°Ñ ÑÐ½ÐµÑÐ³Ð¸Ñ n-ÑÐ³Ð¾Ð»ÑÐ½Ð¾Ð³Ð¾ Ð²ÐºÐ»ÑÑÐµÐ½Ð¸Ñ Ð² ÑÐ¸Ð»Ð¸Ð½Ð´ÑÐµ (ÑÐ¸ÑÐ»ÐµÐ½Ð½Ð¾). ÐÐ¾ÐºÐ°Ð·Ð°Ð½Ð¾, ÑÑÐ¾ Ð² ÑÐ»ÑÑÐ°Ðµ, ÐºÐ¾Ð³Ð´Ð° Ð²ÐµÑÑÐ¸Ð½Ñ n-ÑÐ³Ð¾Ð»ÑÐ½Ð¾Ð³Ð¾ Ð²ÐºÐ»ÑÑÐµÐ½Ð¸Ñ ÑÐ°ÑÐ¿Ð¾Ð»Ð°Ð³Ð°ÑÑÑÑ Ð½Ð° ÑÐ²Ð¾Ð±Ð¾Ð´Ð½Ð¾Ð¹ Ð¿Ð¾Ð²ÐµÑÑÐ½Ð¾ÑÑÐ¸ ÑÐ¸Ð»Ð¸Ð½Ð´ÑÐ°, ÑÐ°ÑÑÐ¼Ð°ÑÑÐ¸Ð²Ð°ÐµÐ¼ÑÐµ ÑÐ½ÐµÑÐ³Ð¸Ð¸ Ð¿ÑÐ¸Ð½Ð¸Ð¼Ð°ÑÑ Ð½ÐµÐ½ÑÐ»ÐµÐ²Ð¾Ðµ Ð·Ð½Ð°ÑÐµÐ½Ð¸Ðµ. Ð ÑÐ»ÑÑÐ°Ðµ Ð¼Ð½Ð¾Ð³Ð¾ÑÐ³Ð¾Ð»ÑÐ½Ð¸ÐºÐ° Ñ Ð±Ð¾Ð»ÑÑÐ¸Ð¼ ÐºÐ¾Ð»Ð¸ÑÐµÑÑÐ²Ð¾Ð¼ ÑÐ³Ð»Ð¾Ð², Ð¿ÑÐ¸ n â â Ð·Ð°Ð²Ð¸ÑÐ¸Ð¼Ð¾ÑÑÐ¸ ÑÐ¿ÑÑÐ³Ð¾Ð¹ ÑÐ½ÐµÑÐ³Ð¸Ð¸ Ð¸ ÑÐ½ÐµÑÐ³Ð¸Ð¸ Ð²Ð·Ð°Ð¸Ð¼Ð¾Ð´ÐµÐ¹ÑÑÐ²Ð¸Ñ ÑÑÑÐµÐ¼ÑÑÑÑ Ðº Ð¸Ð·Ð²ÐµÑÑÐ½ÑÐ¼ Ð·Ð°Ð²Ð¸ÑÐ¸Ð¼Ð¾ÑÑÑÐ¼ Ð´Ð»Ñ ÐºÑÑÐ³Ð¾Ð²Ð¾Ð³Ð¾ Ð²ÐºÐ»ÑÑÐµÐ½Ð¸Ñ; ÑÐ¿ÑÑÐ³Ð°Ñ ÑÐ½ÐµÑÐ³Ð¸Ñ n-ÑÐ³Ð¾Ð»ÑÐ½Ð¾Ð³Ð¾ Ð²ÐºÐ»ÑÑÐµÐ½Ð¸Ñ Ð² ÑÐ¸Ð»Ð¸Ð½Ð´ÑÐµ Ð¸ ÑÐ½ÐµÑÐ³Ð¸Ñ Ð²Ð·Ð°Ð¸Ð¼Ð¾Ð´ÐµÐ¹ÑÑÐ²Ð¸Ñ n-ÑÐ³Ð¾Ð»ÑÐ½Ð¾Ð³Ð¾ Ð²ÐºÐ»ÑÑÐµÐ½Ð¸Ñ Ñ Ð¿Ð¾Ð»ÐµÐ¼ ÐºÐ»Ð¸Ð½Ð¾Ð²Ð¾Ð¹ Ð´Ð¸ÑÐºÐ»Ð¸Ð½Ð°ÑÐ¸Ð¸ Ð² ÑÐ¸Ð»Ð¸Ð½Ð´ÑÐµ Ð¼Ð¾Ð³ÑÑ Ð±ÑÑÑ Ð°Ð¿Ð¿ÑÐ¾ÐºÑÐ¸Ð¼Ð¸ÑÐ¾Ð²Ð°Ð½Ñ Ð¸Ð·Ð²ÐµÑÑÐ½ÑÐ¼Ð¸ Ð²ÑÑÐ°Ð¶ÐµÐ½Ð¸ÑÐ¼Ð¸ Ð´Ð»Ñ Ð°Ð½Ð°Ð»Ð¾Ð³Ð¸ÑÐ½ÑÑ ÑÐ½ÐµÑÐ³Ð¸Ð¹ ÐºÑÑÐ³Ð¾Ð²Ð¾Ð³Ð¾ Ð²ÐºÐ»ÑÑÐµÐ½Ð¸Ñ Ð² ÑÐ»ÑÑÐ°Ðµ, ÐµÑÐ»Ð¸ Ð²ÐºÐ»ÑÑÐµÐ½Ð¸Ñ Ð¸Ð¼ÐµÑÑ ÑÐ°Ð²Ð½ÑÐµ Ð¿Ð»Ð¾ÑÐ°Ð´Ð¸ Ð¿Ð¾Ð¿ÐµÑÐµÑÐ½Ð¾Ð³Ð¾ ÑÐµÑÐµÐ½Ð¸Ñ. ÐÐµÐ»Ð¸ÑÐ¸Ð½Ð° ÑÐ½ÐµÑÐ³Ð¸Ð¸ Ð¼ÐµÐ¶ÑÐ°Ð·Ð½ÑÑ Ð¸ Ð´Ð²Ð¾Ð¹Ð½Ð¸ÐºÐ¾Ð²ÑÑ Ð³ÑÐ°Ð½Ð¸Ñ ÑÐ¸Ð»ÑÐ½Ð¾ Ð²Ð»Ð¸ÑÐµÑ Ð½Ð° Ð¿ÑÐ¾ÑÐµÑÑ ÑÐµÐ»Ð°ÐºÑÐ°ÑÐ¸Ð¸; Ð½Ð°Ð¿ÑÐ¸Ð¼ÐµÑ, Ð² ÑÐ»ÑÑÐ°Ðµ ÑÑÐ°Ð²Ð½Ð¸ÑÐµÐ»ÑÐ½Ð¾ Ð±Ð¾Ð»ÑÑÐ¾Ð³Ð¾ Ð²ÐºÐ»Ð°Ð´Ð° ÑÐ½ÐµÑÐ³Ð¸Ð¸ Ð³ÑÐ°Ð½Ð¸Ñ (~Gb/20) ÐºÑÐ¸ÑÐ¸ÑÐµÑÐºÐ¸Ð¹ ÑÐ°Ð´Ð¸ÑÑ Ð½Ð°Ð½Ð¾Ð¿ÑÐ¾Ð²Ð¾Ð»Ð¾ÐºÐ¸ ÑÐ¾ÑÑÐ°Ð²Ð¸Ñ Ð¿ÑÐ¸Ð¼ÐµÑÐ½Ð¾ 440b, Ð° Ð² ÑÐ»ÑÑÐ°Ðµ ÑÑÐ°Ð²Ð½Ð¸ÑÐµÐ»ÑÐ½Ð¾ Ð¼Ð°Ð»Ð¾Ð³Ð¾ Ð²ÐºÐ»Ð°Ð´Ð° (~Gb/50) â Ð¿ÑÐ¸Ð¼ÐµÑÐ½Ð¾ 180b.
description: The master thesis contains 49 pages, 29 drawings, 20 formulas and 81 sources of literature. Keywords: nanowire; mismatch stresses; stress relaxation; core-shell composite nanowire; mismatch dislocation; inclusion as a polygonal prism. Object of research: relaxation of residual stresses in pentagonal nanowires due to the origin of pentagonal inclusion. The aim of the research is to develop a theoretical model for relaxation of residual stresses in pentagonal nanowires due to the generation of inclusions, taking into account such features of the structure as the real facet of the inclusion. Research result: The proposed theoretical model describing the relaxation of residual stresses in pentagonal nanowire due to the birth of a coaxial dilated inclusion with a cut in the form of a right pentagonal prism, determined by the interaction energy of the n-carbonic inclusions with the field of wedge disclinations in the cylinder (analytically) and the elastic energy of the n-carbonic inclusions in the cylinder (numerical). It is shown that in the case when the vertices of the n-carbon inclusion are located on the free surface of the cylinder, the considered energies take a non-zero value. In the case of a polygon with a large number of angles, for nââ, the elastic energy and interaction energy dependences tend to the known dependences for circular inclusion; the elastic energy of an n-carbon inclusion in a cylinder and the interaction energy of an n-carbon inclusion with a wedge deflection field in a cylinder can be approximated by known expressions for similar circular inclusion energies if the inclusions have equal cross-sectional areas. The energy value of the interphase and double boundaries strongly affects the relaxation process; for example, in the case of a relatively large contribution of boundary energy (~Gb / 20), the critical radius of the nanowire will be about 440b, and in the case of a relatively small contribution (~Gb/50) â about 180b.