Sha W., Malinov S. Titanium Alloys: Modelling of Microstructure, Properties and Applications
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Neural network method 321
example a mechanical property), they can straightforwardly switch to others
to check if the other properties (for example TTT diagram) are satisfactory.
13.3.2 Prediction of properties of existing materials
New materials with different special properties are continuously being
developed to meet engineering requirements. The aim is usually to achieve
desirable values of one or a combination of properties. However, most often,
the other properties of these materials are unknown when they are first
designed and these properties are studied by additional experiments after the
materials are introduced in certain applications. The lack of knowledge of
these other properties inhibits full exploitation of these new materials. The
software developed (Fig. 13.2) can be used to predict unknown properties of
existing materials. For this purpose, the user can input and fix the composition
of the alloy and can predict the unknown property (mechanical, kinetics of
phase transformation, etc., as desired) for different conditions.
One typical example for such use of the software is using the module for
prediction of time–temperature–transformation diagrams (Figs. 13.1 and 13.2).
Experimental investigation of TTT (and CCT) diagrams is both costly and
time consuming. Hundreds of experiments are necessary to construct such
diagrams for a single alloy. For this reason, when a new material is designed,
its TTT diagrams are usually unknown. There is presently still a lack of such
diagrams, even for widely used alloys. Using the software, TTT diagrams
are predicted (Chapter 14) for many existing titanium alloys for which
experimentally determined TTT diagrams are not available in the literature.
These simulation results can be used for explaining the transformation kinetics
during cooling of corresponding alloys. The diagrams will also be useful in
the design of experimental studies of TTT diagrams for these alloys. In this
way, the amount of experimental work could be significantly reduced. In this
respect, it should be mentioned that, for some of the alloys, experimental
TTT diagrams have become available after the simulations and good
correspondence between the predictions and later available experimental
diagrams is demonstrated. These agreements give us confidence in the model
simulations. Other examples of using the software package developed to
predict properties of existing materials are the calculation of fatigue strength
S–N diagrams and mechanical properties (Chapter 15).
13.3.3 New alloy design
Neural network models are usually used to predict outputs for user-defined
combination of inputs. However, very often in practice, it is necessary to
solve the reverse problem, namely to find combinations of inputs which
would produce a desirable output or combination of outputs. For example, it
Titanium alloys: modelling of microstructure322
is of great interest for the theory and the practice to find optimal alloy
composition, processing and environment conditions that would give a
particular desirable property or combination of properties. The background
of new alloy design is the knowledge of the correlations between the alloy
composition and the properties. The optimisation of one or some of the
properties of the material being designed is closely related to optimisation of
its composition. However, new materials are still mainly designed empirically,
by carrying out expensive and time-consuming experimentation on trial alloys.
The software system has assembled results from hundreds of experiments
and is trained with them. As a result, it is capable of predicting properties for
new alloy compositions. It can be used for optimisation of the alloy composition
for the alloy being designed in order to achieve an optimal value for properties
aimed for. Based on the trained neural networks, computer programs for
optimisation of the input values (the alloy composition and processing) in
order to obtain the desired property (or combination of properties) are
developed. The trained neural network is incorporated in the body of the
program and the optimisation criteria can be user defined. This approach
was first applied for the model on mechanical properties of titanium alloys
(Chapter 15). At a later stage, it was incorporated into the other models
described above. In the first instance, the search for the best solution was
based on a simple grid search. Now, the NN models are combined with
efficient optimisation methods for faster discovery of the best solution. The
optimisation programmes are individual for each separate NN model. There
are separate modules for optimisation of mechanical properties, TTT diagrams,
fatigue stress life diagram, etc. The user can use the modules (Figs. 13.1 and
13.2) in this mode by fixing the other inputs (such as temperature, environment
and treatment) at certain levels and varying the composition of the alloy. The
alloy composition can be altered by varying single element concentration
and fixing the others on chosen values or by varying of combination and
ratios of elements. In this way, the user can analyse the influence of the
different elements (or combination of elements) on the output properties,
and can predict the optimal composition of the new alloy that would produce
the desired properties. Usage of the software package in this mode would
allow the amount of experimentation for new alloy design to be reduced.
Examples for such kinds of software application are (Chapter 15): (i)
influence of the aluminium and vanadium contents on the tensile properties
of Ti-xAl-yV alloys; (ii) influence of the contents of Al, V, O, Mo, Sn and Cr
on the isothermal transformation kinetics in different alloys; (iii) influence
of the aluminium content on yield strength, impact strength and hardness of
Ti-xAl-6V-2Sn alloys.
Here, we use one of the modules (Figs. 13.1 and 13.2) to demonstrate how
the software can be used for alloy composition optimisation. For this purpose,
the Ti–Al–Fe system is used, which is a base system for designing a new
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class of low-cost titanium alloys. By varying the alloying element contents,
the program can be used to find the optimal alloy composition that would
result in maximum yield strength (Fig. 13.9). In a similar manner, all modules
can be used to optimise the alloy composition in order to achieve other
desirable properties. Integration of these models would allow simultaneous
optimisation of, for example, different mechanical properties.
13.3.4 Material selection
The material selection procedure has become of extreme importance for
modern engineering. Over recent years, many software systems have been
developed for the selection of materials for user-defined requirements. One
of the popular systems of this kind is ‘Cambridge Engineering Selector’
(developed initially as ‘Cambridge Materials Selector’). Most of these
computer-based systems use a classical approach of searching a database of
materials properties according to user-defined criteria for a combination of
properties.
The neural network software system developed here can also be used for
material selection procedures. For this purpose, a special module and GUI
have been developed (see Figs. 13.8 and 13.10). The user can use the GUI
13.9
Use of the software for optimisation of the alloy composition in
the Ti–Al–Fe system in order to achieve maximal room temperature
yield strength.
Titanium alloys: modelling of microstructure324
developed (Fig. 13.10) to define the working conditions (such as temperature
and environment) and the requirements for materials properties (such as
strength and elasticity). Once these are defined, the user can run the module
by clicking ‘search’. The input information is acquired, organised and processed
to the modules with the trained neural networks. Each input is processed
only to the modules to which it is relevant. The trained neural networks are
the core of the computer program for search of conditions that satisfy the
user-defined criteria. The parameters that are fixed by the user are fixed
inputs of the trained NN. The other inputs, essentially the material composition,
are varied by organised loops, and the trained neural networks are used to
predict properties at each loop. The predicted combination of properties is
compared with the user requirements at each step, and if they are satisfied,
the current combination of material composition and processing parameters
is suggested as a possible solution. The loops are organised so that all possible
combinations between the changeable inputs are attempted. After the
completion of this procedure, material compositions that satisfied the user
13.10
Graphical user interface of module for materials selection
based on trained artificial neural network.
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requirements are suggested, if such are found. In the general case, a list of
possible materials compositions and processing is suggested.
In this mode, the software package developed can be used for materials
selection procedures. For example, it can find material compositions that
satisfy user-defined combination of mechanical properties for any work
temperature. The approach used here that is based on trained artificial neural
networks differs from the approaches that are based on the database search.
In the latter, only a material that exists in the database can be found and
suggested as a material that satisfies the user criteria. In the neural network
approach, along with the existing materials, a composition of material that
satisfies the criteria can be suggested even if such material does not exist. It
should be restated that for this and for all modes, the software package
works only within the ranges of input parameter values that are used for
training.
13.3.5 Optimisation of the processing parameters
The software package can be used for optimisation of the processing parameters
of a titanium alloy in order to achieve a desirable combination of properties
at different working conditions. In this mode, the user can run the chosen
GUI (Fig. 13.2), depending on the property concerned. The alloy composition
and the working conditions (such as working temperature and environment)
should be fixed on the required values. By varying the processing conditions
(such as heat treatment, time, temperature, and cooling), the user can study
their influence on the properties. The user can use these simulations to find
optimal processing and heat treatment procedures that would produce the
desired combination of properties for different working conditions and alloys.
Examples for such usage of the programs are given by Malinova et al.
(2001a), where the ANN model is used to study and optimise the influence
of the processing parameters (time and temperature) on the microhardness
profiles after surface nitrocarburising of steels. Here, we give an example for
use of the software package for simulation of the influence of the processing
route on the fatigue strength of corrosion resistant Ti-6Al-2Sn-4Zr-6Mo
alloy (Fig. 13.11). The alloy composition is fixed. The desired property (in
this case fatigue strength) is selected. This property is studied as a function
of the temperature at different processing procedures, namely α + β annealing,
solution treatment followed by ageing, and duplex annealing. In a similar
way, the modules can be used to study the influences of the processing route
on other selected properties for different alloy compositions.
Titanium alloys: modelling of microstructure326
13.4 Upgrading the software system
13.4.1 Database enhancement and re-training
The model will work with sufficient accuracy within the range of the data set
used in the training. If the user defines input conditions outside this range,
the software will still generate an output, but it may not be correct. In such
a case, the program should give a warning message that the result may not
be reliable. Hence, the software system is restricted to predict with a reliable
accuracy within certain ranges of input parameter values that are limited by
the database used for training. As earlier mentioned, the strategy of the
software developed is to create general models that will be open for constant
upgrade and improvement. Following this aim, modules are developed that
allow users to input their own data and to re-train the ANNs (see left part of
Fig. 13.8).
Input of new data is organised in two ways. The first option is by simple
adding of new data in the spreadsheet files. Since the files are dynamically
linked, the new data are automatically updated in the ASCII file and introduced
in the matrix M that will be used for re-training. This option is more convenient
when new data are inputted in batches and the user already has the data in
electronic form (as a spreadsheet). The second option is by adding data one
by one using the purposely-developed graphical user interface. This option
is more convenient when a single data pair is inputted.
13.11
Use of the software for optimisation of the processing
procedure.
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Once the new data addition process is completed, the modules should be
re-trained so they can absorb the information that is contained in the new
data. This is organised by the graphical user interface for selection of the re-
training parameters. The user has three options for re-training:
• Simple re-training with the optimal combination of network architecture
and training algorithm that has been found in the previous training (see
Section 13.2.3). This is the fastest re-training procedure. However, this
option is recommended only in the cases where the amount of new data
is relatively small. Input of large amounts of new data could require a
different NN architecture and training algorithm.
• User-defined parameters for re-training. In this option the user can define
the number of neurons in the hidden layer, training algorithm, transfer
functions, etc. Advanced users who are familiar with artificial neural
network modelling should use this option. Some recommendations for
training parameters selection are given in Section 13.2.3.
• Re-training with all possible network architecture and training algorithms
for finding the optimal combination. In this option, the program executes
the entire procedure described in Section 13.2.3 for finding the optimal
case of trained neural network. This is the slowest option that requires
significant computational time for re-training, but it is still recommended
because in this option the user can be sure that the best possible combination
in terms of database distribution, network architecture and learning rule
is achieved.
Organised in this way, the software system effectively accumulates and stores
experience intelligently, and will constantly be improved and expanded to
serve the user in the best possible way.
13.4.2 Further developments of the software
The computer programs were developed using a combination of C++ and
MatLab programming language with neural network toolbox. The software
products are available in versions for different platforms including Windows,
UNIX and Apple Macintosh. A web-based version of the software system
can be developed by implementation of Java programming.
At this stage, the models are static neural networks, i.e. they can be used
for computer simulations and predictions. A properly trained and applied
neural network can make decisions by itself. At later stages, the model can
be developed as dynamic, i.e. it can be incorporated to control and optimise
a real production technology.
Titanium alloys: modelling of microstructure328
13.5 Summary
Models and software products are developed for the simulation and prediction
of a variety of properties of titanium alloys and correlations among processing
parameters, microstructure and properties. The software programs and the
models can be used for:
• prediction of mechanical properties of existing titanium alloy materials
as functions of their chemical composition, heat treatment conditions
and working temperature; easy comparison of mechanical properties
corresponding to different conditions by plotting them together; and
investigation of the influence of different factors on the mechanical
properties in titanium alloys;
• simulation of TTT diagrams for titanium alloys as a function of their
chemical composition and design of diagrams for new alloys; investigation
of the influence of different alloying elements on β to α transformation
kinetics in titanium alloys;
• simulation of S–N curves for the Ti-6Al-4V alloy under different input
conditions and practical applications in solving various problems on
fatigue behaviour of the titanium alloy; investigation of the influence of
different factors affecting the fatigue of Ti-6Al-4V;
• significant reduction of the experimental work for measurement of TTT
diagrams, S–N fatigue strength diagrams and other mechanical properties
of titanium alloys;
• new alloys design;
• materials selection;
• optimisation of the alloy composition and processing parameters.
This software can benefit the industry, especially metal and alloy manufacturing
companies. The models and the software are based on artificial neural network.
ANN is the fastest modelling technique with a very quick return for the
practice. Graphical user interfaces are developed for easy use of the models.
The models and software products developed are convenient and powerful
tools for practical optimisation of the composition and processing parameters
of titanium alloys in order to obtain the desired combination of properties at
different working temperatures, with minimum investment in experimental
work. The software products are available in versions for different platforms,
including Windows, UNIX and Apple Macintosh.
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