TWI Industrial Member Report Summary 627/1997
By G I Rees
In recent years, with the increasing availability of computers, a greater emphasis is being placed on the use of numerical techniques and modelling to find solutions to metallurgical problems in welding. Significant progress has been made by some workers, to the extent that the models developed can begin to be used in the design of new alloys (2). One of the most successful of these models is that developed by Bhadeshia and co-workers at the University of Cambridge, in collaboration with ESAB AB (Sweden), for the prediction of microstructure in C-Mn and low-alloy steel weld metal. Despite this model's success, some aspects of the development of microstructure in such welds are not covered by the original theory e.g. the formation of martensite under rapid cooling conditions, and the effect' that nonmetallic inclusion particles have on the final microstructure. While the theory on which this model is based is fully published in open literature, the program itself is not commercially available. However, the thermodynamic calculations on which the model is based can be obtained from Bhadeshia's program entitled 'MUCG46.FOR1, which is freely available. The aim of this work was thereforeto reproduce accurately the calculations of this model, and to incorporate improvements which would begin to allow prediction of effects not previously covered.
To reproduce and validate the weld microstructure prediction model of Bhadeshia et al. Once successfully reproduced, to incorporate improvements into the model to account for phenomena not covered by the original theory. Modelling Work The basic structure of Bhadeshia et al's microstructure prediction model is as follows.
1. Using thermodynamic parameters calculated from the welds chemical composition, an estimate is made of the temperature range over which grain boundary allotriomorphic ferrite and Widmanstatten ferrite form, as the weld cools.
2. By using appropriate solutions to the diffusion equation for carbon, estimates are made of the growth rates of the above phases, over the calculated temperature ranges.
3. Using an idealised model of an austenite grain, the amount of allotriomorphic ferrite and Widmanstatten ferrite which form on the grain boundary surface area is calculated.
4. The austenite remaining after these transformations is assumed to form acicular ferrite and martensite.
New Fortran software routines were written to evaluate growth rates and temperature ranges of formation for the various constituents of weld metal microstructure, during cooling, according to Bhadeshia et al.'s model. The thermodynamic parameters evaluated by Bhadeshia's program MUCG46.FOR, also written in Fortran, were used as a basis for these calculations. A computer program reproducing the microstructure prediction model was thereby produced. Through an analysis of independent data, further work was incorporated into the model in order to account for the formation of fully martensitic microstructures in welds, when cooling conditions are sufficiently rapid. This was achieved by establishing a means of estimating the critical cooling rate at which no constituentother than martensite could form in the weld metal. The compositions for which this relationship was established covered a range of IIW carbon equivalent of 0.27-0.54. By considering the kinetics of acicular ferrite formation, a means of estimating the relative volume fractions of acicular ferrite and martensite in weld metal microstructures was also established. Modifications were further made in order to model the transition between microstructures consisting predominantly of acicular ferrite, to those containing mainly bainite, with an increase in the ratio of aluminium to oxygen in the weld metal.