539.375

антиплоска деформація
пластична смуга
кутова точка
конформне відображення
задача Келдиша-Сєдова
anti-plane deformation
plastic zone
angular point
conformal mapping (angle diagram)
Keldysh-Sedov problem

Отримано аналітичний розв’язок антиплоскої пружно-пластичної задачі про розвиток пластичних шарів для ідеально пружно-пластичної смуги з кутовими точками на її межі. Знайдено довжину пластичних шарів залежно від величини зосередженої сили, прикладеної на великій відстані від вершин кутів. Визначено критичне навантаження, за якого настає пластичне руйнування смуги.
Investigations of plastic areas in the strain concentrators threshold is still the main problem of solid body mechanics and fracture mechanics. They are important because of wide introduction into engineering practice high-plastic materials with high fracture toughness in which while operating considerable plastic deformation can occur. Analytical solution of anti-plane elasto-plastic problem for the ideal elasto-plastic area with angular points on its edges was obtained. Plastic deformations are considered to be localized in the layers of zero thickness on the notch angles bisectrices. The length of plastic layers as the function of concentrated force applied in great distance from angle apexes was found. Maximum load value was found under which the layers coincide, developing from the opposite notch tips and the area loses its load resistance. The less is the angle on notch tips, the less is maximum load. When the notch angle equals zero (the notch changes into mathematical section) it is minimum and equals 78% of the critical load for smooth zone. When the angle value in notch tips approaches its maximum acceptable value 90°, under which angular points disappear and zone edges become smooth, plastic areas gradually disappear as well and stress-strained state gradually becomes homogeneous. Simple formulae for the plastic layer lengths dependence on loading according to the plastic area linear model (PALM) were reduced. Their analysis testified the high accuracy of this model. For steel 0,3X14H7B with shearing yield limit 688 mPa the PALM will provide accuracy not less than 5% until the average shearing load in the zone cross-section does not exceed 75,5 mPa. Carried out investigations consider the case of maximum possible interaction of stress concentrators – the distance between concentrators in infinitely small in comparison with their dimensions. As concentrators interaction decreases the plastic area linear model accuracy, it is reasonable to consider the obtained estimations of accuracy to be the highest and not to be decreased under weaker interactions.

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