Effect of impact angle and velocity in crater circularity in abrasive water jet machining by means of multi-particle impact simulation

Transcription

1 34 Int. J. Machining and Machinability of Materials, Vol. 10, Nos. 1/2, 2011 Effect of impact angle and velocity in crater circularity in abrasive water jet machining by means of multi-particle impact simulation Kyriaki Maniadaki Technological Educational Institute (TEI) of Crete, Romanou 3, Halepa, Chania, Greece Fax: Aristomenis Antoniadis* and Nicholas Bilalis Computer Aided Design Lab, Building D4 009, Department of Production Engineering and Management, Technical University of Crete, Kounoupidiana, Chania, Greece Fax: *Corresponding author Abstract: The present study focuses on the erosion mechanism observed during abrasive water jet (AWJ) machining. An ANSYS/LS-Dyna 3D software-based finite element (FE) model is developed for the representation of the erosion process in a 3D configuration. The proposed FE model s solution, which accounts for the effect of multiple particle impacts on a workpiece made of stainless steel (AISI 304), is obtained using a 16-node cluster system. The influence of impact angle and particle velocity is currently studied, while the material s crater circularity is also evaluated. The results of the present study are found to be in very good agreement with their experimental counterparts. Keywords: AWJ cutting; abrasive; crater; circularity. Reference to this paper should be made as follows: Maniadaki, K., Antoniadis, A. and Bilalis, N. (2011) Effect of impact angle and velocity in crater circularity in abrasive water jet machining by means of multi-particle impact simulation, Int. J. Machining and Machinability of Materials, Vol. 10, Nos. 1/2, pp Biographical notes: Kyriaki Maniadaki is a PhD candidate in Production Engineering and Management Department, Technical University of Crete, since She obtained a degree in Physics from the Department of Physics, University of Crete, (Heraklion-1999) and MSc in Atomic and Molecular Physics (Laser), also from the Department of Physics, University of Crete, (Heraklion-2002). Her research interests are about finite element modelling. She is a member of Design and Manufacturing Lab since 2004, working for the research project Archimedes: Waterjet cutting modelling with finite elements. She gives courses in TEI of Crete, Branch of Chania, current semester Transfer Phenomena (course and laboratory), last semesters Technical Thermodynamics (laboratory), Electrical Circuits (laboratory). Copyright 2011 Inderscience Enterprises Ltd.

2 Effect of impact angle and velocity in crater circularity in AWJ 35 Aristomenis Antoniadis is an Assoc. Professor at the Technical University of Crete, Dept. of Production Engineering and Management. His research interests are on manufacturing, simulation of cutting processes, gear manufacturing, computer numerical control, CAD/CAM, machine design CAE, finite elements analysis and reverse engineering, digitising. Prior to joining the faculty at the Technical University of Crete, he worked in the Technical Education Institute of Crete at Design and Manufacturing Lab. His work there was in the area of production technologies, reverse engineering and mechanical design. Before TEI of Crete, he worked at TEI of Serres, University of Thessaloniki and Thessaly. Nicholas Bilalis is a Professor at the Technical University of Crete, Department of Production Engineering and Management and the Director of CAD Lab. He obtained his Diploma in Mechanical Electrical Engineering, from NTUA (1978), his MSc in Mechanical Engineering Design from Aston University of Birmingham (1979) and his PhD from Loughborough University of Technology (1983). His scientific research is about: CAD/CAM and manufacturing process modelling, new product development and management, tools for product development, rapid prototyping and rapid tooling, virtual prototyping and manufacturing, current electronic based training methods and design for disassembly. 1 Introduction As an advanced manufacturing technology, abrasive water jet (AWJ) cutting is being increasingly used in various industrial applications. A fine nozzle is used to generate a coherent and supersonic water jet, which is followed by the entrainment of abrasive particles to form a very powerful AWJ. Material damage caused by the attack of particles entrained in the fluid system of AWJ, impacting a surface at high speed is called erosion. Erosion is a complex process and it depends on a number of parameters such as, particle speed-size-density-shape, impact angle, mechanical properties of the eroded material, etc. Material is removed when the strain exceeds the material s strain-to-failure value. Material removal occurs due to micro-plastic deformation and/or brittle fracture (El Tobgy et al., 2005). A number of authors attempted to address the problem of describing the abrasive water jet erosion mechanism, by studying the impact of one single particle, based on experimental investigations and microscopic theories. Indeed, Finnie (1958) developed his micro-cutting consideration assuming a plastic behaviour of the target. Bitter (1963) proposed the division of the entire material-removal process into two modes: the first one called cutting wear observed at low-impact angles, and the second one called deformation wear observed at high-impact angles. He also suggested the corresponding mathematical formulas for the evaluation of the removed material volume. Neilson and Gilchrist (1968) proposed a simplified version of Bitter s model, by introducing a simplified ductile erosion mathematical model, while they retained Bitter s model for brittle erosion. Hashish (1984) modified Finnie s erosion model in order to account for the effect of particle shape in the case of brittle materials. Hashish (1984) and Chen et al. (1996) proposed that the erosion mechanism when processing both ductile and brittle materials via AWJs consists of three cutting zones with the first two of them to be

3 36 K. Maniadaki et al. considered as cutting wear and deformation wear, respectively. Hashish (1984), also suggested that the cutting wear mode is characterised by ploughing and cutting deformation. Ploughing occurs at large negative rake angle values, while cutting deformation occurs when the particles impact the material at positive rake angle values. The wear process is similar to that observed in conventional grinding process, however, the explicit description of the erosion mechanism is quite tedious, as the particles may possess both linear and angular velocity (Wang and Wong, 1999). Hutchings and Winter (1974) studied the erosion behaviour of ductile materials processed by spherical particles. They suggested that material removal is due to ploughing. They found that the impact of the first particles resulted to the creation of material lips surrounding the crater, a process that is terminated after the subsequent impact of additional particles. They also found that the deformation mechanism is independent of the particle size. A number of authors have also attempted to address the problem of material deformation caused by AWJ, from a classical mechanics (macroscopic) viewpoint. The majority of these studies include numerical methods based on the finite element method (FEM). Numerical methods may be criticised for not being able to provide detailed microscopic insight like cutting and/or ploughing. Nevertheless, they are characterised by various advantages as they are capable to simulate the erosion behaviour of several materials, under different conditions (particle speed-size-density-shape, impact angle, etc.), thus reducing the requirement of performing various real experiments. In addition, the accuracy of FE-based models may be appropriately refined by using the information attained by experimental applications. El Tobgy et al. (2005), proposed an elasto-plastic finite element (FE) model for the erosion process simulation in a 3D configuration. Their FE model accounted for thermal elastic plastic material behaviour, the effect of multiple particle impacts, as well as material removal. They employed a flow stress material behaviour based on the Johnson Cook material model (Johnson and Cook, 1985). The numerical solution was obtained via the ABAQUS/EXPLICIT software based on the half FE model. In order to accurately describe the erosion mechanism, they considered multiple (three) particles, as the erosion rate was shown to be stabilised after the impact of three particles. Junkar et al. (2006) simulated via FE, the case of single-particle impact and experimentally validated their simulation. They analysed the effect of one single abrasive particle impact on the workpiece material using explicit finite element analysis (FEA). The simulation results were compared and validated with additional experimental results by means of crater s sphericity. They assumed piecewise linear plasticity material behaviour and the solution of their model were obtained via the ANSYS/LS-Dyna software. The impact of a single particle was simulated for the case of three different particle velocity and three different impact angle values (nine simulations in total). In the case of numerical simulation, the particle velocity was considered, while in the experimental case, the corresponding pressure was used instead. During their experimental validation, 200 craters were examined for each of the above test cases. The numerical results (crater sphericity) were found to be in good agreement with their experimental counterparts. Ahmadi-Brooghani et al. (2007) claimed that the achieved numerical solution s accuracy may be improved by adopting a strain rate approach and/or by assuming a Johnson-Cook model for the target material, which is inherently non-linear and strain rate dependant. Indeed, they extended the work of Junkar et al. (2006) by applying the Johnson-Cook model, while the solution of their FE model was obtained using the FEA software ABACUS/CAE on a Pentium 4 computer, for the case of a single

4 Effect of impact angle and velocity in crater circularity in AWJ 37 abrasive particle. Their numerical results were shown to be slightly closer to the corresponding experimental ones of Junkar et al. (2006). Maniadaki et al. (2007) investigated and analysed in detail the workpiece material behaviour under pure water jet impingement. Within the present context, a FE model which accounts for the basic mechanical properties of both the workpiece and the abrasive particle materials, is currently introduced for the case of AWJ machining (AWJM). Indeed, the present study consists of an important extension of the work of Junkar et al. (2006) who investigated the impact of just one single abrasive particle as 20 impacting particles are considered for the first time, allowing for a more detailed and precise determination of the resulting crater geometry and its evolution. Various impact angle and particle velocity are considered and the so called crater circularity is evaluated. The present modelling allows also for the evaluation of the circularity in various points within the crater. Thus, the crater circularity as a function of the penetration depth is also shown. The results of the study indicate a significant variation in the crater geometry during the impact of the first particles, while its shape stabilisation is approximately achieved after the impact of the 13th or 14th particle. The rest of this paper is organised as follows: The proposed FE model is described in Section 2 and its simulation results are presented in Section 3. Finally, the conclusions of the study are summarised in Section 4. 2 FE model description 2.1 Target description The target material considered in the present study is AISI 304 stainless steel, assumed elasto-plastic with material failure criteria capabilities. The target consists of Lagrangian elements, removed when their strain exceeds a predetermined failure threshold strain, called failure strain. The target s mechanical and shape properties are summarised in Table 1 (see also Figure 1). Table 1 Target material and shape properties Target material properties Density 8,030 kg/m 3 Elasticity modulus MPa Poisson s coefficient 0.27 Yield stress 316 MPa Elongation (failure strain) 55% Target meshing properties Type of elements eight-node brick Number of elements 155,595 Number of nodes 147,000

5 38 K. Maniadaki et al. Figure 1 Meshing and material properties of the 20-particles target system (see online version for colours) As in the paper of Junkar et al. (2006), the target consists of eight-node brick elements, allowing for direct comparison with the present results. For numerical accuracy purposes, target meshing is currently adequately dense (the number of FEs was gradually increased until stabilisation of the obtained results). It was accomplished via the ANSYS ICEM CFD pre-processor which allows for the determination of complicate geometries, meshing, boundary conditions (impact angle and particle velocity) and material properties, (ANSYS ICEMCFD 5.1, 2004). The resulting file is subsequently fed to the LS-Dyna solver. Table 2 Abrasive material and shape properties Abrasive material properties Density 4,000 kg/m 3 Elasticity modulus MPa Poisson s coefficient 0.27 Abrasive meshing properties Type of elements Rigid 3D solid (tetrahedral) Number of elements of each particle 482 Number of nodes of each particle 104

6 Effect of impact angle and velocity in crater circularity in AWJ Abrasive description Within the present study, 20 impact particles are considered possessing a spherical scheme characterised by a diameter equal to 0.1 mm (100 μm). Their mechanical and shape properties are summarised in Table 2 (see also Figure 1). Impact particles are assumed to be rigid solid as: a the resulting stresses and strains are of interest for the target only, while the rigid solid assumption leads to zero stresses and strains for the abrasive particles b the computational load is thus significantly reduced c the comparison of the current results with those presented by Junkar et al. s (2006) necessitates the existence of equivalent simulation conditions. As in the target case, particle meshing was accomplished via the ANSYS ICEM CFD pre-processor. 2.3 FE model solution The mathematical solution of the complete (for both the target and the particles) FE model described in the two previous subsections was achieved via the LS-Dyna 3D code (LS-Dyna Keyword User s Manual Version 97). The operating system was a linux86-64 with hpmpi, established on an eight-node parallel processing 64-bit cluster system. The main advantage of this system is its capability of handling large-scale problems characterised by dense grids, small time-step values, large number of FEs, etc., requiring extremely high computing time. This specific system reduces the computational load by a factor of four, when compared with a typical Pentium 4 personal computer (PC). During the solution, the impact of 20 particles was considered for the first time, in contrast to the studies of Junkar et al. (2006) and El Tobgy et al. (2005), who studied the case of just one and three particles, respectively. The algorithm is terminated after the impact of the 20th particle while the total execution time (for the cluster system) varies from 35 min up to 140 min depending on impact angle and velocity. 3 Simulation results The impact of 20 abrasive particles is simulated for three impact velocity values (180, 200 and 220 m/sec) and three impact angle values (30, 60, 90, nine cases in total) similarly to the study of Junkar et al. (2006). The similarity regarding the test cases has been undertaken for comparison purposes. Junkar et al. (2006) studied the erosion wear by simulating the impact of one single particle without considering the potential effects of forthcoming particles, in contrast to the present model which accounts for multiple particle impact. The contact-impact algorithm (Hallquist, 1977) that is used, accounts for the particle s kinetic energy, momentum, inertia and all the forces and moments that affect them. When particles impact the target s surface, some of them may cause only plastic deformation without material removal, while the subsequent particles are responsible for the removal of the plastically deformed zone. The simulation of such a high number of abrasives, aims at the determination of the crater s shape evolution. It

7 40 K. Maniadaki et al. also aims at the investigation for the existence of a potential steady-state limit in terms of crater s geometry. Figure 2 Plastic strain stages after each particle impact to the target (see online version for colours) Figure 3 Von misses stresses after the impact of the 11th particle (see online version for colours) 3.1 Plastic strain stages Figure 2 shows the resulted target s plastic strains as a function of particle number for the case of impact angle equal to 30 and particle velocity equal to 200 m/s. The results

8 Effect of impact angle and velocity in crater circularity in AWJ 41 clearly indicate that an accurate simulation of the erosion process necessitates the consideration of several particles, as both the material s plastic strains and the crater s shape and size vary significantly for at least the first ten to 12 particles. The maximum value of the strain scale is equal to 0.55 representing the material s (AISI 304) failure strain. Complementary to the above figure, the von misses stresses after the impact of the 11th particle are shown in Figure Crater circularity definition and evaluation Crater s circularity is defined as the ratio: C c d1 = (1) d 2 with d 1 representing the diameter of the circle defined by the minor crater dimension and d 2 representing the diameter of the circle defined by the major crater dimension, see Figure 4. Figure 4 Crater circularity definition Top circularity is defined as the circularity measured at the target s top surface. Its evaluation as a function of particle number is shown in Figure 5 for the case of impact angle equal to 30 and particle velocity equal to 200 m/s. Figure 5 indicates a significant variation for the crater circularity, which stabilises after the 12th particle to a value equal to which is quite close to the corresponding experimental result (0.4984) of Junkar et al. (2006). These results justify the author s claim for the simulation of several particles. The target s top surface crater circularity for all the nine test cases considered, are summarised in Figure 6. For comparison purposes, the corresponding experimental values evaluated by Junkar et al. (2006), are also shown (dashed line). As in the previous case, the crater s circularity is shown to vary significantly. The necessity for the simulation of several particles is still apparent. The stabilised circularity values are found to be in good agreement with their corresponding experimental counterparts.

9 42 K. Maniadaki et al. Figure 5 Crater circularity versus particle number (φ = 30, v p = 200 m/s) (see online version for colours) Figure 6 Numerical and experimental crater circularity versus particle number (all test cases) (see online version for colours)

10 Effect of impact angle and velocity in crater circularity in AWJ 43 Particle speed does not significantly affect the circularity s stabilisation limit, except some test cases where the increase of particle speed lead to a partial increase of the stabilisation limit (Figure 6). In some cases the stabilised circularity value was found to be somewhat different from its experimental counterpart (Junkar et al., 2006), since the proposed FE model does not account for phenomena such as particle s kinetic energy reduction due to particle interaction, particle deflection and fragmentation, that take place in real AWJ applications. For the case of φ = 90, the circularity is expectedly evaluated very close to one, since the simulated particles are assumed to be ideally spherical. In the experimental work of Junkar et al. (2006), the aforementioned assumption does not hold, thus the evaluated circularity is expected to be less than one. For the cases of φ < 90, the circularity decreases to values less than one, since the horizontal component of the particle velocity (momentum) drags the material in the velocity direction. In the cases of φ = 60 or φ = 30, the present results approach the theoretical value of sin(φ), as indicated by Figure 7. Figure 7 Geometric determination of crater circularity (φ < 90 ) (see online version for colours) A closer examination of the right hand side of Figure 7 shows that in the cases of φ < 90, the crater circularity may be evaluated as: C c d1 = = sin ( ϕ ) (2) d Circularity evaluation within the crater Within the context of the present study, the circularity inside the crater was also investigated for the first time. Indeed, the circularity is evaluated at specific predetermined planes parallel to the top surface within the crater, after the impact of the last (20th) particle. The planes at which the circularity is evaluated, are determined by the non-deformed target s node points. A side view of the deformed target is shown in Figure 8 (φ = 60, v p = 220 m/sec), where both the depth of the aforementioned planes and

11 44 K. Maniadaki et al. the resulted major crater diameter d 2, are depicted. The lowest point considered, corresponds at the end of the full cut area. Figure 8 Planes used for measuring the crater circularity (see online version for colours) Further details regarding Figure 8, are shown in Figure 9. Its left hand side corresponds to a view point vertical to the impact plane, depicting the evaluated minor crater dimension d 1 along the crater depth, the variation of which is found to be negligible. The major crater dimension d 2 along with the crater circularity versus the crater depth is shown on the right hand side of Figure 9. Figure 9 Circularity measurements inside the crater (see online version for colours) Figure 10 summarises the previous results for the case of φ = 60 (all three particle speeds). A closer examination of Figure 10 shows that the full cut area depth is

12 Effect of impact angle and velocity in crater circularity in AWJ 45 proportional to particle speed, a fact that seems reasonable and also reported by Ahmadi-Brooghani et al. (2007). Furthermore, the crater s circularity tends to unity as the impact velocity increases. Figure 10 Crater circularity versus crater depth

13 46 K. Maniadaki et al. Based upon the previous results, the material removal behaviour was found remarkably different for various impact angles. Indeed, for high impact angles, the material removal mechanism provided by the proposed FE model was found in accordance to that (cutting deformation) proposed by Hashish (1984), while for small impact angles the proposed erosion mechanism seems to be similar to ploughing as suggested by Hashish (1984) and Hutchings and Winter (1974). A potential description of the erosion mechanism for the case of φ = 60 could be as follows: the first particle impacts the target, removes material and is then reflected (with reduced speed) back in the air at about the same direction. The second particle impacts the deformed surface and results to a further crater penetration. The following particles behave similarly. The proposed erosion mechanism seems to be in accordance to the cutting deformation mechanism suggested by Hashish (1984). For the case of φ = 30, a different cutting mechanism was observed. Indeed, the first particle impacts the target, removes material, reduces its momentum and it is reflected back in the air in the opposite direction. The next particles impact the already deformed but not flat surface and are subsequently reflected in various angles. Thus, the resulting penetration depth is negligible, as the particles do not penetrate enough inside the target in order to create a full cut area. This behaviour seems to be similar to ploughing as suggested by Hashish (1984) and Hutchings and Winter (1974). The corresponding results regarding the case of φ = 90 are not presented, since the circularity is always evaluated equal to one, due to the assumed particle sphericity. 4 Conclusions The simulation of the AWJ machining based on a FE model was considered in the present study. The proposed FE model offers an important extension of the models so far presented, as it accounts for the first time in the literature for the simulation of several (20) particles. The results of the study indicated a significant variation of the crater shape and size during the impact of the first ten particles, while its stabilisation was practically achieved after the impact of the 12th up to 14th particle. The crater circularity and its dependence upon both the impact angle and the impact velocity were also studied and the results were found to be in good agreement with their experimental counterparts provided by Junkar et al. (2006). Finally, the results regarding the crater circularity as a function of crater depth were also shown for one simulation case. References Ahmadi-Brooghani, S.Y., Hassanzadeh, H. and Kahhal, P. (2007) Modeling of single-particle impact in abrasive water jet machining, International Journal of Mechanical Systems Science and Engineering, Vol. 1, No. 4, pp ANSYS ICEMCFD 5.1 (2004) Tutorial Manual. Bitter, J.G.A. (1963) A study of erosion phenomena: part I, Wear, Vol. 6, pp Chen, L., Siores, E. and Wong, W.C.K. (1996) Kerf characteristics in abrasive waterjet cutting of ceramic materials, International Journal of Machine Tools and Manufacture, Vol. 36, No. 11, pp El Tobgy, M.S., Ng, E. and Elbestawi, M.A. (2005) Finite element modeling of erosive wear, International Journal of Machine Tools and Manufacture, Vol. 45, pp

14 Effect of impact angle and velocity in crater circularity in AWJ 47 Finnie, I. (1958) The mechanism of erosion of ductile metals, Proceedings of the Third National Congress of Applied Mechanics, New York, pp Hallquist, J.O. (1977) Numerical Procedure for Three-Dimensional Impact Problems, American Society of Civil Engineering, Preprint Hashish, M. (1984) A model study of metal cutting with abrasive water jets, ASME Journal of Engineering Materials and Technology, Vol. 106, pp Hutchings, I.M. and Winter, R.E. (1974) Particle erosion of ductile metals: a mechanism of material removal, Wear, Vol. 27, pp Johnson, G.R. and Cook, W. (1985) Fracture characteristics of three metals subjected to various strains, strain rates, temperatures and pressures, Engineering Fracture Mechanics, Vol. 21, No. 1, pp Junkar, M., Jurisevic, B., Fajdiga, M. and Grah, M. (2006) Finite element analysis of single-particle impact in abrasive water jet machining, International Journal of Impact Engineering, Vol. 32, No. 7, pp LS-Dyna Keyword User s Manual Version 97 (2007) Livermore Software Technology. Maniadaki, K., Kestis, Th., Bilalis, N. and Αntoniadis, A.A. (2007) Finite element based model for pure waterjet process simulation, International Journal of Advanced Manufacturing Technology, Vol. 31, Nos. 9 10, pp (8). Neilson, J. and Gilchrist, A. (1968) Erosion by a stream of solid particles, Wear, Vol. 11, pp Wang, J. and Wong, W.C. (1999) A study of abrasive waterjet cutting of metallic coated sheet steels, International Journal of Machine Tools and Manufacture, Vol. 39, pp