Annals of the CIRP Vol. 56/1/2007 -61- doi:10.1016/j.cirp.2007.05.017

Finite Element Modeling and Cutting Simulation of Inconel 718

E. Uhlmann (2), M. Graf von der Schulenburg, R. Zettier Institute for Machine Tools and Factory Management (IWF)

Technische Universität Berlin, Germany

Abstract Segmented chips are often found in high-speed-cutting. This type of chip formation can be traced back to adiabatic shear bands. The reference workpiece material is the Nickel-based alloy Inconel 718, which shows an affinity to segmented chip formation. A realistic simulation of the chip formation and of the related cutting forces and chip temperatures serve to better process understanding. By implementing a material model into the FE-simulation which besides strain, strain rate and temperature includes ductile damage, a realistic description of the material behavior becomes possible. The results of the experiments and of the 2D- and 3D-simulations correlate well.

Keywords:Turning, Chip formation, Finite Element Method

1 INTRODUCTION In the past decade the essential fundamentals for an industrial implementation of High-Speed-Cutting (HSC) have been developed. The increase of the cutting speed involves an augmentation of the material removal rate and an improvement of the workpiece surface [1]. In this paper the Nickel-based alloy Inconel 718 (IN 718) in a solution annealed state is examined. IN 718 shows an affinity to form segmented chips which is typical for HSC-machining [2,3]. The formation of segmented chips is ascribed to the appearance of shear instabilities during machining [4]. There are multiple surveys and models to describe this phenomenon [4-8]. The finite element method (FEM) is often used to obtain knowledge about the forces and the temperatures occurring during the cutting process and also about the inducement on the emerging workpiece recast layer [9-12]. Since the chip formation mechanisms have a significant influence on the forces appearing in the cutting process a particular importance is ascribed to the simulation of the chip segmentation in this paper. The material law used was developed by the Federal Institute for Materials Research and Testing (BAM), Division Mechanical Behaviour, in collaboration with the Institute for Experimental Physics of the Otto-von-Guericke-University Magdeburg (IEP).

2 EXPERIMENTAL SETUP For an assessment of the cutting simulations experimental testings have been carried out. A description of these tests as well as their results can be found in [13,14]. At this point only the experimental boundary conditions are described. The experimental cutting forces shown in section 4.3 of this paper have been obtained in external cylindrical turning. The depth of cut was ap = 0.5 mm with a feed of f = 0.1 mm/REV. The cutting force vc has been varied between 200 m/min and 800 m/min. The experimental working geometry has been a result of combining the indexable insert type SNGN 120708 T01020 with the insert holder type CSSN L 2020M12. The tool orthogonal rake angle was o = -6° and the tool cutting edge angle rwas 45°. The indexable inserts had a protection chamfer with a chamfer angle of 20° and the cutting material was a

SiC whisker reinforced oxide ceramic of the type CC670, produced by SANDVIK, Sweden. According to the simulations the tests were carried out in dry cutting. IN 718 was used in a solution annealed state as workpiece material in all experiments.

3 MATERIAL LAW For the description of the deformation localization during high speed load the model of Johnson and Cook [15] (equ. 1) turned out to be appropriate because of its viscoplastic flowing regulation in the form of an exponential function.

0ln11)( pCpBA

m

RM

Rnv (1)

with the equivalent stress v, the plastic equivalent strain p, the plastic equivalent strain rate p , the melting temperature M as well as the initial temperature R. The material parameters 0 , A, B, C, n and m of the Johnson-Cook-model [16] are listed in Table 1.

variable 0 A B C n munit 1/s MPa MPa value 1.001 450 1700 0.017 0.65 1.3

Table 1: Johnson Cook material parameters In order to be able to measure the temperatures appearing in the shear bands in situ and to carry out investigations at the chip root, the IEP performed analogy HSC-experiments with the SHPB-technique [17]. The temperatures calculated by the BAM with 2D-cutting simulations regarding the material law described in (equ. 1) amounted to 1000 °C and more. Compared to the measured temperatures the calculated ones were too high [16]. The flow stress of the examined Nickel-based alloy declines by 30 % at the most during high speed deformation (yield rate 10³/s in the range of homogeneous deformation) in the temperature range from 550 °C to 1000 °C [18]. Thus no serious decrease of stiffness appears up to 1000 °C in this workpiece material during high speed load due to thermal softening only.

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Therefore, there has to be another failure mechanism than the thermal softening during the formation of shear bands, which leads to an early decrease of stiffness. The plastic power reduced by the failure mechanism would impede such a temperature boost. A loss of load-carrying capacity up to the total stiffness decay is called ductile damage. Therefore, a model for the ductile damage during high speed load was created [18]. According to the mathematical concept of Lemaitre [19], equation 1 was expanded by a term which contains the degree of the ductile damage D:

DpCpBAm

RM

Rnv 1ln11)(

0 (2)

A direct nonlinear approach for the design of the degree of ductile damage [20] depending on a standardized inner time s, which describes the usage of lifetime [18], was chosen:

ksD (3)

The equation for the development of the inner time is:

ppW

sa

c

effv

v

mm

1

, 1exp (4a)

Dv

effv 1, (4b)

0,

0,:

2

1

m

mm when

when (4c)

33221131

m (4d)

with the effective equivalent stress v,eff, the damage parameters D, k, 1, 2, a and 1, the critical plastic work Wc, a third of the trace of the stress tensor m, the normal stresses 1, 2 and 3. Using the material law expanded by the ductile damage the temperatures in the shear bands as well as the dependency of the cutting forces on the cutting speed established by the BAM could be calculated [18]. The description of the localization due to ductile damage becomes possible by the adjustment of the damage parameters to the smallest element dimension in the FE-net. This offers the possibility to solve problems more efficiently by using larger elements. This is particularly of interest concerning 3D-calculations.

4 SIMULATIONS

4.1 2D-Simulations For simulating the cutting process there are two different FEM-programmes available at the IWF: ABAQUS/Explicit V. 6.4 and DEFORM 2D V. 8.1. In both programmes the material law with ductile damage had been implemented. However, each programme presupposed a unique approach to model the simulation of the chip formation process. Regarding ABAQUS/Explicit, the separation process is based on the deletion of elements. Regarding DEFORM, the same process has been realized by a permanent remeshing. The simulations described in the following paragraphs had – in relation to the external cylindrical turning tests

carried out previously – an undeformed chip thickness of h = 0.072 mm. The tool orthogonal rake angle was

o = -6°. The chamfer of the cutting edge mentioned in section 2 has been disregarded in the modeling process to ease the start of the simulation. Regarding the simulation the tool has been modelled as a rigid body. There was no heat exchange between the workpiece material and the tool or its environment. The following paragraph includes the main characteristics of the ABAQUS-models. ABAQUS/Explicit presupposes the use of an elastic-plastic material behaviour. With regard to the simulations described in [16] only the chip volume has been taken into consideration. Twelve element layers represented the undeformed chip thickness. The height of an element was 6 μm. The bottom layer, which was based on the material model described in equation 1, could be deleted because of a strain- and geometry dependent criterion. With regard to the stability of the simulation, the degree of damage allowed was limited to a maximum of D = 0.8. The choice of the damage parameters and the the critical plastic work Wc for the smallest element edge length of 6 μm shown in Table 2 was made according to [18].

variable D 1 2 k a 1 Wc

unit [1/s] [MPa]value 0.8 1 2 18 0.13 2·104 3000

Table 2: Damage parameters in 2D-ABAQUS simulations The following paragraph deals with the particularities of the DEFORM-model. DEFORM 2D is an implicite FEM-programme. The models include a rigid-plastic material behaviour. The realisation of the material separation process via a permanent remeshing necessitates a consideration of the emerging workpiece recast layer. Therefore, the tool model assumed a rounding of the cutting edge of r = 10 μm. With the help of Mesh Density Windows it is possible to mesh the chip formation zone in more detail. The smallest element edge length was in this case about 7 μm to 10 μm, too. Pretests led to the conclusion, that the frequency of the remeshing if considering the ductile damage indeed has an influence on the simulated chip segmentation. Possibly this is the case due to the high gradients of the ductile damage in the workpiece. The degree of ductile damage D is calculated and stored for each separate element and for each time unit. When the data of D are transferred from the old to the new element mesh, possibly an averaging of the values is performed. Therefore, the clear damage of the material and in turn the chip segmentation is delayed. For this reason, the critical plastic work has been set to a value of Wc = 2100 MPa in this case. The degree of ductile damage that was tolerable at maximum was D = 0.95. Figure 1 shows the simulated chip formation with both FEM-programmes. In both cases the formation of a continuous chip is detectable at cutting speeds of vc = 100 m/min and vc = 200 m/min. At vc = 400 m/min the formation of segmental chips was outright detectable. In further simulations with cutting speeds of up to vc = 1000 m/min segmental chip formation occurred throughout. Hoffmeister found in his investigations, that cutting IN 718 at cutting speeds of under vc = 180 m/min leads to a rather large ratio of continuous chip formation. Above vc = 180 m/min there was segmental chip formation [2]. Komanduri found for IN 718 – however, in fully aged state –, that above a cutting speed of vc = 61 m/min one experiences an intensive formation of segmental chips [3].

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Figure 1: 2D-simulations

4.2 3D-Simulations The 3D-simulation represents an orthogonal cut. Basically the assumptions made in section 4.1 regarding the modeling with ABAQUS/Explicit appeared to be correct. However, the 3D-models have been enlarged to include the workpiece material. Furthermore, the tool orthogonal rake angle was o = 0°, whereas the tool’s chamfer was taken into account. In addition to the rake face the models included two further rigid bodies in the form of planes (Fig. 2). Plane A is supposed to prevent nodes of the chip volume from entering into the workpiece. Plane B is supposed to shorten the initial chip formation procedure and to stabilise the computation.

Figure 2: Layout of the 3D-model for orthogonal cutting

The bottom nodes of the failure element layer in the emerging workpiece surface are constrained in direction 1 whereas these nodes are able to move freely in direction 2 and 3. Therefore, the chip can expand in the direction of the width of the undeformed chip. In [9], a tool model with a stagnation region has been presented for the simulation with a large tool orthogonal rake angle. According to the stagnation region, the additional auxiliary plane at the tool tip is designed to facilitate a sliding of the nodes at the chip bottom along the rake face. A further feature of 3D-modeling was the symmetry plane. The nodes included here, have been constrained in direction 3. The chip volume was made of only eight element layers which means an element height of 9 μm. Therefore, in this case, the critical plastic work was set to a value of Wc = 2400 MPa. Figure 3 contains the simulated chip forms at different cutting speeds vc. At vc = 100 m/min a continuous chip formation was seen whereas at vc = 200 m/min the formation development of a segmental chip denoted. Beginning at a cutting speed of vc = 200 m/min only segmental chips could be found. Also a distinct chip widening was identified.

Figure 3: Chip formation simulated with ABAQUS at different cutting speeds

4.3 Comparison of the simulated forces with experimental forces

To be able to compare the calculated cutting forces with the measured ones the specific cutting forces were consulted. To determine the simulated specific cutting forces the integral average was computed. In the case of the formation of segmental chips the integration of the cutting force took place over the time of the formation of one or more segments. After that the quotient of the integral and the time fragment was calculated. Figure 4 shows the dependency between the specific cutting force and the cutting speed for the experiment and the simulations. All cases show a decrease of the specific cutting force with increasing cutting speed. In the simulations the largest decrease of the cutting force happens at the changeover from a continuous chip to a segmented chip. The specific cutting force in the ABAQUS simulations is almost constant at higher cutting

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speeds whereas it shows a further decrease in the DEFORM simulations. The curve progression of the experimental forces indicates an almost constant level of the cutting force at high cutting speeds as well. This correlates with the observations of Hoffmeister [2].

Figure 4: Comparison of the specific cutting forces

5 CONCLUSIONS The simulations using the described material law depicted the chip formation of IN 718 as well as the occurring cutting forces in both qualitative and quantitative terms well for a broad range of the cutting speed. The differences of the cutting forces in different simulations can be ascribed to differences concerning the modeling.The integration of the tool chamfer into the 3D-simulations led to problems which could only be solved with an additional modeling effort. Statements about the state of stress could not be made for reasons relating to the geometrical boundary conditions. A predefinition of the damage parameters for the DEFORM simulations turned out to be difficult since estimating the influence of remeshing on the ductile damage development is rather problematic. The problems described will be among the main focuses of the modeling of cutting processes at the IWF.

6 ACKNOWLEDGEMENTS The authors gratefully acknowledge the financial support of the German Science Foundation (DFG) and would like to thank very much Prof. Clos, Dr. Schreppel and Dr. Veit from the IEP for conducting the SHPB-Tests and the microstructural investigations as well as Dr. Sievert, Dr. Hamann and Mr. Noack from the BAM for investigating the temperature dependency of the flow stress and developing the material model accordingly. We also thank the staff of the German High-Performance Computer Center North (HLRN) for the allocation of calculating time contingents and for the continuous attendance and the support in the solution of problems.

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[19] Lemaitre, J., 1996, A Course on Damage Mechanics, Springer Verlag, Berlin.

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