# Prediction of Continuous Cooling Diagrams for the Precision Forged Tempering Steel 50CrMo4 by Means of Artificial  Neural Networks

Authors: Florian Nürnberger; Mirko Schaper; Friedrich-Wilhelm Bach; Iryna Mozgova; Kostjantyn Kuznetsov; Anna Halikova; Olga Perederieieva
Journal: Advances in Materials Science and Engineering
 (2009)

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## Abstract

Quenching and tempering of precision forged components using their forging heat leads to reduced process energy and shortens the usual process chains. To design such a process, neither the isothermal transformation diagrams (TTT) nor the continuous cooling transformation (CCT) diagrams from literature can be used to predict microstructural transformations during quenching since the latter diagrams are significantly influenced by previous deformations and process-related high austenitising temperatures. For this reason, deformation CCT diagrams for several tempering steels from previous works have been investigated taking into consideration the process conditions of precision forging. Within the scope of the present work, these diagrams are used as input data for predicting microstructural transformations by means of artificial neural networks. Several artificial neural network structures have been examined using the commercial software MATLAB. Predictors have been established with satisfactory capabilities for predicting CCT diagrams for different degrees of deformation within the analyzed range of data.


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## Body

## 1. Introduction

Precision forging
is a technology for the production of components with near-net-shape geometry such
as automotive gears. High precision forging of the geometry enables the overall
process chain to be reduced since machining before heat treatment is no longer
necessary. This provides the possibility of heat treating directly from the
forging heat, so-called integrated heat treatment. The latter is being thoroughly
investigated within the collaborative research center CRC 489 “Process Chain
for the Production of precision-forged High Performance Components” at the
Leibniz University of Hannover, Germany [1, 2].Microstructural
transformations during integrated heat treatment are influenced not only by
high austenitising temperatures of about1200°C but also by plastic
deformations due to the forging process. Thus, neither the usual isothermal
transformation diagrams nor continuous cooling transformation diagrams from literature, for example, [3, 4], nor deformation diagrams investigated for rolling
processes [5, 6] are suitable for predicting microstructural transformations
during tempering from such hot-forming temperatures. On account of this, the deformation CCT diagrams for the tempering steels 34CrMo4 (SAE 4135), 42CrMo4 (SAE 4140),
50CrMo4 (SAE 4150), 51CrV4 (SAE 6150), and 34CrNiMo6 (1.6582) were determined in
a previous work [7] according to the standards SEP 1680 [8], SEP 1681 [9],
and PN-68/H-04500 [10], respectively. Since such physical experiments are
time-consuming and costly, the capabilities of artificial neural networks were
investigated for predicting deformation CCT diagrams with regard to the
particular processing in precision forging.So far, several
authors have reported on the successful predictions of CCT or TTT diagrams
as a function of chemical composition; however, the influence of deformation
conditions, due to precision forging, has yet to be considered. An overview of
the different fields of applications for neural networks in materials science
is given by [11]. Malinov et al. used
a back-propagation, multilayer feed-forward network to predict titanium alloy
TTT diagrams from their chemical compositions [12, 13]. Calculations of the
initial temperatures of bainite and martensite transformations for a huge
number of steels have been carried out by Garcia-Mateo et al. [14]. Using multilayer perceptrons, the austenite decomposition based on
a large data base of TTT and CCT diagrams was computed by Doktorowski [15]. Based on a hierarchical feed-forward network
using back-propagation, Wang et al.
[16] have shown the influence of carbon concentration on the transformation
characteristics of steels. The capabilities for designing new steels using
neural networks have been demonstrated by Trzaska and Dobrzański [17–19].


## 2. Deformation-Dependent Microstructural Transformations

To physically
simulate the precision forging process, specimens of the investigated melts (see
Table1) were heated to an austenitising temperature of 1200°C
within 30 seconds.Table 1
Chemical
composition
of the investigated melts in mass %.
Melt34CrMo442CrMo450CrMo451CrV434CrNiMo6C0.3250.4100.4910.4670.326Si0.2890.3360.2120.2230.263Mn0.5770.7010.6470.8450.588P0.0070.0110.0050.0060.001S0.0030.0250.0040.0170.004Cr0.9450.9981.0391.0151.433Cu0.2860.3800.2190.2230.260Mo0.1320.1710.1330.0130.126Ni0.0980.1910.0920.0831.469Al0.0250.0290.0240.0180.023Nb0.0190.0190.0200.0020.020Following
isothermal holding for 600 seconds at this temperature, the specimens were
deformed by 30% and 60%, respectively (strain rate 1s−1).
Subsequently these were linearly cooled to room temperature using cooling rates
within the range of 80 Ks−1 to 0.02 Ks−1.
As a reference, continuous cooling transformation diagrams without deformation were
also determined (see Figure 1). Measurements were carried out using a dilatometer DIL 805 A/D made by the company Baehr Thermoanalyse GmbH.Continuous cooling transformation diagrams of tempering steel 50CrMo4
for deformation of 30%, 60%, and 0%, respectively [7].
(a)(b)Initiating the
cooling from temperatures higher thanAc3, the steels’ microstructure
is austenitic or face-centred-cubic (fcc). As the temperature slowly decreases
below this value, austenite will then transform into body-centred-cubic (bcc)
ferrite containing low concentrations of carbon. As a result of this
transformation, the remaining austenite’s carbon content is enriched, and the
austenite therefore transforms into bcc pearlite following completion of the ferrite
formation. With increasing cooling rates, diffusion decreases due to the falling
temperatures, and bainitic structures are formed. With further increase in cooling
rates, the diffusionless transformation of austenite into tetragonal distorted
martensite occurs. This microstructure typically features very high strength
and hardness at the expense of reduced ductility. The aim of the integrated
heat treatment of precision forged components, as in many other heat treatments,
is to create a martensitic surface layer that will significantly increase wear
resistance of highly stressed parts while the core of such components is to simultaneously
possess bainitic or ferritic/pearlitic structures to increase the part’s fatigue
limit. Knowledge of microstructural transformations as a function of cooling rates
thus enables one to realise the aim of an efficient process design.


## 3. Modeling and Implementation of Artificial  Neural Networks

In the following, we consider the task of predicting continuous
cooling transformation diagrams as an
approximation problem. For this reason, we describe each curve, which indicates
the initiation or completion of a microstructural transformation, with a
single-valued functional dependence(1)T=Fi(d,time),i=1,n¯, where n is the number of phase transformations, time is the time of initiation or completion of a microstructural
transformation, T is the temperature, and d the degree of
deformation in percent. Predicting the transformation
curves can then be seen as a task of approximating n functions. For the solution to this problem, splines, wavelets, and fuzzy-logic
methods, and so forth, can be used.The curves for the initiation and completion of microstructural transformations are nontrivial for
classical parametric approximation methods. We therefore use feed-forward neural
networks (FNN) as universal approximators. As shown in [20–22], artificial neural
networks with two-layers—where one is a single sigmoidal hidden layer—can approximate any continuous or discontinuous
function from Rn. Leshno et al. obtained a generalization of these results for
neural networks with arbitrarily limited piecewise continuous activation
functions [23]. According to [23], multilayer perceptrons have the capacity to
approximate any continuous function to a prescribed accuracy. Similar results
were achieved by Huang et al. [24] using
artificial neural networks with radial-based functions (RBF). Analysis of the approximation
possibilities of artificial neural networks is a common, though challenging task.
Figure 2 depicts the model of the feed-forward neural network used in this work, with a single
hidden layer for approximating curves for the initiation or completion of microstructural
transformations for deformation dependent CCT diagrams.Figure 2
Schematic of the model of a feed-forward neural network used for predicting the transformation curves for deformation
dependent continuous cooling transformation diagrams.A general schematic of the
applied approach for solving the approximation
task is given in Figure3.Figure 3
Scheme of the approach
for predicting CCT diagrams.


## 4. Data Extension

Every curve of the
continuous cooling transformation diagrams, which have different percentages of
deformation, has its own time interval. Usually these intervals overlap each
other (see Figure4). We used smooth padding (spd) in order to extend
the data to the common argument range. The procedure spd [25] is a linear extension fit to the first two and last two values (see what follows).Figure 4
Data extrapolation
to the common interval
of microstructural transformations for
different degrees of deformationd using smooth padding.For equidistant
time stepsh, a pair of
variate times Timei and
temperatures Ti, where i=0,n¯;
new values are calculated using the following scheme: (2)ΔTleft=T1−T0,Time−1=Time0−h,T−1=T0−ΔTleft,Time−2=Time−1−h,T−2=T−1−ΔTleft,ΔTright=Tn−Tn−1,Timen+1=Timen+h,Tn+1=Tn+ΔTright.  This method works
well for the approximation of equidistant signals [22]. For this purpose the
function wextend from the Matlab
Wavelet toolbox was used.From physical
experiments, curves were known for three degrees of deformation for each microstructural
transformation of one melt. This data is to be approximated for other degrees
of deformation in order to generate a generalization. Since the cooling trajectory
is linear and starts at an initial temperature of1200°C, we transferred
the data into a new coordinate system (α,time), where α is the cooling rate. For this
purpose, we approximated every curve of a microstructural transformation with a
cubic spline and determined the intersection of the spline and the cooling trajectory
(see Figure 5).Figure 5
Scheme of data transformation into the (α,time) coordinate system.Figure6(a)
shows the curves of martensite initiation
temperatures for different degrees of deformation in the new coordinate system.
Furthermore, T* is a new point for
40% deformation which was calculated according to the linear scheme (see Figure 6(b)). The values for the intermediate points; 10%, 20%, 50%, 70%, 80%, and 90%
deformation were analogously calculated.Figure 6
(a) Curves of martensite initiation temperature in the (α,time) coordinate system.
(b) Scheme of linear data extension.Data inputs and outputs were
normalized by a mean shift followed by a decorrelation and a covariance
adjustment so that the
neural network can learn more accurately.


## 5. Training Algorithm Selection and  Determination of the Optimal  Neural Network Architecture

Two categories of algorithms have
been used. The methods of the first are based on a heuristic analysis of the
behavior of the quickest descent algorithms. This category consists of variable
learning rates, back-propagation, and resilient back-propagation. The second
category of fast algorithms uses methods of numerical optimization. From this
category, we chose three optimization methods for network learning:Powell-Beale conjugate-gradient method, Broyden-Fletcher-Goldfarb-Shanno quasi-Newton, and Levenberg-Marquardt. All the algorithms mentioned work in batch
mode. The algorithm Levenberg-Marquardt showed a good balance between convergence rate and generalization quality. For
this reason, all further studies were carried out with this algorithm. Design
and learning of artificial neural networks were implemented in MATLAB using the Neural Network Toolbox.The
number of neurons in the single hidden layer was varied within the range of two
to fifteen in order to determine an appropriate network architecture. Ten
separate training runs were carried out, and the correlation between outputs of
the net and values from training sets were calculated for all the curves of microstructural
transformations. Figure7 shows the results for the bainite initiation
temperatures for the tempering steel 42CrMo4 with 30% deformation. The red
polylineal curve depicts the maximum values of correlation, and the points
represent the mean correlation with standard deviations calculated from ten
training epochs.Figure 7
Mean correlation values for upper bainite with 30% deformation and varied number of neurons
in the hidden layer.This graph reveals
an acceptable correlation rate of about 0.95 for nine neurons in the hidden
layer. It can be seen that this correlation does not significantly increase with
higher numbers of neurons. It should also be noted that the spread of data decreases at this
number of neurons.Similar results
were obtained for other transformations and alloys. Thus, we used feed-forward neural networks with two inputs (degree of deformation in percent and time), one hidden layer with nine nodes and one node for output (temperature). We also used individual neural networks for each of
the tempering steels and for every transformation curve. Hence, to predict the
overall CCT diagram of 50CrMo4, seven neural networks are necessary. In total, the training
set of every single neural network consists of 1350 to 2700 triplets (time,
deformation, and temperature). The learning process was terminated when the
improvement of the mean square error after 100 consecutive epochs fell below
0.01. The best net was then selected from the ten different trained networks.


## 6. Results

Figure8 depicts the dynamics of microstructural transformations for the steel 50CrMo4. In the graphs on the
left of this figure, the black curves are the network outputs, and the red
curves depict the physically measured diagrams. In the graphs on the right, the
transformation diagrams for unknown degrees of deformation are shown.Dynamics of the microstructural transformations of the tempering steel 50CrMo4.
(a)(b)(c)(d)(e)(f)Figure9 shows the correlation between
measured diagrams and the net outputs.Efficiency of the neural networks for the tempering steel 50CrMo4.
(a)(b)(c)Figures10, 11, 12, and 13 demonstrate
the neural networks’ performances for other types of investigated
steels. Results show that the artificial neural networks used here
are capable of predicting the microstructural transformations within the range
of the investigated degrees of deformation.Results for tempering steel 42CrMo4
with a deformation of 0%.
(a)(b)Results for tempering steel 34CrMo4
with a deformation of 0%.
(a)(b)Results for tempering steel 34CrNiMo6
with a deformation of 0%.
(a)(b)Results for tempering steel 51CrV4
with a deformation of 0%.
(a)(b)For
most of the CCT diagrams, a high correlation coefficient can be achieved between
the networks’ output data and the experimental data.An extrapolation beyond strains of 60% is possible; however, with further increases
of deformation, the transformation lines depicting the completion of ferrite
and the initiation of pearlite then begin to cross each other. This is due to
the approach used
where every net represents one transformation curve of a CCT diagram separated
from the others. Interactions between the nets are not considered and, as a
result, the overlaying effect of the curves may be observed for higher (>80%)
degrees of deformation.


## 7. Further Research

(1) The next stage of our research
will
be concerned with the prediction of microstructural transformations of
tempering steels with lower austenitising temperatures. This will increase the
data base for numerically simulating the processes of precision forging and
integrated heat treatment.Furthermore, artificial neural networks will be used
for the prediction of continuous cooling transformation diagrams, not only for specified
strains but also for strain rates. Investigations
of the CCT diagrams’ strain rate dependence for the tempering steel 42CrMo4 are
also planned for the future. These
experiments may require changes in the architecture of the neural networks used.(2) In addition to this, a certain interest lies in an
alternative data handling scheme for the CCT diagrams’ transformation curves to
reduce the amount of data used in the training set. Therefore an approach
similar to [13] will be implemented. However, we propose an application of the
curves’ critical points (extrema, inflections, and endpoints) of microstructural
transformations.(3) In order to avoid overfitting effects, we propose
applying smoothness criteria to the predicted transformation curves. This
should increase the generalization properties of the networks.(4) The method of data
extension of the current work is not applicable for processes with nonlinear
cooling. For a universal approach of the diagrams generalization, it is
necessary to develop an appropriate method of data extension based on other
principles. Such a principle might be an algebraic method suitable for smoothed
nonlinear approximated functions.


## 8. Summary

Curves
in CCT diagrams for the initiation and the completion of microstructural
transformations were used as training sets for artificial neural networks.  Diagrams with different deformations were
utilized with regard to the process conditions of precision forging with
integrated heat treatment. Predictions could be made within the range of the
investigated deformation conditions. An extrapolation beyond deformations of 80%
leads to inaccuracies.



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*Source: 582739-2009-05-11.xml*