Machining simulation paper

Int. J. Machining and Machinability of Materials, Vol. 14, No. 3, 2013

Finite element simulation of effect of residual stresses during orthogonal machining using ALE approach P. Krishnakumar* Department of Mechanical Engineering, Amrita Vishwa Vidyapeetham, Amrita Nagar, Coimbatore-641 112, Tamilnadu, India Fax: +91-422-2656274 E-mail: [email protected] *Corresponding author

K. Prakash Marimuthu Department of Mechanical Engineering, Amrita Vishwa Vidyapeetham, Bengaluru-560 035, Karnataka, India E-mail: [email protected]

K. Rameshkumar and K.I. Ramachandran Department of Mechanical Engineering, Amrita Vishwa Vidyapeetham, Amrita Nagar, Coimbatore-641 112, Tamilnadu, India E-mail: [email protected] E-mail: [email protected] Abstract: In this paper, a finite element model has been developed to predict the effect of residual stress induced in the work material during multiple pass turning of AISI 4340 steel. Chip morphology and force variation during machining are also quantified using the FE model. Finite element model was developed using arbitrary Lagrangian-Eulerian formulation along with Johnson-Cook material model and Johnson-Cook damage model. The finite element model developed in this study was validated experimentally by studying the chip morphologogy and cutting force variation during the machining. Results indicate that there is good correlation existing between numerical results and experimental results. Keywords: chip morphology; ALE formulation; residual stress; sequential cuts; multi-pass orthogonal machining.

Copyright © 2013 Inderscience Enterprises Ltd.

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P. Krishnakumar et al. Reference to this paper should be made as follows: Krishnakumar, P., Marimuthu, K.P., Rameshkumar, K. and Ramachandran, K.I. (2013) ‘Finite element simulation of effect of residual stresses during orthogonal machining using ALE approach’, Int. J. Machining and Machinability of Materials, Vol. 14, No. 3, pp.213–229. Biographical notes: P. Krishnakumar received his ME in Computer Integrated Manufacturing in 2000. Currently, he is working as an Assistant Professor (SG) in the Department of Mechanical Engineering, Amrita Vishwa Vidyapeetham, Coimbatore. He is pursuing his PhD in the machining field. His research interests include finite element modelling, machining and condition monitoring. K. Prakash Marimuthu received his MTech in Integrated Design and Manufacturing in 2012. Currently, he is working as an Assistant Professor in the Department of Mechanical Engineering, Amrita Vishwa Vidyapeetham, Bengaluru. His research interests include finite element modelling and CAM. K. Rameshkumar received his PhD in Production Engineering in 2007. Currently, he is working as a Professor in the Department of Mechanical Engineering, Amrita Vishwa Vidyapeetham, Coimbatore. His research interests include optimisation and simulation of manufacturing systems. K.I. Ramachandran completed his BTech in Mechanical Engineering at Government Engineering College, Calicut under Calicut University, Calicut in 1986. He received his MTech at IIT Kanpur in 1988. Then, he completed his PhD at IIT Madras in 1993. In 1994, he started his career in teaching profession at Amrita Institute of Technology, Coimbatore. He has published fifteen international journal papers and two books. Currently, he is working as a Professor at Amrita Vishwa Vidyapeetham, Coimbatore.

1

Introduction

Computer simulations helps to predict power requirements, cutting forces and chip formation using numerical models in metal cutting processes. The difficulty of reaching a better theoretical understanding of the metal cutting process impelled researchers in the field to apply the finite element analysis to model the metal cutting process. The advantage of the finite element method is that the entire complicated process can be automatically simulated using a computer. Numerical simulation has the ability to provide a detailed insight into the cutting process. It has the capability to replace costly experiments that are commonly used in design of tools and processes, etc. Due to the complexity of the cutting process it has been difficult to build a comprehensive, reliable and dependable model. From the numerical point of view, there are also aspects of cutting process which make it particularly challenging. Besides challenges like mesh distortion, dynamic boundary conditions another important factor is the cutting action at the tool tip where the material gets branched. Stress and strain field is greatly affected by the model that is being built to understand the cutting process (Movahhedy et al., 2000).

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Finite element formulations

Lagrangian formulation (LF) and the Eulerian formulation (EF) have been traditionally used in modelling of metalworking operations. In the Lagrangian approach, the finite element mesh is attached to the material and follows its deformation, whereas in the Eulerian approach, the mesh is fixed in space while the material flows through the mesh. The former is commonly used in solid mechanics applications and is particularly suitable for cases in which unconstrained flow occurs over free boundaries, because the mesh closely represents material boundaries. The latter, on the other hand, is usually used in fluid mechanics problems that involve a control volume, and is particularly suitable for cases with large material flow, but with minimal change in boundary shape, i.e., when the boundaries of the deformed material are known a priori (Movahhedy et al., 2000). Arbitrary Lagrangian-Eulerian (ALE) approach has been gaining more recognition in structural analysis for its combined advantages of both Lagrangian and Eulerian formulations in a single model. ALE technique combines the features of pure Lagrangian analysis in which the mesh follows the material, and Eulerian analysis in which the mesh is fixed spatially and the material flows through the mesh. ALE formulation is utilised in simulating machining to avoid frequent remeshing for chip separation. Explicit dynamic ALE formulation is very efficient for simulating highly non-linear problems involving large localised deformations and changing contact conditions as those experienced in machining (Özel and Zeren, 2005). The present work uses a plain strain model for the simplification of the analysis along with ALE approach.

2.1 Material models It is very important to use the appropriate material model for better finite element analysis. Johnson-Cook (J-C) material model is used as the constitutive equation for the material (Li et al., 2002). Several models have been developed to represent the rate and temperature dependence of metallic materials during deformation. The J-C material model is perhaps one of the most widely used models because it takes on a simple, yet effective, form that predicts the material behaviour in the static and dynamic modes equally well (Milani et al. 2009). This model (MCclain et al. 2002) uses strain, strain rate and temperature to predict the material responses as given in equation (1).

ε ⎛ σ = ( A + Bε n ) ⎜1 + C ln ε ⎝

o

m ⎞ ⎛ ⎛ T − Tr ⎞ ⎞ ⎜ 1 − ⎟⎜ ⎜ ⎟ ⎟ ⎠ ⎝ ⎝ Tm − Tr ⎠ ⎟⎠

(1)

A, B, C, n and m are material constants that are found by material tests. T is instantaneous temperature, Tr is room temperature and Tm is melting temperature of a given material.

2.2 Damage (failure) models Along with the material model a good damage model is required form the chips during finite element analysis. This means that the material has to fail. Material failure is a phenomenon which has complex physic mechanism. In failure model when a character parameter reach appointed critical value, then the element is completely failed, and FEM deletes it (Yue et al., 2009). Damage modelling in orthogonal cutting has significant

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importance. Plastic deformation and friction are considered as the sources of heat in very small region and cause locally very high temperature. The most part of the failure occurs due to thermal softening. To simulate the appearance of chip formation, the material in the chip should be detached from the work piece material to which fracture criterion should be applied. The chip detachment can be simulated with the progressive damage and failure law. The progressive damage and failure was introduced for composite materials and is extended for ductile material failure. Damage initiation and damage evolution are the two criteria applied for progressive damage and failure of elements in cutting process. For damage initiation the Johnson–Cook criterion is used in the present work. Damage initiation and damage evolution are the two criteria applied for progressive damage and failure of elements in cutting process. For damage initiation the J-C criterion is used as given in equation (2).

ε

f

σ ⎛ = ⎜ D1 + D2 exp D3 m σ ⎝

ε ⎞⎛ ⎟ ⎜1 + D4 ln ε ⎠⎝ o

m ⎞ ⎡⎛ ⎛ T − Tr ⎞ ⎞ ⎤ ⎢ ⎜ ⎟ ⎜1 − D5 ⎜ ⎟ ⎟⎟ ⎥ ⎠ ⎢⎣⎝ ⎝ Tm − Tr ⎠ ⎠ ⎥⎦

(2)

D1, D2, D3, D4 and D5 are the damage criterion constants and that are found by material tests. T is instantaneous temperature, Tr is room temperature and Tm is melting temperature of a given material. This is followed up by the damage evolution to model the progressive damage and failure of elements. The damage evolution capability for ductile material assumes that the damage is characterised by the progressive degradation of the material stiffness. The J-C damage model along with the J-C damage model is well suited (Öpöz and Chen, 2010).

2.3 Friction models In the analysis of orthogonal cutting process using finite element (FE) simulations, predictions are greatly influenced by two major factors; a

flow stress characteristics of work material at cutting regimes

b

friction characteristics mainly at the tool-chip interface.

The uncertainty of work material flow stress upon FE simulations may be low when there is a constitutive model for work material that is obtained empirically from high-strain rate and temperature deformation tests. However, the difficulty arises when one needs to implement accurate friction models for cutting simulations using a particular FE formulation. There is often disagreement between the results of FEM simulations and experiments. Understanding the influence of the inputs upon results can lead to a more reliable FE model for cutting processes. Hence, the analysis of friction on FEM cutting simulation is crucial (Filice et al., 2007). In conventional machining at low cutting speeds, the Coulomb friction can be mostly effective at the tool flank face. In early metal cutting simulation, the simple Coulomb friction model was used on the whole contact zone with a constant coefficient of friction. The model is defined in equation (3).

τ = μσ n

(3)

Here, τ is the frictional stress, σn was used in this case) is the normal stress and μ is the coefficient of friction. (0.1 was used in this case).

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2.4 Chip morphology A good FE model has can used for various purposes like a

chip morphological studies

b

flow stress analysis

c

residual stress analysis

d

force prediction

e

temperature prediction, etc.

Chip morphology and segmentation play a predominant role in determining machinability and tool wear during the machining. Most of the researchers have restricted their studies to the first pass of the orthogonal machining process. Only a couple of works have been published involving sequential cuts. Deshayes et al. (2004) characterised the chip morphology to verify the finite element simulations. The complexity of chip formation in machining processes stems from the confluence of several physical phenomena – mechanical, thermal, and chemical – occurring at very high strain rate. The prediction of chip morphology depends on a fundamental understanding of these phenomena and is of industrial importance for cutting force prediction and surface integrity control (Deshayes et al., 2004). Prediction of chip morphology and segmentation during the machining of titanium alloys were studied by Hua and Shivpuri (2004). They have studied the machinability and tool wear based on the chip morphology. Su and Liu (2010) investigated the effect of work piece material brittleness on segmental chip formation and consequent chip morphology. Effect of the cutting speed on the chip morphology and the cutting forces were studied by Daymi et al. (2009). Chip formation has been simulated by using two different plastic model and damage criteria. J-C plastic model in conjunction with J-C damage is working good when regarding machining process which involves large deformation (Öpöz and Chen, 2010). Different methods have been used to simulate chip formation in machining: pure deformation model, J-C damage model, deformation energy-based criterion, ductile fracture criterion, and more recently, and Baummann-Chiesa-Johnson model (Calamaz et al., 2011). In this study J-C damage model is used to simulate the chip formation in machining of AISI 4340 steel.

2.5 Residual stress modelling Only few studies are available in the literature to model the prediction of residual stress induced during the machining process. The residual stress can augment or blight the functional behaviour of the work piece. The effects of residual stress will influence the deformation, static and dynamic strength, and chemical and magnetic properties of the materials. Also residual stress induced in a particular cutting pass during the machining may induce variation in the cutting forces during machining in the subsequent pass leads to poor surface finish and tool life (Capello, 2005, 2006). Some investigations on predictions of residual stresses due to orthogonal metal cutting using finite element methods were carried out by Shih and Yang (1993). Saoubi et al. (1999) investigated the residual stresses induced by orthogonal cutting in AISI 316L steels. Liu and Guo (2000) carried out finite element analysis to study the effect of sequential cuts and tool-chip friction on residual stresses in a machined layer.

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Quteiro et al. (2006) studied the residual stresses in machined layers of AISI 316L steel. The results show that sequential cut tends to increase superficial residual stresses. A predictive model for residual stresses in orthogonal cutting was presented by Liang and Su (2007). Recently, Miguélez et al. (2009) studied the residual stresses in orthogonal cutting of metals focusing on the effect of thermo mechanical coupling parameters and of friction. In this paper, an attempt is made to study the effect of sequential cuts on residual stresses in a machined layer and the effect of previous cuts on the residual stresses and the chip formation and force.

3

Methodology

The present work deals with the prediction of the chip morphology and force prediction during the multiple pass machining of AISI 4340 steel. The FE model developed will incorporate the ALE approach, J-C material and damage model coupled with adaptive meshing to get more realistic results. The results from the FEA model is compared with the experimental results to validate the FE model developed. The methodology adopted in this work is given in Figure 1. Figure 1

Methodology

FE model

Material model

Damage model

Boundary conditions

Simulation

Work piece material (AISI 4340 steel) Tool material: Tungsten carbide

Turning (experiments) Cutting conditions Speed in rpm = 700 Feed in mm/rev = 0.1 Depth of cut in mm = 0.5

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Residual stress prediction, chip morphological studies, and cutting forces analysis

Finite element model

Adopting the ALE approach a plain strain model is made for the said analysis. 2D model is being used for the analysis. The model is shown in Figure 2. The work piece is modelled as a deformable body and the tool is modelled as a rigid body. Tool is given a rake angle of 2°.

Finite element simulation of effect of residual stresses Figure 2

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2D model of work piece and tool assembled together (see online version for colours)

The material constants, damage constants and material properties for the AISI 4340 are given in Tables 1 to 3 respectively. Table 1

J-C material constants

Material AISI 4340 steel Table 2

A (MPa)

B (MPa)

C

n

m

490

600

0.015

0.21

0.6

D1

D2

D3

D4

D5

0.05

3.44

–2.12

0.002

0.61

J-C damage constants

Material AISI 4340 steel Table 3

Material

AISI 4340 steel

Material property Young’s Poisons modulus ration GPa 210

0.3

Density kg/m

Thermal conductivity W °C m

Specific heat J °C kg

Melting temperature °C

Room temperature °C

7,800

47.7

475

1,525

25

4.1 Boundary condition Boundary conditions are given as shown in Figure 3. The lower end of the work piece is arrested for all degrees of freedom. The tool is not allowed to move in the direction of Y-axis. The tool is given a velocity equivalent to that of the cutting speed in the X-axis, in this case it is 120 m/min. Feed is given as the uncut chip thickness that is 0.1 mm.

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Figure 3

Boundary conditions used in the FE analysis (see online version for colours)

4.2 Meshing Tool is modelled as a rigid by considering cutting tool is extremely harder comparing to work piece material. The work material in 2D model is discredited by using CPE4R element (a 4-node bilinear plane strain quadrilateral reduced integration, hourglass control).

5

Simulation

A dynamic explicit analysis was done using commercially available FEM software Abaqus 6.10. This is done so because of the large deformation which is involved in the simulation. Adaptive meshing is also used to avoid any distortion and to have a realistic simulation.

5.1 Post processing After the successful completion of the simulation post processing was done. The chip formed during the simulation was studied. The chip morphology obtained for the material is given in Figure 4. Along with the chip formation the Von-Mises stress distribution was also recorded. The stress distribution in the material during simulation is given in Figure 5.

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Figure 4

Chip formation during the machining of AISI 4340 steel (see online version for colours)

Figure 5

Von-Mises stress distribution for AISI 4340 steel (see online version for colours)

5.2 Force variation during machining The scope of the present work is to predict the variation of the force during subsequent machining. To predict the force variation, a small variation in the model was made. Instead of having one tool, three tools were considered. Each tool was separated by a distance equal to the uncut chip thickness in the Y-axis and a distance equal to the length of the work piece in the X-axis. This will imitate the real time condition of three passes. In addition to that the mechanical effect on the work piece during the first pass is preserved and the second pass takes place. Subsequently the mechanical effects of the second pass are preserved and serve as the input to the third pass. In this way the force

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variation during the first three subsequent passes were predicted. The FE model was done as shown in Figure 6. All other input to the analysis remains the same. Figure 6

Modified FE model with three tools (see online version for colours)

Figure 7 show the variation of the forces during the first three cuts and their trends are shown in the figure. Figure 7

6

Variation of force for the first three passes in AISI 4340 steel and their trends (see online version for colours)

Experimental work

Experiments were conducted to validate the FE model, developed in this work. Using the FE model simulations were carried out for different cutting conditions and the cutting forces were predicted. To validate the FE model, experimental studies were carried out for same cutting conditions and cutting forces were measured using Kistler dynamometer and the results were compared. A conventional lathe was used for the machining

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operation. The equipment has the capability to measure the forces in the three directions namely, 1

feed force (Fx)

2

radial force (Fy)

3

tangential force (Fz).

The scope of the present work is limited to measurement of cutting force (Fz) only. The experimental setup is shown in Figure 7. The experimental set up shows that the work piece is mounted between centres on a conventional lathe. The Kistler dynamometer is fitted to the tool post in order to make the force measurement. Figure 8

Experimental setup with Kistler dynamometer (see online version for colours)

Figure 9

Machining and force measurement from other view (see online version for colours)

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The specification of the Kistler dynamometer is shown in Figure 10. Figure 10

Specifications of the Kistler dynamometer (see online version for colours)

The force dynamometer is coupled to a computer which facilitates the plotting of the measured force variation. The report from the system has data such as the cutting speed, the feed rate, the rpm of the spindle, the maximum, average and the minimum force measured in Newton and also the time for which the measurement is being carried out.

6.1 Experimental methodology The present work deals with studying the variation of the force during the subsequent cuts. In order to study this, force in the tangential direction was measured during the first three passes using the FE model. Experimental work was carried out in the following manner to validate the obtained results. 1

force measurement was done for the first three passes

2

force measured for the 4th, 5th and the 6th passes. This is done to see how the variation of force as the pass increases.

In all the above cases the chips were collected and compared to that of the chips generated by the FE model.

6.2 Cutting conditions AISI 4340 steel machining was carried out for the cutting conditions as given in Table 4. Three cuts were taken and the force generated was measured using the Dynamometer. Also the chips were collected for comparing with the simulated results.

Finite element simulation of effect of residual stresses Table 4

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Cutting conditions for AISI 4340 stel

Conditions

Value

Speed in m/min

70 m/min

Feed in mm/rev

0.1 mm/rev

Depth of cut in mm Coolant Tool

0.5 mm Yes Carbide tipped

Thus various experiments were conducted for different cutting conditions and the chips obtained were collected for chip morphological studies and the forces during the first three passes were measured. Initial analysis show that there is decreasing trend in the force values for the subsequent passes.

7

Results and discussions

Finite element simulation of cutting process has been accomplished by using abaqus/explicit. 2D analysis has been performed. Both FE simulation and experiments have been done under identical cutting condition. During chip formation, it is observed that machined surface and removed chip surface are not smooth (waviness). It is due to the parameters used in ALE adaptive remeshing. Further studies have to be carried out to optimise the ALE parameters to get high quality mesh. During the sequential cuts, cutting force variation has been studied. The chip morphology and cutting forces were studied using both simulation and experiments.

7.1 Chip morphology The chips obtained during the simulation of machining of the three different materials are compared with that of the chips obtained during actual experiments. The comparison is shown in Figure 11. Since the chip morphology which is obtained through the FE simulation is almost same as the chip morphology obtained through experimentation. This shows that the model is representing the true behaviour of the machining process.

7.2 Force prediction for sequential cuts The force variation during the sequential cuts has been predicted using the FE model. The same has been validated using the experimental results. There is only a slight variation between the predicted force and the actual experimental results. The comparison between these two values is given in Figure 12.

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Figure 11

AISI 4340 steel chip comparison (see online version for colours)

Figure 12

Force variation during sequential cuts of AISI 4340 steel, experimental vs. simulation (see online version for colours)

Finite element simulation of effect of residual stresses Table 5

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simulation vs. experimental force values during subsequent passes Average force value in Newton

Pass number

AISI steel Simulation

Experiment

1

160.00

140.0

2

159.25

147.5

3

164.56

135.0

From Table 5 we understand that the average force values during simulation is close to the experimental values. The number of values taken for calculating the average in case of experiment is fairly high compared to the simulation keeping the simulation time in mind. Also in the FEM model the material is considered to be homogeneous whereas in real time it may not be the case. In the simulation, the tool is assumed to be rigid which is not so in the real sense. All these factors could have effected the variation in the results. However if we see the trend, there is very close agreement between the values.

7.2.1 Causes for the force variation It is observed that there is a slight variation in the force during the subsequent passes. It is the fact that the hardness of the material will increase due to machining which should actually result in the increase in the machining force. But in this case there is a decrease in the force values. This can be attributed to the residual stresses that are formed during machining. The variation of the residual stresses in the depth direction is shown in Figure 13. Figure 13

Residual stress variation across the depth during sequential cuts of AISI 4340 steel

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It can be observed that there are compressive residual stresses for a few microns and there upon the residual stresses are tensile in nature. This might be one of the reasons for the force to show a decreasing trend even though there is increase in hardness of the material. However this requires further probing to understand the exact phenomenon.

8

Conclusions

In this work a finite element model has been developed to predict the chip morphology and force variation during multiple pass turning of AISI 4340 steel. Residual stresses induced during machining are also quantified using the FE model. Experiments were carried out to validate the FEA model proposed in this work. Chip morphological studies have been carried out using the FE model. From the simulation, it is observed that the type of chip formed during the simulation is matching the exact behaviour of the chips formed during the experimentation. During machining, under different cutting conditions cutting force variations were studied. It is found that experimental and values predicted by the FE model are comparable. The numerical results also predict the residual stress distribution and show high magnitude along the cutting direction, on the machined work piece surface. FE model developed in this work may be extended for further studies in the following areas: •

development of a thermo-mechanical model to investigate on the temperature effects on machining

•

measurement of hardness and residual stress after each pass and a correlation has to be drawn between the two values

•

based on the present model and with a few improvements to it, wear model could be developed

•

3D model may be developed to study the effect of depth of cut on force variations and residual stress.

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