ELASTOPLASTIC TENSION PROBLEM FOR A PLATE WITH A CIRCULAR HOLE WITH ACCOUNT FOR CRACK NUCLEATION IN AN ELASTIC DEFORMATI
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ELASTOPLASTIC TENSION PROBLEM FOR A PLATE WITH A CIRCULAR HOLE WITH ACCOUNT FOR CRACK NUCLEATION IN AN ELASTIC DEFORMATION REGION V. M. Mirsalimov
UDC 539.375
Abstract: A plane elastoplastic problem related to stress distribution in a thin plate with a circular hole is considered with account for nucleation and development of cracks in an elastic region. It is assumed that the circular hole is located in the plastic deformation region. It is considered that loading is accompanied by crack nucleation and the fracture of the plate material in the elastic deformation region of the plate. The problem is solved using the perturbation theory and the theory of singular integral equations. Keywords: thin plate, elastoplastic problem, interface between elastic and plastic deformations, pre-fracture zone, crack nucleation. DOI: 10.1134/S0021894420040185
INTRODUCTION A plane stress state occurs in a thin plate loaded with forces acting in its plane. Because the plate thickness is small compared to cross-sectional dimensions and the front surfaces of the plate are free from external loads, stress tensor components σz , τxz , and τyz are small as compared to stress tensor components σx , σy , and τxy , which slightly vary in thickness. Stresses σx , σy , and τxy may be replaced by their average thickness values, and stresses σz , τxz , and τyz may be assumed as equal to zero. Next, the plate thickness is taken to be equal to unity. At sufficiently large external tensile loads, an area of plastic deformation forms around the hole. It is quite important to account for plastic deformation zones when calculating structures and buildings for strength. The complexity of elastoplastic problems is that the shape and size of a plastic region are unknown and should be determined. Solutions of elastoplastic problems for bodies weakened by holes located in a plastic deformation zone are given in [1–4]. In [5, 6], an exact solution of the elastoplastic problem for a thin plate with one circular hole is obtained under the Tresca–Saint-Venant plasticity condition. It is shown that a boundary between the zones of elastic and plastic deformation is an oval. A stress function U representing the stresses in the plastic deformation zone is not biharmonic. In [7–9], problems for determining the boundaries separating the zones of elastic and plastic deformation of an unbounded thin plate being in a plane stress state and weakened by two (periodic and doubly periodic) systems of identical circular holes are considered.
Azerbaijan Technical University, AZ1073 Baku, Azerbaijan; [email protected]. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 61, No. 4, pp. 162–173, July–August, 2020. Original article submitted November 18, 2019; revision submitted November 18, 2019; accepted for publication March 2, 2010. c 2020 by Pleiades Publishing, Ltd. 0021-8944/20/6104-0641
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During the operation of structural elements in the form of thin plates, it was established that a crack nucleates in the plate material, leading to its fracture.
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