PSI - Issue 25

A.Yu. Smolin et al. / Procedia Structural Integrity 25 (2020) 477–485

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A.Yu. Smolin et al. / Structural Integrity Procedia 00 (2019) 000 – 000

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(Kirtane et al., 2013). The development of new coatings that do not cause unpredicted reactions of the body is an urgent task ( Bønaa et al., 2016). One of the promising areas in such an application is the use of porous silicon coatings on self-expanding stents made of nickel-titanium shape memory alloy (nitinol). To create silicon coatings on various substrates, methods of plasma-chemical deposition, gas, liquid-phase or molecular-beam epitaxy, sublimation deposition, sol-gel technology, magnetron sputtering, vacuum arc evaporation, ion beam sputtering and pulsed laser deposition of coatings are used. The structure and properties of the coatings are very sensitive to the methods of application and technological parameters. Kashin et al. (2018) suggested using for this purpose such an effective method for the formation of various coatings as plasma-immersion ion implantation and deposition (Chu, 2013), which is practically not used for the application of silicon coatings. The ultimate goal of the authors of this paper is to clarify the possibility of creating porous silicon coatings on self-expanding titanium nickelide stents, which possess all the requirements for placement of drugs in the pores. The main objective of the present paper is to numerically study the strength properties and the peculiarities of fracture and delamination of a silicon coating on nitinol bar under the three-point flexural test. For detailed modeling the material behavior the multiscale approach should be used (Kondov and Sutmann, 2013). Dmitrirev et al. (2016, 2019) showed that the molecular dynamics method could be effectively used for correct simulation of silica coatings and films at microscale but it strongly depends on the force fields chosen for inter-atomic interaction (Dmitrirev, 2018). Shilko et al. (2015) suggested that particle-based methods could be used for the correct description of the structured materials at meso and macroscale as well. That is why we chose the method of movable cellular automata for this research. Eremina et al. (2017) convinced that this method works well at least for studying the deformation of nitinol stents. Smolin et al. (2014, 2015) made good use of this method for studying the effect of porous space structure of zirconia ceramics as well as the structure of ceramics based composites on the effective elastic and strength properties of the materials. The methods based on a discrete representation of material have been successfully being developed and widely used. The method of movable cellular automata (MCA) is a new and effective method in particle computational mechanics, which assumes that the material consists of a set of elementary objects (automata), interacting with the forces determined in accordance with the rules of many-particle approach. MCA allows one to simulate the mechanical behavior of a solid at different scales, including deformation, initiation, and propagation of damages, fracture and further interaction of fragments after failure as shown by Shilko et al (2015) and Smolin et al. (2018). In MCA, the automaton motion is governed by the Newton-Euler equations: 2. Movable Cellular Automaton Method

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where R i ,  i , m i and Ĵ i are the location vector, rotation velocity, mass and moment of inertia of i th automaton, respectively; F ij pair is the interaction force of the pair of i th and j th automata; and F i  is the volume-dependent force acting on i th automaton and depending on the interaction of its neighbors with the remaining automata. In the latter equation, M ij = q ij ( n ij  F ij pair ) + K ij , where q ij is the distance from the center of i th automaton to the point of its interaction (“contact”) with j th automaton, n ij = ( R j − R i )/ r ij is the unit vector directed from the center of i th automaton to the j th one and r ij is the distance between automata centers (Fig. 1), K ij is the torque caused by relative rotation of automata in the pair as shown below. Note that the automata of the pair may represent the parts of different bodies or one consolidated body. Therefore its interaction is not always really contact one. That is why we put the word “contact” in quotation marks. More of that, as it is shown in Fig. 1, the size of the automaton is characterized by one parameter d i , but it does not mean that the shape of the automaton is spherical. The real shape of the automaton is determined by the area of its “contacts”