Predictive modeling of material removal modes in micro ultrasonic machining

International Journal of Machine Tools & Manufacture 62 (2012) 13–23

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Predictive modeling of material removal modes in micro ultrasonic machining H. Zarepour, S.H. Yeo n School of Mechanical and Aerospace Engineering, Nanyang Technological University, 50 Nanyang Avenue, Singapore 639798, Singapore

a r t i c l e i n f o

abstract

Article history: Received 17 January 2012 Received in revised form 14 June 2012 Accepted 14 June 2012 Available online 26 June 2012

This paper presents a model to predict ductile and brittle material removal modes when a brittle material is impacted by a single sharp abrasive particle in micro ultrasonic machining process. Analyses are performed based on the basic indentation fracture theory for hard angular particles. The conditions required for occurrence of both ductile and brittle removal during the interaction between sharp particles and brittle materials in micro ultrasonic machining are discussed. Subsequently, the quantitative criteria for brittle–ductile transition in material removal are presented using the threshold kinetic energy in promoting radial and lateral cracks. Finally, the adequacy of the proposed model is verified by the experimental results from single particle impingements in micro ultrasonic machining. In the experiments, polycrystalline diamond particles ranging from 0.37 to 3 mm are used for processing of single crystalline /100S silicon and fused quartz. The ultrasonic frequency at 50 kHz is introduced at the horn tip which is set at amplitude from 0.8 to 4 mm. The constellation of the experimental results clearly showed good agreement on the basis of comparative principle for the model validation. The outcome of the present research work can be used as an important platform to build reliable models for prediction of material removal rate based on the mode by which material removal takes place in micro ultrasonic machining process. The proposed model can be employed to enhance surface quality as well as process productivity. & 2012 Elsevier Ltd. All rights reserved.

Keywords: Material removal mode Micro-USM Predictive modeling Ductile mode Brittle mode Single particle impingement

1. Introduction Owing to their unique capabilities in micro-scale material removal, fine abrasive particles are used extensively in the manufacturing of components with high dimensional accuracy and surface quality. As such, machining by abrasive particles, let them be free or fixed, has turned to become a niche micromachining technique. Micro ultrasonic machining (micro-USM) which is a free abrasive process exploits the potential of fine abrasive particles within a fluid for material removal of hard and brittle materials. Since the material removal in USM occurs through mechanical action of particles within the abrasive slurry, no thermal and electrical phenomenon takes place during the process. Therefore, micro-USM is one of the liable candidates to create micro features in hard and brittle materials such as silicon, glass, quartz, and advanced ceramics with minimum thermal damage and in a cost-effective way [1,2]. However, process measures such as surface integrity and material removal rate have been points of concern in microUSM due to increasing demand on quality and productivity of the

n

Corresponding author. Tel.: þ65 67905539. E-mail address: [email protected] (S.H. Yeo).

0890-6955/$ - see front matter & 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.ijmachtools.2012.06.005

emerging micro products [2,3]. On the other hand, material removal mode whether it occurs in brittle or ductile mode and transition between these modes are significant terms with direct impact on both surface integrity and material removal rate associated with process quality and productivity respectively. Based on this rationale, investigation on brittle and ductile material removal modes as well as providing quantitative criteria for brittle–ductile transition based on process parameters seems necessary to further improve the performance of micro-USM technique. A number of studies have been reported in the literature with regards to material removal modes and mechanisms in microUSM processes. Ichida et al. [4] reported on various material removal mechanisms in their proposed non-contact ultrasonic abrasive machining (NUAM) for ultra-precision machining of aluminum alloys. Hu et al. [5] investigated the material removal mechanisms and surface generation in micro-USM. Curodeau et al. [6] proposed an ultrasonic abrasive micromachining process (named as UAmM) and they studied different removal mechanisms in P20 steel under two machining modes namely, hammering (contact) mode and impact (non-contact) mode. Also, in an investigation by the authors [7], material removal modes and their correlation with process parameters were investigated in micro-USM of monocrystalline silicon. However, no studies have

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H. Zarepour, S.H. Yeo / International Journal of Machine Tools & Manufacture 62 (2012) 13–23

Nomenclature a (mm) Amplitude of ultrasonic vibration f (Hz) Frequency of ultrasonic vibration F (mN) Average force per cycle exerted on one single particle rP ðg=cm3 Þ Density of abrasive particles d ðmmÞ Average particles size mp (g) mass of a single abrasive particle dV nR ðm3 Þ Threshold indentation volume for radial/median cracks m Dimensionless constant b Dimensionless constant E (GPa) Young’s modulus of the workpiece material K IC ðMPa m1=2 Þ Fracture toughness of the workpiece material H (GPa) Hardness of the workpiece material dV nL ðm3 Þ Threshold indentation volume for lateral cracks z0 Dimensionless constant a Shape factor of the indenter A Shape factor for the chip of material U (J) Kinetic energy absorbed by workpiece during the particle impact

been reported to date on predictive modeling of brittle and ductile modes of material removal in the micro-USM process. In this paper, a predictive model is introduced to specify brittle and ductile modes of material removal in the process. A series of experiments based on single abrasive particle impingement is conducted as the first attempt in micro-USM to verify the proposed model. Subsequently, the morphology of the craters resulted from single particle impact is studied. The present work serves as a quintessence to the understanding of material removal modes, namely brittle and ductile modes in the micro-USM process.

2. Approach to development of the predictive model Fig. 1 outlines the proposed model for prediction of material removal mode in micro-USM process. The model consists of three parts: estimate the apparent threshold kinetic energy for radial and lateral fracture, estimate the kinetic energy of an impinging particle, and the criteria for deciding on the material removal mode. The analysis to estimate the threshold kinetic energy is performed based on the well-established indentation fracture theory for microcracks initiation by hard angular particles in work materials. The application of this theory to predict the thresholds for ductile and brittle transitions in other processes such as particle erosion have been described by Hutchings [8] and Slikkerveer et al. [9].

P (mN) U nR (nJ) U nL (nJ) vm (m/s) vu (m/s)

Indentation force of the particle Threshold kinetic energy for radial/median cracks Threshold kinetic energy for lateral cracks Maximum velocity of the abrasive particle Velocity of the particle resulted from transmission of ultrasound vc (m/s) Velocity of the particle resulted from cavitation collapse in the slurry m (kg) Mass of the workpiece c (N s/m)Damping coefficient k (N/m) Stiffness coefficient Fv(t) (N) Harmonic force applied to the workpiece by ultrasonic horn F 0 sin2pf t (N) Harmonic external forcing function y (mm) Vertical displacement of the vibrated workpiece a (mm) Amplitude of vibration j (rad) Phase shift v (m/s) Velocity of the vibrated workpiece Up (nJ) Total maximum kinetic energy of a single particle

In the model development, required conditions for ductile and brittle removal in micro-USM are discussed. The model estimates the kinetic energy of a single impinging abrasive particle introduced by the ultrasound. The primacy on the type of material removal mode lies at the foundation of comparative principle between the apparent threshold kinetic energy of the workpiece material and estimated kinetic energy of the impacting particle based on the input parameters. The outcome of the proposed model can be used as a basis for development of predictive models for material removal rate based on the removal mode in the micro-USM process. If the material removal occurs in brittle mode, then the indentation fracture theory could be employed to estimate the material removal rate. On the other hand, if ductile removal mode prevails in the process, then ductile mode abrasion theory might be accommodated to predict the removal rate.

3. Development of the model 3.1. Estimate the threshold kinetic energy for radial/median and lateral fracture When a brittle material is impacted by a hard angular particle, plastic deformation occurs in contact area due to the high compressive and shear stresses. Consequently, a radial/median

Fig. 1. Approach to developing the predictive model for material removal mode in micro-USM.

H. Zarepour, S.H. Yeo / International Journal of Machine Tools & Manufacture 62 (2012) 13–23

crack is formed in the area. Moreover, the plastic deformation results in large tensile stresses which give rise to initiation of lateral cracks and eventually the material removal [10]. It has been demonstrated by Lawn et al. [11] and Marshall et al. [12] that the stress field around the tip of a sharp indenter depends only locally on the shape of indenter tip and it does not extend beyond the plastic zone. The stress outside the plastic deformation zone, which is an indication of the material hardness, is determined mainly by the volume of the indentation zone rather than its shape [9,13]. So, an arbitrary hemispherical shape may be considered for the indentation zone in the models for the crack systems development as proposed in Ref. [12]. The schematic of such an indentation zone and the stress outside the plastic zone during indentation fracture by a sharp particle is shown in Fig. 2. In the analysis that follows, the workpiece hardness is assumed constant throughout the region of the particle indentation. With rise in the indentation force, the volume of the indentation zone as well as plastic zone will increase. At a certain indentation force, the tensile stresses at the boundary of the plastic zone will exceed the fracture limit of the workpiece material and subsequently cracks will initiate. Therefore, the crack initiation can be expressed based on the threshold volume of the indentation zone or briefly ‘‘indentation volume’’ denoted by dV in Fig. 2. Slikkerveer et al. [9] presented the indentation volume related to the crack threshold for radial/median cracks:

dV RT ¼ dV nR ¼



3 2p

3 U

m6 E3=2 UK IC 6 b6

U

H15=2

ð1Þ

3=2

1 z0 E3=2 UK IC 6 U U 3 a1=2 UA3 H15=2

Table 1 Constants for threshold indentation volume in radial/median and lateral cracks. No.

Constant parameter

Value

Reference

1 2 3 4 5

m

0.63 0.096 1.2  103 2 0.75

[9] [14] [12] [11,15] [12]

b z0

a A

If we substitute the respective constants in Eqs. (1) and (2): For radial/median cracks:

dV nR ¼ C R U

E3=2 UK IC 6 H15=2

ð2Þ

The parameter m in Eq. (1) is a dimensionless constant which correlates the size of the indentation zone with that of the plastic zone. Also, parameter b is a constant, independent of material properties and indenter shape. Furthermore, the parameter z0 in Eq. (2) is an empirical constant obtained from experiments with Vickers indenters [12]. Finally, a and A are the shape factor of the indenter and shape factor of the workpiece material chip above the lateral crack respectively. The parametric values in Eqs. (1) and (2) are obtained from an eclectic mix of literature (Table 1).

ð3Þ

and for lateral cracks:

dV nL ¼ C L U

E3=2 UK IC 6 H15=2

ð4Þ

CR and CL in Eqs. (3) and (4) are constants with value of 8694.4 and 23,224.8 respectively. The theory of quasi static indentation can be applied into particle impact phenomenon based on the rationale that speed of the impacting particles (within some hundreds of meters per second) is much smaller as compared to the velocity of elastic and plastic deformation in brittle materials. As such, the energy conservation law can be utilized to equate the kinetic energy absorbed by workpiece material with the work done by particle through the impact event; leading to the following equation [9]: U ¼ HUdV

and by applying the ‘‘apparent threshold’’ for lateral cracks:

dV LT ¼ dV nL ¼

15

ð5Þ

Likewise, during micro-USM process, the speed of the accelerated particles may reach maximum of a few hundred meters per second. When colliding with the target material, the deceleration of the particle generates the indentation force on the workpiece. Therefore, the theory of quasi static indentation is also applicable into the single particle impingement in micro-USM process. Eq. (5) correlates the impact and indentation events of the abrasive particle during the interaction with workpiece material. Thus, in the translation from impact to indentation, the indentation volume (dV) can be calculated as the ratio between the kinetic energy of the impacting particle and the hardness of the workpiece material [9]. Eq. (3) can be rewritten as the required threshold kinetic energy to initiate the radial/median cracks: U RT ¼ U nR ¼ C R U

E3=2 UK IC 6 H13=2

ð6Þ

Similarly, using Eq. (4), the threshold kinetic energy for initiation of the lateral cracks is presented as U LT ¼ U nL ¼ C L U

E3=2 UK IC 6 H13=2

ð7Þ

In order to determine the material removal mode in microUSM, the kinetic energy of the accelerated particle inside the machining zone will be compared with threshold kinetic energy for radial/median and lateral cracks calculated by Eqs. (6) and (7) respectively. 3.2. Kinetic energy of a single impinging abrasive particle

Fig. 2. Indentation and plastic zones beneath a sharp particle during indentation fracture.

The schematic of the micro-USM process with the workpiece vibration method is illustrated in Fig. 3. Workpiece is oscillated vertically and micro tool is pressed against the abrasive slurry by tool infeed. As shown in the enlarged view in Fig. 3, abrasive particles are dispersed in the liquid and they move freely in the

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Fig. 3. Schematic of micro-USM with workpiece vibration, and enlarged view of the machining zone.

machining zone. Vibration of the workpiece introduces the ultrasound into the slurry medium which subsequently leads to acceleration and impact of the particles on the surface of the tool and workpiece. The successive impacts on hard and brittle workpiece material give rise to particles indentation and eventually material removal from the surface. The magnitude of the overall velocity of a single particle at the instant of impact has two coincident components; namely, the velocity of particle originated from transmission of the ultrasonic wave in the slurry, and the velocity created by shock wave from cavitation collapse inside the liquid (hereafter known as cavitation velocity). These velocities are denoted by vu and vc respectively in detailed view of the machining zone in Fig. 3. The maximum velocity of a single particle impinging onto the workpiece surface can be written as vm ¼ vu þ vc

ð8Þ

As discussed earlier, when the workpiece oscillates, its surface comes in contact with abrasive particles dispersed inside the machining zone. Thus, mechanical vibration of the workpiece in the vicinity of slurry medium causes the ultrasound to be transmitted through the slurry. Consequently, every single particle starts to oscillate about its mean position at driving frequency and experiences considerable acceleration [16]. Hence, the speed of the particles resulted from ultrasonic vibration (vu) can be considered the same as the speed of the vibrated workpiece. In the present analysis, the motion of the workpiece can be regarded as forced vibration with single degree of freedom and viscous damping caused by micro-tool which is in indirect contact with the vibrated workpiece via slurry medium. Similar assumption for the vibration of tool in dynamic analysis of the conventional USM based on impact mechanics [17] has resulted in rather accurate estimation of the material removal rate. The schematic of the corresponding spring mass damper model with harmonic force in the present micro-USM system is depicted in Fig. 4. The equation for the vibration motion of the workpiece can be expressed as below my€ þcy_ þ ky ¼ F v ðtÞ

ð9Þ

Eq. (9) can be rewritten as my€ þcy_ þ ky ¼ F 0 sin2pf t

ð10Þ

Using the steady state solution of the Eq. (10), the vertical displacement of the vibrated workpiece is obtained as following: y ¼ a sinð2pf tjÞ

ð11Þ

Eq. (11) indicates that the workpiece will oscillate at the same frequency f, of the applied harmonic force, but with a phase shift j. Therefore, the equation for the velocity of the vibrated

Fig. 4. Schematic of the vibration model in micro-USM with the workpiece vibration method.

workpiece can be written as below v ¼ y_ ) v ¼ 2paf cosð2pf tjÞ

ð12Þ

Thus, the maximum particle velocity originated from transmission of the ultrasound in the slurry medium, may be expressed as vu ¼ 2paf

ð13Þ

The total energy of a vibrating particle in the slurry is equal to the sum of kinetic and potential energies. The kinetic energy is caused by the velocity of the particle, whereas potential energy is due to the displacement of the particle about its mean position during the vibration [18]. The total energy of each particle remains constant. However, the energy of the particle continuously transforms from potential to kinetic and vice versa during the particle movement. Therefore, the energy of a vibrating particle can be determined by calculating its maximum kinetic energy which corresponds to the maximum velocity during the vibration. Besides, if we consider the cavitation velocity of a vibrating particle, the total maximum kinetic energy (Up) of a single abrasive particle upon impacting on the workpiece surface may be presented as 1 U p ¼ mP Uv2m 2

ð14Þ

Eq. (14) can be rewritten using Eq. (8) as following: 1 U p ¼ mP ðvu þvc Þ2 2

ð15Þ

H. Zarepour, S.H. Yeo / International Journal of Machine Tools & Manufacture 62 (2012) 13–23

If the sharp particles are considered as identical cubes with side length (particle size) of d, the mass of a single abrasive particle, m, in Eq. (16) can be written as 3

mP ¼ d UrP

ð16Þ

Considering the Eqs. (13), (15) and (16), the maximum kinetic energy of a single abrasive particle in the micro-USM process can be expressed as 3

U p ¼ 12d UrP ð2paf þvc Þ2

ð17Þ

Accurate calculation of vc is rather complicated as it requires the knowledge of various phenomena involved in the cavitation comprising the formation, growth, and implosive collapse of the bubbles near the particles submerged in the liquid. In order to estimate vc of a single particle in the vicinity of the collapsed bubble, one should consider main forces controlling the interactions and translatory motions of the bubbles including gravity, acoustic streaming, Bernoulli attraction, radiation pressure, and steady forces due to wave-form distortion. Hence, with various forces involved, the interaction of collapsed bubbles with the acoustic field, and with themselves, is a complex theoretical problem [19]. Furthermore, when an ultrasonic wave is introduced into liquids, severe shock waves are formed and transmitted through the liquid at speeds higher than the velocity of sound [20]. The formation of these high speed shock waves results in acceleration and subsequently high velocity impacts among solid particles suspended in the liquid [21]. Taking into account the above implications and with the purpose of simplifying the calculation of the velocity of abrasive particles, alternatively we may use an estimation of vc relative to the value of vu by considering the difference in their order of magnitudes. While the values of particle velocity due to the transmission of ultrasound in the slurry are in order of a few meters per second within the ranges of vibration amplitude and particle size applied in micro-USM, the velocity of the primary cavitation bubbles ranges in the order of a few hundred meters per second [20–22]. Thus, the values of vc may be approximated as two orders of magnitude higher than that of vu. In the present study, the value of vc is considered 100 times higher than that of vu for the purpose of simplicity. The validity of this assumption could be verified through experimental study of the removal modes driven by kinetic energy of the impinging particles associated with the velocity of the particles. 3.3. Criteria for transition between brittle and ductile modes of material removal Threshold kinetic energy for radial/median and lateral cracks could be applied as an indication of the transition points between plastic deformation, radial crack initiation and lateral fracture in processes dealing with particle erosion of hard and brittle materials [9,23]. If the total maximum kinetic energy of an impinging particle which is transferred into the workpiece material upon impact exceeds its threshold kinetic energy for crack initiation, material removal takes place in brittle mode i.e. by lateral fracture; otherwise, material is removed in a ductile mode. Based on this rationale, one can consider three different conditions with respect to resultant material removal mode in microUSM process: (I) U p o U nR : No brittle fracture occurs in workpiece and material is removed by abrasive particle in a pure ductile mode. (II) U nR rU p o U nL : Material is removed partially in ductile mode and radial/median crack occur upon the particle impingement. Lateral fracture is unlikely to occur in this case.

17

(III) U nL r U p : Lateral crack occurs and material is removal by crack propagation in a pure brittle mode. As described in Section 2, the presented model is based on the quasi static indentation theory for sharp particles. It is noteworthy that the indentation theory only holds when the direction of indentation is perpendicular to the surface. According to the discussion presented in Section 3.2, the particle velocity associated with ultrasound transmission in the slurry (vu) can be considered normal to the workpiece surface as it is driven by vertical vibration of the workpiece as a result of the mechanical vibration of the ultrasonic horn with single degree of freedom in vertical direction. As for cavitation velocity (vc), the position of the cavitation collapse and hence the acceleration of the particle due to the resulted shock waves is randomly dispersed throughout the slurry liquid. Therefore, the direction of the particle impact is not constantly perpendicular to the workpiece surface and it may deviate from vertical direction. However, due to a small machining gap which is close to the particle size, and short traveling distance of the abrasive particles before impact, the direction of the particle indentation can be assumed approximately normal to the surface of the workpiece.

4. Modeling results The prediction of material removal modes for silicon /100S and fused quartz are presented in this section. The values of threshold kinetic energy for radial/median and lateral cracks are determined from Eqs. (6) and (7) respectively along with mechanical properties of the materials listed in Table 2. For silicon material, these values are equal to UnR ¼0.215 nJ and UnL ¼0.570 nJ. Also, the corresponding values for quartz material are obtained as UnR ¼0.310 nJ and UnL ¼0.818 nJ. A combination of the process parameters was selected as model input based on the available size of the particles and the range of vibration amplitude which can be set on the developed micro-USM system. Table 3 presents the various parameter settings as well as the calculated values of the particles velocity. The maximum kinetic energy of a single PCD particle for different parameter settings can be estimated using Eq. (17). Table 4 presents the calculated values of UP and corresponding material removal modes predicted by model for silicon /100S and fused quartz. Based on the criteria for brittle–ductile transition, the model suggests that for silicon /100S, using particles with size of 3 mm at vibration amplitudes of 3 and 4 mm results in partially ductile and pure brittle modes respectively. In the case of Table 2 Properties of the workpiece materials. Material

H (GPa)

E (GPa)

KIC (MPa m1/2)

Single crystal silicon /100S Fused quartz

12.6 8.1

166.5 71.7

0.74 0.6

Table 3 Parameter setting and predicted particles velocity. Parameter setting

d (mm)

a (mm)

vu (m/s)

vc (m/s)

vm (m/s)

1 2 3 4 5 6

0.37 1 3 3 3 3

3 3 3 0.8 2 4

0.942 0.942 0.942 0.251 0.628 1.257

94.2 94.2 94.2 25.1 62.8 125.7

95.142 95.142 95.142 25.351 63.428 126.957

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Table 4 Values of UP and predicted material removal modes for silicon /100S and fused quartz. Parameter

setting

UP (nJ)

Predicted material removal mode

Model criteriaa

Silicon /100S

Model criteriab

Fused quartz Pure ductile Pure ductile Partially ductile Pure ductile Pure ductile Partially ductile

1

8  10  4

U p o U nR

Pure ductile

U p o U nR

2

0.016

U p o U nR

Pure ductile

U p o U nR

3

0.428

U nR r U p o U nL

U nR r U p o U nL

4

0.030

U p o U nR

Partially ductile Pure ductile

5

0.191

U p o U nR

Pure ductile

U p o U nR

6

0.761

U nL r U p

Pure brittle

U nR r U p o U nL

a b

U p o U nR

For silicon /100S: UR ¼ 0.215 nJ, UL* ¼ 0.570 nJ. For fused quartz: UR* ¼ 0.310 nJ, UL* ¼0.818 nJ.

fused quartz, either of the above-mentioned parameter settings results in a partially ductile material removal mode. For the rest of the parameter settings listed in Table 4, material removal takes place in a pure ductile regime for both materials.

5. Experimentation Unlike multiple-particle impact, single particle impact has the potential of providing more explicit details on material removal modes and involved mechanisms in studies related to solid particle erosion [24–27]. Therefore, it is postulated that the study of single particle impingement in the micro-USM process could provide more insights into brittle and ductile removal modes and transition between them. As such, validation experiments on single abrasive particle impact are conducted to demonstrate the applicability of the proposed model for determining the material removal modes in the process. 5.1. Experimental setup The schematic of the setup for single particle impact experiments is illustrated in Fig. 5. The high frequency (50 kHz) electrical signal from ultrasonic generator is converted to mechanical vibration by ultrasonic transducer. Then, the vibration is transmitted to the workpiece via booster and horn. The workpiece is held on the face of ultrasonic horn using a vacuum clamping system which includes vacuum pump, liquid separator and flexible tubes. The slurry delivery system consists of magnetic stirrer, peristaltic pump, and flexible tubing to supply fresh abrasive particles to the machining zone. Micro-tooling system employs a precision mandrel with controllable speed up to 6000 rpm. The tooling system is connected to a three-axis stage with piezo-actuators and its position is controlled by computer. 5.2. Materials preparation and process parameters Workpieces were diced from polished /100S silicon wafers and two-side polished fused quartz wafers. Polycrystalline diamond (PCD) powder with angular (sharp) particles in DI water was used for abrasive slurry. The slurry is agitated using an ultrasonic bath for about 15 min in order to wet the particles thoroughly before applying to the machining zone. Tungsten rods with diameter of 300 mm were employed as micro tools. The tool tip was ground and inspected after each experimental run to ensure that the tool face is flat with a

Fig. 5. Schematic of the micro-USM setup for single impact experiments.

Table 5 Process parameters and machining conditions. Ultrasonic characteristics Amplitude Frequency

0.8, 2, 3, 4 mm 50 kHz

Workpiece Workpiece material Dimension Initial surface roughness

Silicon /100S, Quartz 9.5  9.5 (mm2) Ra ¼1–2 nm

Micro tool Tool material Tool size Static load

Tungsten Ø300 mm 1 mN

Abrasive particles Particles type Density Average particles size Concentration

Polycrystalline diamond (PCD) 3.5 g/cm3 0.37 (0.25–0.5); 1 (0.75–1.25); 3 (2–4) mm 0.02, 0.04% wt

burr-free edge. Process parameters and other experimental conditions are listed in Table 5. 5.3. Experimental procedure and characterization method Single particle impact experiments were conducted using the developed micro-USM system. First, the slurry was delivered into the machining zone. Subsequently, a contact force of 1 mN was established between micro tool and abrasive slurry by applying tool infeed with a maximum speed of 20 nm/s in z-axis direction. The amount of force was continuously monitored to maintain its variation within 75% during the experiments. For each set of parameters, particle impingement experiments were carried out for 10 s at the beginning, and increased subsequently with intervals of 10 s. After each stage, workpiece surface was cleaned and observed under confocal imaging microscope to check for the formation of the craters. Experiments continued for each run until single craters were observed. The morphology of the craters resulted from particle impingements is studied using confocal imaging profiler, field emission scanning electron microscopy (FESEM) and atomic force microscopy (AFM). The size of the craters is in the range of 0.25–4.5 mm. Hence, locating the craters under atomic force microscopy is difficult,

H. Zarepour, S.H. Yeo / International Journal of Machine Tools & Manufacture 62 (2012) 13–23

especially when the same crater has to be observed further using the AFM and FESEM. Therefore, PLm confocal imaging profiler was employed as an initial step to map the location of the craters. Also, given the distribution in particles size, the morphology of the resulted craters is expected to vary for a specific particle size. In order to minimize the effect of the variation in particle size and to ensure the selection of the typical representative craters, first the craters with nearly identical size and similar morphology were targeted with a probability of 90% (9 similar craters out of a total of 10) within the impacted area. Subsequently, one crater was scanned using AFM with a very low scan rate.

6. Experimental results 6.1. Material removal modes in single particle impingement of silicon Single particle impact experiments were conducted on silicon /100S material using the same set of the parameters listed in

19

Table 3. Each experimental run was replicated three times and the morphology of the typical representative craters was studied in each parameter setting. Fig. 6 shows the AFM image and cross-sectioned view of the typical craters formed at amplitude of 3 mm using 0.37 mm size particles. No obvious cracked area is observed around the crater. Also, the 3D image shows clearly that material is piled-up at the rim of the crater indicating that the particle impact has resulted in plastic deformation in the impingement site. The depth of the crater and pile-up height are only about 21 and 8 nm respectively. Also, the diameter of the crater is approximately 0.29 mm which can be estimated from cross-sectioned view of the crater in Fig. 6. A similar material removal mode was observed (image not shown) when amplitude of 3 mm and particle size of 1 mm were applied. In this case, craters with relatively smooth rims and free from radial cracks formed in the impinged site. Also, applying amplitudes of 0.8 and 2 mm with particle size of 3 mm resulted in plastic deformation and material pile-up in the impression site.

Fig. 6. AFM image and sectional profile of the craters using particle size of 0.37 mm and amplitude of 3 mm.

Fig. 7. Single crater formed by particles with size of 3 mm at amplitude of 3 mm: (a) AFM image with crater sectional profile; and (b) FESEM image.

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Fig. 7 depicts a typical crater when the surface was processed using particle size and vibration amplitude of 3 mm. As shown in AFM image of Fig. 7(a), the crater edge appears to be rather smooth with no obvious material pile-up at the rim of the crater. However, radial cracks are formed around the impingement site as shown in the sectional profile of the crater. This observation also is confirmed by FESEM imaging with GBhigh mode as depicted in Fig. 7(b). A mixture of plastic deformation and radial cracks are obvious in the crater. Moreover, no lateral cracks or severe brittle fracture is observed in the impacted spots. Fig. 8(a) illustrates the AFM image and sectional profile of the cracks at the rim of a typical crater formed at particle size and vibration amplitude of 3 mm and 4 mm respectively. Also, the FESEM image of the impact site is depicted in Fig. 8(b). The morphology of the crater shows clearly that radial and lateral cracks have formed in the impression site. Also, the crater size is

approximately 4.5 mm i.e. larger than the average particle size by 50%. This difference is attributed to the propagation and intersection of the lateral cracks which leads to brittle fracture and hence increased size of the craters.

6.2. Material removal modes in single particle impingement of fused quartz A set of single impingement experiments were conducted on fused quartz wafer with the purpose of further validation of the model. The selection of this material was due to its high thermal and chemical stability, high tensile strength, unique electrical properties and high optical transmission that make it suitable for a wide range of applications such as biosensors, pressure sensors and microstructures in which the basic component is a resonator.

Fig. 8. Images of a single crater formed by 3 mm size particles at amplitude of 4 mm: (a) AFM image with sectional profile of the cracks; and (b) FESEM image.

Fig. 9. Craters on quartz formed at amplitude of 3 mm: (a) by 0.37 mm size particles; (b) by 1 mm size particles.

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The machining conditions and parameter settings were selected similar to those for silicon. Fig. 9 illustrates the AFM image along with sectional profile of the craters formed at amplitude of 3 mm using different particle sizes. As shown in Fig. 9(a), crater rim is smooth and free from any crack and brittle fracture when PCD particles with size of 0.37 mm are used. Depth of the crater is approximately 14 nm. Also, the diameter of the crater is about 0.38 mm which is close to the average particle size. Fig. 9(b) depicts a typical crater formed by particles with size of 1 mm at amplitude of 3 mm. The diameter and depth of the crater are about 1.19 and 106 nm respectively. No radial and lateral cracks are observed at the impact location and it appears free from brittle fractured zone. Also, plastic deformation is observed clearly at the rim of the crater. Fig. 10 presents the morphology and sectional profile of the craters formed at different vibration amplitudes using particle size of 3 mm. The crater rim formed at amplitude of 2 mm appears to be smooth and free from cracks as depicted in Fig. 10(a). Also, plastic deformation and material pile-up are observed in the impingement site indicating the removal of quartz material under a pure ductile mode. Finally, a partially ductile material removal mode was obtained when 3 mm size particles were impacted on fused quartz at amplitude of 4 mm. As shown in Fig. 10(b), radial cracks have formed around the crater with no lateral crack formation. The depth of the crater is about 660 nm which is relatively close to that of the crater formed at amplitude of 2 mm.

the impinging particles is only about 8  10  4 nJ which is much smaller than the threshold kinetic energy of 0.215 nJ required for initiation of the radial cracks in silicon /100S. This prediction is confirmed by the morphology of the craters formed in single particle impingements as shown in (Fig. 6). Moreover, the morphology of the craters shown in Fig. 7 suggests that the material is removed in a partially ductile regime in silicon /100S when particle size and vibration amplitude of 3 mm are applied in the experiments. This observation is also in agreement with the predicted removal mode by model. In case of applying particle size of 3 mm and vibration amplitude of 4 mm, the calculated kinetic energy of the particles, 0.761 nJ, is noticeably higher than threshold kinetic energy of 0.570 nJ for lateral fracture in silicon /100S. Therefore, a completely brittle fracture mode with lateral cracks is predicted in this parameter setting. The morphology of the craters, observed in Fig. 8, indicates that material has been removed in a purely brittle manner which is consistent with the predicted material removal mode by model.

7. Discussion Fig. 11 illustrates a graphical presentation of the predictive model in silicon /100S materials for different particle sizes and vibration amplitudes. Three distinct regions of material removal modes are also shown with boundaries of the threshold kinetic energy for radial and lateral cracks. Based on the model prediction and the results presented in Table 4, a pure ductile material removal mode is expected in silicon /100S when particles with size of 0.37 mm and amplitude of 3 mm are applied. In this case, the estimated kinetic energy of

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Fig. 11. Graph of the model for material removal modes in silicon /100S.

Fig. 10. Craters formed on quartz using 3 mm size particles: (a) at amplitude of 2 mm; (b) at amplitude of 4 mm.

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With reference to the modeling results for quartz material in Table 4, when amplitude of 3 mm is applied in the process along with particle size of 0.37 and 1 mm, the kinetic energy of a single abrasive particle reaches about 8  10  4 and 0.016 nJ respectively. These values are significantly lower than the threshold kinetic energy of 0.310 nJ for radial cracks in fused quartz. Therefore, a pure ductile removal mode is predicted by the model. This concurs with the morphology of the craters as illustrated in Fig. 9. Furthermore, it is evident from the observed crater morphology in Fig. 10(a) that material removal has occurred in a purely ductile mode when particle size and vibration amplitude are equal to 3 and 2 mm respectively. The same machining mode is predicted by the proposed model at this parameter setting. The kinetic energy of the impinging particles is estimated about 0.191 nJ which is only about 60% of the threshold kinetic energy for initiation of the radial cracks in fused quartz. Finally, the morphology of the craters illustrated in Fig. 10(b) reflects a partially ductile removal mode in quartz material when particle size and vibration amplitude are set at 3 and 4 mm respectively. At this parameter setting, the prediction of the removal mode, based on the comparison made between threshold and particle kinetic energies (Table 4), coincides with the above observation. The kinetic energy of an accelerated particle in the machining zone is calculated as 0.761 nJ which does not exceed the threshold kinetic energy for lateral cracks in quartz. From modeling and experimental results, it is clear that no brittle fracture occurs in fused quartz within the range of particle size and adjustable amplitude of vibration applied in this study. The comparison between predicted material removal modes and experimental results from single particle impingement in silicon /100S and fused quartz shows that despite the observed scatter in the shape and depth of the craters formed at different parameter settings, there is a reasonable indication that the material removal mode can be predicted correctly by the proposed model in the micro-USM process.

8. Concluding remarks The results of this paper can be summarized as following: 1. A new model was developed in micro-USM to predict material removal mode quantitatively based on the properties of the workpiece and particles as well as ultrasonic characteristics of the system. 2. Single particle impingement experiments were conducted to provide more insights into material removal modes and to validate the capability of the proposed model. Single crystalline /100S silicon and fused quartz were used for experiments. 3. The morphology of the craters formed by particle impacts was studied and three modes of material removal were observed; namely, pure ductile, partially ductile (transition mode) and pure brittle. 4. Applying particles with average size of 0.37 mm at an amplitude of 3 mm resulted in a purely ductile removal mode with material pile-up at the rim of the craters in silicon material. The crater depth and pile-up height were as small as 21 and 8 nm respectively. Similarly, a pure ductile removal mode with smooth-edge craters and maximum crater depth of 14 nm was observed in case of fused quartz. 5. Applying particle size and vibration amplitude of 3 and 4 mm respectively resulted in a pure brittle mode in silicon with radial and lateral cracks in the impingement site. Similar parameter setting resulted in a partially ductile removal mode in fused quartz with only radial cracks at the rim of the crater.

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