On different FE-based models to simulate cutting operation of Titanium alloy ( Ti-6 Al-4 V )

Y. Zhang*, D. Umbrello**, T. Mabrouki*, S. Rizzuti***, D. Nelias*, Y. Gong**** *Université de Lyon, CNRS, INSA-Lyon, LaMCoS, UMR5259, F69621, France, E-mail: zyc8910@yahoo.cn **University of Calabria, Department of Mechanical Engineering, 87036 Rende (CS), Italy, E-mail: d.umbrello@unical.it ***Politecnico di Torino, DISPEA, 10129 Torino, Italy, E-mail: stefania.rizzuti@polito.it ****Northeastern University, School of Mechanical Engineering & Automation, Shenyang, 110819, China, E-mail: gongyd@mail.neu.edu.cn


Introduction
As it is known, finite element (FE) method provides precise information concerning variables like plastic strain, strain rate or stress evolutions during toolworkpiece interaction, which are difficult to measure experimentally.After the early FE model [1], many research works about metal cutting process have been performed.Wherein, Mabrouki et al. [2] studied the chip formation and cutting force for dry cutting with thermal physical coupled damage model, they also considered the grain microstructure in the cutting model [3].Filice et al. [4] developed a wear model for the orthogonal cutting using uncoated carbide tools.Outeiro et al. [5] predicted the residual stresses in the cutting process, in particular.Finally, Umbrello et al. [6] incorporated the microstructure transformation for predicting residual stresses.
With these numerical methods, a general understanding of chip formation process can be improved.However, the effectiveness of these models depends, to a large extent, on how accurate are the models used to describe the metal cutting process and also the quality of the input data used in such models, especially when different commercial codes are used to develop the cutting model.
In recent years, researchers tried to find adequate FE-models and simulation parameters for different FE software and metal materials.Deshayes et al. [7] have carried out, based on a FE method comparison, a study dealing with the cutting of AISI4340 steel alloy with AD-VANTEDGE and ABAQUS/EXPLICIT.Similar cutting simulations, with the two cited software, were also performed by Arrazola et al. [8] in the case of AISI4140.Soriano et al. [9] have also presented a comparison of 3D machining models developed under commercially available FE software ABAQUS/EXPLICIT, ADVANTEDGE and DEFORM3D for the machined material Inconel 718.
Considering all above, it is necessary to conduct a comparison study to evaluate the effectiveness of current predictive models not only regarding forces, temperature distribution, chip compression and morphology, but also parameters related with the integrity/quality of the machined surface, such as residual stress, etc.

Aim of study
Benchmark studies are commonly carried out in a manner that all conditions are kept equal for all the models of interest.Nevertheless, it has been proved [10] that for machining process it not possible to conduct a benchmark as usually done for the other manufacturing processes.In fact, it was shown that each model results to be properly predictive only if calibrated in the own simulation strategy.A specific combination of material and damage models furnishes good numerical results when these models are implemented in the same FE-code used for calibrating material constants [10].This happens since mechanical theories, especially for damage models, implemented in FE-codes are different as well as are different the thermal models applied for describing the temperature and its evolution.
In this context, the aim of the study is to develop and calibrate two different simulation models and apply them to predict the most significant cutting parameters, comparing the different predictive capabilities.Thus, for each FE model the most appropriated combination of flow stress model, damage criterion and thermal model has been utilized.Obviously, it is worth pointing out that the proposed flow stress models, although dissimilar in their structure and for material constants, describe equivalent material behaviour.In such circumstances, the study is performed in the optimum conditions for the two different simulation models.In addition, it also permits to highlight the main problems related to current simulations supporting metal cutting researchers for understanding the cutting process and its influence on the material.
This paper is composed of three main parts: after a brief description concerning the material properties of Tialloy, the numerical model setups in ABAQUS/EXPLICIT (v6.7) and DEFORM/IMPLICIT-2D (v10.1) are described.Finally, the numerical and experimental results are detailed, discussed and overall conclusions are pointed out.

Material properties
The workpiece material selected for this study is the Titanium alloy Ti-6Al-4V, which has good specific strength, toughness and corrosion resistance making it attractive for aerospace applications, surgical implants, etc.Consequently, mechanical structure components for these applications have precise requirements in terms of physical, chemical properties [11] (Table 1), and thermo properties [12] (Fig. 1).

Finite element modelling
In order to build a common FE-model for chip formation process during orthogonal cutting process, ABAQUS/EXPLICIT-2D and DEFORM/IMPLICIT-2D software have been adopted.The software ABAQUS/EXPLICIT (V6.7) has been used to set up a FE-model in two-dimensions (2D) as presented in Fig. 2. To control the contact between tool and workpiece during cutting simulation, four parts are participated for the cutting model (Fig. 2) [13].The workpiece is allowed to move with the cutting speed, while the tool is fixed on its top and right sides.

Material constitutive model
Concerning the material behavior of Ti-6Al-4V, the Johnson-Cook (J-C) constitutive model [14] is implemented in ABAQUS and is expressed by the following equation of the equivalent stress: The values of coefficients A, B, C, n and m for the Ti-6Al-4V alloy are reported in Table 2 from the work of [13].In the present model, the adopted numerical methodology is based on the fracture energy as an intrinsic material parameter for controlling damage evolution criterion after damage initiation.

Damage initiation
The strain cumulative damage law is employed for the damage initiation: where  is the equivalent plastic strain increment in one loading increment and 0i  is the equivalent plastic strain is used for determining the damage initiation: The constant parameters for Eq. ( 3) are from [13].Damage initiation is assumed to be activated when ω = 1.

Damage evolution
The evolution of damage is based on the concept of the Hillerborg's fracture energy [15,16], which is presented as a stress-displacement response after damage initiation: where L is the characteristic length presented by the square root of the integration point element area.The linear and exponential damage evolutions are adopted part 3 and part 2 respectively [13].For plane strain condition, the adopted G f can be deduced by: where K C is the fracture toughness [11].Moreover, the classic Zorev's [17] stick-slip friction model is implemented to simulate frictional contact between chip and tool with a constant friction coefficient [13].Finally, the thermo-physical properties of both cutting tool and workpiece are given in Table 2.The contact and damage data can be obtained from [13].

DEFORM/IMPLICIT: Model features
Parallel to the cutting simulations performed with ABAQUS, other FE based simulations were carried out using DEFORM2D, which makes use of an implicit Lagrange formulation.A plane strain coupled thermomechanical analysis is performed in orthogonal cutting conditions.The workpiece is meshed with isoparametric quadrilateral elements and modelled as elastic-viscoplastic, while the tool is modelled as rigid.
The material behaviour for Ti-6Al-4V is modelled with the flow stress developed by Scientific Forming Technologies Corporation (SFTC) based on the works in [18,19].It is important to highlight that such flow stress exhibit similar behaviour for Ti-6Al-4V alloy of the J-C model implemented in ABAQUS.

Constitutive equation An elastic-visco-plastic material model with Von
Mises yield criterion and associated flow rule is used.In the deformation zone, the following equation is given: where: ij  are strain rate components; ij   is the deviatoric stress and  and  are effective stress and strain rate.

Chip formation criterion
The chip segmentation is a consequence of the fracture process that takes place during chip formation.In this research, Cockroft and Latham's fracture criterion (CLFC) [20] (Eq.( 7)) were adopted to present the effect of the stress on the chip segmentation: Where:  f is the effective strain;  1 principal stress and C the material constant representing resistance to failure (sometimes called "damage value").CLFC means that when the integral of the left term (applied state) in Eq. ( 7) reaches the value of C (material state), the fracture occurs and the chip segmentation starts.Usually, the adequate C value is determined by numerical calibration on available experimental data.In this work, C is set equal to 240 MPa as found by SFTC through the above mentioned calibration.This value is chosen on the basis of an iterative procedure aimed at reducing the errors on the predictions of cutting forces, chip morphology parameters and temperature distribution as well as thermal steady-state along primary and secondary shear zones.

Experimental design
To evaluate the robustness of the two simulation models, several numerical tests are taken into account.In particular, the numerical values obtained by means of FE simulation, in terms of cutting force (F c ), thrust force (F t ), cheap peak (h 1 ), chip valley (h 2 ), chip pitch (L 1 ), chip compression ratio (CCR), maximum temperature on workpiece (T W ) and maximum temperature over the tool rake surface (T T ), are considered and compared with those experimentally available in literature [10,18,21,22].Furthermore, numerical residual stress profiles in circumferential direction are numerically extracted from the machined surface and sub-surface and compared with those experimentally measured by X-Ray Diffraction (XRD) technique [10].Schematically speaking, the available experimental data are divided into four groups.
The first group is mainly focused on studying the physical phenomenon accompanying cutting process with positive rake angle of the cutting tool [18].The second group concerns the cutting with negative rake angle [21], and the third group aims to investigate the effect of the tool wear on the residual stress distribution after machining [22].Finally, the fourth group focuses on studying the influence of the V C variation on the residual stress evolution considering a constant tool flank wear [10].The cutting conditions are summarized in Table 3.

Cutting parameters
Group I [18] Group II [21] Group III [22] Group IV [ 4 shows the computed results based on both ABAQUS and DEFORM simulations as far as cutting forces, chip morphology and temperature are regarded.Results concerning principal cutting force allow establishing that the two codes allow a good prediction regarding experimental ones although lowest errors can be obtained by using ABAQUS.In contrast, DEFORM allows to better describe the evolution of thrust forces, even if it is possible to compare the numerical values with only one experimental evidence (Group IV).Furthermore, DEFORM permits to better describe the evolution of both F c and F t instead of ABAQUS, since with increasing of the V C , both the cutting forces decrease (Groups I and II).It is worth pointing out that this well-known behaviour is not observed neither from DEFORM as well as from ABAQUS when Group 4 is considered.In fact, both the FE codes exhibit higher cutting forces when V C rises.
Chip morphology is analysed in terms of chip segment shape (valley, pick and pitch), as shown in Fig. 4. Numerical results are compared with experimental ones for groups I, II and IV (V C = 90 m/min), while the simulation results from group III and the other case of Group IV can be used for qualitative comparison.Analyzing the errors obtained in the predictions of the chip morphology (Table 4), it is possible to state that from a numerical point of view, ABAQUS provided the lowest errors in most of the cases.Regarding the chip formation process, it is worth underlining that in ABAQUS the chip segmentation is the result of a thermal softening state coupled with damage degradation.Moreover, the element deletion is available only in the sacrificial zone, while the other part, which is not deleted, becomes part of the chip.In DEFORM software, the chip formation is obtained by implementing Cockroft and Latham's criterion, thus allowing to describe the effect of tensile stress on the chip segmentation during orthogonal cutting.In addition, in DEFORM, the element deletion feature is also applied in these numerical simula-tions to better describe the chip fracture instead of the remeshing methodology.Finally, for all the investigated cases, both the maximum temperature range on both tool and workpiece are collected.As it can be observed, the results are almost similar although those found in DE-FORM exhibits always higher values of about 50 -100°C compared to those revealed in ABAQUS.Such discrepancy is related to the thermal models used in the cited FE codes as better illustrate in the next paragraph on which the influence of tool wear on thermal field and temperature distribution is investigated. WT, °C: Maximum temperature on workpiece  TT, °C: Maximum temperature over tool rake surface.To analyze the influence of tool wear on temperature distribution beneath the machined surface, the flank wear size of cutting tool is considered as an initial state and kept constant during the cutting simulation.The tools' geometry shapes with flank wear are illustrated in Fig. 5. Fig. 5 shows that both DEFORM and ABAQUS predict similar temperature values on the machined surface.Furthermore, for a given code numerical results present a temperature gradient about 90°C for the two flank wear lengths at the generated surface.Therefore, both DEFORM and ABAQUS take into account the heat generated along the flank face/workpiece interface due to modelled flank wear.In contrast, there is some discrepancy in temperature prediction below the machined surface (Fig. 5) since for both modelled tool flank wears, DEFORM shows higher temperature than ABAQUS.The reason is related to the different heat global coefficient and interface thermal model adopted and implemented in the two used software.Moreover, the difference is also due to the different description of the movements.In addition, the temperature distribution in the whole cutting model is presented in Fig. 6.It can be noted that there is a disagreement between ABAQUS and DE-FORM.Also, it is underlined that a non-concordance in the chip morphologies.Indeed, the chip segmentation morphology obtained by ABAQUS is the result of a thermal softening state coupled with damage degradation.The temperature given by DEFORM modelling is higher at the secondary shear zone and this is due to the fact that the contact is considered as perfect at tool-chip interface.
Besides both DEFORM and ABAQUS show a maximum temperature increase when tool with higher flank wear is used.Except these similarities between the two software, DEFORM shows higher maximum temperatures in both tool and chip.The reason is once again related to the different formulation, interface thermal model and heat global exchange coefficient at the tool/chip interface (the low value of heat exchange coefficient at the tool/chip interface directly leads to the temperature discontinuity at the rake face for ABAQUS, which is assumed that the non-perfect contact condition is considered between tool chip interface under simulation test).

Residual stress distribution considering tool wear
To consider the effect of successive cutting sequences on residual stress distribution, the physical state from the first cut is saved and used as initial condition for the second one.Other cutting conditions of the second cut are the same as those of the first one.In order to predict residual stress based on ABAQUS software, three unloading steps were implemented at the end of each cut in this study: 1. release of the cutting forces; 2. release of the clamping forces; 3. release of the workpiece to the room temperature.
After external force release and cooling down to room temperature, the final residual stress distribution on the workpiece is shown in Fig. 7.The stresses in Region II are selected to evaluate the residual stresses, and the predicted residual stresses should be also averaged over the same volume and the mean value should be taken.The oscillated residual stresses caused by the segmented chip are observed on the machined surface, which present the microstructure of the machined surface.It should be mentioned that the residual stress is extracted from element integration point.Consequently, the stress on the machined surface is located at the centre of the first layer element (4 μm below the machined surface), and the stresses are averaged along 2-3 mm in the circumferential direction after their calculation in element integration points.Vice versa, as far as DEFORM proce-dure since an automatic method for residual stress collection is not yet implemented in SFTC-DEFORM-2D V.10, the following procedure was employed:

Region for RS analysis
1. for several time steps, the tool was released from the machined surface (unloading phase) and the workpiece was cooled down to the room temperature; 2. residual stress profiles at several locations (coincident to Region II, Fig. 7.) of the machined surface were collected and the average values were calculated, as described in the work of Liu and Guo [23].Fig. 8 shows the effect of flank wear length on circumferential residual stress distribution beneath the newly machined surface.As general trends, both the software highlight that when the flank wear was increased from 0.03 to 0.2 mm, the surface residual stress towards the tensile region.This is due to the higher magnitude of temperature generated along flank face/workpiece interface.
Moreover, both DEFORM and ABAQUS show that the maximum compressive residual stress as well as the beneficial depth decreases with increasing of flank wear.In addition, the distance where maximum compressive residual stress is located seems to be not affected by flank wear.However, both the software show some gap between experiments and simulations when considering the influence of first cut.The reason of such discrepancy should be related to firstly the material flow stresses used in both ABAQUS and DEFORM which are not suitable for describing pertinently material states.Secondly, It is worth pointing out that in both computations, the residual stresses due to phase transformation were neglected and, especially in the case of DEFORM (temperature near to phase transformation effect), such assumption is not properly corrected.

Cutting speed effect on residual stress distribution considering a fixed tool wear
To study the influence on circumferential residual stress distribution on the machined surface, different cutting speeds varying from V C = 55 m/min to V C = 90 m/min with constant flank wear are adopted in Fig. 9.It can be noted that, the distribution of the compressive RS computed by ABAQUS is still mainly localized within 60 μm, while the simulation result from DE-FORM extends to 200 μm, which shows an acceptable numerical RS prediction compared to ABAQUS.However, both two codes illustrate that the maximum compressive RS as well as the beneficial depth increases with increasing of the cutting speed, which is in contrast with the experimental facts.It implies that the contact thermal properties between tool/machined surface still need to improve for both codes mentioned above.

Effectiveness and Robustness of FE codes: comparison and overall
Taking into account what it is discussed in the previous paragraphs and in order to complete the assessment of the two described simulation strategies, it is useful at this point to draw an overall comparison between the two used codes for cutting modeling.In order to perform detailed simulations and precise control for the mesh and the boundary conditions, then the software package ABAQUS seems to be adequate.However, if an efficient, easy to setup machining simulation is needed, and then the software package DEFORM seems to be satisfactory.This package allows quick setup of simulations and provides the built in modules for material library, tool and workpiece geometries and process parameters.

Conclusions
In this study, a comparison of four groups of simulations performed with two different 2D FE models is presented in the case of Ti-6Al-4V alloy cutting.The computed results were compared with experimental ones.Some observations concerning the results obtained based on the using of ABAQUS and DEFORM can be pointed following: 1.The serrated chip formation can be modelled using the mentioned two codes with appropriate material and damage models.
2. The temperature distribution at the tool-chipworkpiece interfaces displays that the segmentation is the result of a thermal softening state or/and the coexisting fracture phenomenon, among other phenomena.
3. The simulation results of temperature and residual stress show the similar tendency for two kinds of models, even though there is some gap between them due to the optimal conditions for each of them (material laws, damage criteria, etc.
4. Potentially, these two simulated models can be exploited to perform other numerical comparisons with both commercial and in-house codes.

1
Physical properties of the Ti-6Al-4V alloy as a function of temperature: a) specific heat, C p and b) thermal conductivity, k[12]

Fig. 3
Fig. 3 2D numerical model set up (DEFORM /IMPLICIT) In Fig. 3, the mechanical and thermal boundary conditions of the 2D FE model are schematically shown.As far as friction modeling is concerned, a simple model based on the constant shear hypothesis is implemented with the shear factor kept at m = 0.6, considering as dominant the phenomena appearing in the sticking zone, in which this model is effective.This value is chosen on the basis of an iterative procedure aimed at reducing the errors on the predictions of cutting forces, chip morphology parameters and temperature distribution as well as thermal steady-state along primary and secondary shear zones.

6. 2 .
Temperature distribution due to tool wear Two numerical comparisons were done in order to highlight the evolution of different outputs computed by ABAQUS and DEFORM software: (i) temperatures comparison on machined surface and subsurface near the tool tip for different flank wear; (ii) Temperatures distribution along the primary and secondary shear zones and their maximum values.

Fig. 5
Fig. 5 Temperature distribution beneath the machined surface

Fig. 7
Fig. 7 Residual stress distribution on the workpiece

Fig. 8
Fig. 8 Effect of the flank wear lengths on residual stress profile with V C = 320 m/min: a) VB = 0.03 mm; b) VB = 0.2 mm

Fig. 9
Fig. 9 Effect of the V C on residual stress profile with constant VB = 0.15 mm: a) V C = 55 m/min; b) V C = 90 m/min

Table 2
Thermo-physical parameters for the ABAQUS FE model