METHOD OF ESTIMATING PLASTIC DEFORMATION DISTRIBUTIONS AT THE FATIGUE CRACK TIP BASED ON THE SOLUTION OF LINEAR ELASTICITY THEORY

A.N. Vshivkov, A.Yu. Iziumova, I.A. Panteleev, O.A. Plekhov

Author details

A.N. Vshivkov
Institute of Continuous Media Mechanic Ural Branch of Russian Academy of Science, Perm, Russian Federation
A.Yu. Iziumova
Institute of Continuous Media Mechanic Ural Branch of Russian Academy of Science, Perm, Russian Federation
I.A. Panteleev
Institute of Continuous Media Mechanic Ural Branch of Russian Academy of Science, Perm, Russian Federation
O.A. Plekhov
Institute of Continuous Media Mechanic Ural Branch of Russian Academy of Science, Perm, Russian Federation

https://doi.org/10.15593/perm.mech/2023.6.04

In this paper, an experimental study of the strain fields at the fatigue crack tip was carried out. The strain fields were measured by an optical camera based on the digital image using the correlation method. Images were recorded using a Basler acA2440-75uc optical camera with a TC23007 OptoEngineering lens to achieve a spatial resolution of at least 3 µm. Recording frequency was 100 Hz. The possibility of using the solution of the linear singularity problem of elasticity theory to estimate the distribution of plastic strain at the fatigue crack tip was shown. Mechanical tests of uniaxial cyclic deformation with simultaneous registration of the strain field at the crack tip of different lengths were carried out on flat specimens of titanium alloys Ti Grade 2, Ti-1.1Al-0.9Mn, Ti Grade 9. The specimens were loosened by means of a lateral semicircular notch in order to localize the crack. The solution of the problem of a specimen with a notch in the elastic formulation was carried out numerically in the finite element modelling package Comsol Multiphysics. The peculiarity of the work is the use of the hypothesis of the functional relationship between real deformations and the elastic solution and the value of the secant modulus of the material to estimate the plastic deformation at the crack tip. The size of the zone of intense plastic deformations at the fatigue crack tip for different crack lengths was determined experimentally and numerically. By comparing the calculated and experimental data we showed the possibility of using the proposed dependence to estimate the distribution of the plastic strain field at the crack tip. The results obtained allow the analysis of the irreversible strain fields at the crack tip for mixed mode loading.

Keywords

strain fieldfatigue crack tipDixon theorydigital image correlation

О МЕТОДЕ ОЦЕНКИ РАСПРЕДЕЛЕНИЯ ПЛАСТИЧЕСКОЙ ДЕФОРМАЦИИ В ОБЛАСТИ ВЕРШИНЫ УСТАЛОСТНОЙ ТРЕЩИНЫ НА ОСНОВЕ РЕШЕНИЯ ЗАДАЧИ ЛИНЕЙНОЙ ТЕОРИИ УПРУГОСТИ

Проведено экспериментальное исследование полей деформации в вершине усталостных трещин. Измерение полей деформации проводилось при помощи оптической камеры с использованием метода корреляции цифровых изображений. Запись изображений производилась оптической камерой Basler acA2440-75uc с объективом TC23007 OptoEngineering для достижения пространственного разрешения не менее 3 мкм. Частота записи данных составляла 100 Гц. Показана возможность использования решения линейной сингулярной задачи теории упругости для оценки распределения пластической деформации в вершине усталостной трещины. Механические испытания по одноосному циклическому деформированию с одновременной регистрацией поля деформации у вершины трещины различной длины проводились на плоских образцах из технического титана ВТ1-0 и титановых сплавов ОТ4-0 и ПТ-3В. Для локализации трещины образцы были ослаблены боковым полукруглым вырезом. Решение задачи об образце с боковой трещиной в упругой постановке осуществлялось численно в пакете конечно-элементного моделирования Comsol Multiphysics. Особенностью работы является использование гипотезы о функциональной связи реальных деформаций с упругим решением и величиной секущего модуля материала для оценки пластической деформации в вершине трещины. Экспериментально и численно определён размер зоны интенсивных пластических деформаций в области вершины усталостной трещины при различной длине трещины. В результате сопоставления расчётных и экспериментальных данных была показана возможность использования предложенной зависимости для оценки распределения поля пластической деформации в вершине трещины. Полученные результаты позволят анализировать поля необратимой деформации в вершине трещины для смешанных форм нагружения.

Ключевые слова

поле деформациивершина усталостной трещиныгипотеза Диксонаметод корреляции цифровых изображений

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Article information

Published: 21 December 2023
Issue date: 21 December 2023
Issue: No. 6 (2023)