RPR (2001)

An initial search through the literature and QinetiQ internal databases was carried out to investigate the amount, and more importantly, the quality of data available. Data sources include:

• Superalloys conference proceedings

• Nickel Development Institute (NiDI) Handbook

• QinetiQ reports such as MANDATE Brite EuRam FPIV Programme

• INCO Alloy Datasheets

The first steps taken were to take existing QinetiQ data and build a Microsoft Access database. An extra field was included for the full reference source for each record with hyperlinks to electronic journal papers where applicable. This is particularly valuable information to QinetiQ and proved useful when checking the data for spurious results.

5.4.2 Selection of Inputs

Inputs have been selected to describe the chemical composition, processing route and heat treatment as they all affect the microstructure and therefore strength of the alloy. The roles of alloying additions and processing routes are discussed in section 4.2. Selecting the right number of inputs depends on several factors:

1. There must be enough inputs to adequately describe the alloy composition and other processes that are commonly documented.

2. As the number of inputs increases, so does the complexity of the neural network and the amount of data required to train it.

3. Input data must be consistently recorded for each record used.

Initial models have used the full chemical composition of the alloy with further work being carried out to determine if some elements could be left out of future models. Inputs were chosen based upon information that was readily available in data sources, such inputs could only be used if that particular piece of information was recorded for every alloy. Missing data is difficult to represent in a neural network, a cell cannot simply be left blank. A value of zero is generally not an accurate representation for unknown data. Blank cells can be filled with the average value for that input but this is not desirable as it is not a true result and could be very different from the actual missing value. A better solution is to remove the record containing the missing data.

With this in mind, if the list of inputs was over defined many sources of data would be unusable. The input data has been divided up into 3 categories; Composition, Processing and Heat Treatment. Varying data in each category will have a measurable effect on the strength of the alloy.

5.4.3 Alloy composition

Alloying elements that are included specifically to strengthen the superalloy are discussed in the literature review. To start off with, full compositional information was recorded for each alloy. The initial list comprised of 19 elements: Ni, Cr, Co, Mo, W, Ta, Nb, Al, Ti, Fe, Mn, Si, C, B, Zr, V, Hf, Re, and La.

It is expected that the most important elements will be those that are included for γ’ formation and solid solution strengthening. The removal of some of these elements as

inputs is discussed later in the chapter. Alloy compositions are recorded as weight percent to an accuracy of 2 decimal places.

5.4.4 Processing parameters

Information about the processing route of each alloy was limited to; Cast or cast and wrought as the first input and Polycrystalline (PX), directionally solidified (DS) or single crystal (SX) as the second. These parameters are the only ones which are regularly recorded and they all have a significant effect on material properties which cannot be described by composition and heat treatment alone. Processing parameters are recorded by allocating a number to each parameter as shown:

Process Crystallography Cast 0 P X 0 Wrought 1 D S 1 PM 2 S X 2

The disadvantage with this method is that it infers some sort of numerical ranking to the processes which may adversely affect the model. An alternative method could be used as shown: P1 P2 P3 C1 C2 C3 Cast 1 0 0 P X 1 0 0 Wrought 0 1 0 D S 0 1 0 PM 0 0 1 S X 0 0 1

The problem here lies in the creation of 42 _{more input columns in this case. It was}

decided to use the first method for initial modelling attempts in order to keep the number of inputs to a minimum.

2 _{Whichever method is used to describe level information for processes should also be}

used for cooling rate information (see heat treatments) so the increase in inputs would be by 7 and not 3.

5.4.5 Heat Treatments

The heat treatment used will determine the γ/γ’ microstructure and grain size (where applicable) thus having a large effect on the strength of the alloy. The most common heat treatment cycle is normally a combination of a solution treatment and one or two ageing treatments. Heat treatment information has therefore been split into 9 inputs. Information on heat treatments is recorded with 3 critical parameters (Temperature, Time and Cooling type). Cooling rate is also important but was not often included in papers and specifications and was therefore left out. It is also a function of the cooling method used, so this parameter should adequately describe the process.

Temperature and time inputs are simply recorded in °C and hours respectively. Cooling methods are recorded in much the same way as processing information and are subject to the same decision as to how to record the levels.

Cooling Method

Air cool 0

Furnace cool 1

Water Quench 2

Oil Quench 3

Some alloys have a multi step heat treatment that does not fit the structure of the input database. For these alloys, a method of reducing complex multi step treatments into one equivalent step was used. A single step was calculated to give an equivalent amount of diffusion of Al and Ti in Ni. An example for the treatment of alloy CM247LC DS is given.

The solution heat treatment for CM247LC DS is 1221°C for 2 hours + 1232°C for 2 hours + 1246°C for 2 hours + 1260°C for 2 hours then rapid fan quench in argon. Diffusion of aluminium in nickel (k) has been calculated using the Arrhenius equation.

Equation 29

Where A and Ea are material constants from the literaturexlvii_{, R is the gas constant}

and T the temperature in °Kelvin. The diffusion distance is then calculated:

Distance = √(k.t) Equation 30

Where k has been calculated in Equation 29 and t is the time in seconds. The time required for each step, at the maximum temperature (1260°C) instead of the actual temperature, to give an equivalent diffusion distance was then calculated. An example

is given for diffusion of aluminium in nickel (Figure 27). Values for titanium were very similar. Temp (°C) Temp (°K) R A Q D Time (s) Diffusion distance (cm) Eqiv Time @ 1553°K 1221 1494 1.987 4.41 73160 8.737E-11 7200 0.000793115 3846.2925 1232 1505 1.987 4.41 73160 1.046E-10 7200 0.000867861 4605.438 1246 1519 1.987 4.41 73160 1.311E-10 7200 0.000971433 5770.2683 1260 1533 1.987 4.41 73160 1.635E-10 7200 0.001085128 7200 Total Seconds 21421.999 Hours 5.9505552 Constants

Figure 27 – Excel calculations for solution heat treatment approximation

The 4 step solution treatment is therefore substituted with 1 solution treatment step at 1260°C for 6 hours.