## First Generation Weld Heat Source Models

First Generation weld heat source models are the point, line and plane heat source models of Rosenthal  and Rykalin . They are the first and most famous of weld heat source models. The point source specifies the position of the weld and the net total rate of heat input from the weld source (J/s). This model is useful for shallow weld pools on thick plates. The line heat source specifies a line segment and the net power or net rate of heat input per unit length uniformly distributed along the line segment. This line weld heat source model can be useful for full penetration laser and electron beam welds in sheets and plates. The sheet weld heat source model can be useful for overlay welds made with sheet electrodes on very thick plates.

The point weld heat source models can be quite accurate when they are used to evaluate temperatures sufficiently far from the weld pool. Concentrating the energy in a welding process into a mathematical point can be viewed as simply a mathematical trick to avoid dealing with the real distribution of energy in a weld heat source. If the power in a weld heat source was actually contained in a point, then the power density and the temperature would be infinite which is impossible. In spite of this defect, the value of these models should not be under estimated. They conserve energy which any useful model of a weld heat source must do and they provide quite accurate temperature distributions at distances sufficiently far from the weld. This is a significant accomplishment.

It should also be recognized that the fundamental strength and fundamental weakness to these point, line and plane heat sources is that they ignore and thus they fail to account for the distribution of energy in the real weld heat source. Any significant improvement on these heat sources must account more accurately for the distribution of energy in the weld heat source.

There are other criticisms of these weld heat source models. For example, the analytic solutions based on these models are linear and thus assume temperature independent material properties, and do not deal with phase transformations. Because they are steady state models, they cannot deal with starting and stopping transients. Also they require the weld to be in a prismatic body and the weld to travel parallel to the axis of the prism. Including convection and radiation boundary conditions is awkward. These authors regard these deficiencies as minor in comparison with the need to distribute energy realistically in the weld heat source. If the power density distribution in the weld pool was realistic, most of the other limitations could be handled.

In summary, these models act on very simple geometric domains such as infinite sheets or plates. They only specify the weld position with a straight weld path as a function of time and the total power input. A spiral path on an infinitely long cylinder is also possible. They only determine steady state solutions of the temperature field.

The weld pool is not an essential part of these models. One can of course define the weld pool to be the region with temperature greater than the melting temperature. However, the model itself contains no notion of latent heats or phase transformations.

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