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Quantitative Alloy Design Tools for Ni--Base Superalloys

Final Report EPSRC Grant GR/K23263
Principal Investigator: Dr. H.K.D.H. Bhadeshia


The development of new nickel alloys for aeroengine applications is a difficult taks, frequently achieved by trial and experience. The purpose of this work was to enable a significant proportion of the development procedure to be done by computation. A variety of methods have been used towards this end, ranging from physical models to the power technique of neural network analysis.

A more general method of regression is neural network analysis. As before, the input data xj are multiplied by weights, but the sum of all these products forms the argument of a hyperbolic tangent. The output y is therefore a non-linear function of xj, the function usually chosen being the hyperbolic tangent because of its flexibility. The exact shape of the hyperbolic tangent can be varied by altering the weights. Further degrees of non-linearity can be introduced by combining several of these hyperbolic tangents, so that the neural network method is able to capture almost arbitrarily non-linear relationships. For example, it is well known that the effect of chromium on the microstructure of steels is quite different at large concentrations than in dilute alloys. Ordinary regression analysis cannot cope with such changes in the form of relationships.

A potential difficulty with the use of powerful regression methods is the possibility of overfitting data. For example, it is possible to produce a neural network model for a completely random set of data. To avoid this difficulty, the experimental data can be divided into two sets, a training dataset and a test dataset. The model is produced using only the training data. The test data are then used to check that the model behaves itself when presented with previously unseen data.

Neural network models in many ways mimic human experience and are capable of learning or being trained to recognize the correct science rather than nonsensical trends. Unlike human experience, these models can be transferred readily between generations and steadily developed to make design tools of lasting value. These models also impose a discipline on the digital storage of valuable experimental data, which may otherwise be lost with the passage of time.

We have addressed solid solution strengthening, tensile properties, fatigue, creep, lattice misfit in the context of nickel-base superalloys, and have applied the method to other materials and processes.


A large number of quantitative models have been produced, dealing with the microstructure and mechanical properties of nickel--base superalloys. This is the first time it has become possible to estimate properties as complex as the fatigue crack growth rate as a function of a very large number of variables. The models have been tested successfully against the known principles of physical metallurgy. They have been used already, both in reducing the scale of experimental programmes and in identifying regimes where experiments are essential.

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The work was supported by the Engineering and Physical Sciences Research Council (EPSRC) of the United Kingdom. The results of the project have been assessed by EPSRC referees as follows:

  1. Scientific & Technological Merit: Very significant contribution to the field.
  2. Management and use of resources: Good