PSI - Issue 50

2

Dmitry Parshin et al. / Procedia Structural Integrity 50 (2023) 314–319 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

315

Nomenclature t

time variable

radial and circular (angular) coordinates

,

 

 C specific (per unit load) creep resource of the material at its very large age (Parshin, 2020) C  overall change of the material specific creep resource due to aging (Parshin, 2020) G  overall change of the material elastic modulus of the second kind due to aging (Parshin, 2020) ( ) t  angular velocity of the body rotation during the coating creation 0 a radius of the cylindrical surface to be coated ( ) a t current internal radius of the coating being created  dimensionless spatial variable changing throughout the radial direction in the coating ply ,0   initial hoop stress in the applied material during the process of layerwise coating creation     , current radial and hoop stress in the coating being created ( ) p t law of change of the contact pressure between the body surface and the coating being created on it 1. Introduction The manufacture of a coating on a product surface in any additive technological process occurs by the layerwise creation of a solid ply of the appropriate shape as the result of successive adding thin layers of new material onto the surface of the body representing the considered product. Such bodies with gradually increasing coatings, according to the already established terminology, are commonly called growing bodies in mechanics of solids (Arutyunyan et al, 1991). Due to various physicochemical processes proceeding in the material added to the body during its solidification (the entry of the material into the composition of the solid being created), as well as due to external effects on this material and on the rest of the solid that accompany the performed technological process, significant stresses may evolve throughout the entire compound body during the considered additive manufacture process. The stresses of this kind, being the stresses of technological nature, will cause a certain stress-strain state of the finished product even when any effects on it are absent, which is conditioned by the strain incompatibility in every growing body as a whole continuum (Arutyunyan et al, 1991; Arutyunyan and Manzhirov, 1999). This condition, of course, should not be ignored when analyzing the properties and functional characteristics of the resulting coated product, when calculating its strength and durability, when setting and solving various operational wear and contact problems for it (Manzhirov and Kazakov, 2018; Hakobyan et al, 2020; Kazakov and Sahakyan, 2020; Kazakov and Kurdina, 2021). At the same time, as follows from numerous studies carried out in the field of mechanics of growing deformable bodies (see, for example, articles by Manzhirov and Chernysh (1992), Manzhirov (1995, 2017), Parshin (2017), Manzhirov and Mikhin (2018), Manzhirov and Parshin (2018), Parshin (2020), Kazakov and Parshin (2022) as well as sources cited in these articles), additive technological processes are characterized by many remarkable possibilities for controlling the stress state of the resulting products using a variety of effects on them during their creation including, not least of all, mechanical effects. 2. Aim of the study One of the mentioned effects may be the regulated evoking some non-zero initial stresses in the material added to the growing body, which are to change according to certain given programs during the growth process. The present work aims to demonstrate examples of controlling by means of this type of mechanical effects the resulting stress state of arbitrarily thick coatings being additively (layer-by-layer) created on cylindrical surfaces of structural elements and machine parts. It is assumed that the starting elementary layer of the material is applied to the inner side of a circular cylindrical surface of the radius 0 a belonging to a perfectly rigid body (we neglect the suppleness of this body in comparison with that of the coating created on it). Successive addition of further elementary layers leads to a change over time t in the internal radius a of the product being created. In consequence of the relative thinness of each added elementary layer, this change can be considered continuous.