A one-dimensional heat flow model for calculating the thermal history of welds is investigated in this thesis. The cooling time between 800°C and 500°C (Δτ800-500) and the cooling rate at 704°C (R704°C) parameters are used to describe the thermal cycle. Experimental cooling times (Δτ800-500) and cooling rates (R704°C) for steel welds are compared to values calculated by analytical and numerical methods.
In particular the limitations of the numerical methods caused by using discrete increments for approximating continuous space and time are dealt with in detail. It is found that only two elements in the fusion zone and two elements in the heat-affeected zone are sufficient to provide reliable thermal history calculations (Δτ800-500, R704°C). In addition a time increment of less than 0.04 sec. is necessary to ensure reasonable calculation accuracy. The relatively large space increments and small time increment limits are well suited to the explicit finite difference calculation technique. It is shown in fact that in some cases less computer run time is needed for the easily formulated explicit method where there are space/time calculation limits than for the implicit matrix method where there are no such limits.
While the results presented in this thesis are strictly speaking only valid for welds that can be approximated by one-dimensional heat flow and where the heat input is approximately (810 J/cm^2), this author suggests that the above conclusions most likely apply to a wide range of welding situations.
The one-dimensional analytical relationships established by Passoja and Rajkumar provide cooling times (Δτ800-500) some 100% higher than those measured experimentally. On the other hand numerical calculations and experimental values agree within 20%.