Analysis of cracks in the fields of elastic stresses from wedge disclinations

Sergey V. Kirikov, Aleksandr S. Pupynin, Vladimir N. Perevezentsev

Author details

Sergey V. Kirikov
Mechanical Engineering Research Institute, Nizhni Novgorod, Russian Federation
Aleksandr S. Pupynin
Mechanical Engineering Research Institute, Nizhni Novgorod, Russian Federation
Vladimir N. Perevezentsev
Mechanical Engineering Research Institute, Nizhni Novgorod, Russian Federation

https://doi.org/10.15593/perm.mech/2025.5.02

The article is devoted to the development of mathematical methods for analyzing cracks that occur in polycrystalline solids under the action of stress fields created by wedge disclinations. A method is proposed for calculating the main crack characteristics, such as the density of the Burgers vector of virtual dislocations, stress intensity factors at the crack tips, and the crack faces opening function, for an arbitrary disclination location. The method is based on replacing the solution for the initial disclination with a superposition of the solution for the disclination with a known analytical expression and the solution for a continuous wall of edge dislocations. As a result of applying this method, exact analytical expressions are obtained for the specified parameters in the case where the disclination is located on the crack axis, as well as asymptotic expressions for the stress intensity factors of the crack in the elastic field created by the disclination located near the tip. A comparative analysis of dislocation and disclination cracks is carried out, revealing their fundamental difference: when entering a crack, a dislocation is spread out in the form of a distribution of virtual dislocations along the crack and ceases to exist as a localized defect. In contrast, the disclination remains as an independent source of stress, which is only partially screened by virtual dislocations. The fields of elastic stresses from a disclination crack are calculated, the influence of the disclination position on its interaction with the lattice dislocation is analyzed. It was found that the dependence of the interaction force on the distance between the lattice dislocation and the crack tip is alternating and non-monotonic nature. The results of the study are valuable for developing methods for predicting fracture in materials obtained by severe plastic deformation.

Keywords

disclinationcrackstress intensity factorsdislocationelastic stress fieldssevere plastic deformationfracture.

АНАЛИЗ ТРЕЩИН В ПОЛЯХ УПРУГИХ НАПРЯЖЕНИЙ ОТ КЛИНОВЫХ ДИСКЛИНАЦИЙ

Разработаны математические методы анализа трещин, возникающих в поликристаллических твердых телах под действием полей напряжений, создаваемых клиновыми дисклинациями. Предложен метод расчета основных характеристик трещины, таких как плотность вектора Бюргерса виртуальных дислокаций, коэффициенты интенсивности напряжений в вершинах трещины и функция раскрытия берегов, при произвольном расположении дисклинации. Метод основан на замене решения для исходной дисклинации на суперпозицию решения для дисклинации с известным аналитическим выражением и решения для непрерывной стенки краевых дислокаций. В результате применения данного метода получены точные аналитические выражения для указанных параметров в случае, когда дисклинация находится на оси трещины, а также асимптотические выражения для коэффициентов интенсивности напряжений трещины в упругом поле, создаваемом дисклинацией, расположенной вблизи вершины. Проведен сравнительный анализ дислокационной и дисклинационной трещин, выявивший их принципиальное различие: при попадании в трещину дислокация размазывается в виде распределения виртуальных дислокаций вдоль трещины и перестает существовать как локализованный дефект. В отличие от этого, дисклинация сохраняется как независимый источник напряжений, который лишь частично экранируется виртуальными дислокациями. Рассчитаны поля упругих напряжений от дисклинационной трещины, проанализировано влияние положения дисклинации на ее взаимодействие с решеточной дислокацией. Обнаружено, что зависимость силы взаимодействия от расстояния между решеточной дислокацией и вершиной трещины носит знакопеременный и немонотонный характер. Результаты исследования представляют ценность для разработки методов прогнозирования разрушения в материалах, полученных методами интенсивной пластической деформации.

Ключевые слова

дисклинациятрещинакоэффициенты интенсивности напряженийдислокацияполя упругих напряженийбольшие пластические деформацииразрушение.

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Article information

Published: 17 December 2025
Issue date: 17 December 2025
Issue: No. 5 (2025)