Joanna M Nicholas and David J Abson
Paper presented at the 17th International Conference 'Computer Technology in Welding and Engineering' Held at the University of Cranfield, 18-19 June 2008.
There have been many attempts to model the combined effects of composition and welding parameters on the maximum heat affected zone (HAZ) hardness of C-Mn and low alloy steel welds. Each model has provided a good fit to the data examined, but has not been found to be consistently good for other data. Using over 300 data points for which the composition, welding parameters, cooling time from 800°C to 500°C (t8/5) and maximum HAZ hardness were known, twelve methods for determining the maximum HAZ hardness were examined. The measured and calculated hardness values were compared for each method, and the distributions noted.
No single method was accurate over the entire range, and the statistical parameters did not identify any one method as superior. A range of hybrid methods was also examined, and the same statistical parameters determined. The most successful hybrid model combined a method by Lorenz and Düren with that of Yurioka (1981), and included the estimation of a martensite hardness limit. This hybrid model gave a good fit to the measured data, with a standard deviation of 28HV. The hybrid method requires the value of t8/5. Using the rearrangement of the Rosenthal equations given in EN1011-2 (after Degenkolbe et al), this can be determined from the welding parameters.
Thus, if a welding engineer knows the steel composition, joint configuration and welding parameters, an estimate of the maximum HAZ hardness for a single pass weld (or the final bead of a multi-pass weld) can be derived from this hybrid method. Where a specified value of the maximum HAZ hardness must be met, the approach should substantially reduce the number of welding procedure qualification tests needed.
Many factors influence the hardness of a metal, including the elements present that contribute substitutional strengthening or precipitation hardening to the alloy in question, and the thermo mechanical history of the material. Depositing a weld bead alters the original macroscopic boundaries (preparation edges) and subjects the surrounding material to a thermal cycle, which usually changes the microstructure and hardness of the material. For instances where, in order to avoid a service cracking mechanism (e.g. steels in sour service), it is important to determine what the maximum heat affected zone hardness is likely to be, prediction tools can assist in selecting appropriate welding procedures.
The maximum heat affected zone (HAZ) hardness in C-Mn and low alloy steels is likely to arise from a location within the parent steel that has only experienced one thermal cycle during welding, at temperatures greater than approximately 800°C. If a subsequent thermal cycle is experienced at this location, it is unlikely that the maximum temperature will be >800°C and so some tempering, or reduction in hardness may occur, but an increase is unlikely. In a multiple pass weld, this 'single thermal cycle' location is the parent material adjacent to the capping passes (assuming no further temper beads are deposited).
A number of investigators have published equations to predict HAZ hardness, but it is not clear which of these is the most conservative, or the most appropriate to use for a particular steel. Many of the authors[1-7] have utilised a time-temperature parameter in conjunction with the chemical composition to determine the algorithms for the determination of hardness. The time-temperature parameter selected is the time taken to cool from 800°C to 500°C, a temperature range characterising the transformation temperature range (but not necessarily bounding it). This parameter is known as t8/5.
In order to consider which method of calculation was most appropriate, a validation exercise, considering hardness data, which could be related to composition and t8/5, was used. Over 300 data were used to validate the algorithms, and also provided a base for a neural network analysis.
The relevant equations from each investigation were largely composed of three parts, corresponding to a maximum hardness, low t8/5, 100% martensite regime; a minimum hardness, high t8/5, 0% martensite regime and an in-between regime. As t8/5 increases, the slower cooling rate results in a lower hardness (arising initially from a reduced percentage of martensite). A schematic of such phenomena is given in Fig.1. Data generated at TWI from a number of controlled thermal severity (CTS) tests, (8-15)) in which a single pass fillet weld is made, were used in this validation exercise. In each case, a thermocouple had been lanced into the weld pool, and the t8/5 value had been recorded. Additionally, the full chemical analysis of the parent material and the maximum measured heat affected zone hardness had been recorded.
Fig.1. Diagram illustrating the concept of the change in HAZ hardness with increasing cooling time
Each empirical method was employed, using the input compositional and t8/5 data, to generate a predicted hardness value, and this was compared to the measured hardness data. The relationship of the calculated values with the recorded values was composed with a 1:1 relationship and thus judged as 'conservative' or 'unconservative' (over or underestimations), over the relevant range. Each algorithm was different, and had been originally applied to a limited compositional range. Combinations of various existing algorithms were explored to determine the best match of the data to a combined algorithm, along with a complete reassessment of the data using regression techniques. An estimate of t8/5 would need to be considered for the practical application of the method selected, so consideration was given to the Rosenthal equations, and the rearrangements of them (16-20) for steels.
Neural networks are suited to addressing problems that are difficult to resolve using traditional methods, i.e. those that include noisy or subjective data, and that require classification by pattern recognition.
A neural network is made up of many small processing elements that work in parallel. These elements or neurons are interconnected through connection 'weights' that control the flow of information through the network, and hence its response to input data. The values of the interconnection weights are set by the system during a training process to optimise the network's response to the given problem. The training is an interactive process, and requires a comprehensive set of data that the network is to classify. Once trained, a neural network system has several advantages, namely it is fast, it can generalise (when presented with new data), it is adaptive (being usable even when the dataset is incomplete), and it is easily embeddable.
The same data were used to train, test and validate the neural network as were used for the empirical formulae. The data were separated into three sub-sets in order to facilitate the development of the network. A multi-layer Perceptron type network was used, with a single processing element for the output, and thus only one 'hidden' layer. The quantity of data was relatively small, and so the neural network was not able to be trained to predict effectively the maximum as-welded hardness and was also limited by the scatter in the data.
The data selected had a range of compositions, resulting in a variation in carbon equivalent (International Institute of Welding, CEIIW) from 0.2 to 0.7, and a range of thickness and heat inputs resulting in a range of t8/5 up to 6s. The compositional ranges were shown in Table 1:
Table 1. Range of compositions used.
||less than 0.50%
||less than 0.05%
||less than 0.6%
||less than 0.15%
||less than 0.07%
||less than 0.9%
||less than 0.4%
||less than 0.02%
||less than 0.04%
||less than 0.03%
||less than 0.015%
Only one steel contained boron, at a level of 0.0005%.
Graphical representations of four of the algorithms used are shown in Fig.2-5. The method used by Yurioka in 1981 gave largely conservative (over) estimates of hardness (Fig.2), whereas the other algorithms gave largely unconservative (under) estimates of hardness. The Yurioka algorithm was matched with one by Lorenz and Düren, Fig.3, that had a similar level of under prediction to that of the over prediction and combined on a 1:1 basis. This improved the prediction (Fig.6), but the maximum martensite and minimum bainite hardness was lost due to the combination of the methods. It was considered that bainite could continue to soften with increasing t8/5, due to grain growth, but that the martensite maximum hardness 'plateau' should be re-instated. Using the value of t8/5 to give the maximum hardness in the Lorenz and Düren model, a single value for martensite hardness for the combined algorithm was determined. This is shown graphically in Fig.7. The full algorithm is as follows:
Where C is the carbon content in wt%,
This algorithm gives the predicted hardness with a standard deviation of 28HV. Thus, most points will lie within ±56HV of the prediction.
Fig.2. The results from determining the predicted hardness based on the Yurioka 81 algorithms
Fig.3. The results from determining the predicted hardness based on the Lorenz and Düren algorithms
Fig.4. The results from determining the predicted hardness based on the Suzuki algorithms
Fig.5. The results from determining the predicted hardness based on the Terasaki et al algorithms
Fig.6. Combined algorithm without martensite levelling
Fig.7. Combined algorithm with martensite levelling
In determining a value for t8/5 where no measured data exist, the Rosenthal equations were considered. It is known that there are two solutions for heat flow during steady state welding, for 'thick plate' and 'thin plate' heat transfer conditions. Degenkolbe, Uwer and Wegmann considered the application of Rosenthal's equations to low alloy steels. Their re-arrangement for arc welding gives values of t8/5 which are within 8% of the measured values on average (Fig.8). This method of determining t8/5, when applied to the overall method of determining hardness results in a prediction reasonably close to that of the measured values (Fig.9). Comparing the use of measured or calculated t8/5 data, the spread is similar, although the under and overestimation at the lower and higher ends of the scale respectively skews the data away from a 1:1 correlation slightly. However this skewing of the data is comparable to that generated by the enforced martensite plateau, so where t8/5 data is unavailable, the method can still be employed.
Fig.8. Comparison of calculated values of t8/5 with measured values
Fig.9. Comparison of using a calculated t8/5 to predict hardness against when the value of t8/5 is known, showing a similar spread of values but with greater deviation at high values of t8/5 (low hardness)
Neural network results
Examination of the data revealed significant skew in the data with respect to certain variables, and also that for a single set of variables, the ranges of t8/5 and hardness did not necessarily correlate in the manner expected. All the models developed generated hardness values with a standard deviation of between 25 and 30HV, and a correlation of between 0.8 and 0.88. The best correlation has a standard deviation of 26.1HV, which is close to that of the combined empirical formula. It is not anticipated that any improvement in prediction would arise from using a larger dataset.
The selected method of hardness prediction shows a reasonable agreement with the data. Thus, the method can be used as a predictive tool to indicate trends in hardness, and particularly at the procedure design stage, or procedure modification stage. Welding engineers can establish the effects of small and large changes in parent material composition, and welding parameters, without needing to establish by testing every possible combination. It should be noted that for individual cases, determining the predicted hardness by this method may be 56HV above or below the actual values achieved, and as there seems to be no common factor for these cases, the prediction has limited application for single cases. This would be of particular note for times when the HAZ hardness must be restricted in order to comply with ISO 15156 for example - a steel and welding procedure predicted to give 250HV HAZ hardness may give as low as 194HV, or as high as 306HV. This is mitigated by recognising the limitations of the method and using it primarily as a tool to indicate which factors are most important for the steel composition and welding parameters in question. Thus the prediction cannot replace procedure testing, but can be used to determine whether there could be a problem with the applied procedure. Where the required maximum HAZ hardness has been exceeded in a procedure qualification test, the measured and predicted values can be compared, and further calculations undertaken, to indicate what welding parameter adjustments would be needed to obtain the required maximum hardness. Additionally, when the procedure has been shown to achieve the required hardness levels, any restrictions on composition that may be necessary in order to achieve the requirement in the field can be determined from calculation.
As noted above, the scatter band appears rather large. The following items are considered to contribute to the scatter:
- Errors (including rounding errors) in the coefficients used in the carbon equivalent formulae employed.
- Errors in the cooling time measurements from which the empirical equations were derived.
- Lack of data to fully characterise the empirical equations for an adequate range of t8/5.
- Experimental errors in the 300 data used, either in the determination of maximum hardness or in the measurement of t8/5.
- The effect of elements not accounted for in the empirical equations, such as Ti precipitates and sulphur content.
Additionally, the scatter in hardness measurements may have been influenced by the indenter loads, as at loads <10kg, the scatter in the value determined increases.
From a practical outlook, particularly as the neural network did not demonstrate any improvement over the empirical equations, the translation of the equations into a computer program, or as equations within a spreadsheet package would be sufficient for the requirements of most users.
Following the evaluation of a series of empirical algorithms designed to predict HAZ hardness in steel welds to over 300 data, and neural network modelling of the data, the following conclusions can be drawn:
- None of the empirical equations successfully predicted the as-welded maximum HAZ hardness sufficiently well to provide a satisfactory 1:1 correlation between measured and predicted values.
- A combination of two empirical formulae, namely those from Yurioka 81 and Lorenz and Düren, gave the best correlation, being very close to 1:1, albeit with a standard deviation of 28HV
- The Neural network coding of the hardness values gave a 1:1 correlation with a standard deviation of 26HV.
- The combined empirical formula, used with the method of predicting t8/5 (or a measured value from identical welding parameters) can be used to predict as-welded maximum HAZ hardness, and trends in hardness changes with varying input factors.
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