In order to predict hot deformation behavior of superalloy nimonic 80A, a back-propagational artificial neural network (BP-ANN) and strain-dependent Arrhenius-type model were established based on the experimental data from isothermal compression tests on a Gleeble-3500 thermo-mechanical simulator at temperatures ranging of 1050-1250˝C, strain rates ranging of 0.01-10.0 s´1. A comparison on a BP-ANN model and modified Arrhenius-type constitutive equation has been implemented in terms of

more »

... al parameters, involving mean value of relative (µ), standard deviation (w), correlation coefficient (R) and average absolute relative error (AARE). The µ-value and w-value of the improved Arrhenius-type model are 3.0012% and 2.0533%, respectively, while their values of the BP-ANN model are 0.0714% and 0.2564%, respectively. Meanwhile, the R-value and ARRE-value for the improved Arrhenius-type model are 0.9899 and 3.06%, while their values for the BP-ANN model are 0.9998 and 1.20%. The results indicate that the BP-ANN model can accurately track the experimental data and show a good generalization capability to predict complex flow behavior. Then, a 3D continuous interaction space for temperature, strain rate, strain and stress was constructed based on the expanded data predicted by a well-trained BP-ANN model. The developed 3D continuous space for hot working parameters articulates the intrinsic relationships of superalloy nimonic 80A. Appl. Sci. 2016, 6, 66 2 of 16 obtain an accurate strain-stress relationship becomes critical for the correct calculation of the finite element model [6] . So far, a large amount of research on the characterization for complex non-linear relationships between true stress and deformed parameters such as strain, strain rate and temperature at elevated temperatures has been proposed. Numerous efforts have been made to three types of constitutive models involving the analytical constitutive model, phenomenological constitutive model and artificial neural network [7] . In analytical models, constitutive relations are derived based on physical theories, which require very clear understanding of the processes that control the deformation of the materials. The phenomenological constitutive model is an accurate mathematical model and has relatively many coefficients that need to be calibrated with experimental data. A phenomenological model including the Arrhenius-type equation with hyperbolic laws was proposed to predict flow stress [8] . Furthermore, an improved Arrhenius-type constitutive model incorporating the strain effect on the hot deforming parameters, has been developed to describe and predict the flow behavior for diverse materials or alloys. Lin et al. proposed a modified hyperbolic sine constitutive equation, in which the influence of strain was incorporated to predict the flow stress of 42CrMo steel [9]. Later, the modified Arrhenius-type equation was precise for describing the elevated temperature flow stress of Aermet100 steel [10], Ti60 titanium alloy [11], Al-Zn-Mg-Er-Zr alloy [12], etc. Such constitutive equations are typically only applicable to the limited materials with specific conditions due to the poor adaptability for the new experimental data. Additionally, the artificial neural network (ANN) model with a back-propagation learning algorithm has been successfully used to predict the hot working behavior of material to overcome the gross approximations introduced by the regression methods [6,13-23]. The back-propagational artificial neural network (BP-ANN) is a model emulating some functions of biological neural networks with a data-driven black-box structure [24], thus it merely needs a collection of some typical examples from the anticipant mapping functions for training regardless of explicit professional knowledge of deformation mechanisms. The BP-ANN model with a data-driven black-box provides a novel way to predict the flow stress by learning the complex and non-linear relationships of flow stress, strain rate, strain and temperature with true stress-strain data. Ji et al. applied a feed-forward back-propagation ANN model to predict the flow stress of Aermet100 steel [13]. Haghdadi et al. developed a feed-forward back propagation ANN with single hidden layer to predict the flow behavior of an A356 aluminum alloy [15] . Several such works reveal that the predicted results are well consistent with experimental results; furthermore, the neural network is an effective tool to predict the hot deformation behavior of non-linear characteristic materials. Accordingly, in this work, the stress-strain data of superalloy nimonic 80A were obtained from a series of isothermal compression tests carried out in a wide temperature range of 1050-1250˝C and strain rate range of 0.01-10 s´1 on a Gleeble 3500 thermo-mechanical simulator (Dynamic Systems Inc., New York, NY, United States). A BP-ANN model which takes temperature (T), strain rate ( . ε) and strain (ε) as the input variables, and true stress (σ) as the output variable was established by determining proper network structure and parameters to predict the non-linear complex flow behaviors. Meanwhile, a strain-dependent Arrhenius-type constitutive model was constructed to predict the flow stress of nimonic 80A. Subsequently, a comparative analysis on the performance of two such models has been carried out by a series of evaluators such as relative error (δ), average absolute relative error (AARE) and correlation coefficient (R), which predictably indicates that the former has higher prediction accuracy. In the following, as described previously, a 3D continuous interaction space within the temperature range of 950-1250˝C, strain rate range of 0.01-10 s´1, and strain range of 0.1-0.9 was constructed. Materials and Experimental Procedure The chemical compositions (wt. %) of superalloy nimonic 80A used in this study were as follows: C-0.069, Mn-0.630, Cr-2, Fe-1.260, Ti-2.070, Al-0.680, Si-0.550, S-0.001. Twenty nimonic 80A specimens with a diameter of 10 mm and a height of 12 mm were processed from the same extruded