Numerical modeling of electrical discharge machining of Ti-6Al-4V

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Procedia Manufacturing 00 (2018) 000–000

Procedia Manufacturing 26 (2018) 359–371 Procedia Manufacturing 00 (2017) 000–000

www.elsevier.com/locate/procedia 46th SME North American Manufacturing Research Conference, NAMRC 46, Texas, USA

46th SME North American Manufacturing Research Conference, NAMRC 46, Texas, USA

Numerical modeling of electrical discharge machining of Ti-6Al-4V Numerical modeling of electrical discharge machining of Ti-6Al-4V Han Wua, Jianfeng Maa*, Qingling Mengb, Muhammad P. Jahanc, Farshid Alavid Manufacturing Engineering Society International Conference 2017, MESIC 2017, 28-30 June a a* University, b Saint Louis 3450Meng Lindell Blvd, Saint Louis, MO 63103, USA c, Farshid Alavid Vigo (Pontevedra), Spain Han Wua, Jianfeng Ma , 2017, Qingling , Muhammad P. Jahan b a

Tianjin University, No. 92 Weijin Road, Tianjin, 30072, PRC c High Street, Oxford, OH MO 45056, USAUSA SaintMiami Louis University, 650 3450E.Lindell Blvd, Saint Louis, 63103, db Western Bowling Green, KY30072, 42101,PRC USA Tianjin Kentucky University,University, No. 92 Weijin Road, Tianjin, c Miami University, 650 E. High Street, Oxford, OH 45056, USA d Western Kentucky University, Bowling Green, KY 42101, USA

Costing models for capacity optimization in Industry 4.0: Trade-off between used capacity and operational efficiency A. Santanaa, P. Afonsoa,*, A. Zaninb, R. Wernkeb

* Corresponding author. Tel.: +1-314-977-8441; fax: +0-314-977-9510. E-mail address: [email protected] a University of Minho, 4800-058 Guimarães, Portugal * Corresponding author. Tel.: +1-314-977-8441; fax: +0-314-977-9510. b Unochapecó, 89809-000 Chapecó, SC, Brazil E-mail address: [email protected]

Abstract

Abstract Ti-6Al-4V is one of the most widely used materials for successful applications in aerospace, automotive, and biomedical industries Abstract due to its high specific strength, excellent mechanical and thermal properties, and outstanding corrosion resistance. These properties Ti-6Al-4V is one of thedifficult most widely materials forconventional successful applications in aerospace, automotive, and biomedical industries make Ti-6Al-4V very to beused machined using manufacturing processes. The electrical discharge machining Under concept ofsolution "Industry 4.0", production processes be outstanding pushed to corrosion be increasingly interconnected, due to itsthe specific strength, excellent mechanical and thermal properties, and resistance. These properties (EDM) ishigh a very viable to machine Ti-6Al-4V. However, thewill EDMed surface usually undergoes phase transformation information based ondifficult a due realtotime basis and,using necessarily, moreInefficient. Inthe thiscommercial context, capacity optimization make very tothe be rapid machined manufacturing processes. The electrical discharge machining duringTi-6Al-4V the EDM process heating andconventional coolingmuch in EDM. this paper, FEM software package goes beyond the traditional aim of capacity maximization, contributing also for organization’s profitability and value. (EDM) is a very viable solution to machine Ti-6Al-4V. However, the EDMed surface usually undergoes phase transformation Abaqus used to investigate the effects of EDM conditions on the crater size, phase transformation in HAZ, and the residual stress Indeed, management improvement approaches capacity optimization instead of during thelean EDM processofdue toand the continuous rapid and cooling in EDM. In thissuggest paper, the commercial FEM software package distribution in EDMing Ti-6Al-4V. Theheating phase transformations of Ti-6Al-4V alloy during EDM are modeled based on phase Abaqus is used kinetics toThe investigate thecapacity effects EDM conditions theof crater size, phase transformation in HAZ, thethat residual stress transformation and flow stress isofdescribed using and theonrule mixtures. Experiments are conducted toand validate FEM model, maximization. study of optimization costing models is an important research topic deserves distribution in EDMing of the Ti-6Al-4V. The phase transformations Ti-6Al-4V alloy during EDM modeled based on phase which are then used toboth predict crater size, phase transformation andof residual stress for different discharge energy alevels. contributions from practical and theoretical perspectives. This paper presents and are discusses mathematical transformation kinetics and flow stress is described using the rule ofmodels mixtures. Experiments are conducted to validate FEM model for capacity management based on different costing (ABC and TDABC). A generic model hasmodel, been which are then to predict size,idle phase transformation and residual stresstowards for different discharge energy developed andused it was used tocrater analyze capacity and to design strategies the maximization oflevels. organization’s © 2018The The Authors. Published bymaximization Elsevier B.V. value. trade-offPublished capacityby © 2018 The Authors. Elsevier B.V. vs operational efficiency is highlighted and it is shown that capacity Peer-review under responsibility of thescientific scientificcommittee committeeofofthe NAMRI/SME. Peer-review under responsibility of the 46th SME North American Manufacturing Research Conference. optimization might hide operational inefficiency. © 2018 The Authors. Published by Elsevier B.V. © 2017 The Authors. Published by Elsevier B.V. Keywords: Electrical Discharge Machining Phase Transformation; Ti-6Al-4V; FEM simulation Peer-review under responsibility of the(EDM); scientific committee of NAMRI/SME. Peer-review under responsibility of the scientific committee of the Manufacturing Engineering Society International Conference 2017. Keywords: Electrical Discharge Machining (EDM); Phase Transformation; Ti-6Al-4V; FEM simulation

1. Introduction

and biomedical industries due to its high specific strength (strength-to-weight ratio), excellent 1. Introduction and biomedical industries due to its specific Ti-6Al-4V is one of the most widely used materials mechanical and thermal properties, andhigh outstanding strength resistance (strength-to-weight ratio), sector, excellent for successful applications in aerospace, automotive, corrosion [1]. In the biomedical Ti1. Introduction Ti-6Al-4V is one of the most widely used materials mechanical and thermal properties, and outstanding for successful applications in aerospace, automotive, corrosion resistance [1]. In the biomedical sector, TiThe cost of idle is a fundamental for companies and their management of extreme importance 2351-9789 © 2018 Thecapacity Authors. Published by Elsevier information B.V. Peer-review responsibility of theIn scientific committee of NAMRI/SME. in modern under production systems. general, it is defined as unused capacity or production potential and can be measured 2351-9789 2018 The Authors. Published by Elsevier B.V.hours of manufacturing, etc. The management of the idle capacity in several©ways: tons of production, available

Keywords: Cost Models; ABC; TDABC; Capacity Management; Idle Capacity; Operational Efficiency

Peer-review underTel.: responsibility the761; scientific committee NAMRI/SME. * Paulo Afonso. +351 253 of 510 fax: +351 253 604of741 E-mail address: [email protected]

2351-9789 © 2017 The Authors. Published by Elsevier B.V. Peer-review under responsibility of the scientific committee of the Manufacturing Engineering Society International Conference 2017. 2351-9789 © 2018 The Authors. Published by Elsevier B.V. Peer-review under responsibility of the scientific committee of the 46th SME North American Manufacturing Research Conference. 10.1016/j.promfg.2018.07.044

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Han Wu et al. / Procedia Manufacturing 26 (2018) 359–371 Author name / Procedia Manufacturing 00 (2018) 000–000

6Al-4V is used for the fabrication of both bone and dental implants [2,3]. There have been several studies in recent years that used EDM as a surface treatment process for improving the biocompatibility of titanium alloys. Peng et al. [4] analyzed the recast layer and the microstructural changes and phases on the recast layer after machining titanium alloy using EDM. It was reported that EDM not only generates a nanostructural recast layer, but also converts the alloy surface into a nanostructured oxide surface, increasing the alloy biocompatibility. Otsuka et al. [5] investigated the surface characteristics and biocompatibility of titanium alloy after machining by wire EDM. Janeˇcek et al. [6] used rough EDM by applying high peak current of 29A to increase surface roughness for improved osteointegration. Havilcova et al. [7] applied EDM as a surface treatment process for Ti-6Al-4V alloy and investigated the effect of the EDM-generated surface on osteoblast proliferation and fatigue performance of the material. It was found that EDM and subsequent chemical milling lead to a significant improvement of osteoblast proliferation and viability. Lee et al. [8] applied electrical discharge machining to produce the modified layer on the surface of the Ti6Al-4V specimen and investigated the biocompatibility of the modified surface. It was found that the EDM-generated surface created a thick titanium oxide layer which could facilitate the biocompatibility. Chen et al. [9] used micro-current electrical discharge machining (MC-EDM) technology in titanium powder mixed deionized water to modify the titanium surface. It was reported that the surface micro-cracks were reduced and the wettability of the surface was increased after using powder mixed EDM. The reduction in micro-cracks and improvement in wettability of the surface could positively impact the performance of the materials when they are used as implants. Prakash et al. [10] investigated the effect of surface characteristics generated in powder mixed EDM (PMEDM) on the fatigue endurance and biocompatibility of titanium implants. It was reported that powder mixed EDM could improve the surface roughness, hence improve fatigue performance of the titanium implants. They also reported that the powder mixed EDMed surface promoted osteoblast differentiation activity. With rapid improved computational capabilities and emerging new numerical modeling techniques, many researchers have been developing analytical and numerical techniques to predict EDM machining

performance including surface and sub-surface integrity measures in EDM machined components. Some researchers have used finite difference method (FDM) [11, 14-15, 19, 23, 32-34], finite element method (FEM) [12-13, 16-18, 20-22, 24-28, 30-31, 35-36], CFD [29], and finite volume method (FVM) [37] to predict the temperature distribution [12, 16, 18, 24, 34, 36-37], material removal rate [13-14, 17-20, 22-25, 27-28, 31-33, 35], crater depth/diameter [11, 13-14, 20-21, 23, 25, 28-31, 35-37], recast layer distribution [26, 30], microstructural evolution in heat affected zone [12, 15, 26], residual stress distribution[12, 34], and machined surface roughness of EDM processes [17, 19, 27, 32-33]. In aforementioned references, following workpiece materials have been EDMed: Aluminum alloys [11, 27,], brass [11], steels [11, 12, 14, 22, 28] stainless steel [19, 21, 27, 30, 34, 36], tool/mold steel [16-17, 23, 26, 29, 31-33, 35], iron [25], Inconel 718 [13, 15, 18, 27], Ti-6Al-4V [20, 37], and BeCu alloys [24]. However, phase transformation and EDM induced residual stress in EDMing of Ti-6Al-4V has not been explored. In this study, the FEM software ABAQUS is used to model the effects of EDM parameters on the crater size, phase transformation in the heat affected zone, and residual stress of electrical discharge machining of Ti-6Al-4V. 2. 2D FEM simulation 2.1 Model configuration and mesh design In this research, FEM software ABAQUS/standard is used to model a desk-top die-sinking micro-EDM of Ti-6AL-4V using RC-type pulse generator with EDM oil. Fig. 1 shows the two-dimensional axisymmetric coupled temperature-displacement model, consisting of 13800 linear quadrilateral CPE4T elements, 5934 linear quadrilateral CPE4RT elements, and 462 linear triangular elements of CPE3T. The mesh dimensions are 55 m x150 m, and the minimum element size is 1 m. The top surface, especially the left part, has finest mesh to provide a high spatial resolution.



Han Wu /etProcedia al. / Procedia Manufacturing 26 (2018) 359–371 Author name Manufacturing 00 (2018) 000–000

Fig.1. 2D axisymmetric model for micro-EDM

In EDM process, the workpiece is immersed in dielectric medium and the initial temperature of the assumed to be the ambient temperature (20oC). Consequently, in the FEM analysis, initial temperature of the model is set to be the ambient temperature (20oC). In this study, the distribution of heat flux generated by the electrical discharge is approximated by a heat flux with Gaussian distributed shape, which has been experimentally validated by [38] and has been successfully used by many researchers [11-37]. As seen in Fig. 2, the Gaussian distributed heat flux is applied on the left portion of the top surface using user subroutine DFLUX. The left edge is axis of symmetry, the bottom edge and right edge are insulated boundaries. Convection boundary condition of heat convection is assigned to the top surface to mimic the quenching effect from dielectric flowing. The coefficient of heat convection is calculated as 4.8 ×104 W/m2 K based on laminar flow available in [26]

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plasma channel radius 𝑅𝑅(𝑡𝑡) is determined by Eqn. (3), in which 𝐶𝐶1 and 𝐶𝐶2 are determined based on experiments. Eqn. (2) governs the transient nonlinear analysis of heat distribution in EDM process, where T is the temperature, t is the time, 𝜌𝜌 is density of the workpiece, k is thermal conductivity, C is the specific heat capacity, and r and z are coordinate axes. 𝑄𝑄(𝑟𝑟, 𝑡𝑡) = 1

𝐹𝐹𝐶𝐶 ∗𝑈𝑈∗𝐼𝐼 𝜋𝜋𝑅𝑅(𝑡𝑡)2

𝜕𝜕

exp(−𝑚𝑚 ∗

𝜕𝜕𝜕𝜕

( ) ( ) (𝑟𝑟 ∗ ( )) + 𝑟𝑟

𝜕𝜕𝜕𝜕

3

𝜕𝜕𝜕𝜕

𝜕𝜕2 𝑇𝑇 𝜕𝜕𝑧𝑧 2

𝑟𝑟 2

𝑅𝑅(𝑡𝑡)2

(1)

)

𝜌𝜌𝜌𝜌

𝜕𝜕𝜕𝜕

(2)

= ( )( )

𝑅𝑅(𝑡𝑡) = {𝐶𝐶1 ∗ 𝑡𝑡4 , 0 ≤ 𝑡𝑡 ≤ 𝑡𝑡𝑐𝑐 𝐶𝐶2 , 𝑡𝑡 ≥ 𝑡𝑡𝑐𝑐

𝑘𝑘

𝜕𝜕𝜕𝜕

(3)

In this research, 𝐹𝐹𝐶𝐶 is chosen as 18% in EDM based on previous study [26, 39]. The plasma channel radius model as represented in Eqn. (3) based on previous experiments [40]. The shape coefficient m is set to 2.0. The coefficients 𝐶𝐶1 and 𝐶𝐶2 are selected as 0.12 𝑚𝑚/ 𝑠𝑠 4/3 and 1.2 ×10−4 m based on experimental data [41]. The critical time 𝑡𝑡𝑐𝑐 is estimated as 100 µs. It should be noted that in this research the modeling and its analysis are for a single spark and flushing efficiency is assumed to be 100%. 2.2 Workpiece (Ti-6Al-4V) The mechanical properties of Ti-6Al-4V alloy are given in Table 1. Temperature dependent thermal conductivity (𝑘𝑘) are described using Eqn. (4) and Eqn. (5). In addition, temperature dependent specific heat (𝐶𝐶𝑝𝑝 ) are given by Eqn. (6) and Eqn. (7). Table 1. Mechanical and physical properties of Ti6Al-4V [42]

Fig.2. Thermal model of the EDM process

In Eqn. (1), 𝑄𝑄(𝑟𝑟, 𝑡𝑡) is the time/space-dependent heat flux, r is the radial distance from the plasma center, t is the discharge time, 𝐹𝐹𝐶𝐶 is the fraction of plasma energy to the workpiece. U is the discharge voltage and I is the discharge current. The coefficient m is the shape coefficient of Gaussian curve. The

Property

Notation

Value

Young's modulus

E

113 GPa

Poisson's ratio

ν

0.342

Density

ρ

4428 kg m-3

Melting temperature

Tmelt

1659.85 oC

Boiling temperature

Tboil

2862 oC

𝛼𝛼

9.1 μm m-1 C-1

Thermal expansion coefficient

Han Wu et al. / Procedia Manufacturing 26 (2018) 359–371 Author name / Procedia Manufacturing 00 (2018) 000–000

362 4

For thermal conductivity (k, W/m ℃) [43]:

𝑇𝑇 ≤ 986.85℃, 𝑘𝑘 = 1 ∗ 10−5 𝑇𝑇 2 − 0.00112𝑇𝑇 + 6.651 (4) 𝑇𝑇 > 986.85℃, 𝑘𝑘 = −4 ∗ 10−6 𝑇𝑇 2 + 0.0253𝑇𝑇 − 6.269 (5)

For specific heat (Cp, J/kg ℃) [42]:

𝑇𝑇 ≤ 986.85 ℃, 𝐶𝐶𝑝𝑝 = 0.21𝑇𝑇 + 483.3

𝑇𝑇 > 986.85 ℃, 𝐶𝐶𝑝𝑝 = 0.18𝑇𝑇 + 420.19

(6) (7)

2.3 Phase transformation model

In EDM processes, the phases considered in Ti6Al-4V include 𝛼𝛼 , 𝛽𝛽 , martensite 𝛼𝛼 ′ and the melted material. The basic microstructure of TI-6Al-4V is bimodal and mainly composed of 𝛼𝛼 grains and a low amount of 𝛽𝛽. During heating, the phase transformation 𝛼𝛼 → 𝛽𝛽 takes place when temperature is elevated to the starting point of the transformation, eventually reaching 100% 𝛽𝛽 phase at the 𝛽𝛽 phase transus, which is approximately 1000 °𝐶𝐶 . This transformation involves the nucleation of 𝛽𝛽 phase from 𝛼𝛼 matrix, the growth of the 𝛽𝛽 by diffusion. The volume fraction and the average grain size of these two phases play significant roles in mechanical properties of Ti-6Al4V. In this study, the volume fraction of 𝛽𝛽 is determined via the Avrami model, which is described using Eqn. (8) [44-46]: 𝑇𝑇

𝑓𝑓𝛽𝛽 = 1 − exp {A(T − 𝑇𝑇𝑠𝑠 − 𝑇𝑇𝑠𝑠 )𝐷𝐷 } 𝑒𝑒

(8)

where 𝑓𝑓𝛽𝛽 is the amount of the 𝛽𝛽 phase, T is the temperature, 𝑇𝑇𝑠𝑠 is the initial temperature of the phase transformation and it is equal to 600 °𝐶𝐶 for Ti-6Al-4V. 𝑇𝑇𝑒𝑒 is the complete transition temperature of α → β, which is equal to 980 °𝐶𝐶. The material constants A and D are -1.86 and 4.35, respectively [44]. It should be noted that the initial volume fractions 𝑓𝑓𝛼𝛼 for α phase and 𝑓𝑓𝛽𝛽 for 𝛽𝛽 phase are 75% and 25%, respectively.

During cooling, the 𝛽𝛽 phase can decompose into secondary 𝛼𝛼 or martensitic 𝛼𝛼 ′ depending upon cooling rates. The critical cooling rate is around 410K/s [45]. When the cooling rate is less than the 410 K/s, the transformation is a diffusional process including nucleation and growth process of secondary lamellae 𝛼𝛼 . When the cooling rate is higher than 410K/s, the diffusionless transformation will occur

and the 𝛽𝛽 will transform into martensitic 𝛼𝛼 ′ . The cooling rate of EDM process is much higher than this critical cooling rate. Thus, during the rapid cooling process in EDM, the 𝛽𝛽 will transform into martensitic 𝛼𝛼 ′ and the amount of which 𝑓𝑓𝛼𝛼′ is determined by the Eqn. (6): 𝑓𝑓𝛼𝛼′ = 𝑓𝑓𝛽𝛽′ (1 − exp(−𝑐𝑐(𝑀𝑀𝑠𝑠 − 𝑇𝑇)))

(9)

where 𝑓𝑓𝛽𝛽′ is the volume fraction of the available 𝛽𝛽 phase for martensitic transformation after heating, 𝑀𝑀𝑠𝑠 is the martensitic transformation starting temperature, and 𝑐𝑐 is the material constant [45]. Based on [45, 47], around 10% 𝛽𝛽 phase is retained independent of cooling rate as 𝛽𝛽 phase is cooled to room temperature. This means that only around 90% 𝛽𝛽 phase will transform to martensitic 𝛼𝛼 ′ . In this research, 𝑀𝑀𝑠𝑠 and 𝑐𝑐 are chosen as 827°𝐶𝐶 and 0.003, respectively [45] and 90% 𝛽𝛽 phase is assumed to transform to martensitic 𝛼𝛼 ′ . 2.4 Flow stress

In EDM machining, the total strain increment (∆𝜺𝜺) for Ti-6Al-4V experiencing solid-state phase transformation can be decomposed into the following individual components [48]: ∆𝜀𝜀 = ∆𝜀𝜀 𝐸𝐸𝐸𝐸 + ∆𝜀𝜀 𝑃𝑃𝑃𝑃 + ∆𝜀𝜀 𝑇𝑇ℎ + ∆𝜀𝜀 ∆𝑉𝑉 + ∆𝜀𝜀 𝑇𝑇𝑇𝑇𝑇𝑇 , where ∆𝜀𝜀 𝐸𝐸𝐸𝐸 , ∆𝜀𝜀 𝑃𝑃𝑙𝑙 , ∆𝜀𝜀 𝑇𝑇ℎ , ∆𝜀𝜀 ∆𝑉𝑉 , ∆𝜀𝜀 𝑇𝑇𝑇𝑇𝑇𝑇 represent the strain increments due to elastic, plastic, thermal, volumetric dilatation, and transformation-induced plasticity, respectively. The elastic strain increment ∆𝜺𝜺𝑬𝑬𝑬𝑬 can be computed using the isotropic Hooke’s law in conjunction with the temperature-dependent Young’s modulus and Poisson’s ratio for different constituent phases. The ∆𝜀𝜀 𝑃𝑃𝑃𝑃 is computed based on the constitutive models: for 𝛼𝛼 phase with equiaxed microstructures, the following equation is used as the constitutive model [45]: 𝜎𝜎𝛼𝛼 = [𝐾𝐾𝛼𝛼 𝑒𝑒𝑒𝑒𝑒𝑒 (

273000 𝑅𝑅𝑅𝑅

1 4.6

) 𝜀𝜀̇]

(10)

For 𝛽𝛽 phase, the constitutive model is described as the following equation [45]: 𝜎𝜎𝛽𝛽 = [𝐾𝐾𝛽𝛽 𝑒𝑒𝑒𝑒𝑒𝑒 (

160000 𝑅𝑅𝑅𝑅

) 𝜀𝜀̇]

1 4.2

(11)

where R, T, 𝜺𝜺̇ are the gas constant, temperature, and strain rate, respectively. The strength coefficients 𝐾𝐾𝛼𝛼



Han Wu et al. / Procedia Manufacturing 26 (2018) 359–371 Author name / Procedia Manufacturing 00 (2018) 000–000

is 0.086 and 𝐾𝐾𝛽𝛽 is 6.3 [45]. The ∆𝜀𝜀 𝑇𝑇ℎ is computed based on the following equation: ∆𝜀𝜀 𝑇𝑇ℎ = (𝛴𝛴𝛼𝛼𝑖𝑖 𝑓𝑓𝑖𝑖 )∆𝑇𝑇, where 𝑓𝑓𝑖𝑖 is the phase fraction (phase percentage) of phase i and 𝛼𝛼𝑖𝑖 is the coefficient of thermal expansion for phase i. The strain increment ∆𝜀𝜀 ∆𝑉𝑉 due to volumetric dilatation is given by [48]: ∆𝜀𝜀 ∆𝑉𝑉 =

1 ∆𝑉𝑉

∆𝑓𝑓

(12)

𝜎𝜎𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡 = 𝑓𝑓𝛼𝛼 𝜎𝜎𝛼𝛼 + 𝑓𝑓𝛽𝛽 𝜎𝜎𝛽𝛽

(13)

3 𝑉𝑉

363 5

to define the flow stress of different phase constituents and the phase fractions. During the simulation, the material subroutines are constantly called at all material points of elements to calculate the material flow stresses and the user defined field variables.

where the percent volume change ∆𝑉𝑉/𝑉𝑉 is due to phase transformation from one phase to another and ∆𝑓𝑓 is the phase fraction change during the current time increment. The martensitic transformation plasticity ∆𝜀𝜀 𝑇𝑇𝑟𝑟𝑃𝑃 is equivalent to a reduction in the equivalent flow stress over the phase transformation temperature range [49]. In this research, the flow behavior is computed by first computing the flow stress of each single phase using Eqn. (11) and Eqn. (12), then summing up the contribution of each phase by the rule of mixtures, as shown in the following equation:

In this model, phase fractions, temperature, stress, and strain are all updated at all material points of elements. Consequently, the residual stress on the EDM machined surface, which may affect corrosion resistance of the EDMed parts, can be obtained. 2.5 Simulation procedure The material model is implemented in the commercial software ABAQUS 6.14/STANDARD. The user defined material subroutines of VHARD and VSDFLD are programmed in FORTRAN. Fig. 3 shows schematically how material model is implemented. The phase constituents of 𝛼𝛼 phase, 𝛽𝛽 phase, martensitic 𝛼𝛼 ′ , etc., and their corresponding phase fractions are defined as the state/field variables, which are continually updated in each material element over time in the FEM simulation using Eqns. (8-9) in the user defined subroutine of VSDFLD. The two important state/field variables are SDV11 and SDV1. SDV11 represents the status of the material points. The points that have SDV11 greater than 1.0 are molten material points and will not experience either phase transformation or residual stress. SDV1 represents fraction of martensitic 𝛼𝛼 ′ . The constitutive plasticity models for the phase constituents using Eqns. (10-11) and Eqn. (13) are implemented in the user defined material plasticity subroutine of VHARD

Fig.3. Schematic illustration of material model implementation

3. Experimental validation In this study, to validate the FEM model for EDM machining, a series of experiments have been conducted in Ti-6Al-4V using micro-EDM. A desktop die-sinking micro-EDM machine using RC-type pulse generator was utilized in this study (Model ED009 by Small Tech). The tool electrode used in this study was WC end mills of 300 m diameter and the dielectric was the EDM oil. Fig. 4 shows the photograph of the desktop micro-EDM set-up used in this study.

Han Wu et al. / Procedia Manufacturing 26 (2018) 359–371 Author name / Procedia Manufacturing 00 (2018) 000–000

364 6

sizes for different discharge energy level is shown in Table 4. The crater size of the machined area for each trial was the average of five crater diameters using SEM images. Since there are 3 trials for each level of discharge energy, the average crater size in the last column of Table 4 is the average of 15 measurements of the crater diameter.

Fig. 4. The micro-EDM set-up.

The experiments have been designed by varying voltage, capacitance, and electrode rotational speed. The experimental conditions are listed in Table 2. The discharge energy has been calculated for the RC type pulse generator as D.E. = ½CV2, where C = capacitance, and V = voltage settings, used in the experiment. Table 2. EDM experimental conditions. Discharge Energy (µJ) 8.46 8.46 8.46 4.05 4.05 4.05 19.04 19.04 19.04 6.27 6.27 6.27 29.48 29.48 29.48

Electrode Type WC WC WC WC WC WC WC WC WC WC WC WC WC WC WC

Servo Voltage (V) 60 60 60 90 90 90 90 90 90 112 112 112 112 112 112

Capacitance (pF) 4700 4700 4700 1000 1000 1000 4700 4700 4700 1000 1000 1000 4700 4700 4700

Electrode Rotation (RPM) 1000 2500 4000 1000 2500 4000 1000 2500 4000 1000 2500 4000 1000 2500 4000

After machining, the machined surface was analyzed using the scanning electron microscope (SEM). The diameters of micro-craters for all experiments were measured using SEM. For each experiment, the average of diameters of five craters have been calculated. Fig. 5 shows the sample measurements of the crater size using a SEM image for the first experiment of energy level of 19.04 µJ. Table 3 shows the resulting data of the measurement of crater sizes for each experiment. The average crater

Fig. 5. The crater size measurements using a SEM image.

Table 3. The experimental crater size (diameter) corresponding to the EDM conditions in Table 2. Crater 1 (µm)

Crater 2 (µm)

Crater 3 (µm)

Crater 4 (µm)

Crater 5 (µm)

Avera ge (µm)

8.46

7.97

8.67

9.83

9.11

8.45

8.81

8.46

7.68

7.81

8.09

7.50

7.63

7.74

8.46

10.22

8.27

8.62

9.25

8.02

8.88

4.05

7.18

6.20

6.11

6.50

6.59

6.52

4.05

6.52

6.65

6.73

6.84

6.53

6.65

4.05

6.61

6.39

6.56

6.14

6.53

6.45

19.04

12.35

10.69

10.38

10.30

12.05

11.15

19.04

11.80

11.54

10.26

12.57

11.22

11.48

19.04

10.18

10.67

10.16

11.20

11.34

10.71

6.27

6.94

7.10

7.95

7.33

7.38

7.34

6.27

7.05

7.12

7.21

6.99

7.32

7.14

6.27

6.83

6.82

6.70

6.91

7.39

6.93

29.48

12.39

12.85

12.17

13.87

11.93

12.64

29.48

12.21

12.19

12.57

12.00

12.84

12.36

29.48

11.25

10.54

11.44

10.90

11.03

11.03

Discharge Energy (µJ)



Han Wu et al. / Procedia Manufacturing 26 (2018) 359–371 Author name / Procedia Manufacturing 00 (2018) 000–000

Table 4. Levels of the discharge energy and the average crater size. Experimental Crater Size (µm)

4.05

6.54

6.27

7.14

8.46

8.47

19.04

11.11

29.48

12.01

Experimental Crater size (m)

Discharge Energy (µJ)

6.54 6.064

4.05 μJ

Simulation

8.067 7.14

365 7

12.02 12.0112.1 11.11

8.47 8.01

6.27 μJ 8.46 μJ 19.04 μJ Discharge Energy

29.48 μJ

Fig. 6. Comparison of the crater size between experimental results

Table 5 shows the simulation conditions for different energy levels and the corresponding predicted crater size (diameter). As seen in Table 2, for each experiment, capacitance (pF) and servo voltage (V) are given. To use Eqn. (1) to compute heat flux using discharge voltage (V) and discharge current I, servo voltage is assumed to be the discharge voltage and discharge current is assumed as 1 A. Then the Ton is calculated using Ton=D.E./(V*I). The Toff is selected as around 1.5~2.5 times of Ton. Table 5. Simulation conditions for different energy levels and the corresponding predicted crater size Discharge Energy (µJ)

Discharge Discharge Voltage Current (V) (A)

8.46

60

1

Ton (µs)

Toff (µs)

Predicted crater size (µm)

0.141

0.2

8.01

4.05

90

1

0.045

0.09

6.064

19.04

90

1

0.211556

0.4

12.02

6.27

112

1

0.055982

0.11

8.067

29.48

112

1

0.263214

0.6

12.1

Fig. 6 shows the comparison of the crater size between experimental results and simulation results. The error percentages for these energy levels are 7.2%, 12.9%, 5.4%, 8.19%, and 0.7%. It can be seen very clearly that the coupled temperature-displacement FEM model developed in this research can produce very accurate crater size.

and simulation results.

4. Results and discussions 4.1 Crater size prediction for higher energy levels The validated FEM model are used to predict the crater size for higher energy levels. The simulation conditions and the corresponding predicted crater sizes for the higher energy levels are given in Table 6. Fig. 7 shows the variation of the crater size with the discharge energy. It is manifest that the predicted crater size increases as the discharge energy increases. It is found that as the discharge energy increases from 52.875 µJ to 72 µJ, the crater size increases substantially. In addition, it is noted that the crater sizes for energy levels 46.06 µJ and 39.715 µJ are very close. Table 6. Simulation conditions and predicted crater size for higher energy levels. Discharge Energy (µJ)

Discharge Voltage (V)

Discharge Current (A)

Ton (µs)

Toff (µs)

Predicted crater size (µm)

33.84

120

1

0.282

0.705

16.04

39.715

130

1

0.3055

0.7637

18.066

46.06

140

1

0.329

0.8225

18.06

52.875

150

1

0.3525

0.8812

19.8

72

120

1

0.6

1.5

24.08

84.5

130

1

0.65

1.625

25.04

98

140

1

0.7

1.75

25.4

112.5

150

1

0.75

1.875

26.8

Han Wu et al. / Procedia Manufacturing 26 (2018) 359–371 Author name / Procedia Manufacturing 00 (2018) 000–000

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Predicted crater size (µm)

30

Fig. 8 (a). SDV11 distribution for discharge energy of 8.46 µJ.

25 20 15 10 5 0 Discharge Energy (µJ)

Fig. 7. Variation of the crater size with the discharge energy.

4.2 Phase transformation and residual stress distribution for lower energy levels Fig. 8 (a) shows the SDV11 distribution for discharge energy of 8.46 µJ. SDV11 represents the status of the material points. The points that have SDV11 greater than 1.0 are molten material points and will not experience either phase transformation or residual stress. It should be noted that in this research all crater sizes from simulations are calculated based on SDV11 distribution for these discharge energy levels. The crater radius is calculated first and then multiplied by 2 to get the estimated crater diameter. Fig. 8 (b) shows the SDV1 that represents fraction of martensitic 𝛼𝛼 ′ for discharge energy of 8.46 µJ and the HAZ (Heat Affected Zone) is clearly seen. In the area close to heat source, a substantial amount of martensitic 𝛼𝛼 ′ is formed. It should be noted that the cooling rate in EDM is higher than the critical cooling rate, consequently no secondary 𝛼𝛼 is formed. It needs to be emphasized that for all cooling rates, a small amount of β phase remains after cooling. Outside the HAZ, the β phase remains the initial 25% volume fraction. In addition, the negative SDV1 values (blue area) corresponding to 0% phase fraction for martensitic 𝛼𝛼 ′ . Fig. 8(c) shows the von Mises distribution for discharge energy of 8.46 µJ. It is manifest that residual von Mises stress values in the area close to HAZ are much higher than those in areas far away from HAZ.

Fig. 8 (b). SDV1 (fraction of martensitic 𝛼𝛼 ′ ) distribution for discharge energy of 8.46 µJ.

Fig. 8 (c). The von Mises distribution for discharge energy of 8.46 µJ.

Fig. 9 (a) shows the SDV11 distribution for discharge energy of 29.48 µJ. The same method is used to calculate the crater size (diameter) as in Fig. 8 (a). Fig. 9 (b) shows the SDV1 (fraction of martensitic 𝛼𝛼 ′ ) for discharge energy of 29.48 µJ and the HAZ is clearly seen. Fig. 9 (c) shows the von Mises distribution for discharge energy of 29.48 µJ.

Fig. 9 (a). SDV11 distribution for discharge energy of 29.48 µJ.

Han Wu et al. / Procedia Manufacturing 26 (2018) 359–371 Author name / Procedia Manufacturing 00 (2018) 000–000

Fig. 9 (b). SDV1 (fraction of martensitic 𝛼𝛼 ′ ) distribution for discharge energy of 29.48 µJ.

Fig. 9 (c). The von Mises distribution for discharge energy of 29.48 µJ.

Fig. 11. Representation of the path selected for probing residual stress components on the top surface. 0

2.07

-2E+08

-6E+08 -8E+08 Points from the red starting point

2.05

6.27 µJ

2.04

8.46 µJ

19.04 µJ

Fig. 12 (a). Variations of residual stress 𝜎𝜎11 along the top surface from the red starting point for three different discharge energy levels. 2.00E+08

2.03 2.02 2.01 2

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

-4E+08

2.06

4.05

6.27 8.46 19.04 Discharge Energy (µJ)

29.48

Fig. 10. Predicted HAZ thickness for different discharge levels.

To investigate how EDM changes the residual stresses on the top surface, from this von Mises stress distribution contour below, the red point at the edge of crater and the vertical short line, the farthest point at which substantial high von Mises stress value are identified, as seen in Fig. 11. The length between the

0.00E+00 SigmaXY (Pa)

Predicted HAZ thickness (µm)

Fig. 10 shows the variation of HAZ thickness with discharge energy levels. It can be concluded that the predicted HAZ thickness for all lower discharge energy levels are slightly different and discharge level of 8.46 µJ generates the largest HAZ thickness.

367 9

red point and the vertical short line is L. The points on the top surface within 2L starting from the red point are probed and the residual stress value (𝜎𝜎11 , 𝜎𝜎12 , 𝜎𝜎22 ) are obtained and shown in Fig. 12 (a), Fig. 12 (b), Fig. 12 (c). It should be noted that this method is used for ALL discharge energy levels to draw the residual stress distributions along the top surface of the workpiece. From Fig. 12 (a), Fig. 12 (b), and Fig. 12 (c), the substantially large compressive residuals are obtained in area near the EDMed crater and it is manifest that EDM can induce compressive residual stress on the machined surface. In addition, based on [50], the EDM-induced tensile residual stress can be removed and changed to compressive residual stress using ultrasonic polishing.

SigmaXX (Pa)



-2.00E+08

1

2

3

4

5

6

7

8

9 10 11 12

-4.00E+08 -6.00E+08 -8.00E+08 -1.00E+09

Points from the red starting point

6.27 µJ

8.46 µJ

19.04 µJ

Han Wu et al. / Procedia Manufacturing 26 (2018) 359–371 Author name / Procedia Manufacturing 00 (2018) 000–000

368 10

Fig. 12 (b). Variations of residual stress 𝜎𝜎12 along the top surface from the red starting point for three different discharge energy levels.

discharge energy of 112.5 µJ and the HAZ is clearly seen. Fig. 14 (c) shows the von Mises distribution for discharge energy of 112.5 µJ.

3.00E+08

SigmaYY (Pa)

2.00E+08 1.00E+08 0.00E+00 -1.00E+08

1

2

3

4

5

6

7

8

9 10 11 12

-2.00E+08 -3.00E+08 -4.00E+08

Points from the red starting point 6.27 µJ

8.46 µJ

19.04 µJ

Fig. 12 (c). Variations of residual stress 𝜎𝜎22 along the top surface from the red starting point for three different discharge energy levels.

Fig. 13 (b). SDV1 (fraction of martensitic 𝛼𝛼 ′ ) distribution for discharge energy of 72 µJ.

It should be noted that similar numerical results are also obtained for other energy levels (4.05 µJ, 6.28 µJ, 19.04 µJ), only the size of crater and phase region and residual stress region are different. 4.3 Phase transformation and residual stress distribution for higher energy levels Fig. 13 (a) shows the SDV11 distribution for discharge energy of 72 µJ. The same method is used to calculate the crater size (diameter) as in Fig. 8 (a). Fig. 13 (b) shows the SDV1 (fraction of martensitic 𝛼𝛼 ′ ) for discharge energy of 72 µJ and the HAZ is clearly seen. Fig. 13 (c) shows the von Mises distribution for discharge energy of 72 µJ.

Fig. 13 (c). The von Mises distribution for discharge energy of 72 µJ.

Fig. 14 (a). SDV11 distribution for discharge energy of 112.5 µJ.

Fig. 13 (a). SDV11 distribution for discharge energy of 72 µJ.

Fig. 14 (a) shows the SDV11 distribution for discharge energy of 112.5 µJ. The same method is used to calculate the crater size (diameter) as in Fig. 8 (a). Fig. 14 (b) shows the SDV1 (fraction of martensitic 𝛼𝛼 ′ ) for



Han Wu et al. / Procedia Manufacturing 26 (2018) 359–371 Author name / Procedia Manufacturing 00 (2018) 000–000

369 11

stress on the machined surface. Again, based on [50], ultrasonic polishing can be used to remove and change the EDM-induced tensile residual stress to compressive residual stress using ultrasonic polishing.

SigmaXX (Pa)

0

Fig. 14 (b). SDV1 (fraction of martensitic 𝛼𝛼 ′ ) distribution for discharge energy of 112.5 µJ.

1

2

3

4

5

6

7

8

9 10 11 12 13

-2E+08

-4E+08

Points from the red starting point 39.715 µJ 46.06 µJ 98 µJ 112.5 µJ Fig. 16 (a). Variations of residual stress 𝜎𝜎11 along the top surface from the red starting point for four different discharge energy levels. -6E+08

SigmaXY (Pa)

2.00E+08

Fig. 14 (c). The von Mises distribution for discharge energy of 112.5 µJ.

4 3.5 3 2.5 2 1.5 1 0.5 0

-2.00E+08

Points from the red starting point 39.715 µJ 46.06 µJ 98 µJ 112.5 µJ Fig. 16 (b). Variations of residual stress 𝜎𝜎12 along the top surface from the red starting point for four different discharge energy levels. 2.00E+08 1.00E+08 0.00E+00

Fig. 15. Predicted HAZ thickness for different discharge levels.

Fig. 16 (a), Fig. 16 (b), and Fig. 16 (c) show the residual stress value (𝜎𝜎11 , 𝜎𝜎12 , 𝜎𝜎22 ) distributions of the points on the top surface within 2L starting from the red point (as seen in Fig. 11). It is clearly seen that the substantially large compressive residuals are obtained in area near the EDMed crater and it is manifest that EDM can induce compressive residual

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

-1.00E+08 -2.00E+08

Discharge Energy (uJ)

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

-4.00E+08

SigmaYY (Pa)

Predicted HAZ zone thickness (µm)

Fig. 15 shows the variation of HAZ thickness with discharge energy levels. It can be concluded that the predicted HAZ thickness for all lower discharge energy levels are slightly different and discharge level of 112.5 µJ generates the largest HAZ thickness.

0.00E+00

Points from the red starting point 39.715 µJ 46.06 µJ 98 µJ 112.5 µJ

Fig. 16 (c). Variations of residual stress 𝜎𝜎22 along the top surface from the red starting point for four different discharge energy levels.

It should be noted that similar numerical results are also obtained for other energy levels (33.84 µJ, 52.875 µJ, 72 µJ, 84.5 µJ), only the size of crater and phase region and residual stress region are different. 5. Conclusions In this paper, a coupled temperature-displacement

Han Wu et al. / Procedia Manufacturing 26 (2018) 359–371 Author name / Procedia Manufacturing 00 (2018) 000–000

370 12

FEM model based on Abaqus is used to model electrical discharge machining (EDM) of Ti-6Al-4V to investigate the effects of discharge energy level on crater size, phase transformation, and residual stress. The phase transformations of Ti-6Al-4V alloy during EDM are modeled based on phase transformation kinetics and flow stress of Ti-6Al-4V alloy is described using the rule of mixtures. EDM experiments are conducted to validate the FEM model. The predicted crater sizes are very close to the experimental results. This indicates that the proposed modelling approach can predict crate size, microstructure evolution, and the residual stress in EDM of Ti-6Al-4V. References [1] [2]

[3]

[4]

[5] [6]

[7]

[8]

[9]

[10]

E. O. Ezugwu, Z. M. Wang, Titanium alloys and their machinability-a review. Journal of Materials Processing Technology, 68 (1997) 262-274. H. M. Kim, F. Miyaji, T. Kokubo, S. Nishiguchi, T. Nakamura, Graded surface structure of bioactive titanium prepared by chemical treatment. Journal of Biomedical Materials Research, 45 (2) (1999) 100-107. C. Prakash, H. K. Kansal, B. S. Pabla, S. Puri, A. Aggarwal, Electric discharge machining- A potential choice for surface modification of metallic implants for orthopedic applications: A review. Journal of Engineering Manufacture, 230 (2) (2016) 331-353. P. W. Peng, K. L. Ou, H. C. Lin, Y. N. Pan, C. H. Wang, Effect of electrical-discharging on formation of nanoporous biocompatible layer on titanium. Journal of Alloys and Compounds, 492 (2010) 625–630. F. Otsuka, Y. Kataoka, T. Miyazaki, Enhanced osteoblast response to electrical discharge machining surface. Dental Materials Journal, 31 (2) (2012) 309–315. M. Janeˇcek, F. Nový, J. Stráský, P. Harcuba, L. Wagner, Fatigue endurance of Ti-6Al-4V alloy with electro-eroded surface for improved bone in-growth. Journal of the Mechanical Behaviour of Biomedical Material, 4 (2011) 417-422. J. Havlikova, J. Strasky, M. Vandrovcova, P. Harcuba, M. Mhaede, M. Janecek, L. Bacakova, Innovative surface modification of Ti–6Al–4V alloy with a positive effect on osteoblast proliferation and fatigue performance. Materials Science and Engineering C, 39 (2014) 371–379. W. F. Lee, T. S. Yang, Y. C. Wu, P. W. Peng, Nanoporous Biocompatible Layer on Ti-6Al-4V Alloys Enhanced Osteoblast-like Cell Response. J Exp Clin Med, 5 (3) (2013) 92-96. S. L. Chen, M. H. Lin, C. C. Chen, K. L. Ou, Effect of electro-discharging on formation of biocompatible layer on implant surface. Journal of Alloys and Compounds, 456 (2008) 413-418. C. Prakash, H. K. Kansal, B. S. Pabla, S. Puri, Powder Mixed Electric Discharge Machining: An Innovative Surface Modification Technique to Enhance Fatigue Performance and Bioactivity of b-Ti Implant for Orthopedics Application. Journal of Computing and Information Science in Engineering, 16/041006 (2016) 1-9.

[11] [12]

[13] [14]

[15] [16]

[17]

[18] [19] [20]

[21]

[22]

[23] [24]

[25] [26]

[27]

E. Weingartner, F. Kuster, K. Wegener, Modeling and simulation of electrical discharge machining. Procedia CIRP, 2 (2012) 74-78. R. Perez, J. Carron, M. Rappaz, G. Walder, B. Revaz, R. Flukiger, Measurement and metallurgical modeling of the thermal impact of EDM discharges on steel. Proceedings of the 15th International Symposium on Electromachining, ISEM 2007, 17-22. H. N. Mehta, Modeling of electrical discharge machining process. International Journal of Engineering Research and Technology, 4 (6) (2015) 153-156. S. H. Yeo, W. Kurnia, P. C. Tan, Critical assessment and numerical comparison of electro-thermal models in EDM. Journal of Materials Processing Technology, 201 (2008) 241-251. B. Izquierto, J. A. Sanchez, I. Pombo, N. Ortega, Numerical prediction of heat affected layer in the EDM of aeronautical alloys. Applied Surface Science, 259 (2012) 780-790. M. Shabgard, R. Ahmadi, M. Seyedzavvar, S. N. B. Oliaei, Mathematical and numerical modeling of the effect of inputparameters on the flushing efficiency of plasma channel in EDM process. International Journal of Machine Tools & Manufacture, 65 (2013) 79-87. W. Ming, G. Zhang, H. Li, J. Guo, Z. Zhang, Y. Huang, Z. Chen, A hybrid process model for EDM based on finite element method and Gaussian progress regression. International Journal of Advanced Manufacturing Technology, 74 (2014) 1197-1211. A. Kumar, D. K. Bagal, K. P. Maity, Numerical modeling of wire electrical discharge machining of super alloy Inconel 718. Procedia Engineering, 97 (2014) 1512-1523. C. Mascaraque-Ramirez, P. Franco, Numerical modeling of surface quality in EDM processes. Procedia Engineering, 132 (2015) 671-678. S. S. Mujumdar, D. Curreli, S. G. Kapoor, D. Ruzic, Modeling of melt-pool formation and material removal in micro-electrodischage machining. Journal of Manufacturing Science and Engineering, 137 (2015) 031007-1--031007-9. K. P. Somashekhar, J. Mathew, N. Ramachandran, Electrothermal theory approach for numerical approximation of the micro-EDM process. International Journal of Advanced Manufacturing Technology, 61 (2012) 12411246. S. Vignesh Shanmugam, V. Krishnaraj, K. A. Jagdeesh, S. Varun Kumar, S. Subash, Numerical modeling of electrodischarge machining process using moving mesh feature. Procedia Engineering, 64 (2013) 747-756. A. Tlili, F. Ghanem, N. B. Salah, A contribution in EDM simulation field. International Journal of Advanced Manufacturing Technology, 79 (2015) 921-935. V. A. Jatti, S. Bagane, Thermo-electric modeling, simulation and experimental validation of powder mixed electric discharge machining (PMEDM) of BeCu alloys. Alexandria Engineering Journal (2017) in press. J. Tang, X. Yang, A thermos-hydraulic modeling for the formation process of the discharge crater in EDM. Procedia CIRP, 42 (2016) 685-690. J. F. Liu, Y. B. Guo, Modeling of white layer formation in electric discharge machining (EDM) by incorporating massive random discharge characteristics. Procedia CIRP, 42 (2016) 697-702. H. Huang, Z. Zhang, W. Ming, Z. Xu, Y. Zhang, A novel numerical predicting method of electric discharge machining process based on specific discharge energy. International Journal of Advanced Manufacturing Technology, 88 (2017) 409-424.

[28]

[29]

[30] [31] [32]

[33]

[34]

[35] [36] [37]

[38]

[39]

[40] [41] [42]

[43] [44]

[45]

Han Wu et al. / Procedia Manufacturing 26 (2018) 359–371 Author name / Procedia Manufacturing 00 (2018) 000–000 A. M. Escobar, D. de Lange, H. I. M. Castillo, Comparative analysis and evaluation of thermal models of electro discharge machining. International Journal of Advanced Manufacturing Technology, 89 (2017) 743-754. J. Tao, J., Ni, A. J. Shih, Modeling of the anode crater formation in electrical discharge machining. Journal of Manufacturing Science and Engineering, 134 (2012) 011002-1--011002-11. P. C. Tan, S. H. Yeo, Modeling of recast layer in microelectrical discharge machining. Journal of Manufacturing Science and Engineering, 132 (2010) 031001-1--031001-9. S. N. Joshi, S. S. Pande, Thermo-physical modeling of diesinking EDM process. Journal of Manufacturing Processes, 12 (2010) 45-56. B. Izquierdo, J. A. Sanchez, S. Plaza, I. Pombo, N. Ortega, A numerical model of the EDM process considering the effect of multiple discharges. International Journal of Machine Tools & Manufacture, 49 (2009) 220-229. J. A. Sanchez, B. Izquierdo, N. Ortega, I. Pombo, S. Plaza, I. Cabanes, Computer simulation of performance of electrical discharge machining operation. International Journal of Computer Integrated Manufacturing, 22 (8) (2009) 799-811. N. B. Salah, F. Ghanem, K. B. Atig, Thermal and mechanical numerical modeling of electrical discharge machining process. Communications in Numerical Methods in Engineering, 24 (2008) 2021-2034. S. N. Joshi, S. S. Pande, Development of an intelligent process model for EDM. International Journal of Advanced Manufacturing Technology, 45 (2009) 300-317. B. Shao, Modeling and simulation of micro electrical discharge machining process. PhD dissertation. University of Nebraska-Lincoln. 2015. B. Kuriachen, A. Varghese, K. P. Somashekhar, S. Panda, J. Mathew. Three-dimensional numerical simulation of microelectric discharge machining of Ti-6Al-4V. International Journal of Advanced Manufacturing Technology, 79 (2015) 147-160. A. Descoeudres, C. Hollenstein, G. Wälder, R. Pérez, Time resolved imaging and spatially-resolved spectroscopy of electrical discharge machining plasma. J Appl Phys, 38 (2005) 4066–4073. D. D. DiBitonto, P. T. Eubank, M. R. Patel, M. A. Barrufet, Theoretical Models of the Electrical Discharge Machining Process. I. A Simple Cathode Erosion Model, Journal of Applied Physics, 66 (1989) 4095-4103. W. Natsu, M. Shimoyamada, M. Kunieda, Study on expansion process of EDM arc plasma. JSME International Journal Series C49 (2006) 600-605. A. Kojima, W. Natsu, M. Kunieda, Spectroscopic Measurement of Arc Plasma Diameter in EDM. CIRP Annals – Manufacturing Technology, 57 (2008) 203-207. Y. Zhang, T. Mabrouki, D. Nelias, Y. Gong, FE-model for titanium alloy (Ti-6Al-4V) cutting based on the identification of limiting shear stress at tool-chip interface. International Journal of Material Forming, 4 (2010)11-23. K. C. Mills, Recommended values of thermophysical properties for selected commercial alloys. Woodhead,

Cambridge, 2002

Q. Wang, Z. Liu, D. Yang, A. U. H. Mohsan, Meatallurgicalbased prediction of stress-temperature induced rapid heating and cooling phase transformations for high speed machining Ti-6Al-4V alloy. Materials and Design, 119 (2017) 208-218. Y. Fan, P. Cheng, Y. L. Yao, Z. Yang, K. Egland, Effect of phase transformations on laser forming of Ti-6Al-4V. Journal of Applied Physics, 98 (2005) 013518.

[46]

[47]

[48]

[49]

[50]

371 13

A. Suarez, M. J. Tobar, A. Yanez, I. Perez, J. Sampedro, V. Amigo, J. J. Candel, Modeling of phase transformations of Ti6Al4V during laser metal deposition. Physics Procedia, 12 (2011) 666-673. S. Malinov, Z. Guo, W. Sha, A. Wilson, Differential scanning calorimetry study and computer modelling of β=>α phase transformation in Ti-6Al-4V alloy. Metallurgical and materials transactions. A, Physical metallurgy and materials science, 32 (4) (2001) 879-887. N. S. Bailey, W. Tan, Y. C. Shin, Predictive modeling and experimental results for residual stresses in laser hardening of AISI 4140 steel by a high power diode laser. Surface Coating Technology, 203 (2009) 2003-2012. F. G. Rammerstorfer, D. F. Fischer, W. Mitter, K. J. Bathe, M. D. Snyder, On thermo-elastic-plastic analysis of heattreatment processes including creep and phase changes. Comput. Struct., 13 (1981) 771-779. B. J. Allen, R. E. Williams, J. R. Gilmore. Surface integrity improvement of EDM components by ultrasonic polishing. Proceeding of North American Manufacturing Research Institute of SME (1995) 61-66.