Stress analysis of finned tubes subjected to die expansion

Abstract

In this study, an analytical approach is developed to estimate the force required to expand tubes for different die shapes. The stress distribution in the contact and transition zones is estimated using the analytical approach based on a combined Prandtl Reuss flow rule and self-adaption of the stress strain curve. The driving force is predicted based on the transition and contact zone information. This new approach greatly reduces the difficulty of the analysis and simplifies the calculation. The approach is validated using four different numerical axisymmetric finite element models of different sizes, materials, and die shapes subjected to push and pull of the die. Additionally, stainless steel and copper 3/8 in. diameter tubes are expanded with an oval die in an experimental test bench under both push and pull conditions. The tangential and longitudinal strains and driving force are monitored and recorded during the expansion process. The results from the three approaches show a very good agreement. This research work also investigates the elastics-plastic behavior and estimates the residual stress state of tubes subjected to the die expansion process. The stresses and deformations of the expanded SS316L tube are analyzed numerically using the finite element method. The expansion and contraction processes are modeled considering elastic-plastic material behavior for different die sizes. The maximum longitudinal, tangential and contact stresses are evaluated to verify the critical stress state of the joint during the expansion process. The importance of the material behavior in evaluating the residual stresses using kinematic and isotropic hardening is addressed. Finally, an experiment is conducted to assess the tangential and longitudinal strains of a 3/8 stainless steel subjected to expansion with an oval shape die. Last, the quality of the fin-to-tube assembly is investigated as it is a common type of connection in heat exchangers. During the assembly process, a die or an expander is used to expand the tube and close the gap between the tube and the fin collar for improved heat transfer. The amounts of interference and contact area created depend on both the radial expansion from the die and initial gap, as well as the shape of the fin contact area with the tube before expansion. However, recent research has revealed that the contact adhesion between the surfaces is not consistent across the width. This results in a reduction of heat transfer through conduction and a compromise of the heat exchanger efficiency. The objective of this last part of the research work is to establish a relationship between the fin hole profile shape and contact quality and to provide suggestions for enhancing the tube-to-fin connection. The simulations involve tubes made of various materials, dies of different sizes, and fins with hourglass-shaped collars, all of which are assessed using finite element models. The size of the micro gaps at the tube-to-fin interface is used to determine the quality of the contact surface, while a local transient thermal contact FEA model are used to assess the contact thermal conductive performance in the presence of micro-gaps.

Date	12 Sept 2023
Original language	American English
Awarding Institution	École de technologie supérieure
Supervisor	Hakim A. Bouzid (Supervisor)