INTELLIGENCE OF VARIABLE YOUNG’S MODULUS ON RESIDUAL STRESSES INDUCED BY ROTATIONAL AUTOFRETTAGE OF A TUBE WITH FIXED ENDS

Author details

A.N. Prokudin
Institute of Machinery and Metallurgy, Komsomolsk-on-Amur, Russian Federation

https://doi.org/10.15593/perm.mech/2023.6.09

Autofrettage processes are designed to strengthen hollow cylindrical and spherical parts and usually consist of one load-unload cycle. At the first stage, the workpiece is loaded to cause either partial or complete plastic deformations. During unloading, residual compressive stresses are formed in the vicinity of the inner surface of a part. The present work is devoted to a theoretical study of the process of rotational autofrettage of a hollow cylinder with fixed ends. The formulation of the problem is based on the theory of infinitesimal elastoplastic deformations, the Tresca plasticity condition and the flow rule associated with it. It is assumed that at the loading stage the cylinder material follows the linear-exponential law of isotropic hardening, and when unloaded it behaves as purely elastic body. The effect of a decrease in Young's modulus during unloading as a result of preliminary plastic deformation and its influence on residual stresses caused by rotational autofrettage of the cylinder are studied. To quantitatively describe the variation in Young's modulus, an exponential model with saturation is used. For the load stage, an exact analytical solution is obtained based on the Lambert W-function. Calculation of residual stresses in the cylinder is performed using the Runge-Kutta method. As an example, materials with significant decrease in Young's modulus are considered, namely aluminum alloy AA6022, steel DP980 and manganese steel. It has been established that taking into account the variable Young's modulus can lead to a significant reduction in the calculated level of residual stresses. This effect is especially important for the calculation of thick-walled cylinders and fairly high autofrettage velocities.

Keywords

rotational autofrettageelastoplasticityunloading elastic modulusisotropic hardeninginhomogeneous material

ВЛИЯНИЕ ПЕРЕМЕННОГО МОДУЛЯ ЮНГА НА ОСТАТОЧНЫЕ НАПРЯЖЕНИЯ, ВЫЗВАННЫЕ РОТАЦИОННЫМ АВТОФРЕТИРОВАНИЕМ ПОЛОГО ЦИЛИНДРА С ЗАКРЕПЛЕННЫМИ ТОРЦАМИ

Технология автофретирования предназначена для упрочнения полых деталей цилиндрической и сферической формы и обычно состоит из одного цикла нагрузки-разгрузки. На первой стадии заготовка нагружается с тем расчетом, чтобы некоторая ее часть перешла в пластическое состояние. В ходе разгрузки в окрестности внутренней поверхности заготовки формируется поле остаточных сжимающих напряжений. Настоящая работа посвящена теоретическому исследованию процесса ротационного автофретирования полой цилиндрической заготовки с закрепленными торцами. Постановка задачи основана на теории малых упругопластических деформаций, условии пластичности Треска и ассоциированном с ним законе течения. Предполагается, что на стадии нагрузки материал цилиндра следует линейно-экспоненциальному закону изотропного упрочнения, а при разгрузке ведет себя как чисто упругое тело. Исследуется эффект снижения модуля Юнга при разгрузке в результате предварительного пластического деформирования и его влияние на остаточные напряжения, вызванные ротационным автофретированием цилиндра. Для количественного описания падения модуля Юнга используется экспоненциальная модель с насыщением. Для стадии нагрузки получено точечное аналитическое решение на основе W-функции Ламберта. Расчет остаточных напряжений в цилиндре осуществляется с помощью метода Рунге – Кутты. В качестве примера рассмотрены материалы, у которых достаточно ярко выражено падение модуля Юнга: алюминиевый сплав АА6022, сталь DP980 и марганцевая сталь. Установлено, что учет переменного модуля Юнга может приводить к существенному снижению расчетного уровня остаточных напряжений. Данный эффект особенно важно для расчета толстостенных цилиндров и достаточно высоких скоростей автофретирования.

Ключевые слова

ротационное автофретированиеупругопластичностьмодуль Юнга при разгрузкеизотропное упрочнениенеоднородный материал

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Article information

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