Transport of Metal during welding Part-2

In my previous Blog which was published in May 2010, I had promised that I will write about the work done to explain under what conditions the molten weld metal moves backwards.

In 1970's A number of papers were published exploring how the crater is formed when an electron beam strikes a metal object. But we did not find any published work explaining how the molten metal moves backwards. As suggested by the Physics Professor in Moscow Power Institute we looked at the possibility of Thermocapillary phenomenon playing a part.

It is a well known fact that the surface tension force of metal depends upon upon the temperature. Higher the temperature lower will be the surface tension force. Therefore, in addition to the normal force acting on the molten metal a tangential force along the surface of the molten metal develops.The tangential force is determined by the surface tension gradient.This is represented by the equation
P(t) = grad(sigma)
A positive sign before the gradient indicates that the force P(t) moves the metal from a region of lower surface tension to a region of higher surface tension, i.e the molten metal will move from a region of higher temperature to a region of lower temperature which means from the front of the weld pool to the back of the weld pool.

When the electron beam moves over the metal surface the front portion of the crater is at a higher temperature and back of the crater will be at the melting temperature of the metal. As a result of the temperature gradient thermocapillary effect manifests it self. Hence under thermocapillary forces the molten metal flows from the front of the crater to the back of the crater.

The experiments reported in Part-1 confirmed that Thermocapillary effect is responsible for metal movement.

We also attempted to theoretically examine the metal flow.

To quantify the metal moved from the front to the back of the crater, neglecting the radius of curvature of the crater, as a first approximation, the flow of metal is treated as a two dimensional flow and relevant differential equations with boundary conditions were solved. The solution resulted in calculating velocity of the moving metal and the quantity of metal moved from the front of the crater to the back of the crater. The thickness of the liquid metal in the crater was calculated considering the temperature distribution in the crater. With this input we calculated the volume of metal moved from the front to the back. The theoretical calculations agreed closely with the measured values.

We were the first to identify thermocapillary effect as my Ph.D thesis was defended in 1972 and the work was done in 1971.

We published our work in Svarochnoe Proisvodstvo. Later my professor teamed up with the Professor of Physics mentioned earlier and together they published another paper extending the work to consider the flow as three dimensional. As our work was in Russian it reached not many people. But in spite of the disadvantage of language later I could identify 5 citations of the first paper published on Thermocapillary flow.

A practical application of this work was used to develop welding very thick aluminium blank of over 200mm in single pass by electron beam welding. Here the electron beam was located along the Y-axis as against the convention of beam impinging from top to bottom. In addition to the gravitational force, Thermocapillary force drove the metal away from the molten zone exposing virgin metal which aided in increasing the depth of penetration.