Isothermal constant strain rate compression experiments were carried out on TC20 titanium alloy using a Gleeble- 1500 thermal simulation tester to investigate its high temperature flow behaviour at deformation temperatures of 750 - 900 °C and strain rates of 0,001 - 1 s-1. The results show that the flow stress basically decreases with increasing deformation temperature and increases with increasing strain rate. The correlation coefficients and mean relative errors were 0,998 and 5,06 % respectively, proving that the BP neural network-based intrinsic structure model is effective in predicting the flow stress of the alloy

Miao, J. L.

Xuan, Z. Y.

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65METALURGIJA 63 (2024) 1, 65-68Z. Y. XUAN, J. L. MIAONEURAL NETWORK-BASED INTRINSIC STRUCTURE RELATIONSHIP OF TC20 TITANIUM ALLOY FOR MEDICAL APPLICATIONSReceived – Primljeno: 2023-05-09Accepted – Prihvaćeno: 2023-08-25Original Scientific Paper – Izvorni znanstveni radIsothermal constant strain rate compression experiments were carried out on TC20 titanium alloy using a Glee-ble-1500 thermal simulation tester to investigate its high temperature flow behaviour at deformation temperatures of 750 - 900 °C and strain rates of 0,001 - 1 s-1. The results show that the flow stress basically decreases with increas-ing deformation temperature and increases with increasing strain rate. The correlation coefficients and mean rela-tive errors were 0,998 and 5,06 % respectively, proving that the BP neural network-based intrinsic structure model is effective in predicting the flow stress of the alloy.Keywords: TC20 titanium alloy; hot compression; stress-strain curve; constitutive model; BP neural networksISSN 0543-5846METABK 63(1) 65-68 (2024)UDC – UDK 669.295:620.113:620.16-539.373/513.2.4:621.72=111INTRODUCTIONThe current increase in medical conditions has led to a growing demand for rehabilitation materials for medi-cal use. Because of its high corrosion resistance and high strength, titanium alloy is 2 - 3 times stronger than steel, but lighter than steel, with a long service life and excellent fatigue resistance, while titanium alloy has good wear resistance, its wear resistance is 7 - 8 times that of steel, which can greatly extend the service life of tools. Therefore, titanium alloys are increasingly be-coming the main material used in medical applications.The intrinsic structure relationship of a material, as the link between the plastic deformation behaviour of the material and the various deformation parameters, is an indispensable part of the information related to the material deformation and the finite element simulation study of the material. The flow stress of a material is an important parameter for characterising the material properties during plastic deformation, and is also an im-portant indicator of the physical nature of material de-formation [1,2]. Therefore, the selection of a suitable intrinsic structure relationship model can accurately predict. the material flow behaviour and obtain the cor-responding flow stresses, providing an important refer-ence for the study of metal plastic deformation theory, the formulation of suitable processing parameters, the control of material properties and finite element simula-tion [3,4].Currently, the BP neural network intrinsic structure relationship model has been widely used for the predic-tion of high-temperature flow stresses in metallic mate-Z.Y Xuan (E-mail: xuanzhaoyan@ncst.edu.cn), J. L. Miao, College of Mechanical Engineering, North China University of Science and Tech-nology, Hebei, Tangshan, China.rials due to its ability to quickly and effectively solve complex nonlinear problems with multiple factors [5]. Feng Rui et al [6] predicted the high-temperature flow stress of BT25 titanium alloy based on BP neural net-work and strain-compensated intrinsic structure model and found that the prediction accuracy of BP neural net-work intrinsic structure model was higher than that of strain-compensated intrinsic structure model, and the average relative error was only 3,12 %.CAI et al [7] studied the thermal deformation behaviour of 3Cr23N-i8Mn3N based on the BP neural network intrinsic con-stitutive model and showed that the predicted stress val-ues of the model were in good agreement with the ex-perimental values. However, there are limited studies on the high temperature rheological behavior and intrin-sic structure relationship of TC20 titanium alloy by do-mestic and foreign scholars. Therefore, this paper in-vestigates the high-temperature rheological behaviour of TC20 titanium alloy through hot compression exper-imental data, and uses BP neural network to establish an intrinsic structure relationship model to accurately pre-dict the high-temperature flow stresses and provide a theoretical basis for the reasonable formulation of plas-tic forming process of this alloy in actual production.EXPERIMENTAL MATERIALS AND METHODThe material used in this experiment was TC20 tita-nium alloy (Ti-6Al-7Nb) with good strength, plasticity, toughness and strength, the original organisation of which is shown in Figure 1. The isothermal constant strain rate compression experiments were carried out on a Gleeble-1500 thermal simulation tester with a speci-men size of Φ 8 mm × 12 mm, deformation tempera-tures of 750, 800, 850 and 900, strain rates of 0,001, 66  METALURGIJA 63 (2024) 1, 65-68Z. Y. XUAN et al.: NEURAL NETWORK-BASED INTRINSIC STRUCTURE RELATIONSHIP OF TC20 TITANIUM ALLOY…0,01, 0,1 and 1 s-1 and a 60 % depression rate, and the specimens were heated to the set temperature at a heat-ing rate of 10 °C / s and then held for For 300 s.TRUE STRESS-STRAIN CURVEFigure 1 shows the true stress-strain curves of TC20 titanium alloy at different deformation temperatures and different strain rates. It is clear from the graph that the rheological stress of medical TC20 titanium alloy decreases as the deformation temperature increases and the strain rate decreases. Therefore, medical TC20 tita-nium alloy is a heat-sensitive and strain-rate sensitive material. As the deformation temperature increases, the average kinetic energy of atoms increases and the criti-cal tangential stress for crystal slip decreases, reducing the hindrance of dislocation and intergranular slip. On the other hand, as the deformation temperature increas-es, dynamic reversion and dynamic recrystallisation are more likely to occur, thereby reducing the dislocation density and counteracting the process hardening that occurs during deformation, thereby contributing to the reduction in rheological stress.CONSTRUCTION OF A BP NEURAL NETWORK PRINCIPAL STRUCTURE MODELBP neural network is a neural network obtained by the error back propagation learning algorithm of multi-layer feed-forward network after training, which be-longs to forward neural network.Considering the vari-ous influencing factors of flow stress and the capability of BP neural network, a 3-layer BP neural network with input layer, implicit layer and output layer was estab-lished. The number of neurons in the input layer is set to 3. The number of neurons in the output layer is set to 1, as the output data is the flow stress of TC20 titanium alloy. In general, too many hidden layers will increase the training time and the prediction accuracy is usually not very obvious. In this study, a single hidden layer is used, and the number of neurons in the hidden layer is usually determined according to equation (1).  (1)Where: N is the number of neurons in the hidden layer; n is the number of neurons in the input layer, n = 3; m is the number of neurons in the output layer, m = 1; k is a constant, k  [1,10]. The structure of the neural network in this study is shown in Figure 2, and the number of neurons in the hidden layer of the neural network can be derived from equation (1) in the range 3  12. The number of neurons in the hidden layer was selected as 12 after calculation.In order to ensure the smooth training of the network and the quality of the model, the activation function from the input layer to the hidden layer is the tansig function and the activation function from the hidden layer to the output layer is the purelin function; the learning function Figure 1  True stress-strain curve for thermal deformation  of TC20 titanium alloy (a) 750 °C (b) 800 °C (c) 850 °C (d) 900 °C67Z. Y. XUAN et al.: NEURAL NETWORK-BASED INTRINSIC STRUCTURE RELATIONSHIP OF TC20 TITANIUM ALLOY…METALURGIJA 63 (2024) 1, 65-68is the learngdm function. The learning rate in the range of 0,01  1. In this study, the learning rate was chosen to be 0.3. The target of the training error was set to 10-4 and the number of steps was set to 3 000.In order to enable the BP neural network to achieve high accuracy and meet the requirements of use, the sam-ple data need to be normalised before input and output. In this paper, the mapminmax function provided in Matlab software is used to normalize the input and output data, and the normalization interval is chosen to be [0,1], and the function expression is shown in equation (2).  (2)Where: y is the normalised value of the input and output data; x is the initial value of the input and output data; xmax and xmin are the maximum and minimum values of the corresponding input and output data; ymax and ymin are the maximum and minimum values of the normal-ised interval.In addition, the normalisation is reversed when the data is output.  (3)where:Y is the inverse normalised output data; y0 is the output data normalised in the previous step.VALIDATION OF BP NEURAL NETWORK INTRINSIC STRUCTURE MODELSFigure 3 shows a comparison between the predicted values of flow stresses calculated from the BP neural net-work based intrinsic structure model and the experimen-tal values at different deformation temperatures. Figure 4 shows a plot of the model error analysis. Also in order to measure the accuracy of this intrinsic structure model, the correlation coefficient R (Eq. (4)) and the average relative error AARE (Eq. (5)) are introduced  (4)  (5)Figure 2 BP neural network structureFigure 3  Comparison of experimental and predicted values (a) 750 °C (b) 800 °C (c) 850 °C (d) 900 °C68  METALURGIJA 63 (2024) 1, 65-68Z. Y. XUAN et al.: NEURAL NETWORK-BASED INTRINSIC STRUCTURE RELATIONSHIP OF TC20 TITANIUM ALLOY…where:N is the total number of data; Ei is the experimen-tal value; Pi is the predicted value;  is the mean of the experimental values;  is the mean of thepredicted val-ue i; Ei is the i-th experimental value; and Pi is the first predicted value.The correlation coefficient R and the average rela-tive error AARE of the model were 0,998 and 5,06 % respectively when the data were collated and substitut-ed into equation (4) and equation (5), and the deviation value of the predicted value relative to the experimental value was less than 15 % at 95,2 % of the points, indi-cating that the present structural model has a high pre-diction accuracy.CONCLUSION(1) The flow stress of TC200 titanium alloy is sig-nificantly influenced by the deformation temperature and strain rate during the high temperature deformation process. The flow stress basically decreases with in-creasing deformation temperature and increases with increasing strain rate, and the steady state flow charac-teristics are more obvious at higher deformation tem-peratures.Figure 4 Correlation analysis(2) The BP neural network-based intrinsic structure relationship model has high accuracy, its correlation co-efficient and average relative error are 0,998 and 5,06 % respectively, which can accurately predict the high tem-perature flow behaviour, and the results obtained can provide a theoretical basis for the rational formulation of plastic forming process of TC200 titanium alloy for practical production.REFERENCES[1]  Zhang R , Huang L , Zhao X , et al. Influence of deforma-tion parameters and network structure to the microstructu-re evolution and flow stress of TiBw/Ti64 composite[J]. Materials Science and Engineering A (2021), 809,140997.[2] Fang S, Zhang M , Dong Y . Flow Stress Evolution of P/M Nickel-base Superalloy During High-temperature Plastic Deformation[J]. Journal of Physics Conference Series (2020) 1637,012097.[3] Quan G Z, Wang T, Li Y L, et al. Artificial Neural Network Modeling to Evaluate the Dynamic Flow Stress of 7050 Aluminum Alloy[J]. Journal of Materials Engineering and Performance, 25(2016)2, 553-564.[4] Liu Y, Yao Z, Ning Y, et al. The flow behavior and consti-tutive equation in isothermal compression of FGH4096-GH4133B dual alloy[J]. Materials and Design (2014)63, 829-837.[5] Li Q, Jin Z. Comparative Study of Physical-Based Consti-tutive Model and BP Artificial Neural Network Model in Predicting High Temperature Flow Stress of AZ80 Magne-sium Alloy [J]. Rare Metal Materials and Engineering 50(2021)11, 3924-3933.[6] F Rui, W Kelu, L Shiqiang, et al. Constitutive relationship research on BT25 titanium alloy based on strain compen-sation and BP neural network [J]. Journal of Plasticity En-gineering27(2020)12, 183-190.[7] Cai Z M, Ji H C, Pei W C, et al. Constitutive model of 3Cr23Ni8Mn3N heat-resistant steel based on back propa-gation (BP) neural network(NN)[J]. Metalurgija, 58(2019) 3-4, 191-195.Note:  The responsible translator for English language is Y.F. Meng - North China University of Science and Technology, China

Neural network-based intrinsic structure relationship of TC20 titanium alloy for medical applications

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