Metamodelling the hot deformation behaviour of titanium alloys using a mean-field approach

During the thermomechanical processing of titanium alloys in the β-domain, the β-phase undergoes restoration phenomena. This work describes them by a mean-field physical model that correlates the flow stress with the microstructural evolution. To reduce the computational time of process simulations, metamodels are developed for specific outputs of the mean-field physical model using Artificial Neural Network (ANN) and Decision Tree Regression (DTR). The performance of the obtained metamodels is evaluated in terms of the coefficient of determination (R²), the root-mean-square error (RMSE), and the mean relative error (MRE). No significant difference was observed between R2training and R2testing, meaning that all the metamodels correctly generalise the overall behaviour of the outputs for a wide range of inputs. The evolution of the metamodel outputs is compared with the model predictions in two different situations: 1) at a constant strain rate and temperature, and 2) during Finite Element (FE) simulations of the hot deformation of a hat-shaped sample, where temperature and effective strain rate vary at each element during deformation. The evolution of the outputs at constant and non-constant strain rates and temperature demonstrated the robustness of the metamodels in predicting the heterogeneous deformation within a workpiece. The computational time required by the metamodels to calculate selected outputs can be more than 100 times less than that of the model itself at a constant strain rate using MATLAB® and up to 19% less when coupled with FE simulations. The simulation results combined with microstructural analysis are used to visualise the different restoration mechanisms occurring in different regions of the hat-shaped sample as a function of the local thermomechanical history. The changes in strain rate and temperature during deformation influence the evolution of the wall dislocation density and the immobilisation rate of mobile dislocations at subgrain boundaries, leading to different kinetics of microstructure evolution.Fil: Miller Branco Ferraz, Franz. Graz University Of Technology.; AustriaFil: Sztangret, Lukasz. AGH University of Science and Technology; PoloniaFil: Carazo, Fernando Diego. Universidad Nacional de San Juan. Facultad de Ingeniería. Instituto de Mecanica Aplicada; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Buzolin, Ricardo Henrique. Graz University Of Technology.; AustriaFil: Wang, Peng. Graz University Of Technology.; AustriaFil: Szeliga, Danuta. AGH University of Science and Technology; PoloniaFil: dos Santos Effertz, Pedro. No especifíca;Fil: Macio, Piotr. AGH University of Science and Technology; PoloniaFil: Krumphals, Alfred. No especifíca;Fil: Poletti, Maria Cecilia. Graz University Of Technology.; Austri

Rule-based expert system application to optimizing of multiscale model of hot forging and heat treatment of TI-6AL-4V

Nowadays, multiscale methods are increasingly used in modeling of processes and designing of materials. However, there are two serious obstacles to wider application of such methods. One is a demand of computing power, which is present in almost all applications. Increasing of available computing power is not a solution. Exponential growth of computational complexity with increase of accuracy will always lead exceeding of available resources. Therefore, adaptation of multiscale models is important point of interest. The second obstacle is a difficultness of multiscale model design. Model is an abstraction of reality. Therefore, some assumptions have to be done – which phenomena are important and which do not. There is an additional point of interest in multiscale modeling – in which scale the particular phenomena can be modeled with a good balance of accuracy and computing power demand. Usually, there is no single good answer. Designing of a model can be seen as a kind of an optimization process, where the goal is a function of efficiency and reliability. The need of a such process is pointed out in many publications (e. g. [1]), but in the most of cases it have to be done by a researcher himself

Rule-based expert system application to optimizing of multiscale model of hot forging and heat treatment of TI-6AL-4V

Nowadays, multiscale methods are increasingly used in modeling of processes and designing of materials. However, there are two serious obstacles to wider application of such methods. One is a demand of computing power, which is present in almost all applications. Increasing of available computing power is not a solution. Exponential growth of computational complexity with increase of accuracy will always lead exceeding of available resources. Therefore, adaptation of multiscale models is important point of interest. The second obstacle is a difficultness of multiscale model design. Model is an abstraction of reality. Therefore, some assumptions have to be done – which phenomena are important and which do not. There is an additional point of interest in multiscale modeling – in which scale the particular phenomena can be modeled with a good balance of accuracy and computing power demand. Usually, there is no single good answer. Designing of a model can be seen as a kind of an optimization process, where the goal is a function of efficiency and reliability. The need of a such process is pointed out in many publications (e. g. [1]), but in the most of cases it have to be done by a researcher himself

Phase transformation sequence of Ti-6Al-4V as a function of the cooling rate

The growth kinetics of allotriomorphic α along the prior β grain boundaries and of globular primary α in Ti-6Al-4V during continuous cooling is described. A physical model is developed based on classical nucleation and growth of platelets for the allotriomorphic α. The growth of the primary α is modelled based on the growth of spherical particle immerged on a supersaturated β-matrix. Continuous cooling tests at two different holding temperatures in the α+β field, 930°C and 960°C, and five different cooling rates, 10, 30, 40, 100 and 300°C/min, are conducted to validate the proposed models and elucidate the growth sequence of those α morphologies. Additionally, interrupted tests at different temperatures are conducted to determine the progress of growth of primary α and formation allotriomorphic α during cooling. The size of primary α increases while its size distribution broadens with a decrease in cooling rate. Area fractions of primary α decrease with increasing cooling rate and increasing holding temperature. Moreover, the lower the cooling rate, the thicker the plates of allotriomorphic α. At the beginning of the cooling, growth of primary α, as well as formation of allotriomorphic α plates is observed. The experimental and modelled results show good agreement

Phase transformation sequence of Ti-6Al-4V as a function of the cooling rate

The growth kinetics of allotriomorphic α along the prior β grain boundaries and of globular primary α in Ti-6Al-4V during continuous cooling is described. A physical model is developed based on classical nucleation and growth of platelets for the allotriomorphic α. The growth of the primary α is modelled based on the growth of spherical particle immerged on a supersaturated β-matrix. Continuous cooling tests at two different holding temperatures in the α+β field, 930°C and 960°C, and five different cooling rates, 10, 30, 40, 100 and 300°C/min, are conducted to validate the proposed models and elucidate the growth sequence of those α morphologies. Additionally, interrupted tests at different temperatures are conducted to determine the progress of growth of primary α and formation allotriomorphic α during cooling. The size of primary α increases while its size distribution broadens with a decrease in cooling rate. Area fractions of primary α decrease with increasing cooling rate and increasing holding temperature. Moreover, the lower the cooling rate, the thicker the plates of allotriomorphic α. At the beginning of the cooling, growth of primary α, as well as formation of allotriomorphic α plates is observed. The experimental and modelled results show good agreement

Refinement of the Ti-17 microstructure after hot deformation: Coupled mesoscale model

The thermo-mechanical processing of Ti-alloys comprises several steps where complex deformation and temperature cycles are achieved. In this work, the static recrystallization behaviour of a Ti-17 alloy is investigated using ex-situ characterization and in-situ synchrotron radiation experiments aiming to understand the operating mechanisms and to establish the recrystallization kinetics. Hot compression in the β- field for different strain rates is applied to provide different initial microstructures before isothermal heat treatments and continuous cooling. Strain induced boundary migration is the main operating nucleation mechanism during static recrystallization. A simple mesoscale model is proposed to couple the evolution of the microstructure during hot deformation followed by annealing considering the heterogeneity of deformation within the β-grains, for the nucleation and growth of grains and the formation of the substructure by static recovery. Electron backscattered diffraction measurements are used after isothermal annealing and continuous cooling treatments to validate the model. A strong influence of the localization of deformation in the vicinity of the prior β-high angle grain boundaries is observed and empirically implemented in the mesoscale model. The strong influence of the temperature is attributed to the difference in high angle grain boundary mobility during static recrystallization. Grain refinement is not successfully achieved up to the investigated strain due to the insufficient nucleation rate with respect to the growth rate. However, a homogenous recrystallized microstructure is observed. The model can predict the microstructure for any starting microstructure, even beyond the experimental validatio