A model for the formation and solidification of grain boundary liquid in the heat-affected zone (HAZ) of welds
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INTRODUCTION
G R A I N boundary liquation in the weld heat-affected zone (HAZ) can be either subsolidus or supersolidus. In the supersolidus portion of the HAZ, continuous grain boundary films form by equilibrium melting of the boundary regions. On the other hand, liquation in the subsolidus HAZ occurs by the constitutional liquation of precipitates at temperatures well below the bulk solidus.l~ 71Grain boundary films form in the subsolidus HAZ as a consequence of constitutional liquation. Liquation cracking in the subsolidus portion of the HAZ is due to the formation of grain boundary liquid through constitutional liquation of precipitates and the inability of the liquid films to support tensile stresses which develop during cooling of the weld HAZ. ES-]tl In general, the transient stress in the HAZ becomes tensile only after the HAZ has cooled through a certain temperature below the peak temperature. At any given HAZ location, the time at which the stress becomes tensile depends upon several factors, such as the specific heat input, the thermophysical properties of the alloy, and the alloy's high temperature mechanical behavior, tj2j In the case of high heat input welds, such as a full penetration butt weld in a 1.5-in.-thick section of alloy 718, the time at which transient tensile stress develops in the HAZ could be as high as 6 to 8 scconds after the peak temperature is reached, tt3] In the case of electron beam welds on thin sections, tensile stresses could develop after a much shorter cooling time. However, in both of these extreme situations, the grain boundary liquid film cools through a large temperature range before it is subjected to a tensile stress. Since liquation cracking depends on the simultaneous existence of the liquid film and tensile stress, it becomes
important to be able to predict the rate of formation and solidification of grain boundary films under various welding conditions. I,iquation cracking susceptibility in the subsolidus HAZ can be predicted by appropriately combining models of transient stress generation with a model for microstructural evolution which deals with the formation and solidification of grain boundary liquid. The objective of this article is to present a simple onedimensional (l-D) model for the formation and solidification of the grain boundary liquid in the subsolidus HAZ. For the purposes of modeling, a binary alloy of known composition Co is considered, as shown in Figure I. The HAZ thermal cycle is divided into three distinct stages depending upon the phase transformation which takes place in the microstructure of the alloy. The three stages shown in Figure 1 are defined as follows: Stage 1 corresponds to the portion of the heating cycle during which the matrix coexists with a dissolving precipitate. This stage extends from the ambient temperature to the eutectic temperature TE. Stage 2 corresponds to the portion of the thermal cycle during which liquation takes place. Metastable liquid forms at the interface between the precipitate and the matrix. During th
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