Influences of Cutting Speed and Material Constitutive Models on Chip Formation and their Effects on the Results of Ti6Al4V Orthogonal Cutting Simulation

Nithyaraaj Kugalur-Palanisamy. University of Mons, Faculty of Engineering, Machine Design and Production Engineering Lab – Belgium. Corresponding author: Nithyaraaj.KUGALURPALANISAMY@umons.ac.be Edouard Rivière-Lorphèvre. University of Mons, Faculty of Engineering, Machine Design and Production Engineering Lab – Belgium Pedro-José Arrazola. Mondragon University, Faculty of Engineering, Mechanical and Manufacturing Department – Spain François Ducobu. University of Mons, Faculty of Engineering, Machine Design and Production Engineering Lab – Belgium


Intr Introduction oduction
The Ti6Al4V one of the most widely used titanium alloy. The machining of this expensive alloy remains a major production industry concern because of the poor machinability characteristics. The Finite element modelling is widely employed by researchers [1] to reduce the experimental costs. Due to many factors that affect the machining, the finite element modelling of machining is a very complex process, often limited to the simplified orthogonal cutting configuration. Therefore, a well-defined flow stress model that considers the strain, the strain rate, the temperature, the hardening, the viscosity, and the loading history of the material is necessary in numerical modelling of metal cutting process. Dependency of the results to cutting parameters (and especially cutting speed) are important factors in determining machinability behaviors in addition to mechanical properties of a workpiece. A definitive constitutive model is always a principal factor in developing a finite element model [1]. Many material constitutive models have been developed in the recent years. Because of their simplicity and lucidity empirical models are widely considered.
The aim of this work is to investigate the influence of cutting speed ranging from 30 m/min to 75 m/min on forces and chip morphologies of Ti6Al4V alloy. This paper compares and analyze the finite element simulated results from Johnson-Cook model [2], the modified Johnson-Cook model from Calamaz et al. [3] that takes the strains softening behavior into account and the Modified Johnson-Cook from Hou et al. [4] that takes into account temperature dependent hardening factor and its coupled effects between strain and temperature with the experimental work carried out by Ducobu [5]  The most widely used thermo-mechanical model that links plastic, viscous and thermal aspects observed during orthogonal machining process is the popular Johnson-Cook model [2]. Its flow stress is expressed by the following Eq. (1): Where , , , , are the constants that depend on the material and are determined by material tests. is the yield strength, the hardening modulus, the strain-hardening exponent, the strain rate sensitivity and is the thermal sensitivity. Constants and report the strain hardening. and are the melting temperature and the room temperature respectively, while ɛ0 is the reference strain rate. The parameters for this model are given in Table 1.
The JC model is meaningful in certain operating ranges of strains and strain-rates (strains up to 0.5 and strain rates lower than 10 4 s −1 ) [1] but fails to capture high strain material behavior in machining, where the flow stresses are difficult to measure by existing material testing devices [2].
Thermal softening is defined as the flow stress drops with the increased temperature regardless of plastic strain. JC model does not account for softening observed at the strains and temperatures in the primary shear zone, which is characteristic of metals that exhibit shear banding [1]. This leads to modified or updated versions of Johnson-Cook  Where, 1 is the thermal sensitivity coefficient with the increasing strain, and the rest of all parameters have the same meaning as JC model. The authors concluded that strain hardening rate of Ti6Al4V alloy has no noticeable strain rate sensitivity but evidently temperature sensitivity. The parameters for this model are given in Table 1.
T Table 1. P able 1. Par aramet ameters adopt ers adopted f ed for JC model [6], JC-Calamaz [3] and JC-Hou [4] or JC model [6], JC-Calamaz [3] and JC-Hou [4] The stress vs strain curve evolution for the JC, JC-Calamaz and JC-Hou at fixed temperatures of =573 K and =973 K for strain rate of ɛ=10000 s -1 is plotted in  By comparing the stress-strain evolution curves in Fig.1 it is revealed that JC law, JC-Calamaz law that includes softening behavior and the JC-Hou law that consider temperature dependent hardening effect shows a significant difference in the evolution of stress with respect to strain at high temperature and strain rate. It is significantly important to note that the initial stress value of JC-Calamaz is very low when compared with initial stress value of other two constitutive models considered in this study. This might influence the calculation of forces and chip morphology.

Finit Finite Element Model and C e Element Model and Cutting Conditions utting Conditions
The finite element model (including information on damage model and friction conditions) was adopted from previous authors' work [6]. Tungsten carbide is selected as a tool material and the tool geometry is defined by the rake angle of 15°, the clearance angle of 2°and the cutting edge radius of 20 μm for cutting condition of uncut chip thickness of 60 μm with different cutting speeds of 30 m/min, 50 m/min and 75 m/min which makes a total of nine models.

Experimental r Experimental ref efer erence ence
The experimental reference is considered from the work of Ducobu [5]. The author adopted plunge turning conditions on a lathe to fulfill the hypotheses of the orthogonal cut with a lathe. This allows to evaluate the influence of the

Discussion Discussion
From all the numerically simulated chips it was observed that the temperature in the secondary deformation zone increases with increase of cutting speed. It was explained by the phenomenon that when cutting speed increases, friction force increases and the strain rate in deformation zones also increase, these induce an increase in temperature in the deformation zones. m/min, 75 m/min) was in the range of 5% to 10% and for JC-Calamaz was in the range of 1% to 4%. It is noteworthy that difference in their cutting force value trends is due to modification of thermal softening function of the JC model by adding temperature-dependent strain softening phenomenon, as an effect strain hardening predominates over the effect of thermal softening [8]. The stress strain evolution curve from Fig 1. clearly shows the influence of the strain softening on the stress level. Hence different stresses level leads to different cutting forces. In addition, it was observed that the feed force from JC-Calamaz also shows an increasing trend with cutting speed increment, but still, they are in the uncertainty range nevertheless, those values are far behind the experimental ones. It is also important to note that the difference between the numerically calculated force values and the experimentally measured force values may be due to the choice of the parameters of the constitutive models. Indeed, they are adopted from the references given in Table 1 and were not identified from the material samples employed for the experimental work. Bibliogr Bibliograph aphy y