A numerical approach on parametric sensitivity analysis for an aeronautic aluminium alloy turning process

H. Ijaz*, M. Zain-ul-abdein**, W. Saleem***, M. Asad****, T. Mabrouki***** *Mechanical Engineering Department, University of Jeddah, Jeddah, Saudi Arabia, E-mail: hassan605@yahoo.com **Mechanical Engineering Department, University of Jeddah, Jeddah, Saudi Arabia, E-mail: mzainulabdein@gmail.com ***Mechanical Engineering Department, University of Jeddah, Jeddah, Saudi Arabia, E-mail: waqas95@yahoo.com ****Mechanical Engineering Department, University of Management & Technology, 54770 Lahore, Pakistan, E-mail: masadakhtar@gmail.com *****École Nationale d'Ingénieurs de Tunis (ENIT), Tunis, E-mail: tarek.mabrouki@enit.rnu.tn


Introduction
The usage of aluminum alloys like A2024-T351 as structural parts in aeronautic and avionic industry is very common these days due to its good strength to weight ratio properties.These types of materials undergo numerous dry cutting machining processes before taking final shape [1][2].These materials experience severe cutting forces during the machining processes in the manufacturing industry that may affect the chip formation and work piece distortions [3].In industry, different machining processes are used based on machinist models and empirical studies.High costs of experiments in terms of time, price and availability of expensive materials demand an alternative strategy in the form of finite element analysis to estimate them.Hence optimization of different machining parameters (like cutting speed, feed rate, tool geometry etc) with the help of finite element analysis attains a value of prime importance [4][5].
The cutting process in metals may be described as a crack like entity between the two surfaces i.e. chip and work piece.Two established theories, damage mechanics and fracture mechanics, may be employed to study the crack growth behavior in materials.Fracture mechanics theory established on the basis that a crack like entity already exists in material and it deals with the propagation of crack [6].On the other hand damage mechanics theory not only predicts the propagation of crack but also simulate the process of crack initiation [7].In the present work, Johson-Cook plasticity material model coupled with damage evolution law is adopted to simulate the crack growth behaviour between the two surfaces [8].Johnson-Cook model provides description of metal material behavior by considering large strains, high strain-rates and temperature dependent viscoplasticity.
In the present study 2D finite element analysis of turning process of aluminum alloy A2024-T351 is performed to study the process of chip formation and different parameters affecting the aforementioned process using commercially available FE software, Abaqus/Explicit [9].This particular finite element simulation study will help to understand the turning process of aluminum alloy and to optimize the machining parameters required for the turning process.The authenticity of finite element analysis is verified by comparing the simulation results with the available experimental data [10].
This article is organized as follows: in section 2, mathematical details of employed material model of Johnson-Cook are discussed.Section 3 contains the details of FE model and simulation results.Then a comprehensive parametric study is presented and discussed in section 4. Finally some concluding remarks are given in section 5.

Material model
The Johnson-Cook material model is adopted in the present study for the cutting simulation and chip formation phenomenon.If  is the equivalent plastic flow stress then following expression can be written [8]: where A, B and n are material constants for strain hardening; C is the material constant for strain hardening rate, m is material constant for thermal softening effect, Troom is the reference ambient temperature and Tmelt is the melting temperature of the material.Similarly in the above equation,  is the equivalent plastic strain,   is the plastic strain rate, 0   is the reference strain rate.If 0i   is the plastic strain at damage initiation then it can be expressed by following criteria [8]: constants that can be found from experiments and P is the pressure stress [8].During the analysis, the damage is initiated when a scalar damage parameter ω exceeds 1 and this parameter can be expressed as [11] Based on Hillerborg's fracture energy proposal, the energy Gf required to open a unit area of crack may be written as [12]: In the above equation L is the characteristic length of element and f u is the equivalent plastic displacement at failure and can be computed by the following equation [13]: If E is the modulus of elasticity of material and υ is the Poisson ratio then fracture energy Gf for mode I and mode II crack growth can identified from experiments by the following relation [10]: In the above equation KIC and KIIC are material constants for mode I and mode II crack growth respectively and termed as fracture toughness of the material.(7)

Finite element analysis
2D finite element analysis of turning process is performed using Abaqus/Explicit [9].Johnson-Cook material model along with damage evolution law is available in Abaqus/Explicit.Four node quadrilateral continuum elements with plane strain assumption (CPE4RT) are used for coupled temperature-displacement analysis [15].
The geometry of the model and different boundary conditions are shown in Fig. 1.To optimize the contact conditions between the work piece and tool, the work piece component is divided into three partitions.Different partitions of work piece are: 1) chip 2) tool-tip passage zone and 3) work piece support.To facilitate the chip formation, the thickness of the tool-tip passage zone should be of the order of tool edge radius [16].These three partitions of work piece are joined together using the tie constraint option available in Abaqus/Explicit.During the cutting operation tool comes in contact with the work piece and chip, furthermore chip also makes self contact during the machining process.A coulomb friction model is employed for tool-chip-work piece interaction [17][18].The finite element simulation requires the identification of different damage parameters [19][20][21], The identified Johnson-Cook material parameters used for damage initiation and damage evolution for A2024-T351 are given in Table 1 [14].The different material properties of A2024-T351 are given in Table 2 [14].
In order to authenticate the simulation process, finite element analysis results will be compared with available experimental data on turning machining of A2024-T351.The experimental results of cutting forces against different cutting feeds and velocities are given in Table 3 [10].

Fig. 1 Geometric model of work piece and tool
In order to authenticate the simulation process, finite element analysis results will be compared with available experimental data on turning machining of A2024-T351.The experimental results of cutting forces against different cutting feeds and velocities are given in Table 3 [10].
In this section 2D finite element analysis of cutting process of A2024-T351 is performed for a feed rate f = 0.4 mm and friction coefficient µ = 0.15 against velocity Vc = 800 m/min.Fig. 2 represents the reaction force (Fc) obtained from numerical analysis for cutting speed of 800 m/min.The average cutting force obtained from numerical results is 943.4N and is in good agreement with experimental results.Since the deviation of numerical results from experimental results is of the order of 3.4% which shows the authenticity of simulation work.Fig. 3 shows the resultant Von misses stress profile during the chip formation process.

Parameters affecting the cutting process
In the previous section finite element analysis has been performed on turning simulation for A2024-T351 aluminium alloy and results are successfully compared with experimental results.After verifying the simulation results a comprehensive parametric sensitivity analysis considering different cutting parameters is performed in this section.The effect of different cutting speeds on the reaction force is studied in the present section.The values of feed rate f = 0.4 mm and friction coefficient µ = 0.15 are employed to study the effect of different values of cutting speed.Fig. 4 presents the variation of cutting force with cutting speed.Although from Fig. 4 a slight increasing trend is observed but there is not an appreciable difference in values of cutting force as the cutting speed increases from 200 m/min to 800 mm/min.Similarly temperature profile at different velocities is shown in Fig. 5. From Fig. 5, one can note that by increasing the cutting speed, maximum temperature at the tool-chip interface also increases.In the present case, maximum temperature increases approximately from 231°C for Vc = 200 m/min to 336°C for Vc = 800 m/min.Hence selection of cutting speed can be attributed to total time required to complete a job, machine capability & accuracy, required surface finish and maximum affordable temperature of the work piece.

Effect of feed rate
The effect of feed rate (f) on cutting force is considered in this section.Fig. 6 shows the results of cutting force vs cutting speed for two different feed rate values i.e. f = 0.3 & 0.4 and µ = 0.15.The reaction forces obtained from numerical results are also in good agreement with experimental results, see Table 3 for comparison.
From Fig. 6, it is clear that reaction force decreases considerably as the feed rate (f) decreases.Similarly, temperature profile at different feed rate (f) is shown in Fig. 7. From Fig. 7, one can note that maximum nodal temperature increases with the increase in feed rate.Moreover the difference in rise in temperature at higher velocities is much higher in comparison of lower velocities.At Vc = 200 m/min, the maximum temperature varies from 231°C to 237°C for f = 0.3 and 0.4 respectively.But on the other hand as the cutting speed increases from 200 to 800 m/min, the maximum temperature varies from 301°C to 336 °C for f = 0.3 and 0.4 respectively.Now selection of final cutting feed depends upon the total time to finish the work piece since small feed values will take more time to achieve final dimensions of finished parts.Moreover small feed values also carry the advantage of less cutting force and temperature values.

Conclusions
In this article a comprehensive study is conducted on different parameters that influence the turning process of aluminium alloy using the finite element analysis.The authenticity of finite element work is verified by comparing the results with available experimental data.The effect of four different parameters like cutting speed, feed rate, friction coefficient and rake angle on resultant reaction force is studied.The effect of cutting speed and friction coefficient on the reaction force is not much significant but they appreciably affect the maximum temperature at the tool-chip interface.On the other hand both feed rate and rake angle have strong influence not only on cutting reaction force but also on maximum tool-chip interface temperature.From the conducted study one can say that these parameters may influence the total time required to complete the job and the net resultant force experienced by the tool and work piece.Hence the selection of good parameters for a particular turning process of aluminium alloy may depend on the required total time to finish the job and net resultant forces that work piece and tool can withstand during turning operation.Finally one can also conclude that finite element analysis may replace the critical experimental work and help to save precious time and money.In the present work, a 2D finite element analysis is performed and good numerical results that are comparable with the experimental results are obtained.But the same effort will be made in future on 3D finite element analysis for better and real time analysis of turning process in metals.
. A linear or exponential damage evolution law can be considered for degradation of material under applied force.If D is damage variable, following two equations represent the linear and exponential type of damage evolution law respectively[14]:

Fig. 2 Fig. 3
Fig. 2 Evolution of Reaction Force vs Time for cutting speed of 800 m/min