Effects of the flow stress in finite element simulation of machining

Inconel 718 alloy

Farshid Jafarian1, Mikel Imaz Ciaran2, P.J. Arrazola2, L. Filice1, D. Umbrello1, H. Amirabadi3

1Department of Mechanical, Energy and Management Engineering, University of Calabria, Rende CS 87036, Italy.

2Faculty of Engineering, Mondragon University, Mondragon 20500, Spain.

3Department of Mechanical engineering, University of Birjand, Birjand, Iran

Abstract:

Inconel 718 superalloy is one of the difficult-to-machine materials which is employed widely in

aerospace industries because of its superior properties such as heat-resistance, high melting

temperature, and maintenance of strength and hardness at high temperatures. Material behavior of

the Inconel 718 is an important challenge during finite element simulation of the machining process

because of the mentioned properties. In this regard, various constants for Johnson–Cook’s

constitutive equation have been reported in the literature. Owing to the fact that simulation of

machining process is very sensitive to the material model, in this study the effect of different flow

stresses were investigated on outputs of the orthogonal cutting process of Inconel 718 alloy. For

each model, the predicted results of cutting forces, chip geometry and temperature were compared

with experimental results of the previous work at the different feed rates. After comparing the

results of the different models, the most suitable Johnson–Cook’s material model was indentified.

Obtained results showed that the selected material model can be used reliably for machining

simulation of Inconel 718 superalloy.

1. Introduction

Inconel 718 superalloy is one of the hard materials which among other nickel based alloys used

extensively in many industries. Inconel 718 has superior properties such as wear resistance, high

melting temperature, high corrosion and creep resistance and maintenance of strength and hardness

at the high temperatures. Consequently, this alloy finds a wide range of applications in the

aerospace industries and in rotary parts of gas turbine engines such as blades, shafts and dicks. The

mentioned properties are responsible for poor machinability of Inconel 718 from various points of

view. But it should be noted that, it is very time consuming and expensive to improve and evaluate

machining processes using experimental investigation. Therefore, finite element method (FEM) has

been developed as a beneficial and efficient tool in order to simulation of the cutting processes. In

fact numerical simulation has led to better understanding the chip formation by avoiding

unnecessary experiments. Workpiece material experiences severe loads during the machining which

induce high strain and temperatures to the workpiece. Material constitutive behavior is the most

important pre-requisite for simulation of the cutting process and plays the most important role on

the results of the simulation. Mostly, Johnson–Cook’s (J–C) constitutive equation is used to present

the flow stress of workpiece material during the simulation of cutting process [1]. The suitable

selection of J-C parameters is an essential step for obtaining the reasonable accuracy in simulation

of machining processes. It should be noted that, just few studies are found in the literature for

machining simulation of Inconel 718 alloy. So far, several J-C material models have been proposed

for aged and annealed Inconel 718 superalloy which some of them have been implemented for

cutting simulation. Unfortunately, up to now the efficiency of these models has not been compared

for simulation of machining process. Therefore, identification of the most reliable material model is

the first step for accurate simulation of machining of the Inconel 718 alloy. In this study, different J-

C material models were employed for finite element simulation of orthogonal cutting process of

aged Inconel 718 superalloy (45 HRC). The results of each model were compared with

experimental results of the previous work to identify the most reliable model.

Key Engineering Materials Vols. 611-612 (2014) pp 1210-1216© (2014) Trans Tech Publications, Switzerlanddoi:10.4028/www.scientific.net/KEM.611-612.1210

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2. Overview on Material model of Inconel 718

In this study different J-C material models were employed to simulate thermo-visco plastic

behaviour of Inconel 718 superalloy. This equation can be represented by the following equation:

= + 1 + 1 − (1)

Where σ is the flow stress, ε the plastic strain, ε the reference plastic strain rate (s−1), ε the

strain rate (s−1), T (°C) is the workpiece temperature, Tmelt is the melting temperature of the

workpiece material (1300 °C), and T0 is the room temperature (25 °C). A, B, C, n, and m are the J-

C constants where A (MPa) is yield strength, B is (MPa) the hardening modulus, n is the hardening

coefficient, C is the strain rate sensitivity coefficient, and m is the thermal softening coefficient. In

the literature, different combination of J-C parameters have been reported for Inconel 718 alloy

which seven of them were found for the aged Inconel 718 in 45 HRC (model M1 to M7). Demange

et al [2] conducted SHPB experiment tests at the strain rate up to 1000 (s−1

) and temperature at the

range of 72 to 400 (°C) to identify a new combination of J-C material constants (model M1).

Recently Wang et al proposed a modified J-C model (model M2) in which the Strain rate softening

effect (C constant in J-C equation) was temperature dependent at the different strain rates [3]. They

conducted the SHPB tests at the strain rate of 5000–11000 (s−1

) and the temperature of 500–800

(°C). Klocke et al carried out an inverse methodology to identify J-C constants (model M3) using

finite element simulation of orthogonal cutting process [4]. Pereira et al conducted SHPB tests for

annealed and aged IN718 to determine J-C material model [5]. The experiments were performed

within the room temperature and at the strain range of 1600–5000 (s−1

). A new set of the

constitutive model was suggested by Mitrofanov et al [6] in which A and B parameters of J-C

equation were calculated from quasi-static material property data and C and n parameters (strain

hardening constants) were adopted from the Pereira’s material model. Unfortunately, the thermal

softening effect was neglected in J-C equation in the models of Pereira and Mitrofanov. Lorentzon

et al [7] developed a new J-C material model (model M4) by adding the thermal softening effect to

the Mitrofanov’s equation. In fact, they used the thermal softening effect adopted in Sievert’s study

(m constant in C-J equation). Ozel et al suggested a modified J-C equation for IN718 to present

dynamic behavior of the material [8]. In this model (model M5), in addition to strain and strain rate

hardening and thermal softening, the effect of temperature-dependent flow softening was added to

the J-C material model. In this model A, B, C, n, and m are J-C parameters used in the Lorentzon’s

study and also D, S, s and r are the adopted constants to show the dynamic behavior of IN718 alloy.

Recently, Malakizadi et al [9] implemented an inverse methodology based on the FE analysis and

Response Surface Methodology (RSM) to access new combination of J-C constitutive equation

(model M6). Del Prete et al [10] proposed hardness-based flow stress for Inconel 718 alloy to access

a new material model (M7) at different initial harnesses. The flow stress curves of the different

material models of IN718 (model M1 to M7) is shown in Figure 1. Also, the J-C equation

parameters of the mentioned models are given in Table 1.

Key Engineering Materials Vols. 611-612 1211

Figure 1. The flow stress curves for different material models for the quasi-static tensile test

conditions (model M1 to M7)

Table 1. Different J-C material constants for Inconel 718 alloy (45 HRC)

Material

Model

A(MPa) B(MPa) C n m Other Constants

M1 [2] 1290 895 0.016 0.526 1.55 0.03 -----

M2 [3] 963 937 Variable 0.33 1.3 0.001 C = Function of T and [3]

M3 [4] 1485 904 0.0134 0.777 1.589 0.001 -----

M4 [7] 1241 622 0.0134 0.6522 1.3 1 -----

M5 [8] 1241 622 0.0134 0.6522 1.3 1 D= 0.6, S=0, =5, and r= 1.0

M6 [9] 1562 300 0.0164 0.25 1.7 1 -----

M7 [10] 1241 622 0.0134 0.6522 1.3 1 F=18 and G=1.36

3.1 Numerical modeling and experimental validation

The commercial FEA software DEFORM-2DTM

V-10 was used to simulate the orthogonal

cutting process of Inconel 718. Update-Lagrangian code with remeshing technique was utilized to

achieve mechanical and thermal steady state conditions during the simulation. The tool was

modeled as a rigid body and meshed with 8000 elements. In order to obtain the more precise results

and better chip geometry the workpiece was initially meshed with 15000 isoparametric quadrilateral

elements, and also very fine elements were defined near the cutting zone (0.001 mm element size).

Constant shear friction factor (m) and global heat transfer coefficient (h) were respectively taken

into account for modeling friction and heat transfer conditions between chip, tool, and workpiece

interface. Besides, during the machining of Inconel 718 alloy, adiabatic shear bands with low

thermal conductivity are developed within the chip and lead to the serrated chip formation. In this

case, tensile stress plays an important rule because of its effect on fracture of the material and

starting the segmentation. In this research, Cockroft and Latham’s criterion [1] was considered to

predict chip segmentation during the orthogonal cutting.

3.2 Experimental validation

Experimental results of the previous work [10] including two components of cutting force

(principal Fc and thrust Ff), geometrical characteristics of chip (peak, valley, and pitch), and

workpiece temperature were employed for validating the results of orthogonal cutting simulation of

Inconel 718 alloy (45 HRC). The experiments were conducted by DNMG150616 Sandvik tool with

chip breaker geometry and rake and clearance angles of -6° and 4°, respectively. Testing conditions

of N1, N2, and N3 were conducted with a cutting speed of 60 m/min and feed rate of 0.05, 0.075, 0.1

mm/rev, respectively.

1212 Material Forming ESAFORM 2014

Table 2 Experimental results of the orthogonal cutting [10] Testing

Condition

Forces Chip Geometry Temp

Fc Ff Peak Valley Pitch

N1 472.6 422.1 87.8 64.9 50 876

N2 657.2 560.5 141.9 98.1 87.4 990

N3 795.6 541.5 170.9 113.5 67.8 969

The Experimental results are available in Table 2. Also, an example of predicted temperature

and chip geometry during orthogonal cutting of Inconel 718 (model M2 and feed rate of 0.075

mm/rev) is shown in Fig. 2.

Figure 2. Prediction of temperature and chip geometry during orthogonal cutting

4. Results and discussion

In order to find the most reliable flow stress for machining simulation of Inconel 718 alloy, the

orthogonal cutting process was simulated by using material models of M1 to M7. FORTRAN

subroutines were implemented in Deform software to define the new material models. The

simulations were performed in the three testing conditions of N1, N2, and N3.

Table 3. Results of finite element simulation using different material models

Material

Model

Testing

Condition

Forces Chip Geometry Temp Total

Ave_err (Fc) (Ff) Peak Valley Pitch

M1

N1 6.22 -2.39 -3.19 7.89 -14.0 -17.1

11.9

N2 -6.27 -20.79 -14.7 -12.33 -9.61 -23.4

N3 -1.96 -16.16 -18.0 -3.96 13.57 -22.5

Ave_err 8.9 10.8 21

M2

N1 1.14 -2.77 -0.57 -9.55 21.2 -23.5

16.9 N2 -12.78 -22.43 -17.6 -17.23 7.89 -28.9

N3 -23.58 -15.27 -20.2 -13.48 37.32 -28.5

Ave_err 13 16.1 26.9

M3

N1 9.39 -3.34 -15.7 -26.04 10.0 -14.5

13.39 N2 3.77 -18.30 -18.9 -4.18 -25.63 -21.7

N3 -8.12 -9.51 -11.0 0.44 20.94 -19.4

Ave_err 8.7 14.7 18.5

M4

N1 -14.35 -25.23 -6.61 -9.40 29.6 -27.8

20.62 N2 -22.52 -39.42 -9.65 -3.26 -11.78 -32.5

N3 -32.68 -32.19 -19.8 -5.55 15.63 -32.5

Ave_err 27.7 12.36 30.9

N1 -28.48 -15.19 -21.4 -9.09 6.00 -45.5

Key Engineering Materials Vols. 611-612 1213

M5 N2 -35.33 -35.06 -26.7 -33.74 -14.19 -50.0

29.6 N3 -43.69 -33.89 -26.7 -26.8 32.74 -49.1

Ave_err 31 21 48

M6

N1 -6.05 2.35 -1.14 -8.47 62.60 -30.0

22.4 N2 -21.94 -17.58 -20.3 -19.06 -23.34 -35.8

N3 -31.12 -10.99 -25.6 -24.23 28.32 -34.8

Ave_err 15 23.6 33.5

M7

N1 -2.67 -10.26 -6.49 -8.94 25.80 -23.4

15.72 N2 -14.42 -20.37 -19.0 -3.64 3.50 -28.2

N3 -23.13 -17.56 -22.0 -17.22 10.35 -25.7

Ave_err 14.73 13 25.7

For each testing condition, the parameters of shear friction factor (m), global heat transfer

coefficient (h), and damage value (D) were adopted in accordance with the calibrated results of the

earlier study [10]. Based on this, the constants of (D, m) were considered (120, 0.95) for testing

condition of N1, (220, 0.97) for N2 and (150, 0.98) for N3. Besides, the heat transfer coefficient

between chip-tool-workpiece interfaces was adjusted 100000kW/m2 for all of the testing conditions

[10]. The results of simulations and percentage of errors for each model was reported in Table 3.

As can be seen in Table 3, in model M1 the average of absolute error (for all of the simulations)

is lower than others (11.9%). In general, it’s seems that material model M1 is the most suitable

model for orthogonal cutting simulation of Inconel178 alloy. An example of experimental chip

morphology and predicted chip geometry using the different material models (at the testing

condition N2) is shown in Figure 3.

Figure 3. (a) Experimental [10] and (b) predicted chip geometry using different material models

But, in order to better compare and analysis of the results, average of absolute error for each

testing condition is plotted in the Figure 4(a). As shown in this figure, mainly the results of

simulations are nearer to the experiments when tool feed rate is decreased to 0.05 mm/rev. In

addition, it can be said that both material models of M1 and M3 are better than others, while model

M1 is better than M3 in testing condition N1.

1214 Material Forming ESAFORM 2014

Figure 4. (a) Average of absolute error for each testing condition; (b) average of absolute error for

machining outputs

Models M7 and M5 are hardness-based flow stress and modified J-C constitutive equation,

respectively developed based on the J-C constants in model M4. Comparison between results of

Model M7 and M4 confirm that, developing hardness-based flow stress improves prediction

capability of orthogonal cutting simulation of Inconel 718 alloy. In contrast, comparison between

results of Model M7 and M5 shows that, the results of simulation become worse when temperature-

dependent flow softening effect are included within the J-C constitutive equation. In fact, model M5

is worse than other material models for all of the testing conditions especially for testing conditions

of N2 and N3 (at the higher feed rates). J-C parameters for Models M3 and M6 are accessed by

inverse methodology through FE simulation. The results of Figure 4(a) indicate that, adopted

inverse technique in model M3 is more efficient than the other one due to the significant difference

between estimated results of these models. Also, the result of model M2 is satisfactorily the same as

model M1 at the low feed rate, but it becomes worse when feed rate is increased.

In the rest of the paper, effectiveness of the material models was evaluated separately on each

machining output. The average of absolute error for cutting forces (including Fc and Ff) and chip

geometry (including peak, valley, and pitch) was calculated for each testing condition. Then, for all

of the testing conditions, average error of temperature and calculated values was reported in Figure

4(b). As shown in this figure, for all of the material models predicted results of temperature is

significantly higher than the chip geometry and cutting forces. A reason might be related to

probable error of validated experimental data in [10] because of using thermocouple and inverse

numerical methodology for measuring maximum temperature. the average error of cutting forces

has been satisfactorily predicted using all of the material models except models M4 and M5.

5. Conclusions

In order to accurate simulation of machining processes, identification of the most suitable

material model is one of the first requirements. The aim of the present work is to investigate the

influence of the different J-C material constitutive equation on the chip morphology, forces, and

temperatures in the orthogonal cutting process of Inconel 718 superalloy. The seven sets of material

models (in 45 HRC) were implemented in a numerical machining model and the results were

compared with experimental data. It was shown that the results of simulation are significantly

influenced by J-C parameters used in the material model. In this regard, the obtained results were

compared and discussed to identify the most reliable model. In general, a reasonable prediction of

chip morphology, cutting forces and temperature is obtained when material constants set M1 is used.

Finally, it can be said that, the identified most suitable material model in this study, can be used

Key Engineering Materials Vols. 611-612 1215

efficiently for improving accuracy of machining simulation of Inconel 718 alloy by other

researchers.

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