2212-8271 © 2013 The Authors. Published by Elsevier B.V.Selection and peer-review under responsibility of The International Scientifi c Committee of the “14th CIRP Conference on Modeling of Machining Operations” in the person of the Conference Chair Prof. Luca Settineridoi: 10.1016/j.procir.2013.06.143

Procedia CIRP 8 ( 2013 ) 516 – 521

14th CIRP Conference on Modeling of Machining Operations (CIRP CMMO)

Towards a physical FE modelling of a dry cutting operation: influence of dynamic recrystallization when machining AISI 1045

C. Courbona,b*, T. Mabroukib, J. Rechc, D. Mazuyera, F. Perrardd, E. D’Eramod

aUniversité de Lyon, CNRS, Ecole Centrale de Lyon, LTDS UMR5513, F-69134 Ecully, France bUniversité de Lyon, CNRS, INSA-Lyon, LaMCoS UMR5259, F-69621 Villeurbanne, France

cUniversité de Lyon, CNRS, ENI de Saint-Etienne, LTDS UMR5513, F-42023 Saint-Etienne, France dASCOMETAL-CREAS, F-57301 Hagondange, France

* Corresponding author. Tel.: +33 6 86 94 78 88; fax: +33 4 72 43 89 13; E-mail address: cedric.courbon@free.fr

Abstract

Whether analytical or numerical, models of a machining operation require important input data such as friction laws or material constitutive models to reach accurate results. Recent experimental studies provided a better fundamental understanding of the cutting process especially regarding the thermo-mechanical conditions associated to the chip formation. However, in most of the numerical works, the deformation behaviour of materials is still represented by a simple empirical equation. This contribution therefore aims at improving the physical meaning of a FE cutting model by the use of an advanced constitutive equation. After an emphasis on the microstructural evolutions occurring in cutting, a dynamic compression test campaign is conducted to assess the material behaviour at high strains. A "metallurgy based" constitutive model, taking into account a dynamic recrystallization process, is identified. It clearly leads to a better description of the thermo-mechanical behaviour than the commonly used Johnson & Cook’s model, also identified based on these experiments. Finally, the latter are implemented in a FE code (Abaqus/Explicit©) via a VUMAT© subroutine. An ALE 2D orthogonal cutting model is then involved to assess their performance as well as the effect of the dynamic recrystallization in machining. Numerical results are compared to experimental data in orthogonal cutting conditions as well as identifications of Johnson & Cook’s model conducted in the literature. © 2013 The Authors. Published by Elsevier B.V. Selection and/or peer-review under responsibility of The International Scientific Committee of the 14th CIRP Conference on Modeling of Machining Operations" in the person of the Conference Chair Prof. Luca Settineri Keywords: AISI 1045; cutting; shear zone; dynamic recrystallization; grain refinement;

1. Introduction

Although machining is one of the most aggressive manufacturing processes, modelling of machining, and especially metal cutting, has always been of particular interest for industry. The machined material experiences extreme thermo-mechanical loadings such as strains from 1 to 2, strain rates higher than 104 s-1, temperatures up to 1000 °C and heating rates close to 106 °C.s-1 [1]. Identifying a flow stress model able to provide the material behaviour under those conditions continues to be a challenge whereas it appears as a key input data in any cutting model.

Most of the numerical studies involve empirical

constitutive equations [2][3] identified from Split

Hopkinson Pressure Bar (SHPB) [4][5] or from cutting experiments via in inverse method [6]. Johnson & Cook’s model (JC) [7] is to date the most commonly used due to its simple and uncoupled formulation. The main drawback of empirical models is that their accuracy highly depends on the conditions under which their coefficients have been identified. If they can be definitely suitable when used within their calibration range, an extrapolation outside this domain of validity can be pretty risky. This is inevitably the case when machining is concerned as the loadings are several orders higher than those generated even from the most advanced material testing set-ups. Understanding the deformation mechanisms associated with the chip formation is therefore essential in order to propose advanced constitutive models not only based on

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© 2013 The Authors. Published by Elsevier B.V.Selection and peer-review under responsibility of The International Scientifi c Committee of the “14th CIRP Conference on Modeling of Machining Operations” in the person of the Conference Chair Prof. Luca Settineri

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517 C. Courbon et al. / Procedia CIRP 8 ( 2013 ) 516 – 521

empirical fitting but also on strong physical basis. The latter are expected to limit their dependency on the calibration domain and lead to a larger range of usability and validity. Despite the recent advances in this field, it is regretful to notice that physically-based models are still poorly developed while there continues to be a need for more physical and reliable cutting simulations.

The purpose of the present work is first to emphasise

the deformation mechanisms of carbon steel and especially the dynamic recrystallization process taking place. Secondly, dynamic compression tests are conducted to show how microstructural evolutions induced by high strains can affect the material plastic behaviour and how constitutive model can handle it. A numerical cutting model is finally employed to assess the validity of the proposed equation and compare it to the performance of the JC model.

2. Analysis of the shear regions

2.1. Experimental set-up

All the experiments were carried out in dry orthogonal cutting conditions using normalized AISI 1045 steel with a hardness between 180 and 190 HB (tensile strength - 696 MPa). The ferritic-perlitic microstructure is illustrated in Fig. 1.

A TiN coated carbide insert has been employed with a rake and clearance angles of 0 ° and 11 °, respectively. Tool edge preparation was chamfer and hone (r = 50 μm). Chips have been mounted, mechanically polished and etched in a 2 % Nital solution. Experiments have been carried out over a whole range of cutting speeds [100 - 250] m/min and feed rates [0.1; 0.18; 0.25; 0.32; 0.4] mm/rev.

100 μm 20 μm

a b

100 μm100 μm 20 μm20 μm

a b

Fig. 1. Initial microstructure of the machined material

2.2. Microstructural analysis

All Understanding the cutting mechanisms can only be done by analysing the strain history undergone by the material and especially by observing the deformed microstructure.

A Scanning Electron Microscopy (SEM) combined to

an Electron Back Scattering Diffraction (EBSD) technique have been applied on the samples to investigate the phenomena occurring at a micro scale.

These methods highlighted the microstructural evolutions which occurred in the high deformation zones of the chip. In the Primary Shear Zone (PSZ) (Fig. 2(b)), both ferritic and perlitic phases can be found. If the latter is broken up (splitting of the perlite lamella and dispersion of the carbides), the ferrite grains, with an initial grain size of 10 to 20 μm (Fig. 1), are here found to be considerably refined with a diameter smaller than 1 μm. In the Secondary Shear Zone (SSZ) (Fig. 2(c)), this phenomenon is more pronounced and three deformation regions can be delineated. The furthest from the surface (III) is made of fine equiaxed grains ( 500 nm) mixed with mostly elongated ones. The subsurface layer (I) is formed by nanometric grains, perfectly equiaxed and smaller than 200 nm.

Orthogonal cuttingMaterial: AISI 1045 (180 HB)Tool : Carbide SM30Coating : TiNEdge : Chamfer + radius

n = 0° - s = 0° - n = 11°Vc = 250 m/minf = 0,25 mm/revap = 3 mm - dry

Chip flow

O : Tool-chip interfacePSZ : Prim. shear zoneSSZ : Sec. shear zone

a

O100 μm

O

10 μmSSZ

II

III

IPSZ

1 μm Signal A = SE2EHT = 15.00 kVGrand. = 20.0 K X

Recrystallizedferrite

c

b

Fig. 2. SEM and EBSD analysis showing a recrystallized grain structure

518 C. Courbon et al. / Procedia CIRP 8 ( 2013 ) 516 – 521

Region (II) presents equiaxed grains but with a

slightly larger diameter (0.3 to 1 μm) and seems to provide the transition with the previous ones.

Whether in the PSZ or in the SSZ, the microstructure

of the machined material moves to an equiaxed fine grain structure smaller than 200 nm when extremely deformed. The low intra-granular misorientation observed with the EBSD analysis proves that a rearrangement of dislocations occurred, leading to a more stable configuration. These mechanisms are characteristic of a dynamic recrystallization process (DRX) responsible for the drastic grain refinements.

3. Identification of an advanced constitutive model

DRX greatly depends on the thermo-mechanical loadings applied on the material but is mainly directed by plastic strain and temperature [8]. The objective of this part is thus to investigate the behaviour of the AISI 1045 under really large strains, greater than 40 – 50 % as reached in most of the study.

3.1. Experimental procedure

Uniaxial compression tests have been performed on a servo-hydraulic Gleeble 3800 testing machine in the temperature range of 20 – 600 °C and strain rate of 0.1 to 90 s-1. The specimens ( 8x12 mm) have been resistance heated at a rate of 5 °C.s-1 by thermocoupled feedback-controlled AC current, and held for 2 min at isothermal conditions before compression tests. True strains higher than 100 % have been achieved.

3.2. Flow stress behaviour

Fig. 3(a) presents the evolution of the flow stress at 5 s-1 and different temperatures. If typical hardening curves can be seen for temperatures lower than 400 °C, a peak stress followed by a softening leading to a steady stress appear as the temperature increases.

This evolution is directly connected to different

deformation mechanisms illustrated by Lin et al. [8] in four stages (Fig. 3(b)). Stages I and II corresponds to the work hardening (WH) step combined, from a certain strain, to dynamic recovery (DRV). From a critical strain, dynamic recrystallization (DRX) is activated (Stage III). The competition between the work hardening, and the softening phenomenon induced by

dynamic recovery, as well as the dynamic recrystallization (DRX), takes place.

As strain increases, the flow stress reaches a steady state where DRX prevails and an equilibrium between softening and hardening is obtained. It can be therefore stated that DRX has been activated during the compression tests too.

a

0

200

400

600

800

1000

0 0.2 0.4 0.6 0.8 1 1.2

p

= 5 s-1p = 5 s-1p

Tru

est

ress

(M

Pa)

450 °C500 °C600 °C

200 °C300 °C400 °C

bT

rue

stre

ss (

MP

a)

p

bT

rue

stre

ss (

MP

a)

p

Fig. 3. Flow stress curves obtained from compression tests (a) and stages of the deformation process (b) [8]

3.3. Relevance of the constitutive model

The most commonly used constitutive equations proposed by Johnson & Cook [7] (JC) has first been calibrated from the previously collected data. It is shown to be unable to model the characteristic evolution of the flow stress induced by the DRX (Figs 4(a),(b),(c)) even at strains lower than 0.6. Another approach to consider the work hardening, dynamic recovery and dynamic recrystallization phenomena is thus clearly required.

519 C. Courbon et al. / Procedia CIRP 8 ( 2013 ) 516 – 521

0

200

400

600

800

1000

0 0.15 0.3 0.45 0.6

p

0

200

400

600

800

1000

0 0.15 0.3 0.45 0.6

p

0

200

400

600

800

1000

0 0.15 0.3 0.45 0.6

p

0

200

400

600

800

1000

0 0.3 0.6 0.9 1.2

p

0

200

400

600

800

1000

0 0.3 0.6 0.9 1.2

p

0

200

400

600

800

1000

0 0.3 0.6 0.9 1.2

p

a b c

= 60 s-1p = 60 s-1p= 5 s-1p = 5 s-1p = 20 s-1p = 20 s-1p

y

p

),,( Tppy

y

p

),,( Tppy

d e f

Johnson & Cook (1983) Johnson & Cook (1983) Johnson & Cook (1983)

Kim et al. (2003) Kim et al. (2003) Kim et al. (2003)

= 60 s-1p = 60 s-1p= 5 s-1p = 5 s-1p = 20 s-1p = 20 s-1p

Compression testMaterial : AISI 1045 (180 HB)Device: Gleeble®

Sample: 8 x 12 mmLub. Graphite + TantaleQuenching: Air

Model

20 °C200 °C400 °C500 °C600 °C

Experiments

20 °C200 °C400 °C500 °C600 °C

Tru

e st

ress

(M

Pa)

cT

rue

stre

ss (

MP

a)JC

Kim

Fig. 4. Comparison between the experimental data and the identified Johnson & Cook [7] (a,b,c) and Kim et al [9] (d,e,f) models

A “metallurgy based” model proposed by Kim et al [9] has been identified based on the same data. A description of the model is presented in Fig. 5. Considering that deformation is a thermally activated mechanism, this model is based on the Zener-Hollomon parameter expressed in Eq. 1.

TRQZ exp (1)

With the strain rate, Q an activation energy, R the Boltzmann constant and T the temperature.

Depending on the value of Z, DRX is taken into

account in the model from a critical strain c. The flow

stress (WH+DRV) calculated by a Voce equation (Fig. 5(b)) is lowered by a (DRX) stress depending on a recrystallized volume fraction XDRX. The latter directly drives the drop in the flow stress observed when recrystallization is taking place (Fig. 5(a)) and corresponds to the degree of recrystallization reached in the material. This could further be assimilated to the evolution of the grain size.

Besides a better description of the physical phenomena occurring at high strains, it provides a kinetic equation of the recrystallized volume fraction with the plastic strain in the form of an Avrami type model (Fig. 5(b)).

520 C. Courbon et al. / Procedia CIRP 8 ( 2013 ) 516 – 521

y

sat

p

c

s

c pic p

(WH+DRV)

- DRX

Plastic strain

Tru

est

ress

a

0

)(,,',,,,,

exp

,

,

*

'

*

)(

)(

ZfmmC

X

X

XX

Cexp

csp

mcp

DRX

DRX

spDRXcp

DRXcp

mppDRVWH

DRXDRVWHy

pic

pic

0

00

1

1

0

1

b

Fig. 5. "Metallurgy based" constitutive equation identified in this study [9]

4. Numerical modelling

4.1. Description of the 2D FE cutting model

The proposed model has been implemented in a commercial Finite Element (FE) code Abaqus/Explicit© via a VUMAT® user subroutine and applied on a simple 2D orthogonal cutting model. The ALE approach has been exploited to conduct this coupled thermo-mechanical analysis. The model consists of deformable workpiece and an elastic cutting tool considered as fully embedded. Both solids are meshed using 4-node plane strain thermally coupled quadrilateral elements (CPE4RT).

A user subroutine VUINTER®, based on a master slave penalty contact and a regularized Coulomb friction formulation, has been programmed in order to implement local velocity dependent friction and heat partition models [10]. In order to assess the potential and specificities of this model, numerical simulations have also been performed with common input data from the literature, i.e. the JC model identified in [4], a constant friction coefficient (μ=0.5) and heat partition coefficient (50%) with a thermally perfect contact.

4.2. Numerical results

Integrating the “metallurgy based” constitutive equation described in Fig. 5(b), further named “DRX model”, first leads to a potential prediction of recrystallization occurring during chip formation (Fig. 6). It reveals that it is able to qualitatively predict the region where DRX occurs and the level of recrystallization. Numerical results indeed appear consistent with the observations conducted in section 2: recrystallization is more intense in the SSZ with XDRX

reaching 1 whereas values between 0.5 and 0.75 are computed in the PSZ.

Vc(m/min)

40 250

0.25 0.25 f (mm/rev)

Model : ALE 2DMesh : 20 μmtstep : 10-8 s

XDRX (-)

10.880.750.630.500.380.250.130

XDRX (-)

10.880.750.630.500.380.250.130

Material: AISI 1045Tool: Carbide SM30Coating: TiN

Edge : chamfer + radius

n = 0° - s = 0° - n = 11°ap = 3 mm - dry

Fig. 6. Example of predicted recrystallized areas during chip formation

Averaged outputs such as machining forces are however not drastically affected. Computed values are similar as for the two identified models and appear to be slightly lower than when input data from the literature are used (Fig. 7(a)).

Variable friction and heat partition models greatly

improve the accuracy regarding heat transfers as already reported in [10] but without any clear effect of the selected constitutive model. Chip thickness is still overestimated and results provided by the “DRX model” are found to be closer to the JC model identified in the literature [4].

521 C. Courbon et al. / Procedia CIRP 8 ( 2013 ) 516 – 521

0

100

200

300

400

100 150 200

Cutting speed (m/min)

0 500

10001500200025003000

100 150 200

Cutting speed (m/min)

a b

Model : ALE 2DMesh : 20 μmtstep : 10-8 sMaterial: AISI 1045Tool: Carbide SM30

Coating: TiN - DryEdge : chamfer + radius

n = 0° - s = 0° - n = 11°ap = 3 mm – f = 0.25 mm/rev

ExpeJC (Vsl) (Vsl) h=104

DRX (Vsl) (Vsl) h=104

Jaspers JC =0.5 =0.5 h=108

Ff

Fc

Ff

Fc

c

Ff

Fc

Mac

hini

ng fo

rces

(N

)

Hea

tflu

x (W

)

Chi

p th

ickn

ess

(mm

)

tt

hh

1.2

0

0.2

0.4

0.6

0.8

1

100 150 200

Cutting speed (m/min)

Fig. 7. Comparison between the experimental data and numerical results: a) machining forces, b) heat flux transmitted to the tool and c) average chip thickness.

5. Conclusions

The present paper first described how the machined material is able to sustain the extreme loadings undergone in machining. The SEM and EBSD analyses highlighted a drastic grain refinement leading to grain size lower than 200 nm. It has been shown that a dynamic recrystallization process (DRX) has been activated during cutting. Secondly, dynamic compression tests have been conducted at high strain. A "metallurgy based" constitutive equation has been identified, leading to a better description of the thermo-mechanical behaviour than the commonly used phenomenological models.

A kinetic model of the recrystallized volume fraction has also been introduced. The identified model has been applied in a 2D FE model of a cutting operation. Microstructural evolutions in the shear zones can be predicted whereas no special improvement has been observed regarding the main average outputs of the cutting model. Deeper analyses are required in order to improve this model and also possibly connect the recrystallized volume fraction to a grain size evolution.

Acknowledgements

Authors would like to express their gratitude to the ASCOMETAL CREAS Company for provided steels and the support to this investigation. They also would like to sincerely thank Vincent CHOMIENNE (MATEIS/INSA-Lyon) for his help when conducting the EBSD analysis.

References

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[4] Jaspers S. P. F. C. and Dautzenberg J. H., 2002, Material behaviour in conditions similar to metal cutting: flow stress in the primary shear zone. J. Mater. Process. Technol., 122(2-3), p. 322.

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[6] Pujana J., Arrazola P.J., M'Saoubi R., and Chandrasekaran H., 2007, Analysis of the inverse identification of constitutive equations applied in orthogonal cutting process. Int. J. Mach. Tools Manuf., 47(14), p. 2153.

[7] Johnson G. R. and Cook W. H., 1983, A constitutive model and data for metals subjected to large strains, high strain rates and high temperatures. In Proceedings of Seventh International Symposium on Ballistics, The Hague, The Netherlands, p. 541.

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[9] Kim S.I., Lee Y., and Byon S.M., 2003, Study on constitutive relation of AISI 4140 steel subject to large strain at elevated temperatures. J. Mater. Process. Technol., 140(1-3), p. 84.

[10] Courbon C., Mabrouki T., Rech J., Mazuyer D. and D'Eramo E., 2011, New thermal issues on the modelling of tool-workpiece interaction: application to dry cutting of AISI 1045 steel. Adv. Mater. Res., 223, p. 286.