Three-dimensional monte carlo simulation of grain growth in the heat-affected zone of a 2.25Cr-1Mo steel weld
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I. INTRODUCTION
THE driving forces for grain-size change are classified into two categories. The reduction of grain-boundary energy (or curvature) leads to normal and abnormal grain growth. The reduction of internal defects also leads to changes in grain size due to static and dynamic recrystallization. In most alloys, grain growth occurs due to a reduction in grainboundary curvature.[1,2,3] Computer simulation has been used in recent years to quantitatively study grain growth. In particular, the Monte Carlo (MC) simulation has been widely used to simulate the grain structure under isothermal conditions.[4–7] Apart from grain-growth kinetics, MC simulations also provide information on the evolution of grain morphology which cannot be obtained by analytical equations.[4–7] Recently, MC calculations have also been used to simulate the grain growth in the heat-affected zone (HAZ) of welds.[8–11] In MC simulations, the dimensionless grain size changes with the number of iterations, which is also known as the MC simulation time steps (tMCS). In the MC model, the grainsize variation with tMCS is largely independent of material properties and real-time grain-growth kinetics and is only dependent on the grid system (e.g., the dimensions of the system and total number of grid points). In order to quantitatively predict grain growth for a specific material under given thermal conditions, a relation needs to be established between the simulation steps, tMCS, and real time. So, a kinetic submodel is needed to simulate grain growth using the MC technique. Previous work on modeling grain growth in the weld HAZ using MC simulation included two approaches in relating the tMCS to the real time. Radhakrishnan and Zacharia[10] and Wilson et al.[11] modeled grain growth in the weld HAZ by considering a linear relationship between tMCS and real S. SISTA, Z. YANG, Graduate Students, and T. DEBROY, Professor, are with the Department of Materials Science and Engineering, The Pennsylvania State University, University Park, PA 16802. Manuscript submitted October 29, 1999. METALLURGICAL AND MATERIALS TRANSACTIONS B
time. Gao et al.[9] suggested that there was insufficient evidence to show that the MC simulation time could be linearly related to the real time in all material systems. They proposed three models—the atomistic model, the experimental data–based (EDB) model, and the grain-boundary migration (GBM) model—to relate tMCS and real time to address various situations. One common feature in all the previous work done by both the groups was that the simulation was two-dimensional (2-D) in what was really a three-dimensional (3-D) HAZ. Considering the significant local-temperature gradients in all directions in the HAZ, 2-D simulation of grain growth is inadequate. Furthermore, the width of the HAZ usually varies with the location in the actual weldment. This variation cannot be accounted for in the 2-D simulations, and 3D calculations are needed for a realistic simulation. The phenomenon of “thermal pinning,” in which a grain is physica
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