Eur. Phys. J. Appl. Phys. 44, 317-322 (2008)
https://doi.org/10.1051/epjap:2008177

A dynamical model for investigation of A₃ point maximal spatial evolution during resistance spot welding using Boubaker polynomials

¹ UR Mécanique Appliquée, Ingénierie et Industrialisation (MA2I), ENIT, Tunisia
² ESSTT, 63 rue Sidi Jabeur, 5100 Mahdia, Tunisia

Corresponding author: boubaker_karem@yahoo.com

Received: 12 April 2008
Revised: 26 August 2008
Accepted: 29 August 2008
Published online: 24 October 2008

Abstract

This paper presents a dynamical non linear model of the spatial time-dependant evolution of A₃ point during a particular sequence of resistance spot welding in steel material. The model is based on a solution to the heat equation, expressed in cylindrical coordinates inside the joint area, and when the source term is attributed to the electrical power. By the mean of the steel binary Fe–C diagram and the deduced t-dependant temperature rise profile, an estimation of the A₃ point spatial range date is given and compared to further results. The obtained temperature profile is yielded, taking into account main parameters variations, as a guide to non-destructive protocols and thermal characteristics investigation