Abstract
The two-dimensional temperature distribution in the longitudinal middle section of welding bead under quasi-stationary state during welding can be approximately represented by the following equation referring to the rectangular coordinate (x, y), the origin of which is moving with the heat source towards the positive direction of x-axis,
u=u*+(u0-u*)eh2a2/υ0b xcosμ0(1-y/b),
where u0 is the temperature of welding heat source ; u*, an imaginary temperature at which the temperature of bead is considered to be balanced with that of base metal while the bead is cooling, and this is to be determined experimentally ; b is thickness of bead, that is, distance from the deepest bottom to the top of the bead surface ; ν0, welding velocity ; h2, thermal diffusivity ; α2, coefficient of heat transfer from bead to base metal ; and μ0, minimum positive root of the equation cotμ=μ/α2b,
By this equation the isotherm of the bead may be found as follows :
x=υ0/2h2(b-y)2+ξ ; ξ=-υ0b/h2a2log(u0-u*/u-u*).
Further, the formula which represents the shape of columnar crystal found in the longitudinal middle section of bead is obtained as follows by calculating the orthogonal trajectory of the melting-point isotherm shifting with time :
x=-h2/υ0log(1-y/b).
This describes the shape of practical columnar crystal with near precision and clarifies the following main properties. The higher the welding speed, the larger the thickness of bead and the smaller the thermal diffusivity of weld metal, the nearer the inclination of columnar crystal will be to perpendicular position.
