^{1}

^{1}

^{1}

^{2}

^{2}

^{3}

^{3}

^{1}

^{2}

^{3}

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.

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 [

Microstructural
transformations during integrated heat treatment are influenced not only by
high austenitising temperatures of about

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 [

To physically
simulate the precision forging process, specimens of the investigated melts (see
Table

Chemical composition of the investigated melts in mass %.

Melt | 34CrMo4 | 42CrMo4 | 50CrMo4 | 51CrV4 | 34CrNiMo6 |
---|---|---|---|---|---|

C | 0.325 | 0.410 | 0.491 | 0.467 | 0.326 |

Si | 0.289 | 0.336 | 0.212 | 0.223 | 0.263 |

Mn | 0.577 | 0.701 | 0.647 | 0.845 | 0.588 |

P | 0.007 | 0.011 | 0.005 | 0.006 | 0.001 |

S | 0.003 | 0.025 | 0.004 | 0.017 | 0.004 |

Cr | 0.945 | 0.998 | 1.039 | 1.015 | 1.433 |

Cu | 0.286 | 0.380 | 0.219 | 0.223 | 0.260 |

Mo | 0.132 | 0.171 | 0.133 | 0.013 | 0.126 |

Ni | 0.098 | 0.191 | 0.092 | 0.083 | 1.469 |

Al | 0.025 | 0.029 | 0.024 | 0.018 | 0.023 |

Nb | 0.019 | 0.019 | 0.020 | 0.002 | 0.020 |

Following
isothermal holding for 600 seconds at this temperature, the specimens were
deformed by 30% and 60%, respectively (strain rate 1

Continuous cooling transformation diagrams of tempering steel 50CrMo4
for deformation of 30%, 60%, and 0%, respectively [

Initiating the
cooling from temperatures higher than

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

The curves for the initiation and completion of microstructural transformations are nontrivial for
classical parametric approximation methods. We therefore use feed-forward neural
networks (

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 Figure

Scheme of the approach for predicting CCT diagrams.

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 Figure

Data extrapolation
to the common interval
of microstructural transformations for
different degrees of deformation

For equidistant
time steps

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 of

Scheme of data transformation into the (

Figure

(a) Curves of martensite initiation temperature in the (

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.

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:

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. Figure

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.

Figure

Dynamics of the microstructural transformations of the tempering steel 50CrMo4.

Figure

Efficiency of the neural networks for the tempering steel 50CrMo4.

Figures

Results for tempering steel 42CrMo4 with a deformation of 0%.

Results for tempering steel 34CrMo4 with a deformation of 0%.

Results for tempering steel 34CrNiMo6 with a deformation of 0%.

Results for tempering steel 51CrV4 with a deformation of 0%.

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 (

(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 [

(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.

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.

The authors thank the German Research Foundation for the financial support of the research work within the collaborative research center CRC 489.