A finite element model of ultrasonically assisted drilling in carbon/epoxy composites

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1 Available online at wwwsciencedirectcom Procedia CIRP 8 (13 ) th CIRP Conerence on Modeling o Machining Operations (CIRP CMMO) A inite element model o ultrasonically assisted drilling in carbon/epoxy composites Vaibhav A Phadnis 1,*, Anish Roy, Vadim V ilberschmidt Wolson chool o Mechanical and Manuacturing Engineering, Loughborough University, LE11 3TU, Leics, UK * Corresponding author Tel:+44 () address: vaphadnis@lboroacuk Abstract Ultrasonically assisted drilling (UAD) is a novel machining technique suitable or drilling diicult-to-machine materials such as carbon/epoxy composites, where ultrasonic vibrations are superimposed on the tip o the revolving drill bit Recently, UAD has been shown to possess several advantages in comparison to conventional drilling, including a reduced thrust orce and torque, reduced drilling-induced damage and overall improvement in roundness and surace inish o the drilled hole Here, a inite element model o UAD in carbon/epoxy composite is presented This model accounts or volumetric and thermal sotening phenomena in the workpiece material under the inluence o localized vibro-impacts, which is a characteristic eature o UAD The model was imemented in Abaqus/Exicit and validated with results rom experiments, demonstrating a reasonable correlation between them A parametric study was also carried out to examine the eect o variation in intensity o ultrasonic energy on the extent o sotening in the carbon/epoxy composite or UAD 13 The Authors Published by by Elsevier BV BV Open access under CC BY-NC-ND license election and and/or peer-review peer-review under responsibility under responsibility o The International o The International cientiic Committee cientiic o Committee the 14th CIRP o Conerence the 14th CIRP on Modeling Conerence o Machining on Operations Modeling o in Machining the person o Operations" the Conerence in the Chair person Pro o Luca the Conerence ettineri Chair Pro Luca ettineri Keywords: Carbon/epoxy composite; Finite element analysis; Ultrasonically assissted drilling 1 Introduction Carbon ibre-reinorced polymer (CFRP) composites are widely used in aerospace and automobile industries and several other structural apications owing to their superior mechanical and physical properties CFRPs outperorm structural metals in durability, high strengthto-weight ratio, stiness and density [1-4] In spite o these advantages, machining CFRPs is cumbersome due to highly abrasive carbon ibres, low thermal conductivity o epoxy and a weak interacial bond between reinorced ibres and matrix Parts made o CFRP composite are manuactured to the required inal shape, though machining cannot be avoided to assemble individual components Holes need to be drilled to acilitate riveting and bolting o machined components; to serve this purpose; conventional drilling (CD) methods are oten adopted Apart rom poor geometric tolerance and surace inish, CD can initiate various damage modes in CFRPs such as matrix cracking, burr ormation, interacial de-bonding, delamination and ibre pull-out [1, 4, 11] Consequently, the load-carrying capacity o composite structure is aected Additionally, rapid tool wear is caused by abrasive carbon ibres resulting in requent tool reacement To overcome these issues, a need or alternative drilling technique is recognised Ultrasonically Assisted Drilling (UAD) is a hybrid machining technique, which has been used to improve machining o conventional metals and advanced composites in the recent past [-1] In UAD, highrequency (typically in excess o khz) vibrations generated by a piezoelectric transducer are superimposed on a rotating standard twist drill bit in the axial direction, to enhance the cutting process [5,8] There are several advantages o UAD over CD such as reduction in drilling orces and torque, better surace inish, low tool wear and elimination in burr ormation [11-13] In drilling CFRPs, drilling orces have a direct eect on damage induced in these composites Hence it is considered to be the primary parameter aecting quality The Authors Published by Elsevier BV Open access under CC BY-NC-ND license election and peer-review under responsibility o The International cientiic Committee o the 14th CIRP Conerence on Modeling o Machining Operations in the person o the Conerence Chair Pro Luca ettineri doi:1116/jprocir13679

2 14 Vaibhav A Phadnis et al / Procedia CIRP 8 ( 13 ) o a drilled hole [1, 4, 11] In the experimental study conducted by Hochen and Liu [1] it was concluded that ultrasonic machining had viable advantages over conventional machining processes eg orce and torque reduction Wang [11] perormed several experiments involving UAD in CFRP Using a vibration requency o 3 Hz to excite a high-speed-steel (H) and carbide drill bits o 5 mm diameter; it was observed that thrust orces were reduced relative to those in CD Babitsky and Astashev [5, 8] reported that in UAD, torsional vibration does not contribute much to thrust orce reduction in comparison to the axial direction Very ew researchers have attempted to model a UAD process using a inite element (FE) technique due to the comexity involved in modelling o such processes and the extent o computational resources required, though analytical model [14] to calculate thrust orces in UAD can be ound This paper presents development o a FE model o UAD in CFRP composite using general purpose sotware - Abaqus 611 The experimental results rom our previous work [-4] are presented or the validation purpose FE model o UAD in CFRP 1 Background and assumptions UAD includes superposition o ultrasonic vibration onto the relative cutting motion between a drill bit and the workpiece drilled This collective eect results in the substantial reduction in the drilling orces and torque [- 6] Based on the preliminary observations rom our UAD experiments [-4], a CFRP workpiece undergoes astic deormation under the inluence o ultrasonic vibrations, the extent o which depends on the intensity o vibrations, resulting in sotening the workpiece in the process zone Additionally, surace temperature o the CFRP workpiece oten exceed glass- transition temperature o thermoset epoxy polymer matrix (17-19 C), resulting in matrix burning The reduced thrust orce and torque observed in UAD is claimed to be due to the combined inluence o ultrasonic vibrations giving rise to the vibro-impact and localised heating phenomena In this context, we deine ultrasonic sotening as, the phenomenon in which ultrasonic vibrations reduce the apparent static stress necessary or material to undergo permanent inelastic deormation In this work, a parametric modelling approach was used to account or acoustic (ultrasonic) and thermal sotening phenomena during inelastic deormation o the CFRP workpiece The behaviour o CFRP laminate in elastic regime was deined using the Hill s [13-14] potential theory or anisotropic materials together with the rate-independent asticity criterion incorporating eects o ultrasonic sotening An element-removal scheme was used based on the shear damage-initiation criterion to reicate the hole-making process The temperature rise due to astic straining was modelled assuming adiabatic conditions It should be noted that the temperature is a astic strain work conjugate in the adiabatic system; hence an element was also removed rom the mesh when instantaneous temperature reaches the glass transition limit o the epoxy matrix (irrespective o instantaneous astic strain reaching the racture strain), thus eectively sotening the material at macroscale The primary assumptions o this material model are, Instantaneous intensity o ultrasonic vibrations is proportional to astic strain induced in the CFRP laminate It is deined in terms o ultrasonic energy per unit time transerred to the workpiece and is a unction o instantaneous contact pressure between the chisel edge o the drill bit and the workpiece, the requency and amitude o vibration The strain-rate dependence o CFRP laminate, especially in transverse and through-thickness directions pertaining to matrix dominance, is small enough to be neglected owing to a low loading rate The temperature rise in CFRP laminate during its interaction with the vibrating drill tip is mainly due to astic strain developed locally Constitutive material model The workpiece material used in this study was commercially available quasi-isotropic laminate M1/T7 o thickness 1 mm with individual y thickness o 5 mm The details on the stack sequence and mechanical properties o CFRP laminate emoyed in these simulations can be ound in Phadnis et al [4] The thermo-mechanical asticity model proposed in this work is based on the quadratic yield criterion or anisotropic materials by Hill [13-14] and non-linear isotropic hardening rule or rate-independent asticity The constitutive equations o this model or uniaxial loading are as ollows: The total strain tensor during deormation is the sum o elastic strain tensor and astic strain tensor, given by, el (11) The elastic part o stresses is computed using a constitutive stress-strain relationship; el (1) where, and are the second-order elastic stress and strain tensors while C is the ourth-order stiness tensor The yield unction [13] or orthotropic CFRP

3 Vaibhav A Phadnis et al / Procedia CIRP 8 ( 13 ) material in rectangular Cartesian stress components is given by F ( ) G ( ) ( ) H ( ) L M N 1 y R, (13) where FGHLM,,,, and Nare constants, obtained rom the ollowing equations F G H L M N R R R R R R R R R , 3 R3 3 3, R R 1 1,,, (14) Here is the measured yield stress when apied as the only non-zero stress component, is the initial yield stress and is the shear stress at yield such that, / 3 R ij are anisotropic yield ratios and can be calculated rom the CFRP yield strengths y is the size o an initial yield surace, while R is the isotropic hardening term: where p is the instantaneous contact pressure exerted by the chisel edge o the drill on the CFRP surace; u and a u are the requency and amitude o ultrasonic vibration respectively The standard jobber carbide twist drill (Fig 4) was used in simulations; the details about drill geometry can be ound in [-4] The contact pressure was a direct unction o the chisel edge geometry The magnitude o was calculated using (17) or the eed rate o 8 mm/min and spindle speed o 4 rpm The area o contact and corresponding contact pressure was obtained through a number o drilling simulations u (Hz) Fig1 Eect o amitude u on p c (MPa) (Drill eed 8 mm/min, spindle speed 4 rpm, -to-peak) R (, ) (15) 44 Plastic strain during deormation is deined as (16) D 1, or, 15 a u (μm) p(mpa) 4 c where,,, and D are yield stress at nonzero astic stress, static yield stress, astic strain and sotening parameter respectively D is deined as D D(, ) where is ultrasonic energy per unit time and is the temperature gradient due to work done towards astic straining in an adiabatic system It should be noted that ultrasonic energy per unit time, transmitted to the CFRP surace in the process zone is deined as, Fig Eect o au on (Drill eed 8 mm/min, spindle speed 4 rpm, requency o vibration 5 khz) The eect o a range o requency and amitude o ultrasonic vibration on the magnitude o ultrasonic energy per unit time is shown in Fig 1 and Fig respectively pc u au A (17) c

4 144 Vaibhav A Phadnis et al / Procedia CIRP 8 ( 13 ) Adiabatic heat transer Heat generation caused by mechanical work associated with astic straining was modelled in an adiabatic system The ultrasonic requency used in these simulations was 78 khz resulting in rapid accumulation o ultrasonic energy in a highly localised regime in a very short period o time Hence it was assumed that inelastic deormation due to astic straining occurs so rapidly that heat had hardly any time to diuse through, and, thus, adiabatic analysis was suicient to model the temperature rise in this local regime The model assumed that astic straining gives rise to a heat lux per unit volume, r such that; damage initiation is met when the ollowing condition is satisied: 1 (, ) s s d 1, (111) r :, (18) where is the constant inelastic heat coeicient, is the instantaneous stress state and is the astic strain rate 4 Element-removal scheme Previous UAD experiments preormed on CFRP composite at Loughborough University, UK yielded quasi-continuous chips instead o brittle powder as would be normally expected, emphasising the eect o underlying sotening phenomenon The results showing chip ormation in this process can be ound in Makhdum et al [] Here, simulations o a hole-generation process in CFRP with UAD were accomished with the help o the element removal scheme in Abaqus/Exicit [16] and chip ormation was not modelled This scheme was based on the racture mechanism initiated by shear damage and damage evolution linked to the energy dissipation during degradation o material s stiness The in-built Abaqus shear-damage criterion [16] utilised here is a phenomenological model or predicting the onset o damage due to shear-band localisation It assumes that the equivalent astic strain at the onset o damage is a unction o the shear stress ratio and s instantaneous astic strain such that, where s s (, ), is a shear stress ratio: max (19) (11) Here, s is the total accumulated shear stress at the integration point o an element and max is the corresponding maximum shear stress The criterion or Fig3 tress-strain curve with progressive damage behaviour where s is a state variable that increases monotonically with astic deormation proportional to the incremental variation in the equivalent astic strain The characteristic stress-strain behaviour o a material under uni-axial loading that undergoes progressive damage is shown in Fig3 In case o the elastic-astic material this damage can be decomposed into two parts; sotening o the yield stress and degradation o the elastic modulus The solid curve in Fig 3 represents the damaged stress-strain response, whereas the dashed line represents the undamaged behaviour yo and are yield stress and equivalent astic strain at the onset o damage, while is the equivalent astic strain at ailure, also known as racture strain When material undergoes damage, the stress-strain relationship ails to accurately present its behaviour because o a strong mesh dependency linked to the strain localisation Hence a dierent approach is required to trace the strain sotening branch o the stress-strain curve Thus, Hillerborg s racture energy approach [15] was emoyed in this model, which eventually helped to reduce mesh dependency by ormulating a stressdisacement response ater damage initiation The racture energy was idealised as work required to open a unit area o a crack and expressed as G u y d u, (11) where u is the equivalent astic disacement and can be considered as racture energy conjugate o yield stress ater the damage initiation : u at damage initiation and u L ater it Here L is the

5 Vaibhav A Phadnis et al / Procedia CIRP 8 ( 13 ) characteristic length o an element in a meshed body that depends on its geometry and ormulation D is the overall damage parameter: at damage initiation D, while at comete damage D 1 The residual elastic modulus Er, ater damage initiation can be calculated as: cutting edge and laminate was assumed to be 3 based on the work by Lucas et al [1] E (1 D) E (113) r Evolution o the damage variable d associated with a relative astic disacement was speciied in a linear orm as, d u u, (114) where u is the equivalent astic disacement at ailure and can be calculated as u G y 5 FE model setup (115) 51 Geometric modelling and boundary conditions A 3D geometry o 6 mm twist drill with a point angle o 118 and helix angle o 31 was modelled in Abaqus [16] The drill was modelled as a rigid body The mesh was optimized to reduce the computational cost without compromising accuracy A mesh size o CFRP work piece was reined in the immediate vicinity o the drilled area to capture high stress gradients during the drilling process Elements in the reined cylindrical zone were removed when the ailure criterion was met during simulations using element deletion discussed in section 4 The CFRP laminate was ixed at all our vertical aces, while the drill was constrained to rotate only about its own axis with a speciied speed and ed vertically downwards into the work piece The FE analysis was perormed with experimentally optimised drilling parameters: spindle speed o 4 rpm, eed rate o 8 mm/min, vibration requency o 78 khz, peak-to-peak vibration amitude o 1 μm A time-dependent sinusoidal movement representing a cycle o ultrasonic vibration was imposed on the drill in the axial direction to incorporate the vibrating boundary condition Each wave consisted o 7,8 periodic saming points or one second o simulated period o drilling The drill is thus vibrated along the vertical direction as well as rotated about its own axis independently Contact between the twist drill and the CFRP laminate was deined with general contact algorithm A coeicient o dry riction at the interace between drill s Fig4 Finite element model o UAD in M1/T7 composite laminate 5 Choice o inite elements The Hill s potentential mainly depends on the deviatoric stress components and the astic response becomes almost incompressible [16, 17] The inite elements were selected to accommodate this incompressibility Adiabatic conditions were assumed In an adiabatic heat transer analysis, the heat equation solved at each integration point is given by, c( ) r, (116) where r the heat lux per unit volume due to astic strain is, is the material density c ( ) is speciic heat and is the instantaneous temperature gradient The adiabatic heat was calculated using material properties and no external heat lux was added into the system, thus temperature degrees o reedom were not required In this simulation, eight-node, irst-order, oneintegration point hexahedral elements o type C3D8R were used The CFRP laminate was meshed with 8 elements with the smallest element size o 5 μm The drill was modelled with our-node, 3D discrete rigid elements o type C3D4 and meshed with 35 elements, with the smallest element size o 15 μm 3 FE Results The results obtained rom FE simulations comprise the average o peak thrust orce and torque or UAD in CFRP laminate The thrust orce and torque obtained under similar machining parameters and material properties with conventional drilling technique [5-7] are

6 146 Vaibhav A Phadnis et al / Procedia CIRP 8 ( 13 ) also presented or the comparison purpose and are shown in Fig 5 and Fig 6 Thrust orce (N) Fig5 Comparison o peak thrust orce using experiments and FEA ( a 1 m, 78 khz ) Torque (N-cm) Experimental results FE results Drill eed rate (mm/min) Experimental results FE results Drill eed rate (mm) Fig6 Comparison o peak torque using experiments and FEA ( a 1 m, 78 khz ) [1] R Zitoune, V Krishnaraj, F Collombet, 1 Inluence o machining parameters and new nano-coated tool on drilling perormance o CFRP/aluminium sandwich Composites Part B: Engineering 43:148-8 [] F Makhdum, LT Jennings, A Roy, VV ilberschmidt 1 Cutting orces in ultrasonically assisted drilling o carbon ibrereinorced astics Journal o Physics: Conerence eries;38(1):119 [3] F Makhdum, Dk Nurdiya, A Roy, VV ilberschmidt 1 Ultrasonically assisted drilling o carbon ibre reinorced astics olid tate Phenomena 188:17-5 [4] VA Phadnis, F Makhdum, A Roy, VV ilberschmidt 1, Experimental and numerical Investigations in conventional and ultrasonically assisted drilling o CFRP Laminate Procedia CIRP 1:455-9 [5] VK Astashev, VI Babitsky 7 Ultrasonic processes and machines: dynamics, control and apications Berlin Heidelberg New York: pringer [6] P Thomas, VI Babitsky 7 Experiments and simulations on ultrasonically assisted drilling Journal o ound and Vibration 38:815 [7] K Alam, AV Mitroanov, VV ilberschmidt 11 Experimental investigations o orces and torque in conventional and ultrasonically-assisted drilling o cortical bone Medical Engineering & Physics 33:34 [8] VI Babitsky, VK Astashev, A Meadows 7 Vibration excitation and energy transer during ultrasonically assisted drilling Journal o ound and Vibration 38:85-14 [9] M Wiercigroch, J Wojewoda, A Krivtsov 5 Dynamics o ultrasonic percussive drilling o hard rocks Journal o ound and Vibration 8: [1] H Hocheng, NH Taib, C Liu Assessment o ultrasonic drilling o C/iC composite material Composites: Part A 31:133-4 [11] X Wang, L Wang 4 Investigation on thrust in vibration drilling o iber-reinorced astics Journal o Materials Processing Technology 148():39-44 [1] M Lucas, A, MacBeath, McCulloch, E Cardoni 6 A inite element model or ultrasonic cutting Ultrasonics44:53-59 [13] R Hill 199 Constitutive modelling o orthotropic asticity in sheet metals Journal o the Mechanics and Physics o olids;38(3):45-17 [14] R Hill 1998 The Mathematical Theory o Plasticity: Clarendon Press [15] A Hillerborg1985 Theoretical basis o a method to determine the racture energy concrete Materials and tructures 18(4):91-6 [16] Abaqus 611 User manual 11 Dassault ystem Rhode Islands, U 4 Conclusions A inite element model o UAD in CFRP is developed A constitutive material model suitable to model both volumetric and thermal sotening in CFRP laminate under ultrasonic vibrations is proposed The validated FE model showed good co-relation with the experimental results, demonstrating potential capabilities o this model to predict eatures o UAD Reerences