FLOW STRESS DATA FOR FEM SIMULATION OF INCONEL 718 MACHINING dữ LIỆU ỨNG SUẤT CHẢY CHO mô PHỎNG FEM QUÁ TRÌNH cắt gọt hợp KIM INCONEL 718

FLOW STRESS DATA FOR FEM SIMULATION OF INCONEL 718 MACHINING D Ữ LIỆU ỨNG SUẤT CHẢY CHO MÔ PHỎNG FEM QUÁ TRÌNH CẮT GỌT HỢP KIM INCONEL 718 Nguyen Tuan Anh 1a , Pham Huy Hoang 2b 1Ngu

FLOW STRESS DATA FOR FEM SIMULATION OF INCONEL 718

MACHINING

D Ữ LIỆU ỨNG SUẤT CHẢY CHO MÔ PHỎNG FEM QUÁ TRÌNH CẮT GỌT HỢP

KIM INCONEL 718

Nguyen Tuan Anh 1a

, Pham Huy Hoang 2b

1Nguyen Tat Thanh University, Ho Chi Minh City, Vietnam

2Ho Chi Minh City University of Technology (VNU-HCM), Ho Chi Minh City, Vietnam

a ntanh@ntt.edu.vn; b phhoang@hcmut.edu.vn

ABSTRACT

In recent years, finite element method (FEM) has been applied successfully in studying machining processes, especially machining Inconel 718.The validity of FEM study however depends on the accuracy of the material flow stress data This paper describes a constitutive model for flow stress at machining conditions The equation is a combination of a power law equation and a high-order polynomial equation that are based on velocity-modified temperature

Keywords: finite element method, simulation, flow stress, Inconel 718, machining

TÓM TẮT

Trong những năm gần đây, phương pháp phần tử hữu hạn (FEM) đã được áp dụng thành công để nghiên cứu các quá trình gia công cắt gọt, đặc biệt là hợp kim Inconel 718 Ứng dụng thành công FEM, tuy nhiên, phụ thuộc vào tính chính xác của dữ liệu ứng suất chảy của vật liệu Nghiên cứu này mô tả mô hình toán cho dữ liệu ứng suất chảy trong điều kiện gia công cắt gọt Mô hình này là kết hợp giữa mô hình luật lũy thừa và biểu thức đa thức bậc cao, dựa trên mô hình nhiệt độ điều chỉnh bởi vận tốc

Từ khóa: phương pháp phần tử hữu hạn, mô phỏng, ứng suất chảy, hợp kim Inconel

718, gia công cắt gọt

1 INTRODUCTION

In the last two decades, finite element method (FEM) has been proved a useful tool for investigating and improving machining processes Application of FEM now can be found in studying chip formation mechanism, designing cutting tool, understanding burr formation, improving surface integrity [1,2]

However, the validity of FEM technique depends strongly on the accuracy of the flow stress data used in the simulation Material in machining is subjected to large plastic strain (1 and higher), coupled with high temperatures (200°C to 1000°Cor more) at high strain rates (104 to 106s-1) Moreover, there is a steep stress gradient in front of the cutting tool and a strong stress concentration in chip formation zones [3] Replicating such conditions in material testing is not an easy task A review of the literature shows that flow stress data can

be derived mainly using the following methods: high-speed compression tests, Split Hopkinson’s pressure bar (SHPB) tests, machining tests, and inverse analysis using FEM technique Nevertheless, regardless of the methods in use, the accuracy of the data is hard to verify, which makes stress behaviour is an important challenge for successful FEM simulation

of machining processes [1,4]

In this study, we propose a constitutive model for obtaining flow stress data for FEM simulation of Inconel 718 machining The model is based on a power law constitutive equation with the dependence of stress on velocity-modified temperature It will be shown that the model can describe the viscoplasticity and thermal softening behaviour of the material

2 LITERATURE REVIEW

Inconel 718 is a nickel-based superalloys, widely employed in many applications such

as aircraft gas turbines, hot work tools and dies, space vehicles parts, heat treating equipment, nuclear power plants It is called superalloy due to its superior properties: heat-resistance, high melting temperature, and maintenance of strength and hardness at high temperatures These properties, however, are also the reasons that Inconel 718 is classified as a difficult-to-machine material [5]

Inconel 718 material properties, especially flow stress behaviour, have been the subject

of study for a long time James et al [6] tested annealed, oiled quenched and aged Inconel 718 under tension, creep, cyclic conditions with the temperature of 593°C and the strain rates up

to 7.63x10-6 s-1 Dwivedi et al [7] hot compressed the material at strain rates 0.001, 0.01, 0.1,

1 s-1with strains up to 0.5, and the temperature range was 900, 955, 1010, 1065 and 1120°C Gil et al [8] studied yield of Inconel 718 by axial torsional loading at the temperatures of 23,

454 and 649°C, and the strain rate was 10-5 s-1 Sciuva et al [9] conducted impact tests on Inconel 718 at strain rates of 6, 200 and 500 s-1

The above review points out that most of material tests for Inconel 718 have been conducted at very low strain rates (< 1 s-1) in comparison with the strain rates experienced in cutting processes (> 105 s-1) Only recently, there are available a few flow stress data collected from SHPB tests with strain rate up to 104 s-1 [10,11] A recent comparison of various constitutive models for Inconel 718 highlights the inconsistent influence of the models on FEM results [12]

3 FLOW STRESS MODEL FOR INCONEL 718

In this study, the flow stress data for simulation of machining Inconel 718 is assumed to follow a power law:

where σ is a flow stress, ε is a plastic strain, n is a strain hardening coefficient C is a

stress constant, and can be estimated from Ramburg-Osgood equation [13]

𝐶𝐶 = 𝜎𝜎0�𝛼𝛼𝐸𝐸�𝑛𝑛 (2) where 𝜎𝜎0 is a nominal yield stress, E is Young’s modulus and α a dimensionless constant

The strain rate-hardening and thermal softening behaviour of the material can be taken account by establishing 𝜎𝜎0as a function of on a variable T m:

𝑇𝑇𝑚𝑚 = 𝑇𝑇 �1 − 𝐾𝐾𝐾𝐾𝐾𝐾𝐾𝐾 �𝜀𝜀̇𝜀𝜀̇

where T m called velocity-modified temperature °K, T is temperature, ε is strain rate, ε0

is reference strain rate, and K is material constant

The dependence of 𝜎𝜎0 on T m follows the approach by Hasting et al [14] It was shown that flow stress acquired by this approach gave a better match between FEM and experimental results in comparison with other approaches [15]

3.1 Determination of K

In order to use the above model, it is necessary to determine the value of the material constant K As the material constant K for Inconel 718 is not available, the following procedure is applied to estimate the value of K: (a) Collect flow stress data at strain ε=0 at

various temperatures and strain rates; (b) Set the reference strain rate ε=1s-1; (c) Curve-fit for the flow stress – temperature data at ε=1s-1; (d) Use the fitted curve to estimate the

corresponding values of T m for flow stress at other strain rates; (e) Use equation (3) to find the

value of K from given T, ε and estimated T m

In this study, flow stress data from Dwivedi et al [7] is employed to find K because of its extensive cover of testing temperatures, strains, and strain rates Moreover the testing condition is hot compression, which might be close to machining condition Table 1 gives a sample of the data for strain ε=0

Table 1 Flow stress data at strain ε = 0 Testing

temperature

T,°K

Flow stress σ, MPa

𝜺𝜺̇ = 𝟏𝟏 𝒔𝒔−𝟏𝟏 𝜺𝜺̇ = 𝟎𝟎 𝟎𝟎𝟎𝟎𝟏𝟏 𝒔𝒔−𝟏𝟏 𝜺𝜺̇ = 𝟎𝟎 𝟎𝟎𝟏𝟏 𝒔𝒔−𝟏𝟏 𝜺𝜺̇ = 𝟎𝟎 𝟏𝟏 𝒔𝒔−𝟏𝟏

Figure 1 a) Curve fitting for σ-T m at strain 0and strain rate 1 s -1

. b) A projection of velocity-modified temperatures for flow stress at other strain rates The dots mark the

projection of T m

Figure 1 describes partially the procedure of estimating K In Figure 1a, the values of flow stress at strain 0 and strain rate 1s-1 are display together with the fitted curve The curve

is fitted by using MATLAB curve fitting toolbox Extending the fitted curve, the values of T m

for flow stress at 0.1, 0.01, 0.001 s-1 in Table 1 are found (Figure 1b.)

The above procedure is repeated for flow stress data at other strains Table 2 presents the result of estimating K for different strain values For further derivation of the yield stress equation the average value K=0.09 will be applied

Table 2 K obtained by regression Strain 0 0.04 0.08 0.15 0.22 0.29 0.36 0.43 0.50

K 0.06 0.12 0.09 0.09 0.09 0.09 0.095 0.12 0.1

3.2 Determination of yield stress equation σ0 = f(T m )

The yield stress equation is deduced by fitting a polynomial curve on experimental data of yield stress The data is combined from the literature and shown in Table 3 Except the stress from Dwivedi et al.’s testing [7], which was conducted as hot-compression, all

other tests were tensile The temperature of the tests are converted to T m using equation (3) and K = 0.09

Table 1 Yield stress for curve fitting

T m , °K 426 435 854 1095 1337 1337 1337 1218 1256 1384 1449 1490 1498

Stress, MPa 1280 1260 1120 1073 1028 886 972 893 825 429 351 316 700

T m , °K 1498 1514 1560 1579 1595 1629 1644 1670 1699 1700 1745 1769 1894

Stress, MPa 642 290 211 220 246 141 176 123 123 100 97 92 53

When fitting a polynomial curve to the data, it should be noted that for machining

conditions T m could range from 10 to 900°K However, the data in Table 3 is limited to Tm

>400°K Hence, an extrapolation is required while determining flow stress for simulating machining processes It has been noted that currently all constitutive equations available for FEM present some types of extrapolation as replicating machining conditions in material tests are impossible [1,12] Below are two high-order polynomial equations, fitted for the data in Table 3

σ0 = - 2.23e-17t7 + 1.76e-13t6 - 5.74e-10t5 + 9.98e-7t4 - 10e-4t3 + 0.58t2 - 1.80e2t + 2.44e4 (5) σ0 = - 2.28e-6t3 + 6.49e-3t2 - 6.14t+ 2.96e3

(6)

Figure 2 High-order polynomial fit curves for flow stress data

For the simplicity of later discussion, Equation (5) is called Case A, and Equation (6) – Case B The two cases allow a good fit for the experimental values but varied projection at

lower values of T m (Figure 2) The other parameters required for the model are selected as

follows: the strain-hardening coefficient n=0.056 by estimating from [7], the Young modulus,

which is temperature dependent, is selected from [17], and given in Table 4, α = 3/7 is set following [13, p.18]

Table 4 Young modulus E, GPa [17]

4 FEM SIMULATION FOR SELECTING YIELD STRESS CURVE

The accuracy of FEM simulation requires flow stress information at the velocity-modified temperature Tm from 10 to 900 °K The data from material testing for this range unfortunately is not available at lower 400 °K, hence, an extrapolation is necessary In Section

3, we see that many high-order polynomial curves can be fit to the testing data In order to select the best polynomial curve, an inverse approach is used In an inverse approach, the studied polynomial curve will be used to get the flow stress data, and then FEM simulation is conducted with the obtained stress data The FEM simulation result is then compared with the machining experiment to select the best curve

The simulated machining process is an orthogonal cutting, in which the cutting velocity

is 20 m/min, depth of cut is 1 mm, feedrate is 0.24 mm/rev, the rake and clearance angles of the cutting tool are 5 and 6 degree The simulated machining condition is selected to match the experiment reported in [18]

The FEM undeformed mesh of the workpiece and the cutting tool is given in Figure 3 The chip layer has the height of 0.24 mm and is divided into 10 sub-layers of elements The chip layer is meshed with smaller size elements to accommodate for the complex stress-strain behaviour in the chip The rest of the workpiece has a length of 4.25 mm and a height of 1.24

mm, and has been divided into 10 layers, each having 125 elements along the cutting path The elements have the same width, but the heights increase toward the bottom of the workpiece with the ratio of 1.25 between the layers The elements of the chip sub-layer along the cutting path are defined so that they will fail and be removed from the model when the chip separation criterion is reached The above model has in total 2500 four-node plane strain elements and 2646 nodes

Figure 3 Finite element mesh of workpiece and tool

The cutting tool is considered much harder than the workpiece For the economics of computational time, the cutting tool is modelled by an analytical rigid surface Thus, no stresses and strains for the cutting tool are calculated in the simulation process The boundary

conditions for the chip-workpiece-tool system are given as follows The tool moves as a rigid body with a constant velocity of 20 m/min The bottom of the workpiece is constrained from moving vertically and horizontally since the bottom boundary is expected to undergo very little deformation during cutting The left and right side of the workpiece are considered to be rather far from the cutting zone, thus will be constrained from moving horizontal

For the contact between material and cutting tool, the modified Coulomb friction law with friction coefficient 0.3 is assumed The heating transfer is also considered adiabatic and heat generated from friction is neglected Hence, each finite element integration point is treated as if it is thermally insulated from its neighbours The chip separation criterion employed is the shear failure criterion when a shear strain is met at an element integration point, all the stress components will be set to zero and the material point fails Detailed description of the friction condition, chip separation, heat transfer model can be found in [15]

5 SIMULATION RESULTS AND DISCUSSION

The finite element model was implemented using a commercially available FEM software package ABAQUS/Explicit The flow stress data was tabulated for strain rates from

0 to 106 s-1 and temperatures from 27 to 900°C The simulation was run on a PC Intel Duo Core The stress distributions of the simulation are given in Figure 4 for 2 cases of flow stress data: Case A and Case B

Figure 4 Stress distribution: a) Case A b) Case B

The simulation results show 2 distinctive chip geometries The simulation result of Case

A gives serrated chip geometry while the simulation with Case B displays a continuous chip type It should be noted that serrated chip geometry is typically observed in machining Inconel 718 [19] Analysis of the strain, strain rate, temperature occurred in the simulation reveals that the simulated machining processes are subjected to high strain rates up to 105 s-1 (for Case A) and 104 s-1 (for Case B), strain up to 2.5 (for Case A) and 1.5 (for Case B), temperature in the primary shear zone up 800 °C (for Case A) and 600 °C (for Case B), hence justifying the necessity of obtaining flow stress at large strains and high rates

Figure 5 reports simulated cutting forces for Case A and Case B The average cutting force for Case A is 1250 N while the average value for Case B is 850 N Case A exhibits a fluctuation of the force, which can be explained by local shearing and thermal softening in the primary shear zone associated with the segmentation of the chip On the other hand, smoothness of the cutting force curve for Case B is probably due to the stability of plastic deformation in the chip formation process If comparing with the cutting force of 1350 N reported in [18]for a similar machining condition then Case A gives a closer match

a) b)

Figure 5 Simulated cutting forces: a) Case A b) Case B

Overall, Case A replicates closely the machining experiment reported in the literature in terms of chip geometry, chip formation process, and cutting forces

CONCLUSION

In this study, flow stress data of Inconel 718 for FEM simulation of machining processes is derived By assuming the relationship between flow stress and velocity-modified temperature, high-order polynomial curves are fit on material testing data The selection of appropriate extrapolation is achieved by inverse method with FEM It is shown that flow stress data from 7-order polynomial curve extrapolation gives FEM simulation result in close match with experimental results In order to verify the appropriateness of the flow stress data, more simulation and comparison with machining experiments are needed

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AUTHOR’S INFORMATION

1 Nguyen Tuan Anh, Nguyen Tat Thanh University, ntanh@ntt.edu.vn, 0989619024

2 Pham Huy Hoang, Ho Chi Minh City University of Technology (VNU-HCM),

phhoang@hcmut.edu.vn, 0989166420