Dataset for deformation behavior of pure titanium grade 2 materials during continuous extrusion

There is a huge application and demand for titanium alloys with excellent upgraded mechanical, metallurgical, and material properties in modern industries. To fulfill the demand of modern industries metal forming process is highly desirable. Among all metal forming processes, a special type of cold forming called the continuous extrusion process has been highly appropriate to fulfill the demands. The theoretical analysis has been carried out through Upper Bound Method. The numerical simulation has been carried out through the three-dimensional finite element tool DEFORM-3D. The experimental plan and design have been carried out using Taguchi (2^3) array methods on the MINITAB platform by considering extrusion wheel velocity and feedstock temperature as chief extrusion parameters. The experimental validation process was executed on 12.5 mm CP- Titanium grade 2 feedstock materials using a TBJ350 CONFORM machine setup. The optimization process of parameters for the optimum value of the response variable was carried out through Grey Relational Analysis.


a b s t r a c t
There is a huge application and demand for titanium alloys with excellent upgraded mechanical, metallurgical, and material properties in modern industries. To fulfill the demand of modern industries metal forming process is highly desirable. Among all metal forming processes, a special type of cold forming called the continuous extrusion process has been highly appropriate to fulfill the demands. The theoretical analysis has been carried out through Upper Bound Method. The numerical simulation has been carried out through the three-dimensional finite element tool DEFORM-3D. The experimental plan and design have been carried out using Taguchi (2 ^ 3) array methods on the MINITAB platform by considering extrusion wheel velocity and feedstock temperature as chief extrusion parameters. The experimental validation process was executed on 12.5 mm CP-Titanium grade 2 feedstock materials using a TBJ350 CONFORM machine setup. The optimization process of parameters for the optimum value of the response variable was carried out through Grey Relational Analysis.

Value of the Data
• The dataset helps to realize the optimum parameter conditions of CP-Ti-Grade 2 deformation through the Continuous Extrusion process and achieve better mechanical and metallurgical properties. • The dataset reveals the optimum parameter interaction during the Continuous Extrusion process, which is highly helpful for metal forming researchers and industries in the Continuous Forming process of non-ferrous alloys, especially on titanium feedstock materials. • The dataset presented is analyzed through theoretical analysis, numerical simulation, and experimental validation and optimized using the GRA technique, which can be applied for further analysis using other multivariate optimization techniques like the DEAR approach, Genetic algorithm, and Factor analysis.

Data Description
In this article, both raw and analyzed datasets are accessible, correlated with deformation analysis of Commercially Pure Titanium Grade 2 material through a continuous extrusion process. Table 1 , 2 , 3 , and 4 illustrates the elemental composition, physical, mechanical, and thermal properties of CP-Titanium grade 2 feedstock material. The data presented in this table is    provided by the suppliers CP-Titanium grade 2 feedstock material [1] . The experimental plan and design of the chief parameters of the process have been elucidated using Taguchi L9 (2 ^ 3) orthogonal array, as shown in Table 5 . The theoretical analysis results of CP-Titanium Grade 2 Feedstock material using the upper bound method have been tabulated in Table 5 . Table 6 illustrates the Numerical simulation results of CP-Titanium grade 2 material through DEFORM-3D. Table 7 depicts the Simulation Results for CP titanium grade 2 feedstock material. Finally, Table 8 shows the Experimental validation Results for CP titanium grade 2 feedstock material. The rationale behind the theoretical analysis is to determine and understand the deformation behavior of cp-titanium grade 2 material during continuous forming processes under various ideal assumptions, such as the extrusion wheel (driving wheel) as a rigid and non-friction side plate. The rationale behind running numerical simulations is to determine and understand the deformation behavior of cp-titanium grade 2 material during continuous forming processes through the finite element method through which the results can be approximated to a great extent, including various assumptions such as workpiece material is assumed to be rigid visco-plastic, the material is homogeneous and isotropic, there is no strain hardening, interfaces are either frictionless, or sticking friction prevails.  All in all, the main reasons behind running both methods are to identify and understand the optimum conditions and ranges of each input parameter for the deformation processes of cp-titanium grade 2 material through continuous forming within fewer power consumptions, safe working conditions, especially for extrusion wheel, shoe, and abutment materials and to estimate the differences in results occurring due to these approaches.
The investigation on analysis of a robust new design for titanium alloy prick hole extrusion was carried out through FEA and Taguchi methods. The effect of die semi angle, die hole diameter, friction factor, ram velocity, and temperature of billet were investigated on the strain, stress, and damage value. The optimum value of input parameters was investigated for achieving the perfect extrusion [7] . The multi-response optimization of hot extrusion process parameters using FEA and Grey Relational based Taguchi method was carried out on hot direct extrusion of AA6061alloy. The numerical simulation was carried out through DEFORM-3D. The statistical significance of the process parameters was carried out through Analysis of Variance (ANOVA). The degree of significance of die angle was found to be highest followed by ram speed and coefficient of friction [8] . The investigation on sensitivity analysis of die structural and process parameters in porthole die extrusion of magnesium alloy tube was carried out using the Taguchi method. The simulation of the welding process of metal streams for calculation of peak extrusion load and the temperature was carried out through Lagrangian-Eulerian algorithm. The analysis of welding pressure, temperature, effective strain rate, and stresses on the welding plane were investigated through the J-welding criterion [9] .
The numerical simulation of 12.5 mm diameter Titanium alloy feedstock material has been carried out using the Finite Element simulation tool DEFORM-3D.
The basic equations of the rigid-plastic finite element are as follows [10] : Equilibrium equation: Constitutive equations: Boundary conditions: where σ i j and ˙ ε i j are the stress and the strain rate, respectively, σ and˙ ε are the effective stress and the effective strain rate, respectively . F j is the force on the boundary surface of S F , and U i is the deformation velocity on the boundary surface of S U . The weak form of rigid-plastic FEM can be determined by applying the variation method to Eqs.
Where V and S are the volume and the surface area of the material, respectively, and K is the penalty constant. Yielding criteria which are used for solving the problem is Von Mises (in the Deform3D). Eqs. (6) And (7) show effective strain and effective stress respectively.
Where ε i and σ i are principle strain and principal stress in the direction i respectively.
The upper bound theorem [2] states that among all possible kinematically admissible velocity fields, the one that minimizes the total power ϕ T is the actual velocity field.
The first term expresses the internal power of deformation over the volume of the deformation zone. In contrast, the second term represents the power dissipated in shearing the material over the velocity discontinuity surfaces and at the tool-work interface (i.e., frictional power). Here asterisk ( * ) indicates that the values of stress, strain rate, and velocity discontinuity are obtained from an assumed kinematically admissible velocity field. Table 8 portrays the Experimental validation Results of CP titanium grade 2 feedstock material deformation. Table 9 illustrates the validation of power consumption for deformation of CP-Titanium grade 2 material. Finally, Table 10 represents the Test result of ANOVA for effective stresses of CP-Titanium Grade 2 feedstock material. So as tabulated in Table 10 , ANOVA determines the significance effect and contribution of each (Extrusion wheel velocity, Feedstock Temperature) parameter on the effective stresses of feedstock material during the continuous forming processes to get optimum (minimum) required deformation load and power consumption.
The Theoretical analysis, Numerical Simulation, and Experimental analysis of power consumption results for deformation of CP-Titanium Grade 2 material have been illustrated in Table 11 and Fig. 1 above and are in good agreement, thereby maintaining the error up to 5 %.

Materials
Commercially Pure titanium grade 2 circular rod material size of 12.5 mm diameter was utilized as feedstock material which is deformed through a continuous extrusion process whose elemental composition and properties are depicted in Tables 1 , 2 , 3 and 4 . Fig. 2 depicts the physical appearance of CP-Ti grade 2 feedstock material before the deformation process.

Methods
Theoretical analysis, Numerical simulation and experimental validation were implemented to identify the optimum process parameter conditions of deformation of CP-Titanium grade 2 feedstock material through the Continuous Extrusion Process. [3] The theoretical analysis was analyzed by similarity equations using the upper bound technique as shown in eqns. 1 -5 . The commercial finite element method code was applied through the DEFORM-3D platform [4] to conduct a numerical simulation analysis of deformation behavior by considering the input numerical data values as tabulated in Table 13 . Numerical simulation analysis was evaluated by using the DEFORM-3D platform. The experimental validation process has been examined through commercial continuous extrusion setup TBJ350 machine having specification as shown in Table 12 . Extrusion wheel velocity, feedstock temperature and extrusion ratio are the main parameters in the overall Continuous Extrusion processes of CP-Titanium grade 2 feedstock material.

In the die region
Here, According to the depreciation of the total rate of energy consumption ( d w T dt ), the value of θ min = 90 and a corresponding value of die angle, α = 30. . There are two planes of tangential velocity discontinuity in the die region: AB and BC; while it crosses plane AB, the tangential velocity discontinuity is V AB . Similarly, while it crosses plane BC, the tangential velocity discontinuity is V BC, as shown on the hodograph representation.
Average extrusion pressure in the die region ( p e d ) can be calculated as,

In the groove region
Average extrusion pressure in the groove region ( p e G ) can be calculated as Where m 1 is the friction coefficient on the shoe, m 2 is the friction coefficient inside the groove, m 3 is the friction coefficient on the abutment, k is shear stress of the feedstock material, H is the width of feedstock material, h 0 die chamber height and L is the length of the container (die).
Then, the total extrusion pressure ( p e T ) is the sum of average extrusion pressure in the die and average extrusion pressure in the groove, The force required to carry out the extrusion process can be calculated as, Then, the power required during the continuous forming process can be calculated as, Where F -the force required for deformation, H -the width of material, mm and N -Extrusion wheel velocity, rpm. As illustrated in Table 12 below in the Experimental plan and Design table of the Taguchi L9 (2 ^ 3) orthogonal array two variables are considered as a factor with three levels. Table 13 depicts the numerical simulation data of CP-Ti grade 2 that include geometry data, simulation data and material data. The overall flow processes of the DEFORM-3D tool system have been illustrated in Fig. 4 . Table 14 illustrates details of tetrahedron mesh elements.   Specification and applications of Commercial Setup of TBJ350 machine have been tabulated in Table 15 . Table 16 depicts the experimental validation plans of the process. For the case of experimental validation of power consumption, 10 0 0 °C feedstock temperature and 4 rpm extrusion wheel velocity have been chosen as per the prediction made by theoretical and numerical simulation results of the power consumption. The theoretical and simulation results suggested that the power consumption decreases as the extrusion wheel velocity decreases and feedstock temperature increases. As a result, for experimental validation, the feedstock temperature of the work material has been selected in the form of the average values of hot working condition feedstock of temperature and lower extrusion wheel velocity to get the optimum value (lower) of machine power consumption.

Design of experiments
Design of experiment (DOE) is a method of defining and investigating all possible conditions involving multiple factors, parameters, and variables in the experimental analysis Taguchi method is a commonly used problem-solving tool that can improve the product's performance, process design, and system. And also, it's is a process optimization method that is based on 8steps of planning, conducting, and evaluating the results of matrix experiments to determine the best levels of control factors. The primary goal is to keep the variance in the output very low, even in the presence of noise inputs. As shown below, Fig. 5 . demonstrates the interaction plot of a mean of effective stress. In this interaction plot the lines are not parallel which indicates, the relationship between Extrusion wheel velocity and feedstock temperature on the value of mean effective stress has a significant effect which clarifies the interaction between feedstock temperature and extrusion wheel velocity during the process on the results of effective-stresses of the feedstock material to, optimize the load required for the deformation of feedstock material during continuous forming processes. Therefore, the interaction between extrusion wheel  Interaction plot for Effective-stress velocity at 8 rpm and 600 °C feedstock temperature is the optimum combination of parameters for the deformation of feedstock material during the processes. Fig. 6 . illustrates the interaction plot of a mean of power consumption. It indicates the interaction between extrusion wheel velocity and feedstock temperature on of TBJ350 conform machine during the processes. . In this interaction plot, the lines are not parallel. So, the interaction effect indicates that the relationship between Extrusion wheel velocity and feedstock temperature significantly affects the mean power consumption value, as its displayed in Fig. 6 . below, the combination of extrusion wheel  velocity at 4 rpm and 600 °C feedstock temperature indicates the optimum power consumption of the machine during the deformation process. Fig. 7 shows a contour plot to explore the relationship between three variables. These plots display two independent variables (extrusion wheel velocity, feedstock temperature) and one dependent variable (effective stresses). In addition, the plot shows values of the effective stresses variable for combinations of the extrusion wheel velocity and feedstock temperature variables, it indicates that the lowest effective stresses during the processes occur near (8-12) rpm extrusion wheel velocity and 600 °C feedstock temperature, resulting in the optimum load required for the deformation of feedstock material during continuous forming processes.

Grey relational analysis
Grey relational analysis is the multiple response optimization techniques used for solving interrelationships among the multiple responses. A grey relational grade is obtained to analyze the multiple responses' relational degree in this approach. [6] Have attempted a grey relationalbased approach to solve multi-response problems in the Taguchi methods. The original response data was Transformed into an S/N ratio ( η) using the appropriate formulae depending on the type of quality characteristic. Eqn. 6 expresses the smaller-the better quality characteristics. The S/N ratio ( η) is given by: Where n-is the number of replications Normalization is a transformation performed on a single input to distribute the data evenly and scale it into an acceptable range for further analysis. Normalize Y ij as Z ij (0 ≤ Z ij ≤1) by the following formula to avoid the effect of using different units and to reduce variability, Grey relational coefficient is used for determining how close Y oj and Y ij. Grey relational coefficient can be calculated by using the following relations, Where i = 1, 2… n -experiments and j = 1, 2...., m -responses GCij = grey relational coefficient for the i th experiment/trial and j th dependent variable response = absolute difference between Y oj and Y ij which is a deviation from target the value and can be treated as a quality loss. Y oj = optimum performance value or the ideal normalized value of the j th response Y ij = the i th normalized value of the j th response/dependent variable min = minimum value of max = maximum value of λ -is the distinguishing coefficient which is defined in the range 0 ≤ λ ≤ 1 (the value may be adjusted on the practical needs of the system) Grey relational grade determines the optimum points of multi-response by calculating the average values of grey relational coefficient of responses at each experiment trial. So, the optimum value of each response is considered at the highest value of grey relational grade. The following relation can determine Grey's relational grade, Where GC ij is Grey relational grade and m is the number of responses.

Funding
No funding has been done for this research work.

Declaration of Competing Interest
The authors declare that they have no competing interest.

Data Availability
Dataset for: Deformation behaviour of CP-titanium grade 2 material through continuous extrusion processes (Original data) (Mendeley Data).