An Evaluation of Different Damage Models when ...

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ScienceDirect Procedia CIRP 58 (2017) 134 – 139

16th CIRP Conference on Modelling of Machining Operations

An evaluation of different damage models when simulating the cutting process using FEM Mohamed N.A. Nasr*, Mohamed M.A. Ammar Department of Mechanical Engineering, Faculty of Engineering, Alexandria University, Alexandria 21544, Egypt * Corresponding author. Tel.: +20-3-591-5848; fax: +20-3-590-2715. E-mail address: [email protected].

Abstract The current study compares two damage modeling approaches in metal cutting finite element simulations; the Johnson-Cook shear failure model and the progressive damage model. The first assumes sudden failure when the set criterion is met; however, the second relies on two criteria; one for damage initiation and another for damage evolution. Simulations were performed on AISI 1045 steel, and different process parameters (forces, chip thickness, temperatures and plastic strain) were compared. Also, dry orthogonal cutting tests were performed and cutting forces and chip thickness were compared to the predicted values. The current results showed better predictions when damage evolution was considered. 2017The The Authors. Published by Elsevier B.V. ©©2017 Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the scientific committee of The 16th CIRP Conference on Modelling of Machining Operations, in the under responsibility of theProf. scientifi c committee of The 16thG. CIRP Conference on Modelling of Machining Operations Peer-review person of the Conference Chairs J.C. Outeiro and Prof. Poulachon. Keywords: Machining; Damage; Finite element method (FEM).

1. Introduction Finite element modelling (FEM) has been extensively used for simulating the metal cutting process, and predicting its different aspects. This includes, but not limited to, cryogenic machining [1,2], laser-assisted machining [3,4], surface integrity [5,6], effects of edge preparation [6,7], effects of workpiece material properties [8,9], and sequential cuts [1,10]. When Lagrangian FEM is used, a damage criterion is required for chip separation and segmentation. Furthermore, chip separation requires a parting line to be defined, along which material failure occurs generating the chip [9,11]. One of the most widely used damage models in metal cutting simulations is the Johnson-Cook (J-C) shear failure model [12], which is typically used in conjunction with the J-C constitutive equation [13]. The J-C failure model is based on the magnitude of equivalent plastic strain ( ߝҧ௣௟ ) at the element integration points, where sudden failure is assumed when ߝҧ௣௟ reaches the ௣௟ ௣௟ set value for failure (ߝҧ௙ ); i.e., ߝҧ௣௟ = ߝҧ௙ [12,14]. Examples of using the J-C failure model in metal cutting simulations could be found in [2,10,15,16].

Recently, over the past decade, researchers started to consider progressive damage in finite element (FE) simulations of metal cutting. This was in order to have smooth material degradation, and enhance computational stability [17-20]. To account for progressive damage, two criteria are required; a damage initiation criterion, and a damage evolution law that defines how failure progresses [14]. In the available literature, the J-C shear failure model was used as the initiation criterion, and damage evolution was based on fracture energy [17-20]. Abushawashi et al. [17] examined the effect of using damage evolution on the formation of serrated chips in FE simulations of cutting hardened AISI 1045. Orthogonal dry cutting tests were performed for model validation. The J-C constitutive equation was used to simulate material plasticity, and the J-C shear failure criterion was used for damage initiation. Damage evolution was based on the material fracture energy, where mode I and mode II were used for chip separation (parting line) and serration, respectively. Exponential damage evolution was assumed, and resulted in good agreement with the experimental results, in terms of chip morphology and cutting forces.

2212-8271 © 2017 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the scientific committee of The 16th CIRP Conference on Modelling of Machining Operations doi:10.1016/j.procir.2017.03.202

Mohamed N.A. Nasr and Mohamed M.A. Ammar / Procedia CIRP 58 (2017) 134 – 139

Chen et al. [18] developed FE models and an analytical material flow stress model, which includes plastic flow and failure criterion, to determine the flow stress of Al7075-T6 during cutting. They used the J-C constitutive equation, and presented an improved form of the J-C shear failure model for damage initiation. The improved criterion took into account the effects of variation in strain rate, temperature and stress triaxiality, from one location to another, within the chip region. Damage evolution was modelled using the same approach of Abushawashi et al. [17]. The predicted results, including cutting forces and tool-chip contact length, were found to be in good agreement with experimental results. Mabrouki et al. [19] simulated the process of dry orthogonal cutting of Al2024-T351 using FEM, with special focus on chip formation. Similar to the above works, they used the J-C failure model for damage initiation and fracture energy-based model for damage evolution. However, they used linear and exponential evolution rates in the parting line (mode I) and chip (mode II) regions, respectively. The predicted chip morphology was in good agreement with that obtained experimentally. Chen et al. [20] developed a modified form of the J-C failure model, with an energy-based ductile failure criterion, for Ti-6Al-4V. Again, the fracture energy density was used for damage evolution; however, linear evolution was assumed in both regions. The predicted forces and chip morphology were in good agreement with experimental measurements. After a thorough review, it was found that researchers focused on examining the suitability of using damage evolution models for metal cutting FE simulations. However, they did not examine how this compares to the classical approach, where sudden failure is assumed after initiation. Also, none of them compared linear to exponential damage evolution. Therefore, the current work compares the use of two damage modelling approaches in FE metal cutting simulations. The first uses the J-C shear failure model in its classical form, as a suddendamage prediction criterion; while, the second uses it as a damage initiation criterion accompanied by an energy-based damage evolution criterion. Plane strain FE analysis was used to model dry orthogonal cutting of AISI 1045, and cutting forces, chip thickness, workpiece temperatures and plastic strains were predicted. Also, orthogonal cutting tests were performed, where cutting forces and chip thickness were measured and compared to the predicted results. Nomenclature A,B,C D ‫ܦ‬ሶ E E’ Fc Ft GC Gf KIC L

Johnson –Cook plasticity constants Damage parameter Rate of change of damage parameter (D) Young’s modulus of intact material Young’s modulus of degraded / damaged material Cutting force component Thrust force component Critical fracture dissipation energy Fracture energy dissipation Critical stress intensity factor (mode I) Element characteristic length

T Tr Tm d1-d5 lc r t ‫ݑ‬ത௣௟ ‫ݑ‬ሶ ௣௟ ߝҧ௣௟ ߝҧሶ௣௟ ߝሶ଴ οߝҧ௣௟ ij Ȗ Į ߪത ߪᇱ ߪ௬ ߱

135

Current temperature Reference temperature Melting temperature Johnson-Cook failure parameters Tool-chip contact length Chip compression ratio Uncut chip thickness Equivalent plastic displacement Rate of change of equivalent plastic displacement Equivalent plastic strain Equivalent plastic strain rate Equivalent reference strain rate Equivalent plastic strain increment Shear angle Stress triaxiality ratio Normal rake angle Flow stress of intact material Flow stress of degraded material Yield strength Scalar cumulative damage parameter

Suffix (unless listed above) f Failure 0 State at the onset of damage I, II Mode-I and mode-II fractures, respectively 2. Damage modelling 2.1. Damage in ductile materials When structural failure starts to occur, a material starts losing its load-carrying capacity and resistance to deformation. Accordingly, material damage is typically modelled in terms of stiffness degradation, and when the stiffness is totally lost the part is said to have completely failed. Fig. 1 [14] shows a typical uniaxial stress-strain curve of a ductile material. The curve starts with a linear elastic zone (a-b), followed by plastic yielding with strain hardening (b-c), and then the material starts losing its load-carrying capacity until complete fracture (c-d). In other words, point c represents the onset of damage; i.e., damage initiation, and point d represents complete damage. Region b-c is modelled using a flow stress model, the J-C constitutive equation (for example), and a damage initiation criterion, the J-C failure model (for example), is required for the onset of damage (definition of point c). Region c-d, which can be considered as the degraded response of c-d', which the metal would have followed in case of no failure, is modelled using a damage evolution law [14,17-20]. At any point along the curve c-d, point e for example, the material is said to have a degraded Young’s modulus E’, as given by Eq. 1. In Eq. 1, E represents Young’s modulus of the intact material, and D is a damage parameter that ranges from 0 (case of no failure) to 1 (case of complete failure), as detailed below. At the same time, the flow stress of the degraded material (ı¶) is given by Eq. 2, where ߪത represents the flow stress of the material if failure did not occur (i.e., along the curve c-d'). It is important to note that, structural failure does not affect thermal properties; i.e., the thermal response of the material does not change in region c-d [14].

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‫ ܧ‬ᇱ = (1 െ ‫ܧ)ܦ‬

(1)

ߪ ᇱ = (1 െ ‫ߪ)ܦ‬ത

(2)

accurately represent the material behaviour, as it results in strong mesh dependency due to strain localization. Instead, using a stress-displacement response was found to alleviate mesh dependency, and result in a better representation of material behaviour [14,19]. In this case, such displacement is defined as the equivalent plastic displacement (‫ݑ‬ത௣௟ ) [14]. In order to obtain and implement the stress-displacement concept, the definition of a characteristic length (L), which depends on the type of element, is required [14]. As an example, for a firstorder element, L is the length of a line across the element; values of L for other types of elements can be found in [14]. The relationship between ‫ݑ‬ത௣௟ , L and the material fracture energy dissipation, Gf, is given by Eq. 5. In Eq. 5, ߪ௬ is the ௣௟ yield strength, ߝҧ଴ is the equivalent plastic strain at damage ௣௟ initiation (point c), and ‫ݑ‬ത௙ is the equivalent plastic displacement at failure (point d) as given by Eq. 6. In Eq. 6, ߪ௬଴ is the yield stress at damage initiation (point c). ఌത

Fig. 1. Typical uniaxial stress–strain response of a ductile material [14].

௣௟

There are several damage initiation criteria for ductile materials, where their suitability depends on the mode of failure. One of the most widely used damage criteria in metal cutting simulations is the J-C shear failure model [11]. If it is used by itself, sudden failure occurs; i.e., curve c-d in Fig. 1 will be a vertical straight line. On the other hand, if it is used along with a damage evolution model, it will simply act as a damage initiation criterion. In that case, progressive damage can be modelled, and the material stress-strain behaviour can follow the curve c-d in Fig. 1. The J-C failure model follows a cumulative damage law that is based on the magnitude of equivalent plastic strain at failure ௣௟ (ߝҧ௙ ), as given by Eq. 3 [12], where damage is said to occur when the scalar cumulative damage parameter ( ߱ ), Eq. 4, reaches unity. In Eq. 3, d1 - d5 are material damage parameters, Ȗ represents the stress triaxiality ratio, which is the ratio of hydrostatic pressure to von Mises equivalent stress, ߝҧሶ ௣௟ is the equivalent plastic strain rate, ߝሶ଴ is the equivalent reference strain rate, T is the current temperature, Tr is the reference temperature, and Tm is the material melting temperature. In Eq. 4, οߝҧ௣௟ is the equivalent plastic strain increment [12]. ௣௟

߱ = ȭቆ

୼ఌത ೛೗ ೛೗ ఌത೑

ቇ

ఌതሶ ೛೗ ఌሶ బ

ቁቇ ቀ1 + ݀ହ

ഥ ௨

೛೗

ఌതబ

2.2. Johnson-Cook shear failure model

ߝҧ௙ = (݀ଵ + ݀ଶ ݁ ௗయఊ ) ቆ1 + ݀ସ ݈݊ ቀ

೛೗

‫ܩ‬௙ = ‫ ׬‬೛೗೑ ‫ߪ ܮ‬௬ ݀ߝҧ௣௟ = ‫׬‬଴ ೑ ߪ௬ ݀‫ݑ‬ത௣௟

்ି்ೝ ்೘ ି்ೝ

ቁ

(3)

‫ݑ‬ത௙ =

ଶீ೑

(5)

(6)

ఙ೤బ

The rate of damage evolution, or stiffness degradation, from point c to point d in Fig. 1, is controlled by how the damage parameter D varies with load / equivalent plastic displacement (‫ݑ‬ത௣௟ ). In different commercial FE software, there are typically two damage evolution rates; linear and exponential [14]. In case of linear evolution, D increases according to Eq. 7, where ‫ݑ‬തሶ ௣௟ is the rate of change of equivalent plastic displacement. On the other hand, D is given by Eq. 8 in case of exponential evolution. ሶ ೛೗

ሶ ೛೗

ഥ ௅ ఌത ௨ ‫ܦ‬ሶ = ೛೗ = ೛೗ ഥ೑ ௨

(7)

ഥ೑ ௨

ഥሶ೛೗ ഥ೛೗ ఙ೤ ௨ ௨

‫ = ܦ‬1 െ exp(െ ‫׬‬଴

ீ೑

)

(8)

Finally, in metal cutting simulations, and based on the dominant deformation mechanisms in different parts of the workpiece and chip, mode I fracture dissipation energy (GfI) is used to define damage evolution for chip generation (in the parting line region), while that of mode II (GfII) is used in the chip region (for shear localization and segmentation) [17-20]. Complete failure is achieved when Gf reaches its corresponding critical value (GC). 3. Finite element modelling (FEM)

(4)

2.3. Damage evolution criteria In order to account for progressive damage, a damage evolution criterion needs to be defined in order to control how damage evolves after damage initiation. When damage evolution is considered, the material stiffness degrades progressively based on damage mechanics [14,19]. After the onset of failure (point c in Fig. 1), the use of a stress-strain relationship to model damage evolution was found not to

This section shows how FEM was used in the current work to evaluate the effects of damage initiation and evolution on cutting forces and chip formation in metal cutting simulations, when orthogonal cutting AISI 1045 steel. 3.1. Model description A 2D plane strain Lagrangian FE model was built, using Abaqus/Explicit, to simulate dry orthogonal cutting of AISI 1045 (170 HV). The cutting conditions were selected similar to

Mohamed N.A. Nasr and Mohamed M.A. Ammar / Procedia CIRP 58 (2017) 134 – 139

those used experimentally, Section 4, for model validation. Coupled temperature-displacement analysis was used, along with temperature-dependent material properties, which were obtained from [11]. Workpiece plasticity was modelled using the classical J-C constitutive equation, where the J-C parameters of AISI 1045 were obtained from [10], and presented in Table 1. For chip formation, a parting line was defined, as shown in Fig. 2, which shows the built model with the applied boundary conditions. The workpiece height was 1 mm, and its length was 3 mm. An initial temperature of 20 oC was assumed. Based on the findings of [11], heat transfer to the surroundings was neglected, as it was reported to be negligible compared to heat conduction within the workpiece. Table 1. AISI 1045 (170 HV) J-C plasticity parameters [10]. A (MPa) 553

B (MPa) 600

n

C

ߝሶ଴ (s-1)

m

0.234

0.0134

1

1

3.3. Tool-workpiece interaction and heat generation Surface-to-surface contact pairs were used to define contacts between the tool and workpiece. Even though the simple Coulomb friction model assumes a constant friction coefficient along the whole contact length, which is not the real situation due to the uneven distribution of normal and shear stresses along the tool rake face, it has been widely used in the literature and acceptable results were obtained [2,4,10,11]. Accordingly, and since the actual coefficient of friction is very hard to obtain, the Coulomb friction model was adapted in the current work. A friction coefficient of 0.2 was assumed in the current study, which falls in the same range used in the literature for similar cutting conditions [9,10,11]. All the generated frictional energy was assumed to be converted into heat, which was then spit between the workpiece and tool based on their properties, in a fashion similar to [2,11]. 90% of the plastic deformation energy was assumed to be converted into heat, which agrees with the range used in the literature [9,10]. 4. Experimental work Dry orthogonal cutting tests were performed on AISI 1045 (170 HV) steel disks, using a CNC lathe. Cutting was done using cemented carbide inserts (Sandvik TLG- 4250L-4125) with zero rake angle and 11o flank angle, a cutting speed of 100 m/min, and a feed rate of 0.07 mm/rev. The test was repeated three times, and a fresh insert was used for each cut to avoid tool wear. Cutting forces were measured using a Kistler 9121 dynamometer, and continuous chips were generated. No signs of phase transformation or built-up-edge were found.

Fig. 2. Orthogonal cutting model.

5. Results and discussion

3.2. Chip formation Based on the experimental cutting results, where smooth continuous chips were generated; i.e, no chip segmentation, no failure criterion was defined in the chip region. In other words, failure was defined only in the parting line region. In order to achieve the current objectives, three different models were built, each with a different failure criteria, which are referred to hereafter as: Model-1, Model-2 and Model-3. In Model-1, the classical J-C failure model (Eq. 3 and Eq. 4) was used without any damage evolution criterion; i.e., sudden failure took place after damage initiation. In Model-2 and Model-3, the J-C failure model was used as an initiation criterion, and a fracture energy-based criterion (Eq. 5) was used for damage evolution. Model-2 assumed linear damage evolution (Eq. 7), while Model-3 assumed exponential evolution (Eq. 8). Mode I fracture energy (GfI) was defined based on the material critical stress intensity factor (KIC ZKLFKLV03D¥m [17]. The used J-C damage parameters (d1 – d5) are presented in Table 2. Table 2. AISI 1045 J-C cumulative damage parameters (unit-less) [12]. d1

d2

d3

d4

d5

0.06

3.31

-1.96

0.0018

0.58

5.1. Cutting forces Table 3 compares the predicted cutting (Fc) and thrust (Ft) force components to the experimentally measured values. The reported experimental force represents the average of three tests, with a 5% variation. The presented values represent the specific force values per unit mm of workpiece width. As shown, all the predicted Fc values are in good agreement with the measured force, with a maximum difference of 6% (Model1). Even though the predicted differences are insignificant, being in the same order of experimental variation, cases with damage evolution predicted slightly higher Fc values that are closer to the experimentally measured value, with exponential degradation being the best. The slight increase in Fc is attributed to the delay in achieving complete damage (D = 1). However, it was expected that exponential degradation (Model-3) would predict lower Fc compared to linear degradation (Model-2), due to the difference in degradation rate. Yet, the difference is only 1%. On the other hand, Ft was significantly underestimated, with almost no difference between the three models (with and without damage evolution). Such underestimation is mainly attributed to the tool edge radius effects, as the tool was assumed to be sharp in the current work in order to suit the use

137

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of Lagrangian formulation. It is worth noting that, under the current cutting conditions, the edge radius was found to have a much stronger effect on Ft compared to Fc, as reported in [10]. Table 3. Specific cutting force components. Force

Experimental (N/mm)

Model-1

Model-2

Fc

190

179

183

185

Ft

140

37.15

37.15

37.8

component

FEM (N/mm) Model-3

5.2. Chip compression ratio, shear angle and contact length

a) Model-1

b) Model-2

Table 4 presents the predicted and experimental values of the chip compression ratio (r), shear angle (ij) and tool-chip contact length (lc). First, the chip thickness (t) was measured, then r was calculated as the ratio of t to the uncut chip thickness, and finally ij and lc were calculated using Eq. 9 and Eq. 10, respectively, where Į is the normal rake angle (zero in the current case). tan ߮ =

ୡ୭ୱ ఈ

(9)

௥ିୱ୧୬ ఈ

݈ܿ = ‫ ݐ‬. ‫ݎ‬ଵ.ହ

(10)

c) Model-3 Fig. 3. Workpiece temperature (oC) in the chip formation zone.

5.4. Equivalent plastic strain Table 4. Chip compression ratio (r), shear angle (ij) and contact length (lc). Parameter

Experimental

Model-1

Model-2

Model-3 3.26

r

3.0

3.54

3.31

ij(o)

18.4

15.8

16.8

17.0

lc (mm)

0.363

0.467

0.421

0.413

In general, the three models slightly overestimated r (i.e., thicker chips) and lc, while they slightly underestimated ij; however, better predictions were achieved when damage evolution was considered, with Model-3 (exponential degradation) being the closest to the experimental results. Even though higher r and lc, and lower ij would mean higher Fc, this was not the case (Table 3), which could be attributed to the edge radius effects. As shown, when damage evolution was considered, ij slightly increased and slightly thinner chips (r) were generated, which reflect cutting a slightly harder material. This is a direct result to the delay in achieving complete failure (D = 1) when damage evolution is considered. 5.3. Workpiece temperatures Fig. 3 compares the workpiece temperature distribution in the chip generation zone, where slight differences could be seen. The same applies to the magnitude of maximum temperature (along the rake face), which was slightly changed, where Model-1 (no damage evolution) predicted the highest maximum temperature, with a maximum difference of about 2%. This could be attributed to the slight drop in contact length (lc), which results in lower frictional heat generation.

Fig. 4 presents the distribution of equivalent plastic strain in the chip generation region. As can be seen, no significant differences were noticed in the magnitude; however, slight differences were noticed in the distribution of plastic strain in the chip, especially in the case with exponential damage evolution. In case of no damage evolution (smaller ij), a thicker portion of the chip (rake side) experienced higher strains compared to the cases where damage evolution was considered. In addition, exponential evolution showed a slight intermittent distribution along the rake face. This is because, as opposed to linear evolution where the rate of evolution (‫ܦ‬ሶ ) is constant, exponential evolution results in a steep rate at the onset of damage (D = 0), followed by a slower rate by the end (D = 1). This change in damage rate explains the discontinuity experienced in the strain distribution. Yet, such variations are small in magnitude, and accordingly did not have significant effects on cutting forces and temperature distribution. 6. Summary and conclusions The current paper examined the effects of damage evolution on the prediction of cutting forces and chip formation, when simulating dry orthogonal cutting of AISI 1045 (170 HV) using Lagrangian FEM. Three different damage models were examined; Model-1, Model-2 and Model-3, and their predictions were compared to experimental measurements. Model-1 used the classical J-C shear failure model, as a sudden failure criterion without considering damage evolution. Model2 and Model-3 used the J-C shear failure model as a damage initiation criterion, along with a fracture energy-based damage evolution criterion, where the former assumed linear evolution rate and the latter assumed exponential evolution rate.

Mohamed N.A. Nasr and Mohamed M.A. Ammar / Procedia CIRP 58 (2017) 134 – 139

References

a) Model-1

b) Model-2

c) Model-3 Fig. 4. Equivalent plastic strain in the chip formation zone.

Based on the current findings, the following conclusions were drawn. x Models that considered damage evolution were more successful in predicting cutting forces, shear angle, chip thickness and contact length. However, the differences between different evolution rates as well as the case with sudden failure were in the order of experimental variations; i.e., not very significant. This insignificance could be attributed to: ż The markedly small size of the parting line, being in the order of a few micrometers. It is believed that the results would be more sensitive to the used damage criterion in case of using larger tool edge radii (larger parting lines). ż The significantly high strain rates encountered during cutting, which can be in the order of 106 s-1. x When damage evolution was considered, a thicker portion of the chip (on the rake side) experienced higher strains. x Exponential damage evolution resulted in a slight discontinuity in the plastic strain distribution in the chip along the tool-chip contact length, which is attributed to the non-linear fashion with which damage evolves. An improved model that accounts for edge radius effects is to be developed in order to better evaluate the role of damage evolution.

[1] Pu Z, Umbrello D, Dillon Jr. O.W., Jawahira I.S. Finite element simulation of residual stresses in cryogenic machining of AZ31B Mg Alloy. Procedia CIRP 2014; 13: 282-287. [2] Nasr M, Outeiro J. Sensitivity analysis of cryogenic cooling on machining of magnesium alloy AZ31B-O. Procedia CIRP 2015; 31: 264-269. [3] Dandekar CR, Shin YC, Barnes J. Machinability improvement of titanium alloy (Ti–6Al–4V) via LAM and hybrid machining. Int J of Machine Tools and Manufacture 2010; 50: 174-182. [4] Balbaa M, Nasr M. Prediction of residual stresses after laser-assisted machining of inconel 718 Using SPH. Procedia CIRP 2015; 31: 19-23. [5] Jawahir IS, Brinksmeier E, M’Saoubi R, Aspinwall DK, Outeiro JC, Meyer D, Umbrello D, Jayal AD. Surface integrity in material removal processes: recent advances. CIRP Ann - Manuf Techn 2011; 60: 603-26. [6] Rizzuti S, Umbrello D, Filice L, Settineri L, Finite element analysis of residual stresses in machining. Int J Mat Forming 2010; 3 (1): 431-434. [7] Parida AK, Maity M. Effect of nose radius on forces, and process parameters in hot machining of Inconel 718 using finite element analysis. Eng. Sci. Tech., Int. J. 2016; http://dx.doi.org/10.1016/j.jestch.2016.10.006. [8] Nasr M, Ng EG, Elbestawi M. Effects of strain hardening and initial yield strength on machining-induced residual stresses. J Eng Mater – T ASME 2007; 129: 567-79. [9] Nasr M. Predicting the effects of grain size on machining-induced residual stresses in steels. Advanced Materials Research 2014; 996: 634-639. [10] Nasr M. Effects of sequential cuts on residual stresses when orthogonal cutting steel AISI 1045. Procedia CIRP 2015; 31: 118-123. [11] Nasr M. PhD thesis. McMaster University, Hamilton, ON, Canada 2008. [12] Johnson GR., Cook WH. Fracture characteristics of three metals subjected to various strains, strain rates, temperatures and pressures. Eng. Frac. Mech. 1985; 21: 31-48. [13] Johnson GR, Cook WH. A constitutive model and data for metals subjected to large strains, high strain rates and high temperatures. Seventh Int. Symposium on Ballistics Hague, Netherlands. April 1983; 541-547. [14] Abaqus Analysis User’s Guide, version 6.11. [15] Bacaria JL, Dalverny O, Pantalé O, Rakotomalala R, Capéraa S. 2D and 3D numerical models of metal cutting with damage effects. European Congress on Computational Methods in Applied and Engineering. 2000. [16] Mabrouki T, Rigal JF. A contribution to a qualitative understanding of thermo-mechanical effects during chip formation in hard turning. Jour. of Mat. Proc. Tech. 2006;176: 214–221. [17] Abushawashi Y, Xiao X, Astakhov VP. FEM simulation of metal cutting using a new approach to model chp formation. Int. J. Adv. Mc. For Ope. 2011; 3: 71-92. [18] Chen G, Li J, He Y, Ren C. A new approach to the determination of plastic flow stress and failure initiation strain for aluminum alloys cutting process. Com. Mat. Scie. 2014; 95: 568–578. [19] Mabrouki T, Girardin F, Asad M, Rigal JF. Numerical and experimental study of dry cutting for an aeronautic aluminium alloy (A2024-T351). Int. J. Mach. Tools Manuf. 2008; 48:1187–1197. [20] Chen G, Ren C, Yang X, Jin X, Guo T. Finite element simulation of high-speed machining of titanium alloy (Ti–6Al–4V) based on ductile failure model. Int. J. Adv. Manuf. Technol. 2011; 56: 1027–103.

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