Numerical investigating the effect of machining parameters on residual stresses in orthogonal cutting

Simulation Modelling Practice and Theory 18 (2010) 378–389

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Numerical investigating the effect of machining parameters on residual stresses in orthogonal cutting M. Mohammadpour, M.R. Razfar *, R. Jalili Saffar Department of Mechanical Engineering, Amirkabir University of Technology (Tehran Polytechnic), 424-Hafez Ave., 15875-4413 Tehran, Iran

a r t i c l e

i n f o

Article history: Received 12 April 2009 Received in revised form 25 September 2009 Accepted 9 December 2009 Available online 13 December 2009 Keywords: Residual stress Finite element Orthogonal cutting Cutting parameters

a b s t r a c t The aim of the present study is to develop a finite element analysis based on the nonlinear finite element code MSC.Superform for investigating the effect of cutting speed and feed rate on surface and subsurface residual stresses induced after orthogonal cutting. Basically, the present analysis is a coupled thermo-mechanical dynamic-transient problem. The results from the model are compared to experimental measurements available in the literature, concerning orthogonal cutting of steel AISI 1045 and are in good agreement with experimental data. Ó 2009 Elsevier B.V. All rights reserved.

1. Introduction Residual stress is defines as the stress state which exists in a body after all the external loads are removed. When assessing surface integrity, residual stress is often considered as one of the most critical parameters since it has a direct effect on the fatigue life of a machined component. The effects of residual stress could be both positive and detrimental on the deformation behavior, fatigue life, dynamic strength, chemical resistance and magnetic properties of machined components. Tensile residual stresses on the surface of components dangerously affect the life of them in operating conditions. After machining operations a thin layer (around 100 lm thick) on the surface can be found in traction with remarkable residual stresses of up to 800 MPa. In machining, the source of residual stress includes plastic deformation of the material and high thermal gradients in the cutting zone. These two sources are complex and do effect each other. Plastic deformation occurs during chip formation when the material is being sheared in the cutting zone. Additional plasticity occurs due the rubbing contact between the tool and the newly machined surface. Thermal gradients are caused by plastic deformation and frictional heating. When the thermal gradients are sufficiently high, phase transformation at the surface or near subsurface of the machined part will occur. Such change in material structure will alter the mechanical properties of the workpiece at the surface region. Consequently, the plastic deformation will be affected. Such complexity in the surface causing residual stress has made modelling the post-process stress in a machined part a challenging task. As can be probably deduced, the plastic deformation and the thermal gradient are directly dependent on how the cutting and tool geometry parameters, and the materials both for the tool and the workpiece were selected. A finite element method could be a good tool for selecting the best working cutting parameters, which induce a limitation of the tensile residual stress state [5].

* Corresponding author. Tel.: +98 2164543458. E-mail address: [email protected] (M.R. Razfar). 1569-190X/$ - see front matter Ó 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.simpat.2009.12.004

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Research in the field of metal cutting has traditionally been based on experimentation and prototyping, which means it has been expensive and rather slow. Nevertheless, the study of metal cutting has been going on for decades, due to the interest of the manufacturing sector in having a better understanding of this process and solving specific problem. In literature, most studies on surface integrity and, more specifically, on the residual stresses are experimental. Liu and Barash [11,12] found three quantitative measures to define the surface integrity of a machined layer: the apparent strain energy density, the strain-hardening index and the residual stress distribution. They also found there is a size effect in chip-removal, namely the deformation work per unit volume increases as the depth of cut decreases. Liu and Barash [13] investigated the impact on residual stresses by the tool flank wear, which causes subsurface heating and make residual stresses go deeper into the bulk of the workpiece; the origins of residual stresses proved to be predominantly mechanical with a slight thermal influence. Wu and Matsumoto [29] studied the effect of hardness on residual stress patterns after orthogonal machining; the shear angle remarkably increased with a higher material hardness. Fuh and Wu [3] presented a mathematical model for predicting residual stresses due to end-milling operations. They proposed a polynomial form that include the cutting speed, the feed rate, the cutting depth, the tool flank wear and nose radius as input parameters. M’Saoubi et al. [18] investigated residual stresses induced by orthogonal cutting in steels, analyzing the effect of the cutting speed, the feed rate, the tool geometry and coating; high residual stresses up to 960 MPa were observed, as well as a strong hardening. Jacobus et al. [6] developed a model to predict the full-biaxial surface and subsurface residual stresses; they found that an increase in feed rate or in depth of cut leads to an increase in the tensile character of normal stresses. El-Axir [2] tested five different materials and developed a model capable for predicting both the maximum value and the patterns of residual stress, on the basis of main cutting parameters. Recently, more and more FEM-based studies have turned up in literature and nowadays it is in all probability the only tool to provide models of fully predicting all the relevant variables in metal cutting. Strenkowski and Carrol [25] developed a finite element model based on the updated Lagrangian formulation, using an effective plastic strain criterion for chip separation; chip formation occurred along a pre-defined path and adiabatic heating conditions were assumed. Strenkowski and Moon [26] presented a steady-state Eulerian orthogonal cutting model; which neglected elasticity and consequently could not allow for residual stresses evaluation. Shih [23,24] showed the importance of the effects of thermal stresses and of cutting and clamping forces in predicting residual stresses. Ceretti et al. [1] modeled chip separation by removing elements that exceeded a threshold level for specific damage criteria. Lin and Lin [14] developed a three-dimensional model, keeping into account both convective and radiative heat transfer; chip separation was forced to occur along a pre-defined surface according to some geometrical and physical criteria. Liu and Guo [15] investigated the impact of sequential cuts and tool–chip friction on residual stresses, still employing a pre-defined path for chip separation. Kalhori [9] conducted different studies on metal cutting; adaptive remeshing was employed in two models developed for the FEM codes SiMPle and AdvantEdge. Movahhedy et al. [16,17] studied on the chip-removal process, simulating sharp, blunt and chamfered tools; such analysis was based on ALE formulation. Yang and Liu [27] focused on the impact of the friction coefficient on residual stress patterns, presenting a new stress-based polynomial model of friction; the main drawback of their approach was the need to have an experimental evaluation of the friction coefficient all along the tool rake face for a particular cutting condition and a specific workpiece material. In the present study a FEM model for orthogonal cutting of AISI 1045 mild steel is presented. This model is based on the updated Lagrangian formulation. The results of the model are validated through comparisons with the results of experimental measurements available in the literature.

2. FE simulation 2.1. Numerical model and parameters The essential and desired attributes of the continuum-based FEM models for cutting are: (1) the work material model should satisfactorily represent elastic plastic and thermo-mechanical behavior of the work material deformations observed during machining process, (2) FEM model should not require chip separation criteria that highly deteriorate the physical process simulation around the tool cutting edge specially when there is dominant tool edge geometry such as a round edge or a chamfered edge is in present, (3) interfacial friction characteristics on the tool–chip and tool-work contacts should be modelling highly accurately in order to account for additional heat generation and stress developments due friction [21]. In this paper, a two-dimensional strain–stress integration finite element model in MSC.Superform 2005 was developed for the nonlinear implicit finite element analysis. The chip formation is simulated via adaptive remeshing and plastic flow of work material by considering round tool edge geometry. Therefore, no chip separation criterion is needed. The aim is the simulation of orthogonal cutting of AISI 1045 steel, in order to predict the residual stress state beneath the machined surface. The effect of cutting speed and feed rate will be investigated and other parameters such as tool geometry do not change. The geometry of cutting tool is given in Table 1 and numbers of analyses as well as cutting conditions are given in Table 2. The cutting edge geometry indicates TNMG-432 of Sandvic Inserts. Meanwhile for simplicity the cutting tool is considered rigid. Due to high deformations during the simulation of the cutting process, the quality of the mesh is repeatedly checked and modified through adaptive remeshing: when the mesh quality becomes inadequate (that is when a specific criterion is not

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met, as later explained), the analysis is stopped and a remeshing is automatically prompted. After that, rezoning is performed, so that all parameters from the old mesh are transferred to the new one; at this point, the analysis can proceed. An advancing-front meshing technique has been used, which starts creating elements along the boundary and then fills up the entire region ending in the middle.

Table 1 Cutting tool geometry. Parameter

Value

Unit

Rake angle Clearance angle Edge radius

7 0.5 15

° °

lm

Table 2 List of analyses as well as cutting conditions. Analysis no.

Cutting speed (m/min)

Uncut chip thickness (mm)

Depth of cut (mm)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

135 135 135 135 175 175 175 175 215 215 215 215 265 265 265 265

0.05 0.1 0.2 0.3 0.05 0.1 0.2 0.3 0.05 0.1 0.2 0.3 0.05 0.1 0.2 0.3

3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3

Table 3 Johnson–Cook model constants for various steels. Steel

Ref.

A (Mpa)

B (MPa)

n

C

m

AISI 4340 AISI 4340 AISI 1045

[19] [4] [7]

950.0 792.0 553.1

725.0 510.0 600.8

0.375 0.26 0.234

0.015 0.014 0.013

0.625 1.03 1.000

Fig. 1. Illustration of the deformation zones and simulated slip-line fields in orthogonal cutting [21].

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The remeshing criteria implemented in this investigation and used in this analysis are three: (1) element-distortion criterion: all element angles are checked at every increment and changes in angles are estimated for the following increment; (2) contact penetration criterion: the relative distance between the edge of an element and the edge of a body in contact with it is checked at every increment and it must not exceed two times the contact distance tolerance; and (3) frequency criterion: remeshing is performed every ten increments, whatever the mesh quality. Model involves three stages. In stage I, the tool is advanced incrementally in the cutting direction until a steady-state condition is attained. In stage II, the tool is retracted. In stage III, the workpiece is incrementally cooled down to room temperature. At the end of this stage, residual stresses and strains are obtained. 2.2. Material properties Accurate and reliable flow stress models are considered highly necessary to represent work material constitutive behavior under high-speed cutting conditions especially for a new material. The constitutive model proposed by Johnson and Cook [8] describes the flow stress of a material with the product of strain, strain rate and temperature effects that are individually determined as given in Eq. (1). In the Johnson–Cook (JC) model, the parameter A is in fact the initial yield strength of the material at room temperature and a strain rate of 1/s and e represents the plastic equivalent strain. The strain rate e_ is normalized with a reference strain rate e_ 0 . Temperature term in JC model reduces the flow stress to zero at the melting temperature of the work material, leaving the constitutive model with no temperature effect. In general, the parameters A, B, C, n and m of the model are fitted to the data obtained by several material tests conducted at low strains and strain rates and at room temperature as well as split Hopkinson pressure bar (SHPB) tests at strain rates up to 1000/s and at temperatures up to 600 °C. JC model provides good fit for strain-hardening behavior of metals and it is numerically robust and can easily be used in FEM simulation models. JC shear failure model is based on a strain at fracture criteria given in Eq. (2). Many researchers used JC model as constitutive equation for high strain rate, high temperatures deformation of behavior of steels [19,4,7] (see Table 3).

" !#  m   e_ T  T room n   1 r ¼ A þ BðeÞ 1 þ C ln _ T melt  T room e0 !#   "  _ e p T  T room 1þ ef ¼ d1 þ d2 ed3 1 þ d4 ln reff T melt  T room e_ 0

ð1Þ ð2Þ

Fig. 2. Normal and frictional stress distributions on the tool rake face [21]. Table 4 Friction characteristics determined for AISI 1045 using carbide cutting tool. Material

AISI 1045

Vc (m/min) tu (mm) rNmax (MPa) lp (mm) lc (mm) a kchip (MPa)

135–265 0.05–0.3 1312.63 0.639 3.122 0.183 202.95 0.5

le

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2.3. Friction law Several researchers have used Oxley’s parallel-sided shear zone in which the primary shear zone is assumed to be parallel-sided and the secondary zone is assumed to be of constant thickness, in order to obtain work flow stress data. In order to successfully determine flow stress for JC material model and friction characteristics at the tool–chip interface, Özel and Zeren [22] proposed some modifications and improvements to Oxley’s model [20], that includes integration of

Fig. 3. Temperature distribution in different stages of chip forming.

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Johnson–Cook constitutive model as for the flow stress and triangular shaped secondary shear zone as it was confirmed via FEM simulations (Fig. 1). The basic concept of this methodology is the use of orthogonal cutting experiments and inverse solution of Oxley’s model in order to determine the flow stress and friction conditions experimented in the range of highspeed cutting. As commonly accepted, in the tool–chip contact area near the cutting edge, sticking friction occurs, and the frictional shearing stress, sint is equal to average shear flow stress at tool–chip interface in the chip, kchip. Over the reminder of the tool–chip contact area, sliding friction occurs, and the frictional shearing stress can be calculated using the coefficient of friction le. The normal stress distribution on the tool rake face can be described as:



rN ðxÞ ¼ rNmax 1  ðx=lc Þa



ð3Þ

Fig. 4. Surface and subsurface residual strain profile in the cutting (circumferential) direction.

Fig. 5. Illustration of circumferential and axial directions [9].

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Normal stress distribution over the rake face is fully defined and the coefficient of friction can be computed, once the values of the parameters rNmax and a are found. The shear stress distribution on the tool rake face illustrated in Fig. 2 can be represented in two distinct regions:

Circumferential Residual Stress 600 500 400 S11(MPa)

300 200

Experiment

100

FEM

0 -100 -200 -300 -400 0

0.2

0.4

0.6

0.8

1

Depth(mm) Fig. 6. Comparison of results from FEM and experimental for analysis no. 5.

Axial Residual Stress 450 350 S22(MPa)

250 150

Experiment FEM

50 -50 -150 -250 0

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

1

Depth(mm) Fig. 7. Comparison of results from FEM and experimental for analysis no. 5.

Circumferential Residual Stress 1000 800

S11(MPa)

600 400 Experiment

200

FEM

0 -200 -400 0

0.2

0.4 Depth(mm)

0.6

0.8

Fig. 8. Comparison of results from FEM and experimental for analysis no. 8.

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(a) In the sticking region:

sint ðxÞ ¼ kchip ; le rN ðxÞ P kchip ; 0 < x 6 lP

ð4Þ

(b) In the sliding region:

sint ðxÞ ¼ le rN ðxÞ; le rN ðxÞ < kchip ; lP < x 6 lC

ð5Þ

In Eqs. (4) and (5), kchip is the shear flow stress of the material at tool–chip interface in the chip. Based on the JC material model for AISI 1045 steel, the calculated friction characteristics include parameters of the normal and frictional distributions on the rake face are given in Table 4 [21]. 2.4. Heat transfer modelling In this simulation two sources of heat are considered: (1) heat due to sliding at the tool–chip interface; and (2) heat due to the plastic deformation work. The heat partition during cutting depends on several factors. The problem has been analyzed in detail in [28], where the authors have developed a method to estimate heat partition called ‘‘microstructure based method”. The method is based on experimental observation on a test case of flank wear land length and thickness of the white layer in the chip. Their results suggest that the heat partition is strongly dependent upon the development of the flank wear. The method could not be applied about the machined object in orthogonal cutting, i.e. the disk or tube, because no data about flank wear land length and white layer thickness of the chip were available. A rough assumption was then adopted: friction-related thermal energy is supposed to go in equal parts into the chip and the tool. On the other hand, as in most studies in literature [26,23,1,15,9,27]; it is assumed that 90% of the plastic work is converted into heat.

Axial Residual Stress 600 500

S22(MPa)

400 300

Experiment

200

FEM

100 0 -100 -200 -300 0

0.2

0.4

0.6

0.8

Depth(mm) Fig. 9. Comparison of results from FEM and experimental for analysis no. 8.

Table 5 Maximum values of residual stress components. Analysis no.

S11 (MPa)

S22 (MPa)

S33 (MPa)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

360.77 464.653 480.313 499.269 562.173 613.825 777.662 760.206 598.346 718.575 797.219 779.415 642.837 749.391 819.619 781.663

273.004 343.096 344.804 366.217 315.999 348.55 360.052 364.876 404.16 416.96 477.778 434.965 406.782 418.134 510.117 499.998

644.083 678.832 725.011 692.855 716.592 933.11 1033.94 1034.13 759.167 1023.87 1086.83 1100.56 803.306 1074.38 1068.02 1002.99

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In the software by selection of heat transfer option and giving convection and emissivity coefficients, the cooling simulation process of workpiece to the environment was carried out. The convection coefficient for arbitrary heat transfer equals to 4 mW 2 K and emissivity coefficient for AISI 1045 equals to 0.3 [20].

Circumferential Residual Stress 900

S11(MPa)

800 700

f=0.05mm/rev

600

f=0.1mm/rev f=0.2mm/rev

500

f=0.3mm/rev

400 300 100

150

200

250

300

Cutting Speed(m/min) Fig. 10. Maximum value variations of S11 with incrementing the cutting speed in different feed rates.

Axial Residual Stress 550

S22(MPa)

500 450 f=0.05mm/rev f=0.1mm/rev f=0.2mm/rev f=0.3mm/rev

400 350 300 250 100

150

200

250

300

Cutting Speed(m/min) Fig. 11. Maximum value variations of S22 with incrementing the cutting speed in different feed rates.

In-Depth Residual Stress 1100

S33(MPa)

1000 f=0.05mm/rev

900

f=0.1mm/rev f=0.2mm/rev

800

f=0.3mm/rev

700 600 100

150

200

250

300

Cutting Speed(m/min) Fig. 12. Maximum value variations of S33 with incrementing the cutting speed in different feed rates.

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3. Simulation and results, comparison between experimental and numerical results The simulations were conducted and the chip formation process from the incipient to the steady-state for analysis no. 5 was fully observed as shown in Fig. 3. The final residual surface and subsurface strain in the cutting direction for analysis no. 5 has shown in Fig. 4. S11 is the residual stress component in cutting or circumferential direction. S22 is the residual stress component in axial direction and S33 is the residual stress component in the normal (to the depth of cutting) direction. For better understanding, the circumferential and axial directions [10] are shown in the Fig. 5. Model is validated by comparison of residual stress profiles in circumferential and axial directions with experimental measurements available in Ref. [10] for analyses nos. 5 and 8 as shown in Figs. 6–9. In all of the cases, the maximum of residual stress components have occurred in the surface of the part and their values are given in Table 5. Figs. 10–12 show the variations of maximum values of stress components with incrementing the cutting speed in different feed rates. S11 in Fig. 10 increases with increasing cutting speed in all of the feed rates and the rate of increment in lower cutting speeds is more obvious. Also this subject is true for S22, but the rate of increment in average cutting speeds is more obvious and in lower feed rates, increasing the cutting speed more over a specific value does not have important effect and stress almost remains constant. The behavior of S33 in Fig. 12 is similar to the case of S11, but in upper feed rates, increasing the cutting speed more over a specific value lowers the level of tensile residual stress. Figs. 13–15 show the variations of maximum values of stress components with incrementing the feed rate in different cutting speeds. In Fig. 13, increasing the feed rate to 0.2 mm/rev causes the increment in S11, but increasing the feed rate over this value has negligible effect and in some cases lowers the level of tensile residual stress and is more obvious in higher cutting speeds.

Circumferential Residual Stress 900

S11(MPa)

800 700

v=135mm/min v=175m/min v=215m/min

600

v=265m/min

500 400 300 0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

Feed(mm/rev) Fig. 13. Maximum value variations of S11 with incrementing the feed rate in different cutting speeds.

Axial Residual Stress 550

S22(MPa)

500 450

v=135mm/min v=175m/min

400

v=215m/min v=265m/min

350 300 250 0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

Feed(mm/rev) Fig. 14. Maximum value variations of S22 with incrementing the feed rate in different cutting speeds.

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In-Depth Residual Stress 1100

S33(MPa)

1000 v=135mm/min

900

v=175m/min v=215m/min

800

v=265m/min

700 600 0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

Feed(mm/rev) Fig. 15. Maximum value variations of S33 with incrementing the feed rate in different cutting speeds.

Also this subject is strongly true for S22, excepting a little difference in v = 175 m/min. A regular procedure is not seen for S33 in Fig. 15. Increasing the feed rate more over 0.2 mm/rev lowers the level of tensile residual stress a little in the case of v = 135 m/min and almost constant in the case of v = 175 m/min and increments a little in the case of v = 215 m/min. The maximum value of stress occurs at f = 0.1 mm/rev in the case of v = 265 m/min and after that, the level of tensile residual stress falls down.

4. Conclusion A two-dimensional finite element model of orthogonal cutting of AISI 1045 has been presented and the numerical solution using the implicit FEM has been fully reported in the paper. Johnson–Cook work material model and a detailed friction model have been also used and work material flow around the round edge of the cutting tool was simulated in conjunction with an adaptive remeshing scheme. With increasing cutting speed and feed rate the maximum value of tensile residual stresses were increased. The simulation of the chip formation as well as predictions of the stress distributions on the machined surface was successfully achieved. This study establishes a framework for further study machining induced residual stresses accurately and process design via optimization of cutting conditions, tool edge geometry for high-speed machining applications.

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