When a real weld is started, the weld pool is not formed instantly. First, a Gaussian flux distribution heats the solid to the melting point, then a thin layer of molten metal forms. This grows in width and depth with time. With increasing depth, the weld pool surface is depressed and stirring is induced by […]

The welding path is assumed as any valid geometric curve in space on which a local coordinate system moves. From the local coordinate system, a tangential vector and principal normal can be computed at any point on the curve. Typically, a point is calculated according to the velocity and the time as the leading weld […]

The net power input for the weld, volt x amp x efficiency/speed, should equal the total thermal load reaction or sum of the Lagrange multipliers at the nodes connected to the prescribed temperature field in the weld pool. This is a consistency check and a redundant measure of correctness. Since the total heat input is […]

The most popular model for the heat input is double ellipsoid, because for many arc welds the double ellipsoid shape is a good approximation. It shows that a Gaussian distribution of power density inside a double ellipsoid moving along the weld path was convenient, accurate and efficient for most realistic welds with simple shapes. Since […]

When analyzing a given weld, one is not required to remain faithful to a single model. Clearly, unless one wishes to analyze the interior of the weld pool, it is sufficient for all analyzes outside of the weld pool to specify the geometry of the weld pool as a trimmed surface patch preferably in the […]

Fifth Generation models make a serious effort to include a model of the arc in the heat source model. This adds the equations of magneto — hydrodynamics to the equations in the previous models. Although these Fifth Generation models are very general, they face even more serious mathematical difficulties than the Fourth Generation Weld Heat […]

Fourth Generation models are distinguished by adding the equations of fluid dynamics to the modeling of the weld heat source. Recall that the First, Second and Third Generation models have no fluid velocity. The most general equations for macroscopic fluid dynamics are the Navier-Stokes equations. They can include buoyancy and Lorentz forces acting on the […]

The next advance in weld heat source models, Third Generation models, was initiated by Ohji et al. [21]. They predicted the liquid weld pool shape. The distinguishing feature of Third Generation models is that they must solve the Stefan problem for the weld pool liquid-solid free boundary. Recall that First and Second Generation models need […]

These models treat the weld heat source as a sub-domain in which the temperature or specific enthalpy in the weld pool is known as a function of (x, y,z, t). Since the temperature is known, it need not be solved. Instead, the boundary of this sub-domain can act as a Dirichlet BC for the complement […]

The first second Generation models define a distributed heat source function. The best known example of such a function is the double ellipsoid model, see Figure 2-9. Another example is a conical model for deep penetration electron or laser beam welds, see Figure 2-11. These were the first weld heat source model capable of simulating […]