Recent advances in the mathematical modeling of fundamental phenomena in welds are summarized. State of the art mathematical models, advances in computational techniques, emerging high-performance computers, and experimental validation techniques have provided significant insight into the fundamental factors that control the development of the weldment. The current status and scientific issues in the areas of heat and fluid flow in welds, heat source-metal interaction, solidification microstructure, and phase transformations are assessed. Future research areas of major importance for understanding the fundamental phenomena in weld behaviour are identified.
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