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Influence of alumina particles on the mechanics of machining metal matrix composites
International Journal of Machine Tools & Manufacture 45 (2005) 389–398 www.elsevier.com/locate/ijmactool
Influence of alumina particles on the mechanics of machining metal matrix composites Y. Zhu, H.A. Kishawy* Mechanical Engineering Department, University of New Brunswick, P.O. Box 4400, Fredericton, NB, Canada E3B 5A3 Received 5 July 2004; accepted 7 September 2004 Available online 12 November 2004
Abstract A plane-strain thermo-elasto-plastic finite element model has been developed and used to simulate orthogonal machining of alumina/aluminium 6061 metal matrix composite using a tungsten carbide tool. Simulations were carried out employing temperaturedependent material physical properties. The interface failure mode between the aluminium matrix and alumina particles was incorporated in this model. The model is used to investigate the effective and shear stresses on the alumina particles. Detailed results of the cutting forces generated during the machining process are presented and a comparison has been made with the experimental results for a range of feeds. Of particular interest are the contact stress distributions and alumina particle’s interface failure. Normal and shear stresses and cutting temperatures were investigated. q 2004 Elsevier Ltd. All rights reserved. Keywords: Metal matrix composite; Alumina particle; Aluminium matrix; Machining
1. Introduction Metal-matrix composites are either in use or being prototyped for the Space Shuttle, commercial airliners, electronic substrates, bicycles, automobiles, golf clubs, and a variety of other applications [1]. While the vast majorities are aluminium matrix composites, a growing number of applications require the matrix properties of superalloys, titanium, copper, magnesium, or iron. The term Metal Matrix Composite (MMC) covers various types of systems, and also a wide range of scales and microstructures. Common to them all is a metallic matrix, which is normally contiguous. The reinforcing constituents are in most cases a ceramic, intermetallics or semiconductors. MMC types are commonly subdivided according to whether the reinforcement is in the form of (a) particles, which are at least approximately equiaxed, (b) short fibers (with or without a degree of alignment), or (c) long aligned fiber matrix and reinforcement. Specifications of the way in which the composite material is to be synthesized, and the manner in * Corresponding author. Tel.: C1 506 458 7767; fax: C1 506 453 5025. E-mail address: [email protected] (H.A. Kishawy). 0890-6955/$ - see front matter q 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.ijmachtools.2004.09.013
which a stock item or component is to be fabricated from this material, are key interwoven issues for technologists interested in product development [2]. Compared to monolithic metals, MMCs have higher strength-to-density ratios, better fatigue resistance, better elevated temperature properties (such as high strength and low creep rate), lower coefficients of thermal expansion, high thermal conductivity, good damping characteristics, excellent wear properties and flexibility in design attributes. However, the utilization of the MMC in different industries is not as generalized as expected due to difficulties encountered with the machining of MMC materials. Cost effective machining of aluminium MMC has not been proven. Capable machining practices established in the past decade have not been optimized. Studies of advancements in the materials show promise for machinability but have not been incorporated into any modeling activity. The same holds true for tooling. New coatings for tools show great promise for advancing the machinability of this class of material, but have not been investigated in detail. In addition to the tool coatings, no optimization has been done on the presentation of the tool to the material. Effects of approach geometry (i.e. rake, lead) have not been incorporated into
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past studies, nor has the geometry of the cutting edge of the insert. Past studies show a significant initial breakdown of the cutting edge. From that point, wear statistics show a gentler slope of the wear development line until end of life is reached. This indicates that some edge preparation, other than ‘up sharp’ may be beneficial. The main problem when machining MMC is the extensive tool wear caused by the very hard and abrasive reinforcements. Several studies have been performed in order to examine the efficiency of different cutting materials, such as cemented carbide and diamond, in turning, milling, drilling, reaming and threading of MMC materials [3,4]. The test results showed the influences of the reinforcement material on tool wear and the surface integrity of MMC. In the subsurface zone, when the workpiece was machined with worn cutting tools, the reinforcements are fractured. Damage of the reinforcements, caused by the machining process, can lead to significant deterioration in the properties of the components [5]. To optimize the machining process for MMC a better understanding of the interaction physics between the tool and the workpiece is required. This can be achieved through proper modeling of the metal removal of the MMC materials. There are few publications which are concerned with the mathematical modeling of the MMC machining process [6]. The cutting forces, tool wear and surface roughness during the turning and drilling of the particulate metal matrix composite A356/20/SiCp-T6 was measured and the results were used to develop a methodology for optimizing the process parameters in turning and drilling. Since there are contradictory objectives, such as maximization of tool life and minimization of tool wear, the concept of the Pareto optimum solution was considered in the optimization procedure. A solid, accurate, understandable model for the chip formation of this material has not yet been developed to the point of general acceptance. Although, the finite element (FE) method is a commonly used approach for metal cutting modeling, literature available on FE modeling of metal matrix particulate composite machining is very diminutive. A complex micro-mechanical process for a normally loaded particulate reinforced metal matrix composite against a tungsten carbide cutting tool has been modeled using FEA [7]. Thermal load effect and residual stresses were analyzed using a thermo-elasto-plastic FE code [8], and it was concluded that the thermal load could be ignored for specific ranges of process parameters. The results obtained from the above mentioned investigations indicate that there is a need for more thorough FE modeling activities to study the particle behavior in the matrix when it contacts the tool rake face. Investigating the particle behavior during machining will help in identifying the optimum tool geometry and process parameters to reduce the cost of machining MMC materials. A transient dynamic finite element analysis was carried out to investigate the mechanics of diamond turning of an aluminium 6061/silicon carbide [9]. Based on this
model, a new chip separation criterion, a two-dimensional link element, was employed to analyze the normal and shear stresses along the cutting tool rake face. Mofid Mahdi and Liangchi Zhang [10] modeled the orthogonal cutting of fiber-reinforced composites. The variation of the cutting force was investigated carefully against the cutting conditions with the following development: a failure model of the work-material based on the Tsai-Hill criterion and a contact model of the mechanisms of the cutting process. Further investigation is required to understand the behavior of the particles in the parent matrix since they are the main parameters for tool wear. In this paper, a finite element model was developed using commercial software (ABAQUS/Explicit) by incorporating a thermo-elasto-plastic material model and a thermo-elastic cutting tool model with special emphasis on the stresses acting on the particles and the aluminum matrix.
2. Finite element modeling 2.1. Modeling solver The modeling of the two-dimensional orthogonal cutting process was simulated using a commercially available general-purpose finite element solver, ABAQUS/Explicite, version 6.2. An updated Lagrangian formulation is employed. The momentum equation discretized for a Lagrangian formulation is shown in Eq. (1). M u€ Z f ext K f int
(1)
where M is the diagonal or lumped mass matrix, u€ is the acceleration at the beginning of the increment, f ext is the externally applied load and fint is the internal load. The explicit central difference integration rule, with a lumped mass matrix and an explicit forward difference time integration rule, are used to obtain the mechanical responses [11]. The central difference integration rule advances the kinematics state (velocities and displacements) explicitly through time using known values of acceleration. DtðiC1Þ C DtðiÞ € N N N U_ ðiC1=2Þ Z U_ ðiK1=2Þ C U ðiÞ (2) 2 _ U € are the nodal displacement, velocity and where U, U, acceleration, respectively; Dt is the time increment, N is a nodal degree of freedom, the subscript i represents the increment number, and (iK1/2) and (iC1/2) are midincrement values. 2.2. Material formulation Modeling the real material behavior and dealing with the plastic deformation of 6061 aluminium matrix mainly depends on the input of material properties, therefore, the Johnson-Cook constitutive equation was employed in this
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Table 1 Physical properties of aluminium and aluminium oxide particle [12] Properties 3
Density (kg/m ) Possion’s ratio Thermal expansion (10K6) Thermal conductivity (W/mk) Elastic constant (GPa)
Al 6061
Alumina
2700 0.34 23.5 180 71.9
3700 0.22 8 30 370
Table 2 Physical properties of tungsten carbide cutting insert [12] Fig. 1. Geometry and boundary conditions.
Physical properties of tungsten carbide Density (kg/m3) Possion’s ratio Thermal expansion Thermal conductivity (W/mk) Elastic constant (GPa)
19,700 0.22 4.5!10K6 173 700
(CPE4RT) were used to discretize both the workpiece and the elastic insert. The tool shank was modeled as a twodimensional rigid body with two-node rigid link element (R2D2). 2.4. Modeling of aluminium oxide particle
study [12] (Tables 1 and 2). Eq. (3) shows the Johnson-Cook constitutive equation, which is a function of plastic strain 3pl, strain-hardening index n, strain-rate 3_, temperature T and strain rate sensitivity index m. The constants C1, C2 and C3, strain hardening index n and strain rate sensitivity index m are obtained from literature as shown in Table 3. T K 20 m 3_ s Z ðC1 C C2 3npl Þ 1 C C3 log 1K Tm K 20 3_0 (3) 2.3. Geometrical modeling and boundary conditions The geometrical modeling and discretization of the workpiece and cutting tool are shown in Fig. 1. The model presented here used a constant rake angle of 308 and a sharp tool. A cutting speed of 85 m/min and a range of feeds (0.1–0.3 mm/rev) were used. The workpiece was created as a single two-dimensional solid while the cutting tool was modeled as a twodimensional assembly of a rigid shank and an elastic insert as shown in Fig. 1. A plane strain condition was assumed in this work. The workpiece was constrained against movement in any direction at the bottom, left-hand side and the lower portion of the right-hand side. To avoid the tool rotational and translational movement in the y-direction, constraints were input on the shank reference node in this direction, while it was given a pre-described translational rigid-body motion in the x-direction. Two-dimensional, four-node displacement and temperature continuum element featuring reduced integration and hourglass control
In order to create a more realistic model, the hard particles embedded in the workpiece were utilized and its shape and position were assumed to be random. The average size of these alumina particles was defined as 15 mm. Multiple point constraints were employed to model the constraints between the alumina particles and aluminium matrix. In the multiple point constraints, nonlinear constraints are specified, in which the penalty contact algorithm between hard particles and aluminium matrix is adopted for nodes involved in multiple point constraints and contact pair definitions. The alumina particle’s interface, which has the same hardness as that of the particles, was modeled. The thickness of this interface was defined as 1 mm. Fig. 2 shows the interface modeling and the material definition. 2.5. Chip separation criterion In this simulation physical chip separation criterion available with ABAQUS/Explicite was used. According to this criterion, chip separation occurs when the critical value
Table 3 Material constants [12] C1 (MPa)
C2 (MPa)
C3
n
m
428.5
328
0.008
1.01
1.4 Fig. 2. Alumina particle’s interface modeling.
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between the leading node and the tool edge is less than or equal to a given value. The chip separation developed in the study was based on the shear failure mode using the SHEAR FAILURE, ELEMENT DELETIONZYES module [11]. The shear failure module is based on the effective plastic strain, 3pl. When an element of the workpiece mesh reaches the damage plastic strain value, 3dpl , the damage parameter D in Eq. (4) equals to one. When this occurs, the corresponding element will be deleted. DZ
3pl Z1 3dpl
(4)
The heat distribution depends on the cutting speed and the thermal conductivity of the workpiece and the cutting tool materials. The heat rate per unit area, which is released at the chip/tool interface, is given by [11] qf Z hf tc g_
where qf is the frictional heat rate per unit area, hf is the fraction of the frictional energy converted into heat, tc is the frictional shear stress, and g_ is the slip rate. Depending on the heat absorption co-efficient of the cutting tool material, the heat conducted into the cutting tool is based on the fraction of heat energy channeled into the chip (b) and can be given as
2.6. Chip/tool interface bZ Friction along the chip/tool interface plays a very vital role in the metal cutting process. It determines the power required for removing a given volume of metal, controls the surface quality of the finished product, and affects the rate of wear of the cutting tool. In order to explore the effect of friction along the tool–chip interface, a modified friction model is employed in this study based on the Coulomb friction model in ABAQUS and can be used with all contact options in the code. According to the Coulomb friction law, the sticking region is assumed near the cutting tool edge and the sliding region takes place beyond the sticking region on the rake face. Usually, the Coloumb law is described by the following equation tc Z minðmp; tth Þ
(5)
where p is the normal pressure across the chip/tool interface, m is the coefficient of friction, tth is the threshold value for the conventional coulomb friction stress that is provided by the product of mp. The limiting shear pffiffiffi stress, tmax, used in this study was calculated from sy = 3. As the hard particle slides against the cutting tool, the coefficient of friction between them was assumed to be 0.15 [13]. 2.7. Heat generation
EC ET C EC
ET;C Z
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi KT;C rT;C CpT;C
qt Z qc K bqf
(9)
(10)
2.8. Experimental set-up and results Orthogonal cutting tests were performed on a 10% Al2O3/6061 aluminium metal matrix composite bar with a diameter of 32 mm. The cutting parameters, 85 m/min cutting speed, 3 mm depth of cut and a range of feeds from 0.1 to 0.3 mm/rev, were adopted in this experiment. Coated tungsten carbide cutting tools with a sharp cutting edge were used. Cutting forces were measured using a 3-component piezoelectric dynamometer connected to a series of charged amplifiers. An A/D converter was used to convert the voltage output from the charge amplifiers to digital format. Chips were collected after each cutting experiment and analyzed under the optical and SEM microscope. Cutting force data was captured, plotted and analyzed (Fig. 3).
(6)
where qpl is the heat rate generated per unit volume, hm is the fraction of dissipated mechanical energy converted to pl heat, spl eqv is the equivalent stress, and 3_ is the plastic strain rate. The chip carries away a high fraction of the heat and the rest is dissipated into the workpiece and the cutting tool.
(8)
The heat flux density leaving the tool/chip interface as a function of frictional heat generation qf, heat flux due to deformation of the chip material at the sticking friction region qc and b is given by
In machining, most of the energy spent in deforming the material to generate chips and to sliding the chip along the rake face is converted into thermal energy. The heat generated during machining is one of the main parameters that govern the tool wear mechanisms and failure. As a result of plastic deformation, the heat generated gives rise to heat rate per unit volume pl qpl Z hm spl eqv 3_
(7)
Fig. 3. Orthogonal cutting experimental set-up.
Y. Zhu, H.A. Kishawy / International Journal of Machine Tools & Manufacture 45 (2005) 389–398 Table 4 Experimental results for cutting force and feed force
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the deformed chip thickness and the chip–tool contact length can be estimated.
Feed (mm/rev)
Cutting force (N)
Feed force (N)
0.1 0.2 0.3
118 187 247
62 96 121
The measured cutting force and feed force under different feeds are illustrated in Table 4.
3. Results and discussions 3.1. Overview The cutting tool is advanced incrementally into the workpiece from the initial position as shown in the Fig. 4(a–d). The chip is formed gradually until the steady state is attained and the cutting forces reach constant value. For each increment in the simulation, the shape of the deformed chip, the stress and strain distributions in both the chip and workpiece, as well as the temperature distribution in the workpiece/chip/tool interface are predicted. At the initiation of the incipient stage, the chip/tool contact area is small, which is subjected to a high concentrated load as shown in Fig. 4(a). As the tool advances, penetrating deeper into the workpiece, more plastic deformation of the workpiece material is generated along the rake face as shown in Fig. 4(b). The chip flow over the rake face was initiated when the full chip/tool contact area was achieved as can be seen in Fig. 4(c). Thus the resistance to the tool penetration decreases, which in turn results in a thinner primary deformation zone as shown in Fig. 4(d). Moreover, when the steady state condition is achieved, shown in Fig. 4(d),
3.2. Cutting and feed forces In order to validate this model, a comparison between the predicted and experimental cutting and feed force was made as shown in Fig. 5. The cutting and feed forces, as predicted by the finite element method, were found to increase almost linearly with increasing feed rate, thus, conforming to the results obtained in experiments. Moreover, the predicted and measured results show a divergence of about 9%, which was assumed to be an acceptable level of agreement. Due to the different tool/hard particle interaction mechanisms operating in the machining process, the cutting forces generate peaks and troughs which is in good agreement with the observations in the literature [14]. These fluctuations achieved in the cutting forces have been analyzed using a spectrum analysis [9]. The existence of the hard particles lead to large fluctuations in the cutting forces. In addition, it was found that the position of the hard particle relative to the tool motion also affects the magnitude and frequency of these fluctuations. There can be three possible encounters of the cutting tool: (1) insert cutting through the matrix alone, (2) insert encountering aluminium oxide particle and debonding and/or particle pullout, (3) tool ploughing through the matrix or aluminium oxide. This finite element model is able to predict the effect of alumina particles and encountering conditions on the fluctuations of cutting forces during machining with a tungsten carbide cutting tool. 3.3. Von Mises equivalent stress distribution on the workpiece and cutting tool Von Mises equivalent stress contours at steady state are shown in Fig. 6(a) for the case of feedZ0.2 mm/rev.
Fig. 4. Chip formation during machining process. (a) Chip formation at tZ2.2 ms. (b) Chip formation at tZ11 ms. (c) Chip formation at tZ33 ms. (d) Chip formation at tZ99 ms.
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particle was found to have the highest value in the primary deformation zone which is due to the high compressive stress exerted by the cutting tool tip. The stress at the cutting tool tip depends on the tool encountering different constituents of the workpiece. The value is found to be high as the tool tip encounters a hard particle and is low as it shears through the soft ductile matrix. In the secondary deformation zone, similar observations are made. A gradual decrease of equivalent stress from the cutting tool tip into the insert is observed in all three feeds.
Fig. 5. Measured and predicted cutting forces.
During the orthogonal machining of MMC’s with a sharp tool, the chip is formed by shearing in the primary deformation zone. As a result of very high shear stresses and pressures at the chip–tool interface, a secondary deformation zone along the chip–tool interface also occurs. The magnitude of the Von Mises equivalent stress increases while the workpiece element goes through the primary deformation zone. In the primary shear zone, the value of Von Mises was in the range of 1080–1200 MPa, while, the secondary deformation zone had a higher value of 1320– 1758 MPa for different feeds from 0.1 to 0.3 mm/rev. The analysis reveals that high levels of work hardening exist in the matrix around the hard particles and thus high stresses are developed. This result is in agreement with the work of [15], who solved the problem of a plate with a circular elastic inclusion using Airy stress functions. However, with the irregular-shaped particles employed in this work, extremely high local stresses are developed at the particle corners. Particle clustering also leads to an increase in the stress on and around the hard particles. The Von Mises stress distribution on the alumina particle at different positions is presented on the un-deformed chip (A), primary zone (B) and secondary shear zone (C) as shown in Fig. 6(b). The equivalent Von Mises stress on the hard
3.4. Shear stress distribution on the workpiece and cutting tool The contours of shear stress in the workpiece are shown in Fig. 7(a) for the feed of 0.2 mm/rev. The shear stress changes from positive in the secondary deformation zone, with the values of 551, 968 and 607 MPa to negative in the primary deformation zone with the values of 447, 470 and 532 MPa for the feeds of 0.1, 0.2 and 0.3 mm/rev, respectively. The size and position of the hard particles not only change the magnitude of the stresses but also the pattern and trend, which can be visualized clearly in Fig. 7(b). The shear stress value is found to increase with increasing feeds. The shear stress on the hard particle, which is in the undeformed chip, primary deformation zone and secondary deformation zone, depicts negative shear stress values in the primary zone (B), ahead of the cutting tool and positive values in the secondary deformation zone (C). The highest shear stress on the alumina particle shows maximum value which is due to shearing. The shear stress ranges from 874 to 1100 MPa in the cutting tool for different feeds 0.1–0.3 mm/rev. By increasing the feeds, the increase of the shear stress can be attributed to the increase in the chip–tool interfacial friction due to the rubbing action of the abrasive particles.
Fig. 6. Von Mises stress distribution on the matrix and hard particle. (a) Contours of Von Mises equivalent stress distribution for feedZ0.2 mm/rev. (b) Von Mises stress distribution on the particles.
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Fig. 7. Shear stress distribution on the matrix and hard particle. (a) Contours of shear stress distribution for feedZ0.2 mm/rev. (b) Shear stress profile on the particles.
3.5. Temperature distribution on the workpiece and cutting tool Three main heat sources exist in the secondary deformation zone: plastic deformation within the chip that is in contact with the rake face, tool–chip interface friction, and chip sliding velocity. Among the above-mentioned sources the results indicate that the tool–chip interfacial friction is the most important factor in increasing temperature value. The contours of temperature in the workpiece are shown in Fig. 8(a–c) for different feeds from 0.1 to 0.3 mm/rev. The temperature generated along the tool–chip interface is
substantially higher than that in the primary shear zone. At 85 m/min cutting speed, maximum temperatures of 380, 390 and 398 8C were predicted along the chip–tool interface for different feeds 0.1–0.3 mm/rev. A large amount of heat is generated in the primary shear zone and the increase in temperature is entirely related to plastic deformation. Generally, the temperature is higher as the feed increases because of the increase in the rate of plastic deformation, which leads to a higher magnitude of energy input into the system. The temperature distributions on the cutting tool rake face for feed rates of 0.1, 0.2 and 0.3 mm/rev are shown
Fig. 8. Temperature distribution on the matrix. (a) Temperature contour for feedZ0.1 mm/rev. (b) Temperature contour for feedZ0.2 mm/rev. (c) Temperature contour for feedZ0.3 mm/rev.
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Fig. 9. Temperature distribution along the contact length.
in Fig. 9. As expected, the maximum temperature occurs on the area of the rake face, a distance away from the cutting edge. The location of maximum temperature depends on the condition encountered at the interface due to the existence of alumina particles, which will be discussed in Section 3.6. 3.6. Tool/particle contact mechanisms along interface High contact stresses between the hard particle and rake face are primarily responsible for the development of tool wear when machining metal matrix composites. Therefore, a better understanding of the phenomena occurring at the chip/tool interface should be useful in predicting and reducing tool failure. The alumina particles’ interface fails as it goes through the secondary shear zone. Thus, the hard particle is out of control by the aluminium matrix and scratches along the cutting tool rake face. A high shear stress, 785 MPa, on the alumina particle is generated due to the scratching between the hard particle and tool rake face. As part of the interface
fails, the alumina particle is still partly bonded by aluminium matrix. The hard particle scratches along the cutting tool rake face and generates high shear stress, 947 MPa, leading to abrasive wear. After experiments, the microstructure of the chips was investigated. Fig. 10(a) and (b) indicate the partly debonded and fully debonded particle. The interface failure was modeled in this work and analysis was incorporated in this paper. There are two main mechanisms between tool and hard particles observed in this work. As the chip is formed, the hard particles are sliding along the rake face and scratching as they move upward as shown in Fig. 11(a) and (b). Some fluctuations are observed in the contact stresses distribution due to the matrix hardening. After scratching a certain distance, the hard particle is pushed inside the chip. The contact between the cutting tool and the hard particle is lost and thus creates a gap between them as shown in Fig. 12(a) and (b). These two mechanisms have been confirmed by the experimental results. After experiments, the chips were collected and the microstructure observations were analyzed. Fig. 10(c) shows tracks caused by the particle’s scratching and being pushed inside the chip.
4. Conclusions The following conclusions can be drawn from this analysis: 1. A finite element model is developed and used to simulate orthogonal machining of aluminium/aluminium oxide particulate composite. It is believed that details afforded by this FE analysis will be of great importance for better
Fig. 10. SEM images showing different possible particles conditions and motions during machining. (a) Partly debonded alumina particle. (b) Fully debonded alumina particle [16]. (c) Hard particle is pushed inside the chip.
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Fig. 11. Schematic drawing of the chip/tool interaction and the corresponding stress distribution. (a) Contact condition between tool and hard particle. (b) Normal/shear stress distributions corresponding to the case in (a).
Fig. 12. Schematic drawing of the chip/tool interaction and the corresponding stress distribution. (a) Contact condition between tool and hard particle. (b) Normal/shear stress distributions corresponding to the case in (a).
2.
3.
4.
5.
understanding of the particle’s behavior during machining of MMC and can help in optimizing the process parameters. For all the feeds employed in this analysis, the predicted cutting force components increased with feed and the discrepancies between the predicted and measured values were within 9% errors. The simulation results of the Von Mises equivalent stress distributions on the aluminium oxide particles depict a gradual increase in the stress on particles in the undeformed chip and reach a peak value when the particles are in the primary shear zone. The shear stress distributions on the aluminium oxide ceramic particles show a reversal from negative stress values in the primary shear zone to a positive maximum in the secondary shear zone. There are some fluctuations of normal and shear contact stress values along the chip/tool interface, which corresponds to the different alumina particles/tool conditions. Due to the failure of alumina particle’s interface, the hard particles are debonded or partly debonded and scratch
the tool rake face, leading to a high tool wear that was shown by the high shear stress on the alumina particle.
Acknowledgements This research was supported by the NCE and AUTO-21C08 ‘High Speed Machining of Light Materials for Automotive Application’.
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Influence of alumina particles on the mechanics of machining metal matrix composites Y. Zhu, H.A. Kishawy* Mechanical Engineering Department, University of New Brunswick, P.O. Box 4400, Fredericton, NB, Canada E3B 5A3 Received 5 July 2004; accepted 7 September 2004 Available online 12 November 2004
Abstract A plane-strain thermo-elasto-plastic finite element model has been developed and used to simulate orthogonal machining of alumina/aluminium 6061 metal matrix composite using a tungsten carbide tool. Simulations were carried out employing temperaturedependent material physical properties. The interface failure mode between the aluminium matrix and alumina particles was incorporated in this model. The model is used to investigate the effective and shear stresses on the alumina particles. Detailed results of the cutting forces generated during the machining process are presented and a comparison has been made with the experimental results for a range of feeds. Of particular interest are the contact stress distributions and alumina particle’s interface failure. Normal and shear stresses and cutting temperatures were investigated. q 2004 Elsevier Ltd. All rights reserved. Keywords: Metal matrix composite; Alumina particle; Aluminium matrix; Machining
1. Introduction Metal-matrix composites are either in use or being prototyped for the Space Shuttle, commercial airliners, electronic substrates, bicycles, automobiles, golf clubs, and a variety of other applications [1]. While the vast majorities are aluminium matrix composites, a growing number of applications require the matrix properties of superalloys, titanium, copper, magnesium, or iron. The term Metal Matrix Composite (MMC) covers various types of systems, and also a wide range of scales and microstructures. Common to them all is a metallic matrix, which is normally contiguous. The reinforcing constituents are in most cases a ceramic, intermetallics or semiconductors. MMC types are commonly subdivided according to whether the reinforcement is in the form of (a) particles, which are at least approximately equiaxed, (b) short fibers (with or without a degree of alignment), or (c) long aligned fiber matrix and reinforcement. Specifications of the way in which the composite material is to be synthesized, and the manner in * Corresponding author. Tel.: C1 506 458 7767; fax: C1 506 453 5025. E-mail address: [email protected] (H.A. Kishawy). 0890-6955/$ - see front matter q 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.ijmachtools.2004.09.013
which a stock item or component is to be fabricated from this material, are key interwoven issues for technologists interested in product development [2]. Compared to monolithic metals, MMCs have higher strength-to-density ratios, better fatigue resistance, better elevated temperature properties (such as high strength and low creep rate), lower coefficients of thermal expansion, high thermal conductivity, good damping characteristics, excellent wear properties and flexibility in design attributes. However, the utilization of the MMC in different industries is not as generalized as expected due to difficulties encountered with the machining of MMC materials. Cost effective machining of aluminium MMC has not been proven. Capable machining practices established in the past decade have not been optimized. Studies of advancements in the materials show promise for machinability but have not been incorporated into any modeling activity. The same holds true for tooling. New coatings for tools show great promise for advancing the machinability of this class of material, but have not been investigated in detail. In addition to the tool coatings, no optimization has been done on the presentation of the tool to the material. Effects of approach geometry (i.e. rake, lead) have not been incorporated into
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past studies, nor has the geometry of the cutting edge of the insert. Past studies show a significant initial breakdown of the cutting edge. From that point, wear statistics show a gentler slope of the wear development line until end of life is reached. This indicates that some edge preparation, other than ‘up sharp’ may be beneficial. The main problem when machining MMC is the extensive tool wear caused by the very hard and abrasive reinforcements. Several studies have been performed in order to examine the efficiency of different cutting materials, such as cemented carbide and diamond, in turning, milling, drilling, reaming and threading of MMC materials [3,4]. The test results showed the influences of the reinforcement material on tool wear and the surface integrity of MMC. In the subsurface zone, when the workpiece was machined with worn cutting tools, the reinforcements are fractured. Damage of the reinforcements, caused by the machining process, can lead to significant deterioration in the properties of the components [5]. To optimize the machining process for MMC a better understanding of the interaction physics between the tool and the workpiece is required. This can be achieved through proper modeling of the metal removal of the MMC materials. There are few publications which are concerned with the mathematical modeling of the MMC machining process [6]. The cutting forces, tool wear and surface roughness during the turning and drilling of the particulate metal matrix composite A356/20/SiCp-T6 was measured and the results were used to develop a methodology for optimizing the process parameters in turning and drilling. Since there are contradictory objectives, such as maximization of tool life and minimization of tool wear, the concept of the Pareto optimum solution was considered in the optimization procedure. A solid, accurate, understandable model for the chip formation of this material has not yet been developed to the point of general acceptance. Although, the finite element (FE) method is a commonly used approach for metal cutting modeling, literature available on FE modeling of metal matrix particulate composite machining is very diminutive. A complex micro-mechanical process for a normally loaded particulate reinforced metal matrix composite against a tungsten carbide cutting tool has been modeled using FEA [7]. Thermal load effect and residual stresses were analyzed using a thermo-elasto-plastic FE code [8], and it was concluded that the thermal load could be ignored for specific ranges of process parameters. The results obtained from the above mentioned investigations indicate that there is a need for more thorough FE modeling activities to study the particle behavior in the matrix when it contacts the tool rake face. Investigating the particle behavior during machining will help in identifying the optimum tool geometry and process parameters to reduce the cost of machining MMC materials. A transient dynamic finite element analysis was carried out to investigate the mechanics of diamond turning of an aluminium 6061/silicon carbide [9]. Based on this
model, a new chip separation criterion, a two-dimensional link element, was employed to analyze the normal and shear stresses along the cutting tool rake face. Mofid Mahdi and Liangchi Zhang [10] modeled the orthogonal cutting of fiber-reinforced composites. The variation of the cutting force was investigated carefully against the cutting conditions with the following development: a failure model of the work-material based on the Tsai-Hill criterion and a contact model of the mechanisms of the cutting process. Further investigation is required to understand the behavior of the particles in the parent matrix since they are the main parameters for tool wear. In this paper, a finite element model was developed using commercial software (ABAQUS/Explicit) by incorporating a thermo-elasto-plastic material model and a thermo-elastic cutting tool model with special emphasis on the stresses acting on the particles and the aluminum matrix.
2. Finite element modeling 2.1. Modeling solver The modeling of the two-dimensional orthogonal cutting process was simulated using a commercially available general-purpose finite element solver, ABAQUS/Explicite, version 6.2. An updated Lagrangian formulation is employed. The momentum equation discretized for a Lagrangian formulation is shown in Eq. (1). M u€ Z f ext K f int
(1)
where M is the diagonal or lumped mass matrix, u€ is the acceleration at the beginning of the increment, f ext is the externally applied load and fint is the internal load. The explicit central difference integration rule, with a lumped mass matrix and an explicit forward difference time integration rule, are used to obtain the mechanical responses [11]. The central difference integration rule advances the kinematics state (velocities and displacements) explicitly through time using known values of acceleration. DtðiC1Þ C DtðiÞ € N N N U_ ðiC1=2Þ Z U_ ðiK1=2Þ C U ðiÞ (2) 2 _ U € are the nodal displacement, velocity and where U, U, acceleration, respectively; Dt is the time increment, N is a nodal degree of freedom, the subscript i represents the increment number, and (iK1/2) and (iC1/2) are midincrement values. 2.2. Material formulation Modeling the real material behavior and dealing with the plastic deformation of 6061 aluminium matrix mainly depends on the input of material properties, therefore, the Johnson-Cook constitutive equation was employed in this
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Table 1 Physical properties of aluminium and aluminium oxide particle [12] Properties 3
Density (kg/m ) Possion’s ratio Thermal expansion (10K6) Thermal conductivity (W/mk) Elastic constant (GPa)
Al 6061
Alumina
2700 0.34 23.5 180 71.9
3700 0.22 8 30 370
Table 2 Physical properties of tungsten carbide cutting insert [12] Fig. 1. Geometry and boundary conditions.
Physical properties of tungsten carbide Density (kg/m3) Possion’s ratio Thermal expansion Thermal conductivity (W/mk) Elastic constant (GPa)
19,700 0.22 4.5!10K6 173 700
(CPE4RT) were used to discretize both the workpiece and the elastic insert. The tool shank was modeled as a twodimensional rigid body with two-node rigid link element (R2D2). 2.4. Modeling of aluminium oxide particle
study [12] (Tables 1 and 2). Eq. (3) shows the Johnson-Cook constitutive equation, which is a function of plastic strain 3pl, strain-hardening index n, strain-rate 3_, temperature T and strain rate sensitivity index m. The constants C1, C2 and C3, strain hardening index n and strain rate sensitivity index m are obtained from literature as shown in Table 3. T K 20 m 3_ s Z ðC1 C C2 3npl Þ 1 C C3 log 1K Tm K 20 3_0 (3) 2.3. Geometrical modeling and boundary conditions The geometrical modeling and discretization of the workpiece and cutting tool are shown in Fig. 1. The model presented here used a constant rake angle of 308 and a sharp tool. A cutting speed of 85 m/min and a range of feeds (0.1–0.3 mm/rev) were used. The workpiece was created as a single two-dimensional solid while the cutting tool was modeled as a twodimensional assembly of a rigid shank and an elastic insert as shown in Fig. 1. A plane strain condition was assumed in this work. The workpiece was constrained against movement in any direction at the bottom, left-hand side and the lower portion of the right-hand side. To avoid the tool rotational and translational movement in the y-direction, constraints were input on the shank reference node in this direction, while it was given a pre-described translational rigid-body motion in the x-direction. Two-dimensional, four-node displacement and temperature continuum element featuring reduced integration and hourglass control
In order to create a more realistic model, the hard particles embedded in the workpiece were utilized and its shape and position were assumed to be random. The average size of these alumina particles was defined as 15 mm. Multiple point constraints were employed to model the constraints between the alumina particles and aluminium matrix. In the multiple point constraints, nonlinear constraints are specified, in which the penalty contact algorithm between hard particles and aluminium matrix is adopted for nodes involved in multiple point constraints and contact pair definitions. The alumina particle’s interface, which has the same hardness as that of the particles, was modeled. The thickness of this interface was defined as 1 mm. Fig. 2 shows the interface modeling and the material definition. 2.5. Chip separation criterion In this simulation physical chip separation criterion available with ABAQUS/Explicite was used. According to this criterion, chip separation occurs when the critical value
Table 3 Material constants [12] C1 (MPa)
C2 (MPa)
C3
n
m
428.5
328
0.008
1.01
1.4 Fig. 2. Alumina particle’s interface modeling.
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between the leading node and the tool edge is less than or equal to a given value. The chip separation developed in the study was based on the shear failure mode using the SHEAR FAILURE, ELEMENT DELETIONZYES module [11]. The shear failure module is based on the effective plastic strain, 3pl. When an element of the workpiece mesh reaches the damage plastic strain value, 3dpl , the damage parameter D in Eq. (4) equals to one. When this occurs, the corresponding element will be deleted. DZ
3pl Z1 3dpl
(4)
The heat distribution depends on the cutting speed and the thermal conductivity of the workpiece and the cutting tool materials. The heat rate per unit area, which is released at the chip/tool interface, is given by [11] qf Z hf tc g_
where qf is the frictional heat rate per unit area, hf is the fraction of the frictional energy converted into heat, tc is the frictional shear stress, and g_ is the slip rate. Depending on the heat absorption co-efficient of the cutting tool material, the heat conducted into the cutting tool is based on the fraction of heat energy channeled into the chip (b) and can be given as
2.6. Chip/tool interface bZ Friction along the chip/tool interface plays a very vital role in the metal cutting process. It determines the power required for removing a given volume of metal, controls the surface quality of the finished product, and affects the rate of wear of the cutting tool. In order to explore the effect of friction along the tool–chip interface, a modified friction model is employed in this study based on the Coulomb friction model in ABAQUS and can be used with all contact options in the code. According to the Coulomb friction law, the sticking region is assumed near the cutting tool edge and the sliding region takes place beyond the sticking region on the rake face. Usually, the Coloumb law is described by the following equation tc Z minðmp; tth Þ
(5)
where p is the normal pressure across the chip/tool interface, m is the coefficient of friction, tth is the threshold value for the conventional coulomb friction stress that is provided by the product of mp. The limiting shear pffiffiffi stress, tmax, used in this study was calculated from sy = 3. As the hard particle slides against the cutting tool, the coefficient of friction between them was assumed to be 0.15 [13]. 2.7. Heat generation
EC ET C EC
ET;C Z
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi KT;C rT;C CpT;C
qt Z qc K bqf
(9)
(10)
2.8. Experimental set-up and results Orthogonal cutting tests were performed on a 10% Al2O3/6061 aluminium metal matrix composite bar with a diameter of 32 mm. The cutting parameters, 85 m/min cutting speed, 3 mm depth of cut and a range of feeds from 0.1 to 0.3 mm/rev, were adopted in this experiment. Coated tungsten carbide cutting tools with a sharp cutting edge were used. Cutting forces were measured using a 3-component piezoelectric dynamometer connected to a series of charged amplifiers. An A/D converter was used to convert the voltage output from the charge amplifiers to digital format. Chips were collected after each cutting experiment and analyzed under the optical and SEM microscope. Cutting force data was captured, plotted and analyzed (Fig. 3).
(6)
where qpl is the heat rate generated per unit volume, hm is the fraction of dissipated mechanical energy converted to pl heat, spl eqv is the equivalent stress, and 3_ is the plastic strain rate. The chip carries away a high fraction of the heat and the rest is dissipated into the workpiece and the cutting tool.
(8)
The heat flux density leaving the tool/chip interface as a function of frictional heat generation qf, heat flux due to deformation of the chip material at the sticking friction region qc and b is given by
In machining, most of the energy spent in deforming the material to generate chips and to sliding the chip along the rake face is converted into thermal energy. The heat generated during machining is one of the main parameters that govern the tool wear mechanisms and failure. As a result of plastic deformation, the heat generated gives rise to heat rate per unit volume pl qpl Z hm spl eqv 3_
(7)
Fig. 3. Orthogonal cutting experimental set-up.
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the deformed chip thickness and the chip–tool contact length can be estimated.
Feed (mm/rev)
Cutting force (N)
Feed force (N)
0.1 0.2 0.3
118 187 247
62 96 121
The measured cutting force and feed force under different feeds are illustrated in Table 4.
3. Results and discussions 3.1. Overview The cutting tool is advanced incrementally into the workpiece from the initial position as shown in the Fig. 4(a–d). The chip is formed gradually until the steady state is attained and the cutting forces reach constant value. For each increment in the simulation, the shape of the deformed chip, the stress and strain distributions in both the chip and workpiece, as well as the temperature distribution in the workpiece/chip/tool interface are predicted. At the initiation of the incipient stage, the chip/tool contact area is small, which is subjected to a high concentrated load as shown in Fig. 4(a). As the tool advances, penetrating deeper into the workpiece, more plastic deformation of the workpiece material is generated along the rake face as shown in Fig. 4(b). The chip flow over the rake face was initiated when the full chip/tool contact area was achieved as can be seen in Fig. 4(c). Thus the resistance to the tool penetration decreases, which in turn results in a thinner primary deformation zone as shown in Fig. 4(d). Moreover, when the steady state condition is achieved, shown in Fig. 4(d),
3.2. Cutting and feed forces In order to validate this model, a comparison between the predicted and experimental cutting and feed force was made as shown in Fig. 5. The cutting and feed forces, as predicted by the finite element method, were found to increase almost linearly with increasing feed rate, thus, conforming to the results obtained in experiments. Moreover, the predicted and measured results show a divergence of about 9%, which was assumed to be an acceptable level of agreement. Due to the different tool/hard particle interaction mechanisms operating in the machining process, the cutting forces generate peaks and troughs which is in good agreement with the observations in the literature [14]. These fluctuations achieved in the cutting forces have been analyzed using a spectrum analysis [9]. The existence of the hard particles lead to large fluctuations in the cutting forces. In addition, it was found that the position of the hard particle relative to the tool motion also affects the magnitude and frequency of these fluctuations. There can be three possible encounters of the cutting tool: (1) insert cutting through the matrix alone, (2) insert encountering aluminium oxide particle and debonding and/or particle pullout, (3) tool ploughing through the matrix or aluminium oxide. This finite element model is able to predict the effect of alumina particles and encountering conditions on the fluctuations of cutting forces during machining with a tungsten carbide cutting tool. 3.3. Von Mises equivalent stress distribution on the workpiece and cutting tool Von Mises equivalent stress contours at steady state are shown in Fig. 6(a) for the case of feedZ0.2 mm/rev.
Fig. 4. Chip formation during machining process. (a) Chip formation at tZ2.2 ms. (b) Chip formation at tZ11 ms. (c) Chip formation at tZ33 ms. (d) Chip formation at tZ99 ms.
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particle was found to have the highest value in the primary deformation zone which is due to the high compressive stress exerted by the cutting tool tip. The stress at the cutting tool tip depends on the tool encountering different constituents of the workpiece. The value is found to be high as the tool tip encounters a hard particle and is low as it shears through the soft ductile matrix. In the secondary deformation zone, similar observations are made. A gradual decrease of equivalent stress from the cutting tool tip into the insert is observed in all three feeds.
Fig. 5. Measured and predicted cutting forces.
During the orthogonal machining of MMC’s with a sharp tool, the chip is formed by shearing in the primary deformation zone. As a result of very high shear stresses and pressures at the chip–tool interface, a secondary deformation zone along the chip–tool interface also occurs. The magnitude of the Von Mises equivalent stress increases while the workpiece element goes through the primary deformation zone. In the primary shear zone, the value of Von Mises was in the range of 1080–1200 MPa, while, the secondary deformation zone had a higher value of 1320– 1758 MPa for different feeds from 0.1 to 0.3 mm/rev. The analysis reveals that high levels of work hardening exist in the matrix around the hard particles and thus high stresses are developed. This result is in agreement with the work of [15], who solved the problem of a plate with a circular elastic inclusion using Airy stress functions. However, with the irregular-shaped particles employed in this work, extremely high local stresses are developed at the particle corners. Particle clustering also leads to an increase in the stress on and around the hard particles. The Von Mises stress distribution on the alumina particle at different positions is presented on the un-deformed chip (A), primary zone (B) and secondary shear zone (C) as shown in Fig. 6(b). The equivalent Von Mises stress on the hard
3.4. Shear stress distribution on the workpiece and cutting tool The contours of shear stress in the workpiece are shown in Fig. 7(a) for the feed of 0.2 mm/rev. The shear stress changes from positive in the secondary deformation zone, with the values of 551, 968 and 607 MPa to negative in the primary deformation zone with the values of 447, 470 and 532 MPa for the feeds of 0.1, 0.2 and 0.3 mm/rev, respectively. The size and position of the hard particles not only change the magnitude of the stresses but also the pattern and trend, which can be visualized clearly in Fig. 7(b). The shear stress value is found to increase with increasing feeds. The shear stress on the hard particle, which is in the undeformed chip, primary deformation zone and secondary deformation zone, depicts negative shear stress values in the primary zone (B), ahead of the cutting tool and positive values in the secondary deformation zone (C). The highest shear stress on the alumina particle shows maximum value which is due to shearing. The shear stress ranges from 874 to 1100 MPa in the cutting tool for different feeds 0.1–0.3 mm/rev. By increasing the feeds, the increase of the shear stress can be attributed to the increase in the chip–tool interfacial friction due to the rubbing action of the abrasive particles.
Fig. 6. Von Mises stress distribution on the matrix and hard particle. (a) Contours of Von Mises equivalent stress distribution for feedZ0.2 mm/rev. (b) Von Mises stress distribution on the particles.
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Fig. 7. Shear stress distribution on the matrix and hard particle. (a) Contours of shear stress distribution for feedZ0.2 mm/rev. (b) Shear stress profile on the particles.
3.5. Temperature distribution on the workpiece and cutting tool Three main heat sources exist in the secondary deformation zone: plastic deformation within the chip that is in contact with the rake face, tool–chip interface friction, and chip sliding velocity. Among the above-mentioned sources the results indicate that the tool–chip interfacial friction is the most important factor in increasing temperature value. The contours of temperature in the workpiece are shown in Fig. 8(a–c) for different feeds from 0.1 to 0.3 mm/rev. The temperature generated along the tool–chip interface is
substantially higher than that in the primary shear zone. At 85 m/min cutting speed, maximum temperatures of 380, 390 and 398 8C were predicted along the chip–tool interface for different feeds 0.1–0.3 mm/rev. A large amount of heat is generated in the primary shear zone and the increase in temperature is entirely related to plastic deformation. Generally, the temperature is higher as the feed increases because of the increase in the rate of plastic deformation, which leads to a higher magnitude of energy input into the system. The temperature distributions on the cutting tool rake face for feed rates of 0.1, 0.2 and 0.3 mm/rev are shown
Fig. 8. Temperature distribution on the matrix. (a) Temperature contour for feedZ0.1 mm/rev. (b) Temperature contour for feedZ0.2 mm/rev. (c) Temperature contour for feedZ0.3 mm/rev.
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Fig. 9. Temperature distribution along the contact length.
in Fig. 9. As expected, the maximum temperature occurs on the area of the rake face, a distance away from the cutting edge. The location of maximum temperature depends on the condition encountered at the interface due to the existence of alumina particles, which will be discussed in Section 3.6. 3.6. Tool/particle contact mechanisms along interface High contact stresses between the hard particle and rake face are primarily responsible for the development of tool wear when machining metal matrix composites. Therefore, a better understanding of the phenomena occurring at the chip/tool interface should be useful in predicting and reducing tool failure. The alumina particles’ interface fails as it goes through the secondary shear zone. Thus, the hard particle is out of control by the aluminium matrix and scratches along the cutting tool rake face. A high shear stress, 785 MPa, on the alumina particle is generated due to the scratching between the hard particle and tool rake face. As part of the interface
fails, the alumina particle is still partly bonded by aluminium matrix. The hard particle scratches along the cutting tool rake face and generates high shear stress, 947 MPa, leading to abrasive wear. After experiments, the microstructure of the chips was investigated. Fig. 10(a) and (b) indicate the partly debonded and fully debonded particle. The interface failure was modeled in this work and analysis was incorporated in this paper. There are two main mechanisms between tool and hard particles observed in this work. As the chip is formed, the hard particles are sliding along the rake face and scratching as they move upward as shown in Fig. 11(a) and (b). Some fluctuations are observed in the contact stresses distribution due to the matrix hardening. After scratching a certain distance, the hard particle is pushed inside the chip. The contact between the cutting tool and the hard particle is lost and thus creates a gap between them as shown in Fig. 12(a) and (b). These two mechanisms have been confirmed by the experimental results. After experiments, the chips were collected and the microstructure observations were analyzed. Fig. 10(c) shows tracks caused by the particle’s scratching and being pushed inside the chip.
4. Conclusions The following conclusions can be drawn from this analysis: 1. A finite element model is developed and used to simulate orthogonal machining of aluminium/aluminium oxide particulate composite. It is believed that details afforded by this FE analysis will be of great importance for better
Fig. 10. SEM images showing different possible particles conditions and motions during machining. (a) Partly debonded alumina particle. (b) Fully debonded alumina particle [16]. (c) Hard particle is pushed inside the chip.
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Fig. 11. Schematic drawing of the chip/tool interaction and the corresponding stress distribution. (a) Contact condition between tool and hard particle. (b) Normal/shear stress distributions corresponding to the case in (a).
Fig. 12. Schematic drawing of the chip/tool interaction and the corresponding stress distribution. (a) Contact condition between tool and hard particle. (b) Normal/shear stress distributions corresponding to the case in (a).
2.
3.
4.
5.
understanding of the particle’s behavior during machining of MMC and can help in optimizing the process parameters. For all the feeds employed in this analysis, the predicted cutting force components increased with feed and the discrepancies between the predicted and measured values were within 9% errors. The simulation results of the Von Mises equivalent stress distributions on the aluminium oxide particles depict a gradual increase in the stress on particles in the undeformed chip and reach a peak value when the particles are in the primary shear zone. The shear stress distributions on the aluminium oxide ceramic particles show a reversal from negative stress values in the primary shear zone to a positive maximum in the secondary shear zone. There are some fluctuations of normal and shear contact stress values along the chip/tool interface, which corresponds to the different alumina particles/tool conditions. Due to the failure of alumina particle’s interface, the hard particles are debonded or partly debonded and scratch
the tool rake face, leading to a high tool wear that was shown by the high shear stress on the alumina particle.
Acknowledgements This research was supported by the NCE and AUTO-21C08 ‘High Speed Machining of Light Materials for Automotive Application’.
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