PSI - Issue 44

Ivan Marenda et al. / Procedia Structural Integrity 44 (2023) 2152–2157 Ivan Marenda et al./ Structural Integrity Procedia 00 (2022) 000–000

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2.1. Axial Behaviour In the static condition, the deformability of the joint in the axial direction is limited. The experimental observation shows that the real contact area is given by the sum of small areoles distributed at each asperity. In the hypothesis of plastic model, Cooper, Miki and Yovanovich developed a model of contact between rough surfaces. The model, although developed for the study of thermal behaviour, showed a good correspondence also in the mechanical contact field. The relationship between the real contact area and the apparent area is therefore: ! ! ! " = # " #$% (1) Furthermore, supposing that the rough surface is characterized by a Gaussian distribution of the heights starting from the mean line, we obtain ! ! ! " = √& $ ' ∫ ( ' & ( ' ' * ) = $ & ) √ * &+ * (2) The number and the average radius of the contact area are: , = ) - + . * & ( √ & '( ( ( & ' ' / ) √ * &+ * (3) = . ' / . + ( √ & '( ) √ * &+ * (4) 2.2. Tangential Behaviour If the joint is subjected to a force in the tangential direction, the relative displacement is due to the deformation of the bodies (stick condition) and the relative sliding between the surfaces (slip condition). Oden and Martins propose to divide the friction phenomenon into three categories: quasi-static, dynamic and wear-abrasion problems. In the dynamic case, after a certain number of cycles, the surfaces reach a steady state in which they do not undergo further plasticisation, so these phenomena can be treated with elastic models. In this case it shall be considered that the polymeric surfaces react with the metal modifying its friction coefficient. Furthermore, transfer phenomena may occur during sliding due to the abrasive action carried out by the asperities of the metal. In some areas the contact becomes polymer-polymer, and the friction coefficient decreases. The initial roughness of the joint is very important, and an optimal roughness value is observed at which friction reach a minimum value. For instance, European code (EN 1337-2) prescribes for a roughness (R y5i ) of the metal surface in contact with the PTFE a value of 1 µ m. In addition, another parameter to be considered in these phenomena is the operating and the glass transition temperature. The friction coefficient remains almost constant until the glass transition temperature is reached. The classic Coulomb’s theory defines a linear relationship between frictional and axial force. The friction coefficient is different in static and dynamic condition. The theory of Bowden and Tabor (1950) and Kragelskii, Dobychin and Kombalov (1982) hypothesize that the sliding resistance is due to two main causes: the development of bonds between the asperities and the mutual indentation of the asperities. Neglecting the second effect, the tangential tension results: t = 0 t 1 (5) and the coefficient of friction is: = ! ! 2 * ! ! # #$% = t * # #$% (6)