Monte Carlo simulation of grain boundary pinning in the weld heat-affected zone
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I.
INTRODUCTION
THE mechanical properties of a weld heat-affected zone (HAZ) are largely influenced by the grain size and grain size distribution. The peak temperature, the heating rate, and the cooling rate in the HAZ are all decreasing functions of the distance from the heat source. The gradients in the preceding parameters give rise to a gradient in the HAZ grain size, with the coarsest grains typically forming near the fusion line. In alloy systems where there is a solid-state transformation from a high-temperature to a low-temperature phase, the kinetics of formation and the morphology of the low-temperature phase are determined, to a large extent, by the parent-phase grain size. A common example is found in steels where the kinetics of austenite transformation on cooling is sensitive to the prior austenite grain size. m Several studies that deal with the estimation of grain size in the HAZ are available in the literature.[ 2,3,4~ These studies are generally based upon the use of the well-known equations describing curvature-driven grain growth given by Om - D ~ ' = k t
[1]
where D is the average grain size at time t and Do is the average initial grain size. When D > > Do, Eq. [1] can be approximated as O
= kt"
[2]
where n is the grain growth exponent which is equal to 1/m in Eq. [1]. In Eqs. [1] and [2], the quantity k is a temperature-dependent boundary mobility given by
where Ko is a constant, Q is the activation energy for grain growth, T is the absolute temperature, and R is the universal gas constant. Nonisothermal grain growth is modeled by
B. RADHAKRISHNAN, Research Staff Member, and T. ZACHARIA, Group Leader, are with the Metals and Ceramics Division, Oak Ridge National Laboratory, Oak Ridge, TN 37831-6140. Manuscript submitted June 30, 1994. METALLURGICAL AND MATERIALS TRANSACTIONS A
using the differential form of Eq. [1] or [2] and then integrating it over the thermal cycle. However, it has been recognizedt41 that the use of Eqs. [1] or [2] and [3] for calculating the HAZ grain size is not strictly correct, because it assumes an average thermal cycle for a HAZ width equal to the grain size. Often, the temperature gradient in the weld HAZ can be so steep that the temperature can vary across a single grain. This is especially true near the fusion line where the grains are the coarsest and the temperature gradient steepest. Under such conditions, the quantity k in Eq. [2] varies across a grain, and hence, the grain growth rate can be significantly different than the estimates obtained using Eq. [1]. The preceding phenomenon, termed "thermal pinning," was first reported in the weld HAZ of a 0.5Cr-Mo-V steel by Alberry et al. t21 Although the effect of thermal pinning on the HAZ grain size has been recognized for quite some time, the phenomenon has not been quantitatively modeled. The Monte Carlo (MC) technique has been used to simulate grain growth in single-phase and two-phase materials under isothermal conditions.tS-~8] As a first step, the technique involves the mapping of a grain structure
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