al carry heat from underneath the heat source to all other locations within the weld pool. Its circulation determines the melting pattern of the various regions of the workpiece, the shape and size of the weld pool, and the structure and properties of the welded joint. But the weld metals are opaque and very hot. As a result, the actual velocities and temperatures within the weld pool have not been experimentally measured so far. A welcome recourse emerged in the 1970s. Advancements in computer hardware and software (Fig. 4) made fluid flow and heat transfer calculations accurate and affordable. Engineers now routinely use these calculations in critical designs in aeronautical, aerospace, civil, and other engineering disciplines. In welding, there are many important problems that cannot be solved without these calculations, at least not easily. Billions of Equations Solved Instantly Evolution of computational hardware and software from mechanical to analog to digital calculations has improved both the theory and practice of welding. The combination of digital computers and robots has improved joint quality, enhanced safety, and taken the boredom out of repetitious welding in automotive and other industries. Clearly, a new manufacturing 60 WELDING JOURNAL / APRIL 2015 paradigm has emerged. What is less apparent but equally important is the advancement of analytical ability for problem solving and design based on fundamental principles. There are compelling reasons for detailed understanding of heat transfer and fluid flow in welding. Both the temperatures and velocities at all locations in the weld pool affect not just its shape and size, but the mixing of the filler metals, cooling rates at different locations, vaporization of alloying elements, weld metal composition, and the structure and properties of the joint. Local temperatures and velocities can be calculated by solving equations of conservation of mass, momentum, and energy (Ref. 4). Since these equations are too complex to be solved analytically, an appropriate numerical method is needed. A typical numerical solution procedure starts by dividing the workpiece into many small volumes or cells, typically about 250,000 cells. For each cell, an algebraic equation relates the local values of a variable with its values at the neighboring cells (Ref. 5). Typically, the variables include three components of velocities, enthalpy or temperature, and pressure, which are solved repeatedly until correct solutions are obtained. For these five variables, a total of 5 × 250,000 or 1.25 million equations have to be solved for each attempt at solution, commonly called an iteration. In most cases, several thousand iterations are needed before correct solutions for the variables at all cells are obtained. So, several billion equations are solved cumulatively to get temperatures and velocities in the entire workpiece. Today, about a billion such linear algebraic equations can be solved in about two minutes using inexpensive laptops. Typical computed temperature and velocity fields during gas tungsten arc welding are shown in Fig. 5. The figure shows regions of different temperatures by specific color bands. Since the heat source is moving, the temperature changes rapidly in the cold workpiece ahead of the moving weld pool. Behind the weld pool where the material has already been heated, the metal cools slowly in air and the temperatures change more gradually. On the weld pool surface, liquid metal moves away from the low surface tension region under the heat source to other regions where the surface tension is higher. The surface is depressed below the arc because it exerts pressure on the liquid surface and forms a small hump behind the arc. The velocities range from a few tens of centimeters per second to about a meter per second, and the liquid metal carries a significant amount of heat from under the heat source to all other locations within the weld pool. Fig. 5 — Computed flow of weld metal during arc welding. The colors represent temperatures in K and the dotted lines represent the lines of flow of liquid. The two loops shown near the surface are from the Marangoni flow and the two loops below the surface result from electromagnetic force (Ref. 4). Fig. 6 — Weld cross sections of 15-mm-thick, high-speed steel plates containing 0.9%C, 3.9%Cr, 6.3%W, 4.8%Mo, 1.8%V, 4.6%Co, 0.2%Mn, 0.5%Si by weight containing 20 ppm sulfur (left) and 150 ppm sulfur (right) spot welded at a laser power of 5200 W for 5 s (Ref. 11).
Welding Journal | April 2015
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