3D FE modelling of the cutting of Inconel 718

Journal of Materials Processing Technology 150 (2004) 116–123

3D FE modelling of the cutting of Inconel 718 S.L. Soo a,b,∗ , D.K. Aspinwall a,b , R.C. Dewes a,b a

School of Engineering (Mechanical and Manufacturing), University of Birmingham, Edgbaston, Birmingham B15 2TT, UK b Interdisciplinary Research Centre (IRC) in Materials Processing, Birmingham B15 2TT, UK

Abstract Following a literature review, the paper outlines the development of a 3D finite element model for the turning of Inconel 718 using ABAQUS/Explicit as a precursor to ball end milling simulation. The model employed a Lagrangian formulation. The workpiece material property data were determined from experimental work on a Gleeble thermo-mechanical simulator using uniaxial compression testing, with temperatures and strain rates of up to 850 ◦ C and 100 s−1 , respectively. Predicted and measured forces were within 6% for the tangential component, while feed forces were within 29%. The actual chip morphology determined from quick-stop experiments was segmented, whereas the predicted profile was continuous, irrespective of the cutting speed. It is likely that the discrepancies were a result of over-simplification of the friction model together with inadequacies in the algorithms describing the material behaviour. A user sub-routine which contains a ‘damage criterion’ to initiate crack propagation has been highlighted as a requirement to simulate chip segmentation. Details of preliminary work on the 3D ball nose end milling of Inconel 718 are also presented, which underline the difficulties inherent in this approach, together with geometry and mesh considerations. © 2004 Elsevier B.V. All rights reserved. Keywords: Cutting; FE modelling; Chip formation; Crack propagation

1. Introduction Traditionally, experimentation has been the main avenue for research and development. Escalating costs in terms of time, equipment, materials and manpower have, however, encouraged alternative methods of analysis to be explored, in particular computer based simulation. Within this area, finite element modelling (FEM) is pre-eminent. First developed in the 1950s, it has now evolved into an extremely sophisticated and advanced tool for analysing and solving a multitude of problems and is accepted in many branches of industry, including the automotive and aerospace sectors [1]. Finite element analysis was first applied to study metal cutting in the early 1970s, when Tay et al. [2] developed a two-dimensional (2D) finite element model of the orthogonal turning of a free-machining steel, in order to determine the temperature distribution in the chip and cutting tool. This pioneering work triggered a flurry of interest from the machining fraternity, as witnessed by the large number of publications on the subject in the last three decades. With ∗ Corresponding author. Present address: School of Engineering (Mechanical and Manufacturing), University of Birmingham, Edgbaston, Birmingham B15 2TT, UK. Tel.: +44-121-414-4201; fax: +44-121-414-4201. E-mail address: [email protected] (S.L. Soo).

0924-0136/$ – see front matter © 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.jmatprotec.2004.01.046

continuous upgrades in computing power, the potential and efficiency of FEM for evaluating bigger and more complex problems exists. Much of the literature on FEM in metal cutting up to the early 1990s was mainly 2D in nature, allowing comparison with orthogonal turning. As cutting is essentially a chip formation process, one of the most important considerations when modelling is the method by which elements of the workpiece material separate as the cutting tool advances. For Lagrangian based models, these have included node separation; Shet and Deng [3], element deletion; Ceretti [4], and adaptive remeshing; Marusich and Ortiz [5]. Here, elements of the workpiece material flow around the cutting edge and ‘reposition’ themselves to form the chip and machined surface. The triggering of material fracture is then governed by a ‘separation criterion’, which is generally a function of the finite element software used. Strenkowski and Carroll [6] applied a chip separation criterion based on effective plastic strain, while Komvopoulos and Erpenbeck [7] defined a separation criterion based on distance. More recently, a comprehensive analysis of chip separation criteria has been presented by Zhang [8]. The choice of implicit or explicit time integration to solve the equilibrium equations of motion in an FE analysis is another consideration for the modeller. Both approaches are valid for almost any type of problem, however, there are

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major advantages to be gained if the appropriate time integration procedure is applied for a given class of analysis. Although many of the early FE models simulating metal cutting used implicit integration (usually inherent in the software employed), there is currently a move towards utilising the explicit method, especially for 3D analysis. For a non-linear problem, the implicit mode has to solve a set of simultaneous equations for each time increment in order to obtain a solution. This usually involves a significant number of iterations within an increment before convergence is achieved, which can be costly, depending on the size and complexity of the model. Conversely, with explicit time integration, a solution is obtained by advancing the kinematic state (accelerations, velocities and displacements) of the model at the beginning of each time increment by very small amounts. This invariably results in the simulation requiring a very large number of increments (typically several orders of magnitude more than for the implicit routine), however, each increase is relatively efficient computationally, due to the fact that no iterations are required to solve the equations of motion. The nature of the explicit technique makes it suitable for modelling aspects such as high-speed dynamic events, complex contact and post buckling problems, highly non-linear incidences and material degradation/failure [9]. With metal cutting being classified as a highly non-linear, dynamic, bulk material deformation process, there is a strong case for supporting the use of explicit FE codes in simulating these operations. Early FEM work centred primarily on continuous chip formation, however, several researchers have developed 2D models that simulate segmented/serrated chips since the mid-1990s. Ceretti [4] used an implicit finite element code DEFORM 2D to model the segmented chips formed when turning a low-carbon free cutting steel AISI 1045, at relatively high cutting speeds of 150 and 200 m/min. Hua and Shivpuri [10] also used DEFORM 2D to study chip segmentation when machining titanium alloy Ti–6Al–4V over a range of cutting parameters. Ng [11] modelled the turning of AISI H13 hardened steel with polycrystalline cubic boron nitride (PCBN) tooling using an explicit based software, which detailed the transition of chip morphology from continuous to segmented as the cutting speed was increased and the hardness of the workpiece material varied. Other work concerning segmented as well as discontinuous chips has been published by Bäker et al. [12], Marusich and Ortiz [5] and Obikawa et al. [13]. Park and Dornfeld [14,15] employed FEM to assess the development of burr formation when cutting AISI 304 stainless steel. More recently, the emphasis has shifted towards 3D formulations involving other cutting processes than turning. The transition from 2D to 3D simulation in terms of computing time and model complexity (geometry and contact conditions) is significantly more tedious, although developments in computer technology have alleviated some of these aspects.

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Ceretti et al. [16] developed a 3D turning model using DEFORM3D to predict cutting forces, temperature and stress distributions, together with chip flow, when machining aluminium alloy under orthogonal conditions and also low-carbon steel with an oblique cutting configuration. Guo and Dornfeld [17] presented a 3D model using ABAQUS/Explicit to simulate burr formation when drilling stainless steel. Sohner et al. [18] utilised the same software to produce a 3D simulation of the face milling process for machining Ck 45 steel (AISI 1045 medium carbon steel equivalent). A recent 3D FE model by Guo and Liu [19] addressed the finish ‘hard turning’ (facing operation) of AISI 52100 steel using PCBN tooling. The model was used to predict the temperature distribution over the cutting edge, the residual stress distribution on the machined surface and the cutting forces. Additionally, the sensitivity of the output results to several of the model parameters such as material strain failure, material flow stress and the friction coefficient, were evaluated. The authors of the current paper are also aware of on-going FEM research involving high-speed end milling at institutions in Germany (Aachen) and the USA (Ohio State University). The present paper details a 3D FE model for the turning of Inconel 718 using ABAQUS/Explicit, based on earlier work previously published in [20]. The research was undertaken as a precursor to the simulation of high-speed ball nose end milling, of which initial work on the model geometry and mesh considerations are also presented. Experimental cutting force data, together with chip micrographs from turning quick-stop tests, are compared with the predicted output from the model. A key aspect of the work is the use of experimentally determined high strain rate data obtained at elevated temperatures.

2. Experimental work 2.1. Force measurement and quick-stop tests The workpiece material used for the experimental trials was a 150 mm diameter × 200 mm length bar of wrought Inconel 718 nickel based superalloy, with a chemical composition of 19% Cr, 18.3% Fe, 5.1% Nb, 3% Mo, 0.9% Ti and Ni balance. The material was solution treated and aged and had a hardness of 44 ± 1 HRC when measured with an Emcotest ET 11 portable hardness tester (Maier and Co.). The tungsten carbide cutting tool inserts used were manufactured by Sandvik Coromant (94% WC, 6% Co), and initially conformed to product code SPUN 120304 (12 mm square insert). However, the inserts were subsequently ground down to 9.5 mm square together with a sharp cutting edge to fit a custom made toolholder, closely conforming to ISO code CSGOR 2525H09. The toolholder provided a 0◦ inclination angle, 10◦ top rake angle and 6◦ clearance angle. Cutting force experiments were performed on a 17 kW Dean Smith and Grace 1910 lathe having continuously

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Fig. 2. Schematic diagram of the orthogonal configuration for cutting force and quick-stop tests.

2.2. Elevated strain rate and temperature compression tests Fig. 1. Explosive bolt quick-stop arrangement.

variable speed control from 0 to 2000 rpm. Force components were measured via a Kistler three-component piezoelectric dynamometer (9257A) and charge amplifiers (5011A). The data from the dynamometer was acquired using a Keithley DAS1601 analogue/digital board together with Dynoware; a Windows based data acquisition software on a PC. Quick-stop tests were carried out using an in-house designed explosive bolt device, with the cutting tool supported on a shear pin, see Fig. 1. A rectangular groove was cut into one end face of the workpiece to provide the necessary orthogonality during cutting, see Fig. 2. This gave a width of cut of 2.0 mm, while a constant feed rate of 0.2 mm/rev and cutting speeds of 50 and 80 m/min were employed for both cutting force and quick-stop experiments. All the tests were carried out under dry cutting conditions. The quick-stop chips were removed by electrical discharge wire machining, mounted in Bakelite and then ground, polished and etched to reveal their morphology and microstructure.

A Gleeble 3500 thermo-mechanical simulator was used to carry out a series of preliminary uniaxial compression tests to obtain flow stress data at elevated strain rates and temperature for the Inconel 718 material, see Fig. 3. The machine is capable of exerting a maximum static force of 100 kN, a stroke rate of 2000 mm/s and heating rates of up to 10 000 ◦ C/s using direct resistance heating. The test specimens were designed to conform as near as possible with ASTM Standard E9 and E209, being cylindrical bars measuring 5 mm diameter and 9 mm length. Bars of approximately 130 mm length and 5.2 mm diameter were initially electro-discharge wire machined. These were then centreless ground, using a low stress regime, to the required diameter and concentricity, followed by further wire machining to lengths of 9.2 mm. Finally, the ends of the individual specimens were finish ground to length while ensuring parallelism. Especially designed anvils (ISO-T anvils) were used to maintain uniform temperature over the specimen during the compression cycle. Control and temperature measurement was achieved through K-type thermocouples, which were resistance welded to the centre of the specimens. Thin graphite

Fig. 3. Gleeble set-up for elevated strain rate and temperature compression tests.

S.L. Soo et al. / Journal of Materials Processing Technology 150 (2004) 116–123 Table 1 Test matrix for uniaxial compression tests Temperature (◦ C)

Strain rate (s−1 ) Quasi-static

1

10

100

20 400 550 700 850

TC TC TC TC TC

TC TC TC TC TC

TC TC TC TC TC

TC TC TC TC TC

TC: test completed.

foils were placed at the ends of each specimen to reduce friction at the specimen/anvil interface in order to ensure more uniform deformation and reduce barrelling. Experiments were carried out to 30% strain at temperatures of 20, 400, 550, 700 and 850 ◦ C with strains rates of 10−3 (quasi-static), 1, 10 and 100 s−1 . Table 1 details the test parameters used, each test being replicated once.

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The workpiece material was modelled as elastic–plastic, with isotropic hardening and the flow stress defined as a function of strain, strain rate and temperature, based on results from elevated strain rate compression tests on the Gleeble. The cutting tool was considered as a stiff elastic material, for which the mechanical properties were obtained from Brookes [21]. Within the linear elastic regime, the total stress is related to the total elastic strain by the following equation: σ = Del εel

(1)

where σ is the total true stress, Del the elasticity matrix and εel the total elastic strain. The plastic regime was modelled using the classical metal plasticity constitutive relationship in ABAQUS, which is a standard Von Mises yield surface. This is generally accepted as suitable to describe the behaviour of most metallic materials. Very high strain rates are encountered during the metal cutting process, which significantly change the flow properties of the workpiece material. In this simulation, the strain effects were considered using the following relationship:

3. Finite element model

εrate = D(R − 1)n

3.1. Initial configuration and formulation

where εrate is the equivalent plastic strain rate, R the ratio of the yield stress at non-zero strain rate to the static yield stress, and D and n are material parameters. The values of D and n were calculated by curve fitting the data obtained from the Gleeble tests and are functions of temperature. The specific heat capacity values for the workpiece material were defined as functions of temperature and were calculated using the following equation:

Fig. 4 shows the initial mesh of the workpiece together with the cutting tool in isometric view. This was meshed using 8-noded, 3D solid elements; with the chip having a higher mesh density compared to the rest of the model. This resulted in 9072 nodes and 8120 elements. Appropriate boundary conditions were applied to constrain the movement of the bottom, front and left faces of the workpiece (viewed from the current perspective). Additionally, the cutting tool was constrained to move only in the positive z-direction. Although the configuration was essentially orthogonal, the geometry was such that the model also simulated the separation of material in the radial (x-axis) direction. The tool geometry and machining parameters were identical to those used in the experimental trials.

ρC = k1 + k2 T + k3 T 2

(2)

(3)

where ρ is the density, C the specific heat, T the temperature of the body under consideration and k1 , k2 , and k3 are material coefficients. The coefficients for Inconel 718 were obtained by fitting standard values of specific heat capacities obtained from handbooks. Eq. (3) was also used by Stephenson [22] for comparing several analytical metal cutting temperature models with experimental measurements and was found to give reasonable results. The model was assumed to be adiabatic such that no heat was transferred between the workpiece free surface and the surroundings. This assumption is typically used when simulating high-speed manufacturing processes. Adaptive meshing was also applied to the model, to help to maintain the aspect ratio of the elements, which were subject to severe material deformation during cutting. 3.2. Chip formation

Fig. 4. Isometric view of the initial tool/workpiece mesh configuration.

Chip formation was achieved through a shear failure criterion where the equivalent plastic strain was taken as the failure measure. This was done by defining a series of short link elements (∼2 ␮m high) in the vicinity where the chip was

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expected to detach from the workpiece. ABAQUS/Explicit allows for automatic deletion of the link elements when the damage parameter exceeds 1, as the cutting tool shears the material and thus initiates separation of the chip from the workpiece. The damage parameter ω was defined by the following equation:  
εpl ω= (4) pl εf where εpl is an increment of the equivalent plastic strain, pl and εf the strain at failure, with summation being performed over all increments in the analysis. Fig. 5. Sample stress–strain curves at 100 s−1 over the range of test temperatures.

3.3. Friction modelling The contact at the tool chip interface was analysed using Coulomb’s friction law, which relates the shear (frictional) stress τ across the interface to the normal stress p acting between the contacting bodies. This model defines a critical − shear stress τcrit which is equal to a fraction of the normal − stress (τcrit = µp), where µ is the coefficient of friction. Slipping is said to occur when the computed frictional stress − τ is greater than or equal to τcrit , while sticking conditions dominate when τ is less than the critical shear stress. In this study, the value of µ was calculated using Merchant’s circle with experimentally obtained cutting forces.

4. Results and discussion Fig. 5 details the stress–strain curves of Inconel 718 when compressed at a strain rate of 100 s−1 over the range of temperatures tested. Due to commercial sensitivity, the exact values of the stresses cannot be given. The graphs indicate that the material exhibits strain hardening, irrespective of the testing temperature. As expected, the strength of the material decreased with temperature, but it was not until the temperature exceeded approximately 700 ◦ C that the stress dropped drastically, demonstrating the high tempera-

ture strength of Inconel 718 (a tensile strength of 1020 MPa at 650 ◦ C) [23]. The data also show that the strength of the material increases with higher strain rates, and this trend was repeated throughout the test temperatures. Fig. 6 shows the deformed mesh for the model run at 50 m/min cutting speed after machining a distance of 1.7 mm. Successful separation of the material from the workpiece, together with smooth chip flow up the rake face of the tool, is observed. The simulation run at 80 m/min also produced a similar result with a continuous chip being formed. Fig. 7a and b shows micrographs of the chip morphology obtained from the quick-stop experiments when turning at 50 and 80 m/min, respectively. At 50 m/min, the etched chip profile showed a transition between a continuous and a segmented chip, with initial shear localisation taking place. At 80 m/min, a fully segmented chip with significant shear localisation between the segments was formed. Obviously, this was not reflected by the results in the FE model. Segmented or saw-tooth chips are usually formed when machining hardened steels and ‘difficult to cut’ aerospace alloys, under certain operating conditions. Hardened AISI

Fig. 6. Predicted mesh deformation (chip) at a cutting speed of 50 m/min.

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Fig. 7. Etched chip micrographs at cutting speeds of: (a) 50 m/min and (b) 80 m/min.

4340, H13 and 52100 demonstrate this behaviour, as do Inconel 718 and titanium Ti–6Al–4V [24–27]. There are two prevailing theories that claim to explain the occurrence of chip segmentation, the first involving adiabatic shear, and the second periodic crack initiation and propagation from the workpiece free surface [28]. Publications suggesting either or both theories are extensive, those given the above representing only a fraction of the literature available. Chip morphology studies carried out by Komanduri and Schroeder [29] over a range of cutting speeds (15.25–213.5 m/min), suggest that intense shear localisation and thermoplastic instability along the shear plane due to an upsetting process, aided by contained thermal softening, causes segmented chip formation with Inconel 718. The inability of the FE simulation to predict the correct chip morphology was due to a number of factors, not least an appropriate algorithm to describe the onset and propagation of chip segmentation. Material models available in commercial FE software such as ABAQUS/Explicit are designed for use across a wide spectrum of applications, and are usually insufficient to simulate a problem such as chip segmentation on its own. For ABAQUS to model this phenomenon, a suitable ‘damage criterion’ is necessary to trigger element deletion after severe localised deformation, in order to form the segments. The shear failure criterion that was used to define chip separation from the workpiece did not accommodate chip segmentation due to the fact that the underlying mechanisms are vastly different. Whereas in the first case, chip formation occurs as a result of shearing/tearing of the workpiece material as a harder body (cutting tool) moves through it, the latter case is characterised by heavy and localised thermoplastic deformation together with crack propagation along the primary shear zone. Researchers who have previously been successful in modelling 2D segmented chips have confirmed the need for customised sub-routines to be written and incorporated into the original input code [4,10,11]. Work is currently being undertaken to develop a user sub-routine, which would enable the prediction of chip segmentation.

Fig. 8. Predicted and measured cutting forces.

Fig. 8 details the tangential (Fz ) and feed (Fy ) forces predicted by the FE model, together with corresponding experimental data. Predicted data were obtained by summation of all the nodes on the rake face of the cutting tool. Force Fz showed very good agreement with the experimental results with an error of <6%. FE simulation, however, under-predicted the feed forces (Fy ) for both cutting speeds between 13 and 29%. It is likely that the discrepancy was in part due to the simplified Coulomb friction model employed to relate the interaction between the tool and chip during machining. It was also observed that the change in cutting speed did not have a significant effect on the magnitude of the cutting forces.

5. 3D modelling of ball nose end milling As stated earlier, the research on turning simulation was a precursor for modelling the high-speed ball nose end milling process. This section describes some initial work concerning the model geometry, together with meshing aspects carried out by the authors. The geometry of a ball nose end milling cutter can be extremely complex, hence advanced CAD packages are required to help to create appropriate

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Fig. 9. Wire frame model of a ball nose end mill.

Fig. 11. Imported solid CAD model in ABAQUS CAE.

Fig. 10. A commercial end mill with equivalent geometry to the CAD model.

models. Fig. 9 shows a wire frame surface model of a typical ball nose end mill produced in AutoCAD (dxf file type). The geometry (ball and flute rake angle, helix angle, relief angle, etc.) reflects commercial tools, samples of which have been used for cutting experiments, see Fig. 10. The initial model had to be imported into a pre-processor before any analysis could be carried out. This was done using ABAQUS CAE 6.2, however, a number of obstacles were encountered during the importation process: (a) ABAQUS CAE only allowed import of IGES or ACIS type files; (b) a solid model was required for the 3D analysis; and (c) further ‘repair’ of the model was required after the file type conversion process.

AutoCAD’s Mechanical Desktop software was utilised to convert the initial surface model into an IGES format solid model. This was followed by the repair and patching of gaps in the CAD model that arose due to the conversion process. PowerSHAPE software provided by Delcam was employed for this purpose. The successfully imported CAD model is shown in Fig. 11. Fig. 12 illustrates the initial mesh and assembly of the 3D FE model for ball nose end milling. The end mill was modelled as a rigid body using rigid elements. This was done to increase computational efficiency, as deformation within the workpiece was the main focus for the current investigation. Solid deformable elements were employed in the mesh of the workpiece, giving a total of 7600 elements. The formulation with regards to thermo-elastic–plastic and strain rate behaviour was the same as that applied in the turning simulation. Similarly, a shear failure criterion was applied to instigate the deletion of elements as the milling cutter passes through the material. The mesh in the region where cutting takes place was made more dense, compared to the rest of the workpiece. The model is currently still under investigation and the results will be communicated in future publications.

Fig. 12. Initial mesh and assembly of the ball nose end mill model.

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6. Conclusions 1. A 3D finite element model to simulate turning of Inconel 718 superalloy has been developed using ABAQUS/Explicit, employing experimentally determined mechanical properties at elevated strain rates and temperatures. 2. The cutting forces predicted by the FE models showed good agreement with experimentally measured data, with an error of <6% for forces parallel to the cutting direction. In contrast, predicted feed forces were under-predicted by 13–29% which was probably due to an inadequate friction description. 3. The simulation was unable to predict chip morphology due to the lack of a suitable sub-routine to properly define the onset and propagation of shear localisation and fracture along the shear plane.

Acknowledgements The authors wish to thank Rolls-Royce plc, SNECMA, Matsuura Machinery plc and Technicut Ltd. for financial/technical support. Additionally, they would also like to express their gratitude to Mr. Steve Hobbs from Delcam plc for help in the repair of the CAD file. Finally, thanks go to the Engineering and Physical Sciences Research Council (EPSRC) and Universities, UK (Overseas Research Studentship Award Scheme)/School of Engineering, University of Birmingham, for financial support.

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