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International Journal of Machine Tools & Manufacture 40 (2000) 1351–1366 Non-conventional machining of particle reinforced metal matrix composite F. Mu ¨ller, J. Monaghan * Department of Mechanical and Manufacturing Engineering, Parsons Building, Trinity College, Dublin, Ireland Received 7 July 1999; accepted 26 November 1999 Abstract Particle Reinforced Metal Matrix Composites (PRMMC’s) have proved to be extremely difficult to machine using conventional manufacturing processes due to heavy tool wear caused by the presence of the hard reinforcement. This paper presents details and results of an investigation into the machinability of SiC particle reinforced aluminium matrix composites using non-conventional machining processes such as Electro Discharge Machining (EDM), laser cutting and Abrasive Water Jet (AWJ). The surface integrity of the composite material for these different machining processes are examined and compared. The influ- ence of the ceramic particle reinforcement on the machining process was analysed by tests performed on samples of the non-reinforced matrix material. 2000 Elsevier Science Ltd. All rights reserved. Keywords: Metal matrix composites; Laser machining; Electro-discharge machining; Abrasive water jet machining; Material removal rate; Surface quality/topography; Heat affected zone/re-cast layer 1. Introduction Particle Reinforced Metal Matrix Composites (PRMMC’s) are a class of materials with a wide potential for application in the automotive and aerospace industries. However, the full potential of these materials is hindered by the high manufacturing costs associated with the difficulties experienced in machining these composites. Machining PRMMC’s using conventional machining processes such as turning, drilling etc., generally results in excessive tool wear due to the presence of the hard particles which results in a very abrasive nature of this material [2,17]. Consequently non-conventional machining processes such as Electro Discharge Machining (EDM) [9,12,14], laser cutting [11,13] and Abrasive Water Jet (AWJ) [6] techniques are increasingly being used * Corresponding author. Tel.: + 353-1-6081936; fax: + 353-1-6795554. E-mail address: [email protected] (J. Monaghan). 0890-6955/00/$ - see front matter 2000 Elsevier Science Ltd. All rights reserved. PII:S0890-6955(99)00121-2
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International Journal of Machine Tools & Manufacture 40 (2000) 1351–1366

Non-conventional machining of particle reinforced metalmatrix composite

F. Muller, J. Monaghan*

Department of Mechanical and Manufacturing Engineering, Parsons Building, Trinity College, Dublin, Ireland

Received 7 July 1999; accepted 26 November 1999

Abstract

Particle Reinforced Metal Matrix Composites (PRMMC’s) have proved to be extremely difficult tomachine using conventional manufacturing processes due to heavy tool wear caused by the presence ofthe hard reinforcement. This paper presents details and results of an investigation into the machinabilityof SiC particle reinforced aluminium matrix composites using non-conventional machining processes suchas Electro Discharge Machining (EDM), laser cutting and Abrasive Water Jet (AWJ). The surface integrityof the composite material for these different machining processes are examined and compared. The influ-ence of the ceramic particle reinforcement on the machining process was analysed by tests performed onsamples of the non-reinforced matrix material. 2000 Elsevier Science Ltd. All rights reserved.

Keywords:Metal matrix composites; Laser machining; Electro-discharge machining; Abrasive water jet machining;Material removal rate; Surface quality/topography; Heat affected zone/re-cast layer

1. Introduction

Particle Reinforced Metal Matrix Composites (PRMMC’s) are a class of materials with a widepotential for application in the automotive and aerospace industries. However, the full potentialof these materials is hindered by the high manufacturing costs associated with the difficultiesexperienced in machining these composites. Machining PRMMC’s using conventional machiningprocesses such as turning, drilling etc., generally results in excessive tool wear due to the presenceof the hard particles which results in a very abrasive nature of this material [2,17]. Consequentlynon-conventional machining processes such as Electro Discharge Machining (EDM) [9,12,14],laser cutting [11,13] and Abrasive Water Jet (AWJ) [6] techniques are increasingly being used

* Corresponding author. Tel.:+353-1-6081936; fax:+353-1-6795554.E-mail address:[email protected] (J. Monaghan).

0890-6955/00/$ - see front matter 2000 Elsevier Science Ltd. All rights reserved.PII: S0890-6955(99)00121-2

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Nomenclature

hd Average dross height (mm)ie Discharge current (A)PL Average laser power (W)Ra Average roughness value (µm)tc Pulse on-time; discharge duration (µs)tw Thickness of workpiece (mm)ui Open circuit voltage (V)v Feed rate (mm/min)wk Average kerf width (mm)a Deviation from the right angle (°)

for the machining of PRMMC’s. However, most of these non-conventional machining processesstill need to be investigated in detail in order to assess the “optimal” machining conditions andachieve cost efficient machining in combination with high process reliability and reproducibility.

This paper reports on an experimental test program involving EDM, laser and AWJ machiningof SiC ceramic particle reinforced aluminium alloy matrix composites. The different machiningprocesses are based on different removal mechanisms and lead therefore to different results, e.g.surface integrities. The differences in surface quality, including surface roughness, surface top-ography and sub- surface damage were investigated. Furthermore the influence of the reinforce-ment on the machining process was studied by performing comparative tests on samples of non-reinforced aluminium alloy.

2. Experimental procedure

Two types of composite material, AA2618/SiC/20p and A356/SiC/35p, were selected for inves-tigation. The AA2618/SiC/20p composite consists of an aluminium alloy AA2618 (2.3% Cu, 1.5Mg, 1.2% Fe, 1.1% Ni, bal. Al) reinforced with 20% SiC particles of approximately 10–13µmsize. This composite was produced by spray deposition followed by an extrusion process. TheA356/SiC/35p composite consists of A356 aluminium alloy (7% Si, 0.2% Cu, 0.6% Fe, 0.35%Mn, 0.35% Mg, 0.35% Zn, bal. Al) reinforced by 35% 13µm SiC particles. This material wasproduced by a powder metallurgy route involving hot-isostatic pressing. Tests were also performedon the non-reinforced aluminium alloys (AA2618 and A356).

The EDM process was performed using an ARD M50E die-sinking machine. Paraffin oil, speci-fication 72K supply by Fuchs Lubrication (electrical conductivityk=5×1024 µS/cm) was used asthe dielectric fluid, in a reverse flow (suction flow). The machining settings are displayed in thevarious graphs below. The tool electrodes used were machined from copper, each of which was10 mm square and 5 mm in thickness. The PRMMC workpieces were 10 mm thick plates withpre-drilled 9 mm diameter holes. Each of these circular holes was changed into a square holeusing the EDM process through the use of square shaped electrodes.

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Table 1Results of laser cuts using a CO2 Laser

Material (tw=3 mm) Output Feed ratev Surface Average Average Average DeviationpowerPL [mm/min] roughness thickness dross kerf width from right[W] Ra [µm] of heighthd wk [mm] anglea [°]

deposition [mm]layer [µm]

PRC LaserAA2618/SiC/20p 1600 400 5.28 30 0.98 0.37 2°429AA2618/SiC/20p 1600 600 6.59 35 1.1 0.32 1°469AA2618/SiC/20p 2000 600 5.11 35 1.14 0.36 1°569AA2618a 2000 600 7.15 not 0.56 0.25 2°439

identifiablyTRUMPF Laser TFL 1200AA2618/SiC/20p 1100 600 4.2 25 0.62 21°619AA2618/SiC/20p 1100 1000 4.76 23 0.46 21°999AA2618/SiC/20p 1100 2000 4.42 25 0.24 21°169AA2618/SiC/20p 1100 2500 4.65 17 0.17 0.25 21°299AA2618/SiC/20p 1100 3000 4.81 19 0.19 21°079

a Other settings for the non-reinforced aluminium were also investigated, but the laser did not cut at these settings.The surface was barely scratched, which is explained by the very high optical reflectivity of the aluminium. Reinforcingwith the SiC particles reduces the reflectivity.

Laser cutting was performed using a CO2 laser (wavelength 10.6µm). Two different laserswere used, firstly a PRC Laser (max. power 2.2 kW/hyper pulse mode) and secondly a TrumpfLaser (max. power 1.2 kW/TEM01). The tests were performed under a coaxial jet of Nitrogengas at a pressure of 1.3 MPa (PRC Laser) and 0.8 MPa (Trumpf Laser). Process parameters suchas laser power and feed rate were varied, as displayed in Table 1. Each PRMMC workpiece was3 mm thick.

The results of the Abrasive Water Jet cutting relate to a test program performed on an AWJmachine developed by the EREDIS society, France. The following cutting parameters wereapplied: 300 MPa water pressure, 1.1 mm nozzle diameter, 1 mm stand-off distance, and 80-meshgarnet flowing at 450 g/min as abrasive particles. Feed rate was varied, as displayed in Table 2.The workpiece thickness was 3 mm thick.

Following machining the workpieces were sectioned and geometrical features were measured

Table 2Results when cutting PRMMC using AWJ

Material (tw=3 mm) Feed ratev Max/min kerf width Deviation from right Surface roughness[mm/min] wk [mm] anglea [°] Ra [µm]

AA2618/SiC/20p 250 1.98/1.12 28°049 4.51AA2618/SiC/20p 350 1.92/1.1 28°339 4.81AA2618/SiC/20p 450 1.94/1 28°039 5.98

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using a Mitutoyo toolmakers microscope. The surface finish of the machined holes was measuredusing a Hommel T1000 stylus type instrument set to a cut-off length of 0.8 mm and a tracinglength of 4.8 mm. The microstructure of the material was investigated using a BX60 Olympusoptical microscope and a 440 Stereo Scan Electron Microscope with which the EDS–XR (energydisperse spectroscopy-X-ray) analysis was also performed. The topography of the samples wereinvestigated using a ZYGO Newview 100 white light interferometer.

3. Results and discussion

3.1. Electro Discharge Machining (EDM)

The results obtained indicate that Al/SiC PRMMC’s can be machined using EDM, despite thelow electrical conductivity and the high thermal resistance of the SiC particles. The EDM processis however slow and the material removal rate does not exceed the value ofVw=35 cm3/min underthe conditions used [14]. The material removal rate increases with increasing discharge currentand increased pulse duration up to an optimal value and thereafter decreases for any pulse on-time greater than this value [14]. It has also been shown that the material removal rate decreaseswith increased SiC ceramic contents. This can be explained by a number of factors. Firstly, theelectrical conductivity of the aluminium matrix decreases due to the presence of the ceramicreinforcement. Furthermore, because of the low thermal conductivity, and the much higher thermalresistance of the SiC, the aluminium alloy between the ceramic particles is preferentially removed.It was observed that the SiC-particles were not melted during the machining process since theirfull size and sharp corners were still visible in the machining debris, Fig. 1, as well as in the re-cast layer (see later paragraph in this section). This appears to suggest that the removal of thecomposite material occurs through the process of melting and vaporising the matrix materialaround the ceramic particle and at some point the entire SiC-particle becomes detached. This“shielding” effect of the SiC ceramic is followed by a decreased removal rate with increased SiC

Fig. 1. Debris of EDM process: PRMMC containing SiC ceramic particles (back-scattered electron image).

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particle content [14]. The exposure of entire SiC particles during EDM when machining thePRMMC results in a tendency for arcing to occur. This arises under inadequate flushing conditionsduring which the removed ceramic particles trap sufficient molten aluminium droplets to form aconductive path between the electrodes, and this leads to abnormal arcing.

The machined surface of a material generated using EDM is composed of many microscopiccraters associated with the random spark discharge between the electrodes. Such an EDM topogra-phy is presented in Fig. 2, the crater structure with its high peaks adjacent to valleys of removedmaterial is clearly evident. The size of the craters produced on the workpiece surface dependsmainly upon the energy of the discharge.1 The change in surface finish, as a function of machiningcurrent and pulse on-time, is illustrated in Fig. 3. It can be seen that the surface roughness valuesvary betweenRa=1.5 µm andRa=7.5 µm. It is evident that with increasing current, the surfaceroughness value increases. Higher current results in a higher thermal loading on both the cathodeand anode, followed by a higher amount of material being ejected. This results in a larger cratersize and thus the surface finish becomes rougher. Furthermore, it is evident that machining withlonger pulse duration also brings about an increase in surface roughness. Longer pulse durationresults in a larger removal per discharge. The crater size therefore increases and consequently thesurface roughness value increases. These results do not follow the findings of Hung et al. [9],who maintained that the current alone dominates the surface finish.

It can be seen from Fig. 3 that surfaces obtained for the non-reinforced matrix material (A356aluminium alloy) are rougher than those observed for the composite materials machined underthe same conditions. As mentioned previously, the present investigations indicate that the SiC-particles seem to shield and protect the aluminium matrix from being removed. It is suggestedthat this results in less material becoming superheated or molten during the discharge phase.Furthermore, the SiC particles were not melted during the machining process. The molten materialis therefore more viscous, which results in a decrease in removal efficiency.2 Consequently, whilstmachining the composite, less material is removed and a smaller crater is produced. In contrast,due to the absence of the SiC particles in the non-reinforced material, the EDM process is able

Fig. 2. Crater topography of EDMed PRMMC (workpiece mat: A356/SiC/35p;ie=6A; tc=300 µs; Ra=5.3 µm).

1 Discharge energy is determined by the gap voltage during discharge, the discharge current and the pulse on-time [10].2 Removal efficiency may be defined as the ratio of material removed per pulse to the volume of molten material during the dis-

charge.

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Fig. 3. Surface roughness when EDM PRMMC’s and non-reinforced aluminium.

to concentrate the energy of a spark on the aluminium alone and therefore produce a larger crater,resulting in a higher surface roughness value.

During EDM an extremely high temperature is produced at those areas where the plasma chan-nel strikes the electrodes. However, as a result of the high-pressure field around the dischargechannel, the main removal process takes place after the interruption of the discharge. Sub-sequently, not all the material melted during the discharge phase is removed. The remainingmolten material will resolidify by quenching at an extremely high rate due to the flushing by thedielectric, and hence a layer of re-cast material is formed [3].

Fig. 4 shows the re-cast layer of the AA2618/SiC/20p composite material. One of the featuresof this re-cast layer are the voids formed due to imperfect joining of the molten aluminiumdroplets. As can be seen from Fig. 4 the effects of gas bubbles are also obvious in the re-castlayer, where they produce a kind of porosity. This porosity is a consequence of the gas/vapour,resulting from the extremely high temperature, which is trapped during the rapid re-solidification.Furthermore it was observed that the SiC-particles were not melted during the machining process,as mentioned previously. This was also observed by Le Roux et al. [12] and Hung et al. [9].From Fig. 4 it can also be seen that the rapid cooling rate results in a change in the microstructureof the matrix material. It is evident, that the white spots found in the non-affected bulk materialdisappear within the re-cast layer. Fig. 5 shows the silicon, aluminium, copper, magnesium, ironand nickel content maps of Fig. 4 (EDS–XR — analysis). The content maps indicate that thewhite spots shown in the electron microscope image contain higher percentages of copper, ironand nickel, compared to the other areas within the matrix. Since these white spots disappear inthe matrix material within the re-cast layer it can be assumed that the iron, nickel and copperdiffuse into the aluminium, resulting in a homogenised alloy structure due to melting and fast re-solidification of the material. Furthermore, silicon was also found in the matrix material within

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Fig. 4. Microstructure of re-cast layer of a SiC particle reinforced aluminium matrix composite (AA2618/SiC/20p).

Fig. 5. Silicon, aluminium, copper, magnesium, iron and nickel content maps of section shown in Fig. 4/darker areasindicate a high content of the particular element.

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the re-cast layer (arrow in the Si contents map). This indicates that some silicon diffused fromthe SiC-particles into the matrix alloy (shown in more detail by Mu¨ller [15]). The thickness ofthe re-cast layer increases with increased discharge current and longer pulse on-times [14].

By contrast EDM of a non-reinforced aluminium alloy produces no significant re-cast layer.This confirms the fact that reinforcing with ceramic particles brings about a decrease in removalefficiency. As explained earlier, the SiC-particles were not melted during the machining process.The melt of the composite material is therefore much more viscous. As a result, only a smallamount of the material which was melted or superheated during the discharge is expelled withthe interruption of the discharge. This results in a comparatively thick re-cast layer on the com-posite, compared to that obtained whilst machining the non-reinforced aluminium alloy.

3.2. Laser cutting

To date MMC has been used in the production of relatively thick components but more recentlyattempts have been made to use this material in thin sheet form [7]. Conventional cutting usingdiamond tools is costly and/or technically difficult. Since Wire-EDM is slow, laser cutting isconsidered as a possible alternative. However, the surface quality of a laser made cut is usuallyrelatively poor. The availability of information on the surface quality after laser machining isimportant since this knowledge makes it possible to decide if secondary machining is necessarywhen laser machined samples are to be used for particular application.

The surface roughness is one of the most important quality indices of a laser cut surface andis related to the appearance of the typical surface striations. These striations occur as a result ofthe intermittent flow of the molten material during cutting. A number of different factors areresponsible for the existence of these striations. However, side way burning seems to be themain reason for the formation of the striation, however with changing cutting conditions differentmechanism are predominant [4]. Figs. 6 and 7 show the topography of the cut surfaces obtainedusing a white light interferometer as well as an electron microscope. The following remarks canbe made in connection with the observed surface roughness valueRa in Table 1. By decreasingthe cutting feed rate a smoother surface is obtained. With a higher feed rate laser cutting tends

Fig. 6. Striation pattern on Laser cut surface (workpiece mat: AA2618/SiC/20p; PRC CO2 Laser;PL=1.6 kW; v=600mm/min; Ra=6.6 µm).

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Fig. 7. Surface topography on cut PRMMC (Trumpf CO2 Laser; PL=1.1 kW; v=3000 mm/min; workpiece mat:AA2618/SiC/20p).

to be intermittent, which results in a rougher surface, also found by Lau et al. [11]. A smoothersurface can also be obtained by machining at a higher output power.

Fig. 8 shows the topography of the cut surface of the non-reinforced Al alloy matrix. It wasobserved that the surface at the entrance of the laser is relatively smooth (averageRa=3.5 µm),but at approximately 2/5 of the height of the cut the surface roughness is increased noticeably(averageRa=8.98 µm). Due to the nature of the process it is suggested that the upper part of thekerf3 is cut by vaporising the aluminium alloy producing a smooth surface. However, in the lowersection of the plate thickness the material is melted by the laser and swept downwards by thenitrogen jet (fusion cutting). In contrast when machining the PRMMC the SiC particles hinderthe vaporising process of the material, therefore the main removal occurs by fusion cutting (meltand blow). The smoother striation surface obtained on the PRMMC can be attributed to the moreviscous melt, which hinders the striation formation (critical droplet size [16]).

The poor surface quality is also due to the damage produced by the excessive heating of thesub-surface layer of the material. Fig. 9 shows an electron microscope image (back scattered) ofthe heat-affected sub-surface layers observed following machining of the PRMMC. It is evident

3 Kerf might be defined as the slot produced by the laser.

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Fig. 8. Surface topography on cut aluminium alloy (PRC CO2 Laser; PL=2 kW; v=600 mm/min; workpiece mat:AA2618).

from Fig. 9 that the microstructure of the matrix material is changed by the heat generated bythe machining process. It can be seen that the matrix material shows white lines in its structurewhich are more prominent in Fig. 10. An extensive X-ray (energy dispersive spectroscopy X-ray/EDS XR) analysis was undertaken and Fig. 11 shows the aluminium, silicon, copper and zinccontent and their locations within the thermally affected sub-surface layer. The results shown inFigs. 10 and 11 indicate that the heat generated during laser machining results in the depositionof copper and zinc along the aluminium grain boundaries. It can be seen from Table 1 that thethickness of this deposition layer decreases with increased feed rate.

Beside the rough surface the resulting cut also shows a burr and the so-called dross attachmentat the bottom of the cut surface is also evident in Fig. 7. It can be seen from Table 1 that theaverage dross height decreases with increased feed rate. These results confirm that the dross heightand the extent of the thermal damage are directly proportional to each other: minimising oneresults in minimising the other [1]. No dissolving of SiC particles was observed under thesemachining conditions, such dissolving was observed when blind hole drilling PRMMC [15]. Thisis a result of the less efficient removal of the molten material when blind hole drilling is comparedto the cutting process where the melt can be more easily blown out of the cutting kerf.

One of the advantages of laser cutting is the narrow width of the cut opening, called kerf width.As can be seen in Table 1 the kerf width varies betweenwk=0.25 mm andwk=0.37 mm. The cut

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Fig. 9. Sub-surface layer of PRMMC after Laser cutting (workpiece mat: AA2618/SiC/20p; PRC CO2 Laser;PL=2kW; v=600 mm/min).

obtained was nearly parallel sided, Table 1, with high laser power and lower feed rate resultingin a wider underside of the cut, probably due to side burning [16].

3.3. Abrasive Water Jet (AWJ)

Machining with an Abrasive Water Jet (AWJ) has many advantages compared to other machin-ing technologies. In comparison to thermal machining processes (laser, EDM) AWJ does notinduce high temperatures and as a consequence there is no thermally affected zone. Furthermoresince high feed rates are possible AWJ can be considered to be a very efficient machining process.

The surface quality of the AWJ cut is characterised by a rough surface as presented in Table2. This is one of the drawbacks of this machining process, a smoother surface can be obtainedwith lower feed rates [6]. Figs. 12 and 13 show the surface topography of the cut surface, obtainedusing a white light interferometer and an electron microscope. Since the thickness of the cutcomposite is relatively small (tw=3 mm), no striation pattern was apparent on the cut surface. Theformation of striation is presumed to be as a result of a cutting lag and step removal [8] and isgenerally present when machining thicker material. The absence of striations also indicates thatthe removal process occurs mainly by cutting the material and deformation wear is negligible.The ductile shearing of the aluminium is evident from the abrasive scooping and ploughing path

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Fig. 10. Microstructure of deposition layer, Fig. 9 (workpiece mat: AA2618/SiC/20p; PRC CO2 Laser,PL=2 kW;v=600 mm/min).

Fig. 11. Aluminium, silicon, zinc and copper contents maps of Fig. 10 (EDS–XR analysis).

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Fig. 12. Surface topography of AWJ cut surface (water Pressure=300 MPa; 80mesh garnet;v=450 mm/min; workpiecemat: AA2618/SiC/20p).

Fig. 13. Surface topography of an AA2618/SiC/20p PRMMC after cutting using AWJ (water pressure=300 MPa;80mesh garnet;v=450 mm/min).

(micro-cutting) of the garnet, Fig. 12. The SiC particles are probably pulled out by the muchbigger garnet particles (80-mesh refers to an approximate particle diameter of 190µm). One ofthe major advantages of the AWJ process is the absence of any thermal damage to the surface[15]. Furthermore no burr attachment was observed. The top edge of the cut surface is howevercharacterised by a radius as well as slotted edge damage, as shown in Fig. 14.

As can be seen in Table 2 the kerf is characterised by a larger width (average kerf width around

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Fig. 14. Slotted edge damage after machining a PRMMC using AWJ.

wk=1.5 mm) than that obtained when using the laser process. Furthermore, Table 2 shows thatthe kerf width of the bottom of the cut surface was less than that at the top, as indicated by thenegative sign of the deviation of the right angle. A possible reason for this effect is the loss ofpenetration velocity with increasing penetration depth [5,6]. A relatively straight kerf can howeverbe obtained with lower feed rates. Hamatani et al. [6] obtained a straight kerf for similar machiningconditions but with a feed rate ofv=75 mm/min.

4. Conclusion

The results obtained indicate that Al/SiC PRMMC can be machined using non-conventionalmachining processes such as EDM, laser and AWJ. However the different removal mechanismsresult in different surface qualities and the following conclusion can be drawn from the results:

O The EDM process is suitable for machining PRMMC’s, however, the process is very slow.EDM results in a crater-like surface, the size of the crates increases with increased dischargeenergy. EDM produces a relatively small amount of sub-surface damage on the cut surfaces(depending on the chosen machining settings).

O Laser machining offers significant productivity advantages for rough cut-off applications. It isapparent that a laser is very suitable for high feed rates (up tov=3000 mm/min) and can producea cut with a narrow kerf width (wk#0.4 mm). Reinforcing the aluminium matrix with SiC

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ceramic particles improves the machinability of the composite, due to the reduction in theoptical reflectively of the material. However quality of the laser cut surface is relatively poor.Striation patterns on the cut surface and burrs at the exit of the laser (dross attachment) wereobserved. Significant thermal induced microstructural changes were also observed within thePRMMC.

O As in the case of the laser machining process, AWJ is very suitable for rough cut applications(feed rates up tov=450 mm/min), but with the difference that AWJ cutting did not result inany thermal damage within the composite. No burr attachment was observed, however, thesurface was relatively rough and slotted-edge damage was observed on the top of the cut sur-face.

Acknowledgements

The authors would like to thank Materials Ireland Materials Processing Research Centre atTrinity College Dublin for financial and technical support. The authors also would like to thankAxel Demmer from IPT Aachen, Germany, and the EREDIS society, France, for their contributionto this research project.

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