Abrasive Waterjet Machining of Polymer Matrix Composites Cutting Performance, Erosive Process and Predictive Models

Transcription

1 Int J Adv Manuf Technol (1999) 15: Springer-Verlag London Limited Abrasive Waterjet Machining of Polymer Matrix Composites Cutting Performance, Erosive Process and Predictive Models J. Wang School of Mechanical, Manufacturing and Medical Engineering, Queensland University of Technology, Brisbane, Queensland, Australia An investigation of the cutting performance and erosive process in abrasive waterjet (AWJ) machining of polymer matrix composites is presented. It shows that AWJ cutting can produce good quality kerf at high production rates if the cutting parameters are properly selected. Plausible trends of the cutting performance are discussed, as assessed by the various kerf geometry and quality measures, with respect to process parameters. The traverse speed, water pressure and abrasive flowrate are found to have a profound effect on the total depth of cut and kerf taper angle, while the first two variables also have a large effect on the kerf width. The study shows that the optimum jet forward impact angle in the cutting plane is about 80 which increases the total depth of cut only marginally, and has little effect on the other kerf characteristics. It is found that good quality kerf without delamination can be achieved if through cut is attained. A scanning electron microscopy (SEM) analysis of the cut surfaces reveals that the erosive process for the matrix material (resin) involves shearing and ploughing as well as intergranular cracking. Shearing or cutting is found to be the dominant process for cutting the fibres in the upper cutting region, but the fibres are mostly pulled out in the lower region. Mathematical models for the total depth of cut are finally developed and verified, together with empirical models for the other kerf geometrical features. Keywords: Abrasive waterjet; Cutting of composite materials; Cutting performance; Kerf characteristics; Waterjet cutting mechanism; Waterjet modelling 1. Introduction Polymer matrix composites are being used increasingly in various applications owing to their superior physical and mechanical properties. It should be realised, however, that the processing of polymer matrix composites relies primarily on Correspondence and offprint requests to: Dr J. Wang, School of Mechanical, Manufacturing and Medical Engineering, Queensland University of Technology, GPO Box 2434, Brisbane, Queensland 4001, Australia. j.wang@qut.edu.au the traditional band saw cutting. This process is associated with low quality cut, low productivity and inflexibility in the cut geometry. A study [1] to apply laser cutting technology to polymer matrix composites has shown that the cut quality is extremely poor with excessive burr formation, large dimensional errors, a large heat-affected-zone, and severe thermal damage to the cutting front. By contrast, the unique cold abrasive waterjet (AWJ) cutting technology has the distinct advantages of no thermal distortion, high machining versatility, high flexibility and small cutting forces [2] and offers the potential for the processing of polymer matrix composite materials. This paper presents a study of the cutting performance and erosive mechanisms in abrasive waterjet machining of polymer matrix composites. Based on an experimental investigation, the cutting performance as assessed by the kerf profile and geometry as well as by the quality of the machined surfaces with respect to the process parameters, are discussed. A scanning electron microscopy (SEM) analysis is then carried out to study the cutting process and cutting mechanisms. Predictive models for the depth of cut are finally developed, and verified by comparing the predicted values with the corresponding experimental results. Empirical equation for the other performance measures are also developed for process control and optimisation. For the purposes of this study, some background and a brief review of the previous investigations are considered first. 2. Background and Review of Previous Work AWJ cutting technology uses a jet of high pressure and velocity water and abrasive slurry to cut the target material by means of erosion. In early investigations, it has been found [3,4] that three cutting zones exist in the processing of ductile and brittle materials with abrasive waterjets, i.e. the cutting zone at shallow angles of attack, the cutting zone at large angles of attack, and the jet upward deflection zone. The attack angle is defined as the angle between the initial jet direction and the particle cutting direction at the point of attack. Based on the proposal by Bitter [5] and Finnie [6] for particle erosion of materials,

2 758 J. Wang Hashish [3] claimed that the cutting mechanisms in the first two zones could be considered as cutting wear and deformation wear, respectively. It is proposed that the cutting wear mode is characterised by ploughing and cutting deformation by which the ploughing process occurs at large negative rake angles on the abrasive particles, whereas cutting deformation occurs when the particles cut the material at positive rake angles. Although the cutting wear process is similar to that in the conventional grinding process, it is very difficult to describe since the particles may have linear velocity as well as angular velocity. The surface generated by cutting wear is generally of a good finish which can be assessed by a surface roughness measure. In the steady cutting stage, the particles will change the attack angle between the initial jet and cutting directions from shallow to large, and have a reduced kinetic energy. Under this condition, material is removed by the cutting wear as well as by the deformation wear processes where the particles push the material into a plastic state until it is removed. Chen et al. [4] show that as the jet penetrates further into the workpiece, deformation wear is the dominant cutting mechanism. This is associated with striations (or wavinesses) formed at the lower portion of the cut surface, although the response mechanism has not been fully investigated. In the jet upward deflection zone, the cutting process is considered as being controlled by erosive wear at large particle attack angles. This process is associated with jet upward deflection which increases the local rate of change of momentum. This zone is responsible for the raggedness of the cut at the bottom of the kerf and occurs only when the material is thick enough to prevent complete penetration. The kerf geometry of a through cut generated by abrasive waterjets may be described as in Fig. 1. It is characterised by a small rounded corner at the top edge owing to the plastic deformation of material caused by jet bombardment. The kerf is wider at the top than at the bottom so that a taper is produced. In addition, the plastically deformed material rolls over at the bottom of the kerf forming burrs at the jet exit side when cutting ductile materials. Hashish and du Plessis [7] have proposed a model for jet spreading profile and strength zones, as shown in Fig. 2. Hashish [8] later used this model to explain the kerf characteristics in abrasive waterjet cutting. These authors, as well as Chen et al. [9], believed that the particle velocity at any cross-section of the jet should vary from zero at the nozzle wall to a maximum at the jet centre. This velocity distribution corresponds to an energy or strength distribution in the jet. The Fig. 2. Relative strength zones in a waterjet. inner contoured regions of the jet, as shown in Fig. 2, that have higher velocities and are convergent, can result in tapered cuts on the material. The kerf width is dependent on the effective width (or diameter) of the jet, which in turn depends on the jet strength in that zone and the target material. It is noted that the study of cutting mechanisms for AWJ cutting of ductile and brittle materials has been comprehensive. In addition, a considerable amount of work has been carried out in the modelling studies for AWJ cutting of these types of materials [3,4,10], although most of these studies use a semi-empirical approach in which the constants are determined from the cutting tests. Studies have also been reported on enhancing the AWJ performances using various techniques, such as nozzle oscillation [11] and improving machine capability [12]. It is interesting to note, however, that the work on AWJ cutting has been primarily directed towards hard or difficult-to-cut materials with little attention paid to the machining of soft materials [13 18], such as polymer matrix composites. It appears that more work is required to study the cutting performance and cutting mechanisms of the soft materials under abrasive watejet as well as to develop mathematical models for the prediction of the cutting performance in process planning. 3. Experimental Work An experiment was conducted on a Flow Systems International waterjet cutter to cut mm 2 test specimens of 16 mm and 20 mm thick. The waterjet cutter was equipped with a model 20X dual intensifier high output pump (up to 380 MPa) and a five-axis robot positioning system. The specimens were Bear Brand Phenolic Fabric Polymer Matrix Composites which are non-metallic laminated sheets made by impregnated layers of fibre (cotton) reinforcement with resin matrix. This material finds extensive application in various industries and its major mechanical and physical properties are given in Table 1. Table 1. Major properties of the test material. Fig. 1. Schematic and definition of kerf geometry. Impact strength 11 MPa Compressive strength (flatwise) 290 MPa Compressive strength (edgewise) 210 MPa Shear strength 100 MPa Maximum working temperature 130 C

3 Abrasive Waterjet Machining of Polymer Matrix Composites 759 It should be noted that AWJ cutting involves a large number of variables and virtually all these variables affect the cutting results. These include the design and dimensional sizes of the orifice, mixing tube and nozzle, the properties of the workpiece material, and the abrasive material and particle size, the abrasive mass flowrate, the jet velocity or water pressure, the traverse or feed speed, the jet impact angle, and the stand-off distance. To allow for all these variables implies an unmanageable amount of work. Therefore, only the major and easy-toadjust dynamic variables were considered in the present study. These were the water pressure, the nozzle traverse speed, the abrasive flowrate and the jet forward impact angle. Two sets of tests were conducted. In the first set, four levels of each of the first three variables were considered at a 90 jet impact angle on the 16 mm specimens. The water pressures were selected within the common ranges of application and the equipment limit, i.e. at 230, 280, 330 and 380 MPa. The traverse speeds tested were 400, 1000, 1600, and 2000 mm min 1 and the abrasive flow rates were 0.1, 0.2, 0.3, and 0.4 kg min 1. For these tests, a 4 mm stand-off distance between the nozzle and the workpiece was used. It should be noted that the selection of the stand-off distance was to prevent contact between the nozzle and the specimen as delamination may occur, although a smaller stand-off distance was found to be preferred [13]. Consequently, 64 tests were conducted for straight cuts of 60 mm long in the first set of tests. The second set of tests was intended to study the effect of jet forward impact angle on the cutting performance. For this purpose, five levels of jet angles at 50, 60, 70, 80, and 90 were tested at three levels of water pressures (280, 330, and 380 MPa), three levels of traverse speeds (1000, 1600, and 2000 mm min 1 ) and a single level of stand-off distance (4 mm). Since the machine was reconfigured for hard material processing after the first set of tests and could not be changed at the time of the experiment owing to technical and commercial reasons, the abrasive flowrate could not be selected to be consistent with the first set. Therefore, an abrasive flowrate of 0.6 kg min 1 was selected, and 20 mm thick specimens were used. Thus, a further 45 tests were carried out and the results were processed separately to examine the effect of the jet impact angles. For all the tests, the other parameters were kept constant using the system standard configuration, i.e. the orifice diameter = 0.33 mm, the mixing tube diameter = 1.27 mm, the length of mixing tube = 88.9 mm, the nozzle diameter = 1.02 mm and the nozzle length = 76.2 mm. The abrasive used was 80 mesh almandite garnet sand. It should be noted that the nozzle was made from tungsten carbide whose chemical composition remains commercially confidential. This nozzle material and the design provide very good wear resistance. With 80 mesh almandite garnet sand as abrasives and the normal production condition, its life is in excess of 30 hours of actual cutting time if the jet is focused properly. During the course of the experiments, care was taken to ensure that the wear of the nozzle did not have a large effect on the cutting performance. Frequent checks were made of the wear, and when it became significant, the nozzle was replaced. 4. Cutting Performance and Analysis A number of measures can be used to assess the cutting performance in abrasive waterjet cutting. As material removal rate (MRR) is not a major concern in the present work and the nozzle wear is beyond the scope of this study, the cutting performance is assessed by the various kerf characteristic measures, i.e. kerf profile and geometry and the quality of the machined surfaces. 4.1 Kerf Profile for Through and Non-through Cuts An observation of the cuts has revealed that there are two types of kerf produced within the range of the parameters used in the present study, namely through cuts and non-through cuts, as shown in Fig. 3. When the jet was provided with sufficient energy (e.g. at high water pressure and slow traverse speed), a through cut was formed where the kerf is characterised by a wider entry and then a gradual reduction towards the exit so that a taper is generated. Taper angle, as shown in Fig. 1, can be used as a measure of the kerf width variation. The experimental results show that the taper angle increases as the traverse speed increases, but the reverse is seen with increases in the water pressure and abrasive flowrate. When the jet was unable to penetrate the specimen, a nonthrough cut was formed. In this case, the geometry of the kerf resembles that of a through cut in the upper cutting region, but a later cut at the bottom causes the kerf to widen forming an enlarged pocket with an irregular shape. This is attributed to the reduced jet stability and effectiveness, jet side deflection and the particles rebounding from the bottom of the kerf. It is found that the traverse speed has a strong effect on the pocket formation, as a lower traverse speed permits a longer interaction time between the abrasive particles and the work material, resulting in a larger pocket. The effect was found to be more pronounced when a lower traverse speed was used in combination with a higher water pressure and abrasive flowrate. At a higher traverse speed and a lower abrasive flow rate, non-through cuts show very little widening at the bottom owing to less particle interaction. An analysis of the effect of the process variables on the depth of cut (or penetration) has shown that the total depth of cut increases almost linearly with the water pressure but the rate of increase declines above certain pressure setting. Particle fragmentation at high pressure is believed to be the main reason for this decline. The total depth of cut also increases with an increase in the abrasive flowrate but with a decrease in the traverse speed. This is because changes in these two settings caused changes in the density of particles impacting on the material, which affects the depth of cut. However, the experimental results show that the depth of cut does not increase linearly with the abrasive flowrate but increases at a reduced rate. This is attributed to the fact that increasing abrasive flowrate increases interference between the particles and, hence, reduces the cutting efficiency of individual particles. The relationship between the depth of cut and traverse speed is rather complex. A faster traverse speed allows less

4 760 J. Wang Fig. 3. Kerf profile for through and non-through cuts. (a) Through cut. P w = 380 MPa, M a = 0.4 kg min 1, U = 1000 mm min 1 (left), U = 400 mm min 1 (right). (b) Non-through cut. P w = 280 MPa, M a = 0.1 kg min 1, U = 2200 mm min 1 (left), U = 1600 mm min 1 (right). overlapping cutting action and fewer particles to impinge on the material, resulting in reduced depth of cut. Hashish [3] pointed out that the cutting mechanism is affected by the traverse speed, so that the depth of cut will not decrease linearly with the cutting speed. The current study has found that the rate of decrease of the depth of cut decreases with an increase in the traverse speed. In general, the entrance kerf edges were relatively smooth with a parallel opening, as shown in Fig. 4(a). For through cuts, the jagged kerf edge at the jet exit side may be formed dependent on the selected cutting conditions. A sample of such a case is given in Fig. 4(b). The jagged edge at the bottom appears to be a manifestation of decreasing jet energy as the jet cuts into the material. However, relatively good exit kerf edges can be achieved, as shown in Fig. 4(c), by properly Fig. 4. Entrance and exit kerf characteristics for through cuts. (a) Entrance kerf, P w = 330 MPa, U = 1000 mm min 1, M a = 0.2 kg min 1. (b) exit kerf. P w = 330 MPa, U = 1000 mm min 1, M a = 0.2 kg min 1. (c) Exit kerf. P w = 380 MPa, U = 400 mm min 1, M a = 0.4 kg min 1. selecting the cutting parameters, which are often high water pressure, slow traverse speed and high abrasive flowrate. The top kerf width shows an increasing trend with the water pressure initially, but then becomes flattened. This is due to the fact that an increase in the water pressure increases the effective jet width (Fig. 2) for the target material, which in turn increases the kerf width. When the whole jet width becomes effective at the location of initial jet material interaction (top kerf), a further increase in the water pressure will have little effect on the top kerf width. In addition, the kerf width is dependent on the abrasive flowrate and the traverse speed. At higher traverse speeds and lower abrasive flowrates, fewer particles will be available for erosion, opening a narrower slot. 4.2 Machined Surface Characteristics An AWJ machined surface generally consists of two regions depending on the energy level of the jet. The upper region is

5 Abrasive Waterjet Machining of Polymer Matrix Composites 761 Fig. 5. Machined surface characteristics. P w = 280 MPa, U = 1000 mm min 1, M a = 0.2 kg min 1. dominated by roughness and the lower region is characterised by a waviness component, although a clear transition between the two regions is difficult to discern, as shown in Fig. 5. When analysing the depth of the smooth region from the top edge to where clear striation marks can be seen, it is found that this depth is mainly affected by the traverse speed and abrasive flowrate. At a slower traverse speed and a higher abrasive flow rate, the density of particles impacting to the exposed material increases, extending the smooth depth by refinishing and smoothing the cut surfaces. An increase in the water pressure resulted in an increase in the smooth depth of cut, owing to the increase in the particle energy, but to a lesser extent compared to the above two variables. The trend of the surface roughness measured at a location of 2 mm from the top edge is found to be similar to that of the smooth depth of cut with respect to the three variables, i.e. it decreases with an increase in the water pressure and abrasive flowrate and a decrease in traverse speed. For all the cuts, the measured surface roughness (centre-line average R a ) ranges from 4 m to 13 m. It has been found that in the striation or waviness region, a peak on one side of the cutting wall corresponds to a valley on the other side. This follows the findings of Guo et al. [19] and can be explained as a result of jet oscillation in the plane normal to the cutting plane, although Arola and Ramulu [15] proposed that jet instability and fluctuation in abrasive distribution at the bottom region could be the cause of striation formation. The present study has found that the amplitude of the striation increases as the depth of cut increases and can be minimised with a lower traverse speed, and higher water pressure and abrasive flowrate. integrity. This phenomenon is greatly dependent on the properties of the composite materials being processed, particularly the bonding strength between the layers, and the waterjet properties in the cutting front. Hashish [8] postulated that at a certain depth within a kerf, the abrasive waterjet deflects and will penetrate between the layers causing delamination when the jet pressure is sufficiently high. In a study on fibre reinforced plastics, Capello et al. [16] proposed that excessive loading on the material owing to factors such as workpiece vibration causes failure in bonding or delamination in the lower region of the cutting. Delamination was observed on some specimens in the present study, as shown in Fig. 6. It was found that some process variables significantly affect the occurrence of delamination and this undesired phenomenon can be avoided if the cutting parameters are properly selected. In particular, this study shows that delamination occurs only on specimens with non-through cuts. Furthermore, with the same setting of abrasive flowrate, traverse speed and jet angle, the possibility of delamination appears to be higher at higher water pressures, while nonthrough cuts at lower water pressures do not show any sign of delamination. Water pressure is a critical factor to be considered in avoiding this mechanical defect. In practice, water pressure has to be selected to be high enough to attain through cuts at a reasonably high traverse speed. This points to a need to develop predictive models for the depth of cut, which will be considered later in the paper. 4.3 Delamination Delamination is a failure in the bonding between layers in layered material processing. It is seen as a crack perpendicular to the grain of the materials and affects the overall workpiece Fig. 6. Delamination on non-through cut specimens. (a) P w = 280 MPa, U = 1600 mm min 1, M a = 0.3 kg min 1. (b) P w = 330 MPa, U = 2200 mm min 1, M a = 0.2 kg min 1.

6 762 J. Wang Although delamination was found at the end of some nonthrough cuts at high water pressures, in most cases it occurred where the jet was on the verge of cutting and close to the end of cut. This is probably because the jet does not have enough energy to delaminate the material when it is at the end of a cut. This finding is similar to that reported by Capello et al. [16]. Whereas no obvious relation can be established between the cutting parameters and delamination, the results again show that delamination can be avoided if clear through cuts are achieved by correctly selecting the cutting parameters. Table 2. The effect of water pressure and traverse speed on fibre burr formation. Water pressure Traverse speed (mm min 1 ) (mpa) Burr Formation Burr formation is a common problem in most cutting processes. Burrs affect part functionality and assemblability and have to be removed by deburring or finishing operations. Burr formation in cutting processes is generally related to the process conditions and the work material properties. Ductile materials tend to form burrs while brittle materials generally present no burrs. However, there is little understanding of what is involved in the processing of polymer matrix composites. The specimens used in the present study were fabricated by impregnating layers of fibrous material (i.e. cloth) with resin, and may not be classified as a ductile or brittle material. Yen and Kharan [20] suggest that the wear of polymer composites is cyclic in nature and that the wear starts with the polymer matrix material (resin) at the initial stage. The fibres are then exposed and finally fail owing to buckling or fracture at locations close to where the fibres are still supported by the resin. If the fibres do not fail completely, they remain on the materials as hairline burrs. An SEM analysis in the present study has revealed similar findings. Loose hairline burrs (fibres) were formed mostly at the bottom of the cutting front. It has been found that at higher water pressure, burrs are almost absent from the specimen so that a clear exit edge can be formed. At a lower pressure, however, burrs were clearly visible at the exit edge. Hairline burrs were also found on the specimens when the cutting was performed with a higher traverse speed. It may be deduced that burr formation is dependent on the jet energy level at the bottom region of the cut. For the range of abrasive flowrates used in this study, this parameter does not show any apparent effect on burr formation. In addition, some small fragments of the resin material were found at the exit edge on some of the specimens. These fragments cling loosely onto the exit edge and the fibre burrs and can be removed easily. Owing to the irregularity of the burrs formed, a quantitative assessment has been difficult. Table 2 summarises the qualitative trends of hairline burr formation in relation to the two major influencing parameters. It can be seen that no burrs were generally observed when a traverse speed of 400 mm min 1 or the water pressure of 380 MPa was used. When a higher traverse speed or lower water pressure was used, these two factors combined in affecting burr formation. The jet energy must be maintained above a threshold level if hairline burrfree cuts are desired. 4.5 Effect of Jet Impact Angle on the Kerf Characteristics It can be seen from Fig. 5 that as the abrasive particles cut into the workpiece, the direction of cutting changes. This reduces the component of energy for cutting the material. It is thus suggested that a jet forward impact angle (the angle between the nozzle direction and the material surface) in the cutting plane may be introduced to compensate for this drag angle so as to improve the cutting performance. In this study, the jet forward impact angle was varied from 50 to 90 (orthogonal cutting) in increments of 10 with a view to examining the effect of this angle on the kerf characteristics and suggesting the appropriate angle to be used for the material. Figure 7 shows the relationships between the five major kerf characteristic measures and the jet impact angle. It can be seen from Fig. 7(a) that the total depth of cut increases as the jet impact angle increases from 50 upward, but the rate of the increase reduces. It has also been found from the experimental results that a peak value of the depth of cut occurs at about 80 for most cases, which shows a marginal improvement as compared to a 90 jet impact angle. This is attributed to the distribution of the particle energy as the jet angle varies. Reducing the jet angle will reduce the tangential component of the particle velocity along the cutting wall in the top cutting region, nevertheless, this component is sufficient for the cutting action. The improved effectiveness of the jet angle used occurs in the lower cutting region where it compensates for the jet drag angle so that the tangential component of the particle energy is increased. This increase is particularly important when the jet energy is about the threshold value for cutting the material. As a result, the total jet penetration is increased. However, a further reduction in the jet impact angle will not only reduce the cutting effectiveness in the upper but also in the lower cutting region owing to over compensation. Therefore, an optimum jet impact angle exists, as shown in Fig. 7(a). It follows from the above analysis that the jet impact angle does not affect significantly the smooth depth of cut in the upper region within the range tested, as shown in Fig. 7(b). Figure 7(c) shows a small variation in the top kerf width with respect to the jet impact angle. However, this variation is only about 0.1 mm when the jet angle increases from 50 to 90 and, hence, the kerf width may be considered as independent of the jet angle. This trend may be anticipated since the kerf width is highly dependent on the properties of

7 Abrasive Waterjet Machining of Polymer Matrix Composites 763 Fig. 7. Effect of jet impact angle on kerf characteristics. M a = 0.6 kg min 1.(a) Total depth of cut vs. jet angle (U = 1600 mm min 1 ). (b) Depth of smooth cut vs. jet angle (U = 1000 mm min 1 ). (c) Kerf width vs. jet angle (U = 1600 mm min 1 ). (d) Kerf taper vs. jet angle (U = 1600 mm min 1 ). (e) Surface roughness vs. jet angle (U = 1600 mm min 1 ). the material and the jet structure (i.e. the effective diameter) [8,14]. A similar trend was also noted for kerf taper, as shown in Fig. 7(d). This is again because the jet structure or energy distribution determines the kerf width while the jet angle has little effect on it. By contrast, the jet angle shows a marked improvement (up to 50% reduction) in the surface roughness when it increases from 50 to 70, as shown in Fig. 7(e). This improvement vanishes as the jet angle is further increased to 90. This is consistent with the finding reported by Hashish [21] and is due to the fact that at a small jet angle, the reduction in the tangential component of particle energy results in a significant change in the cutting wear mode erosion, which increases the surface roughness. 4.6 Concluding Remarks on Cutting Performance The above analysis has shown that the kerf profile generated in polymer matrix composites by AWJ is similar to that in ductile and brittle materials reported in the literature. The kerf also exhibits similar characteristics for these materials. It is found that AWJ can produce good quality cuts although delamination may occur for some of the non-through cuts. If the cutting parameters can be selected so that the abrasive waterjet can penetrate the workpiece, kerfs with no delamination can be achieved. The development of the depth of cut models to select the parameters for through cut will be presented later in the paper. The above analysis also suggests that an optimum jet impact angle of about 80 exists, which marginally increases

8 764 J. Wang the total depth of cut while not significantly affecting the other kerf characteristic measures. 5. Morphology of the Machined Surfaces and Cutting Analysis An analysis of the cut surfaces and the cutting or erosive process was carried out on some selected and representative samples at 90 jet impact angle with the assistance of a JEOL JEM-35CF scanning electron microscope. These samples were selected to cover the various water pressures, traverse speeds and abrasive flowrates and include through and non-through cuts. Some selected SEM photomicrographs of the cut surfaces are given in Fig. 8. Figures 8(a) and (b) show the cut surfaces at 20 magnification. The cutting marks as well as the fibres and matrix (resin) are clearly visible, and the split ends of the fibres on the surface appear in a waved pattern. At the upper region (Fig. 8(a)), it appears that the fibres and the resin were removed with a small-scale plastic deformation. It can also be seen that the fibres were cut at somewhere slightly above the surface of the resin and there are a negligible number of loose burrs. Generally, the surfaces at this region are smooth and are of good quality. At a larger magnification (Fig. 8(c)), it appears that the resin was removed by shearing and ploughing actions together with fatigue pitting or cracking, the latter showing an increased trend from the upper to the lower region of the cutting front. The faint traces of the ploughing action, marked by ridges formed on the surface, are clearly visible. This suggests that resin plastic deformation is the dominant process in this region. In addition, some resin flakes and craters are also seen in the resin area. This is presumably due to intergranular cracking which usually occurs in brittle material erosion. The photographs also show that the fibres in the upper region were more evenly trimmed and less fibrillated than those in the lower region. When cutting further down in the lower region, it is apparent that some fibres were pulled out, rather than cut off, and some were not cut completely, leaving loose hairline burrs on the surface, as shown in Fig. 8(b). In addition, ploughing marks and striations become evident and the cutting direction (or particle trace) varied. In the lower region, pulling out is the primary process for removing the fibres, particularly for nonthrough cuts as shown in Fig. 8(f), and the fibres were broken somewhere inside the resin. The surface in this region is rougher than in the upper region. At 240 and 480 magnifications, as in Figs 8(d) and 8(e), it appears that intergranular cracking is increased on the resin area. This is attributed to the fact that the particles with reduced energy cannot cut the material effectively, but fracture it eventually. In addition, the resin area is not as smooth as the upper region with an increased number of pits and flakes as well as cracks, as evidenced in Fig. 8(e). Shearing and ploughing actions are still seen on the surfaces. Consequently, the cutting or erosion in the middle region involves plastic deformation which usually occurs in processing ductile materials, as well as involving the erosive process which is often seen when cutting brittle materials. It is also noticed that debonding between the fibre layers and resin matrix occurred on some of the samples where the particles pushed and deformed the fibres, as shown in Fig. 8(d). This phenomenon is partly dependent on the bonding strength between the two materials and the extent of the deformation of the fibres. Moreover, there are an increased number of particles embeded on the cut surface as the depth of cut increases. The photomicrographs for the surfaces of some non-through cuts show that in the lower region, both the resin and the fibres experienced massive destruction and were badly deformed. There are large and long deformation marks on the resin area. Delamination and loose burrs can be seen over the region, as shown in Fig. 8(f). The delamination appears as cracks across the interface of the resin and the fibre layers, while the loose burrs are a result of the incomplete cutting and pulling out of the fibres. The cutting process on the resin seems to be dominated by fracturing rather than shearing and ploughing. This is due to the reduced particle energy which is unable to shear, but the impact results in the resin fracturing. For the specimens with through cuts, the texture of the cut surfaces in the lower region is shown to be similar to that of non-through cuts, but a reduced extent of deformation with no considerable delamination was observed. Loose hairline burrs also exist in this region, and intergranular cracks as well as ploughing actions are found in the resin area, presumably because of the higher particle energy available. 6. Development of Predictive Models 6.1 Depth of Cut Model From the foregoing analysis, it is evident that mathematical models for predicting the depth of cut are required for process planning and to avoid delamination. However, the SEM analysis has shown that neither the erosive mechanism for ductile materials nor that for brittle materials apply for polymer matrix composites containing resin matrix and cotton fibres. Thus, it does not appear to be appropriate to use the erosive theory (i.e. the cutting wear and deformation wear models) [3] or the fracture mechanics-based approach [22] in developing the depth of cut model for polymer matrix composites. The assumption used in the present study is that the rate of material removed from the workpiece is proportional to the kinetic energy of the abrasive particles, i.e. dv dt = C dk e (1) dt where C is a proportionality factor to allow for the variation in material properties, and the other symbols are as defined in the nomenclature. The material removal rate can be calculated by multiplying the cross-sectional area of the cutting front by the jet traverse speed. By ignoring the variation of the kerf width along the depth, it can be given by dv dt = D t d j U (2)

9 Abrasive Waterjet Machining of Polymer Matrix Composites 765 Fig. 8. Photomicrographs of machined surfaces when jet angle is 90. (a) and (c) P w = 380 MPa, U = 400 mm min 1, M a = 0.4 kg min 1.(b) and (e) P w = 230 MPa, U = 400 mm min 1, M a = 0.1 kg min 1.(d) and (f) P w = 280 MPa, U = 1600 mm min 1, M a = 0.2 kg min 1.

10 766 J. Wang The rate of kinetic energy of the abrasive particles in the jet stream can be expressed as dk e =. m dt a V 2 a (3) Consequently, Eq. (1) becomes D t d j U =. Cm a V 2 a (4) or D t = Cm a 2d j U V2 a (5) The velocity of the particles V a is assumed to be equal to the velocity of the slurry and can be approximated by the momentum transfer equation considering the incoming waterjet and the exit slurry jet momentum: m w V j = k 1 (m w + m a )V a (6) where k 1 is a factor allowing for momentum transfer efficiency. Thus, the velocity of the slurry jet can be found to be m V a = k 1 w m w + m j (7) a V Solving equation (7) has resulted in a very complex V a equation, so an attempt has been made to simplify this equation. It is assumed that the mass of the abrasives is only a very small proportion of the mass of the abrasive slurry, so the ratio term in the bracket is approximately constant for a given water pressure and system configuration (i.e. the m a variation is ignored). Thus, V a = k 1 k 2 V j = k 3 V j (8) This assumption was found to result in an error of less than 4% for the range of process variables used in the experiment, and an even smaller error may be expected for the final depth of cut. By assuming that the water is incompressible and the frictional loss in the system is negligible, the velocity of the waterjet may be approximated by using Bernoulli s equation and is given by V j = (2P w / w ) 0.5 (9) Thus, substituting Eqs. (8) and (9) into equation (5) gives Cm D t = k 2 a 3 2d j U 2P w w (10) or D t = k m ap w (11) d j U w where k generalises all the constants in equation (10), and has been determined statistically from the experimental data to be Consequently, equation (11) can be rewritten as D t = m ap w (12) d j U w In order to check the adequacy of the depth of cut model, a comparison between the values predicted from the model Fig. 9. Percentage deviations of predicted and experimental depth of cut values. and those from the experiment has been carried out based on percentage deviation of the predicted value with respect to the corresponding experimental value, as shown in Fig. 9. This study has shown that while an acceptable average percentage deviation of 7.5% is achieved, the standard deviation is 30.09% which is considered to be high for an adequate estimation of the depth of cut. Thus, this model may be used for rough estimation, but a modification to the model is required in order to improve the model s predictive capability. A detailed analysis of the experimental data has indicated that the effect of traverse speed on the depth of cut is not quite hyperbolic as in equation (11). It is proposed that this phenomenon is a result of the effect of traverse speed on the energy loss as the jet flows through the kerf and an exponential term may be used to reflect this effect [23]. Thus, an exponent ( 1 ) is introduced in the traverse speed in the equation. In addition, the experimental data show that the relationship between the abrasive mass flowrate and the depth of cut cannot be best represented by a linear equation. This is because the cutting efficiency of individual particles will decrease with an increase in the abrasive mass flowrate owing to the increased interference between the particles. Therefore, the term m a in equation (11) was modified to include an exponent ( 2 ). Consequently, equation (11) becomes P w D t = k m 1 a (13) d j U 2 w The constants, k, 1, and 2 in the equation were determined by the regression technique which yielded the following model for the total depth of cut: P w D t = m0.407 a (14) d j U w A comparison study was again carried out, and the results are shown in Fig. 10. It can be seen from the histogram that the modified model yields an average deviation of 0.3% with the standard deviation of 8.17%. A statistical analysis has also confirmed the predictive capability of the model with a coefficient of determination (R 2 ) of Consequently, this model

11 Abrasive Waterjet Machining of Polymer Matrix Composites 767 T a = U 0.507m a (6.701E-06)P 2 w (16) 0.240U 2 (2.221)m a U 3. Surface roughness R a (at 2 mm from the top edge): R a = P w U m a (17) 0.702U m 2 a 4 Depth of smooth cutting region: D s = m a U 2 (18) + (4.259E 05)P 2 w (0.011)P w U (6.521)m a U Fig. 10. Percentage deviations of the modified model prediction from experimental depth of cut values. can be used for adequate prediction of the depth of cut in process planning for the ranges of parameters used in this study for a 90 jet impact angle. 6.2 Empirical Models for Kerf Characteristics If the kerf width and kerf taper can be predicted, they may be compensated for in the design and process planning stages and also by controlling the nozzle side angle in the machine. Likewise, knowing the surface roughness and the smooth depth of cut prior to cutting will enhance the likelihood of accomplishing the required smooth region at the required surface finish. For these purposes, a regression analysis has been carried out to establish empirical models relating these kerf characteristics to the process variables when cutting at a 90 jet angle. The regression procedure was carried out using an SPSS package. Five different possible models were tested for each of the four quantities at a confidence interval of 95%. They were straight-line model, exponential model, power model, logarithmic model and quadratic model. Examining the coefficients of determination (R 2 ) showed that the quadratic model gave the highest R 2 values of 80%, 94%, 93%, and 95% for the top kerf width, kerf taper, surface roughness R a, and the depth of smooth cutting zone, respectively. Thus, a further analysis was made on the quadratic models with interactions. For a three-factor experiment, nine estimated parameters are needed to fit a quadratic model. However, not all of the nine variables will be significant for predicting the process outcome. Therefore, the backward elimination procedure available in the SPSS package was used and the final simplified models for the top kerf width, kerf taper, surface roughness R a and the depth of smooth cutting zone were obtained and are given as follows: 1. Top kerf width: W T = P w 0.092U m a (15) (1.155E-05)P 2 w 2. Kerf taper angle: These equations are applicable for the test conditions and the ranges of variables specified in Section 3 for a 90 jet angle. The R 2 values for the four simplified equations are respectively 80%, 94%, 93%, and 93%. F-tests have been conducted and showed strong evidence of the utility of the models. Similarly, t-tests have indicated that there is strong evidence of linear relationships between the response variables (top kerf width, kerf taper, surface roughness, and smooth depth) and all the individual explanatory parameters in the final equations. In addition, comparisons between the predicted and experimental results have shown that the empirical models correlate very well with the experimental data. Consequently, the established empirical equations can be used in process control and optimisation. 7. Conclusions A study of AWJ cutting of polymer matrix composites has been presented. It has been shown that AWJ cutting is an effective technology for polymer matrix composite processing with good quality kerf and production rates. The kerf produced on polymer matrix composites exhibits similar trends and characteristics to those on ductile and brittle materials, such as steels and ceramics. The SEM analysis of the machined surface has shown that the cutting of the resin matrix involves shearing and ploughing as well as intergranular cracking processes, the former two being dominant in the upper region whereas the latter is the main cutting process in the lower region. It has been found that in the upper region, the fibres are removed by shearing or cutting at somewhere slightly above the resin surface. In the lower cutting region, some fibres are pulled out leaving hairline burrs on the cut surface. The optimum jet forward impact angle has been found to be about 80 which improves the total depth of cut marginally and has little effect on the other kerf characteristics. The study has also shown that delamination defects may occur for some of the non-through cuts so that a depth of cut predictive model for through cuts to avoid delamination is required. A mathematical model for the total depth of cut has been developed using the energy approach. While this model can provide an estimation for the total depth of cut, it has been modified to arrive at a new model in order to provide adequate predictions. Numerical studies have verified the predictive capability of the models. The depth of cut models together with the empirical models established for the other kerf characteristics provide a means for process control and optimisation.

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