Modeling the microstructure of heat-affected zone (HAZ) in weld area can be useful in predicting mechanical behavior of the weldment. A multi-scale model is proposed to calculate the temperature distribution and to predict the microstructure evolution within the HAZ. Finite difference method was used to develop a computer model for studying the cooling curves during welding, and a stochastic method to analyze the austenite formation and its grain growth in HAZ. The droplet of liquid metal detached from electrode in manual arc metal welding is an important concern in studying the temperature distribution and the austenite grains growth. Both heat content of liquid metal detached from electrode and heat generated by electrical arc were used in calculation of temperature distribution. The stochastic model simulates the austenite phase formation and its growth during welding based on the kinetics of these processes. With this model, it is possible to visualize the topology of austenite phase. This multi-scale model was applied to the welding of low alloy steel. The observed morphology was in good agreement with that predicted by the model. © 2008 Elsevier B.V. All rights reserved. 1. Introduction Microstructure of a welded joint has a significant effect on its mechanical properties. Grain growth of the austenite phase near the fusion line due to the welding heat input has detrimental effect on toughness of the welded joints. Before welding, low alloy steels mainly contain ferrite and pearlite phases (Fig. 1a). Oliveira et al. (2007) studied the kinetics and microstructural evolution of austenite formation in a low carbon steel, with initial microstructure composed of ferrite and pearlite, during continuous heating, by using dilatometric analysis and measurements of microstructural parameters. They observed that austenite formation occurs in two stages. The first stage is the dissolution of pearlite, followed by the ferrite to austenite transformation (second stage). Both transformations take place by nucleation and growth processes. ∗ Corresponding author at: Department of Metallurgy and Materials Engineering, Faculty of Engineering, Ferdowsi University of Mashhad, Mashhad, P.O. Box: 91775-1111, Iran. Fax: +98 5118763305. E-mail address: haddadm@ferdowsi.um.ac.ir (M. Haddad-Sabzevar). During welding, the pearlite starts to dissolve at about 725 ◦C (Fig. 1b) and mainly completes 750 ◦C following by austenite formation from ferrite which finishes at 860 ◦C. Different stochastic models have been developed to simulate the HAZ microstructure. In a stochastic method, a set of probabilistic numbers must be defined based on physical variables such as temperature. Therefore, in order to set up a stochastic model, the spontaneous temperature during welding must be calculated to simulate the microstructure. Shi et al. (2004) discussed the grain structure of ultra fine grain steel in weld HAZ during welding thermal cycle. They used an analytical equation for the temperature distribution. A stochastic model on the grain growth during GTA welding of titanium has been proposed by Yang et al. (2000). They calculated the effect of turbulence of liquid metal in weld pool on temperature distribution based on numerical methods. Both of these 0924-0136/$

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