Multi-step 3-D finite element modeling of subsurface damage in machining particulate reinforced metal matrix composites

Composites: Part A 40 (2009) 1231–1239

Contents lists available at ScienceDirect

Composites: Part A journal homepage: www.elsevier.com/locate/compositesa

Multi-step 3-D finite element modeling of subsurface damage in machining particulate reinforced metal matrix composites Chinmaya R. Dandekar, Yung C. Shin * Center for Laser-based Manufacturing, School of Mechanical Engineering, Purdue University, West Lafayette, IN 47907, United States

a r t i c l e

i n f o

Article history: Received 21 October 2008 Received in revised form 27 April 2009 Accepted 18 May 2009

Keywords: C. Finite element analysis Damage prediction E. Machining A. Metal matrix composites

a b s t r a c t A multi-step 3-D finite element model using the commercial finite element packages Third Wave Systems AdvantEdgeÓ and ABAQUS/ExplicitÓ is developed for predicting the sub-surface damage after machining of particle reinforced metal matrix composites. The composite material considered for this study is an A359 aluminum matrix composite reinforced with 20 vol% fraction silicon carbide particles (A359/SiC/ 20p). The effect of machining conditions on the measured cutting force and damage is modeled by means of a multi-step fully-coupled thermo-mechanical model. Material properties are defined by applying the Equivalent Homogenous Material (EHM) model for the machining simulation while the damage prediction is attained by applying the resulting stress and temperature distribution to a multi-phase sub-model. In the multi-phase approach the particles and matrix are modeled as continuum elements with isotropic properties separated by a layer of cohesive zone elements representing the interfacial layer to simulate the extent of particle–matrix debonding and subsequent sub-surface damage. A random particle dispersion algorithm is applied for the random distribution of the particles in the composite. Experimental measurements of the cutting forces and the sub-surface damage are compared with simulation results, showing promising results. Ó 2009 Elsevier Ltd. All rights reserved.

1. Introduction Metal matrix composites offer high strength to weight ratio, high stiffness and good damage resistance over a wide range of operating conditions, making them an attractive option in using these materials for structural applications. Particulate reinforced composites offer higher ductility and their isotropic nature as compared to fiber reinforced composites makes them an attractive alternative. Popular reinforcement materials for these composites are silicon carbide and alumina particles, while aluminum, titanium and magnesium constitute as the most common matrix materials. Although these composites are generally processed near net shape, subsequent machining operations are inevitable. The inherent challenge in machining of these composites is the excessive tool wear and the subsequent damage in the material sub-surface. This paper deals with a multi-step 3-D finite element modeling approach for predicting the sub-surface damage of machined particulate reinforced composites. Machining of particulate reinforced metal matrix composites has been extensively studied experimentally [1–5] and numerically [6–10] in the past to assess the attendant tool wear, surface roughness, sub-surface damage and to predict cutting forces. Silicon carbide particle reinforced aluminum matrix composites * Corresponding author. Tel.: +1 765 494 9775; fax: +1 765 494 0539. E-mail address: [email protected] (Y.C. Shin). 1359-835X/$ - see front matter Ó 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.compositesa.2009.05.017

(SiCp/Al) have been the most popular amongst these studies, where the primary focus of experimental data was on the characterization of the excessive tool wear caused by the highly abrasive silicon carbide (SiC) particles, as severe tool wear usually resulted in the creation and progression of surface and sub-surface flaws. In terms of modeling machining of metal matrix composites (MMC), following strategies have been employed; (a) a micromechanics based approach (b) an equivalent homogeneous material (EHM) based approach and (c) a combination of the two approaches. The micromechanics and the equivalent homogenous material (EHM) based approaches have their respective advantages and disadvantages [11,12]. The micromechanics approach describes the material behavior locally, and hence it is possible to study local defects such as debonding. However it is computationally intensive and hence cannot be used for large scale deformation simulations. On the other hand the EHM approach loses the ability to predict the local effects, namely, the damage observed at the interface separating the two phases [11], while it is more computationally efficient for machining simulations. Therefore there is a need to harness the advantages of both the continuum and micromechanics models in their capability of predicting cutting forces and sub-surface damage. A number of attempts have been made in modeling machining of MMCs [7–10]. Although the results reported in these works seem reasonable, these studies have primarily focused on 2-D modeling of orthogonal cutting which is not realistic for actual

1232

C.R. Dandekar, Y.C. Shin / Composites: Part A 40 (2009) 1231–1239

machining. The modeling work has been focused on studying the failure at particle–matrix interface [7], the tool–particle interaction [8,9] and residual stresses with sub-surface damage [7,10]. The studies focused on predicting sub-surface damage have so far lacked in their representation of the interface, since the particles are considered to be perfectly bonded to the matrix. It is clear that the presence of reinforcement makes MMCs different from monolithic materials due to incorporation of superior physical properties into the MMC [13]. On the other hand, these reinforcement particles are responsible for very high tool wear and inferior surface finish when machining MMCs. Typical sizes of reinforcing particles are in the order of 10–30 lm diameter with reinforcements ranging from 5 to 30 vol%. Understanding the various failure mechanisms during machining of MMC’s is crucial in formulating a valid and representative machining model. Li et al. [14] characterized the different failure mechanisms during dynamic loading of MMC’s: (i) cracking of the reinforcing particles; (ii) partial debonding at the particle/matrix interface resulting in the nucleation of voids and (iii) the growth and coalescence of voids in the matrix. A good FEM model would be able to incorporate all the above failure modes based on the stress/strain state prevalent at the time of loading. This can be achieved by having a number of failure criteria by incorporating user defined material parameters for the different phases of the particle and matrix. The interface can be modeled using a cohesive zone model [11,15] to facilitate in capturing the interface mechanics. Prediction of damage based on either analytical or numerical studies helps in better design of tool geometry and selection of cutting parameters. In this paper, 3-D numerical simulations are conducted and compared with experimental measurements of cutting force and sub-surface damage for an A359/SiC/20p composite. 2. Modeling of 3-D machining of particulate reinforced metal matrix composites The multi-step approach utilizes a two step approach to predicting the behavior of composites during machining. In the first step an EHM model is used for the overall prediction of cutting forces, temperature and the stress distributions in the composite undergoing machining. The second step then involves applying the predicted stress and temperature distributions to a local three phase finite element mesh. The mesh is based on distinct properties of the particulate, matrix and particulate–matrix interface. The particulate is modeled as a linearly elastic isotropic material until failure. The matrix material on the other hand is considered as thermo-elastic–plastic and isotropic in nature while the particulate–matrix interface is modeled using cohesive zone elements. The continuum elements account for the deformation present in the particulate and matrix, while the cohesive elements account for the occurrence of debonding. 2.1. Matrix material modeling For modeling initiation and progression of damage in the A359 aluminum matrix, a thermo-elastic–plastic material model with isotropic and kinematic hardening is coded in FORTRAN in the form of a user material (VUMAT). The model is suitable for simulating processes involving high adiabatic shear localizations as observed in metal matrix composite machining. The first step in the trial stress radial return method for thermoelastic–plastic material implementation is calculating the trial stress [16,17]. The strain can be segregated into two parts; the elastic and the plastic part as given in Eq. (1) in indicial notation. The trial stress is then calculated from Eq. (2), where dij is the usual notation for the Kronecker–Delta symbol, and k and l are the Lame’s constants. K is

the bulk modulus, a is the coefficient of thermal expansion, T is the material temperature and Tr is the reference temperature.

eij ¼ eeij þ epij rij ¼ kekk dij þ 2leij  betaðT  T r Þdij b ¼ 3aK

ð1Þ ð2Þ ð3Þ

On determining the trial stress from Eq. (2), back stress (x) due to kinematic hardening and the deviatoric part of the back stress ðr  xÞ0 are obtained. The effective stress (re) as per the von Mises criterion is then calculated using Eq. (4), where ‘:’ denotes the double contracted dot product, of two second order tensors.

re ¼

 12 3 ðr  xÞ0 : ðr  xÞ0 2

ð4Þ

The plasticity is then checked by Eq. (5), where f is the yield function.

f ¼ re  R  ry

ð5Þ

where R is the isotropic hardening parameter and ry is the yield stress. Eq. (6) is then used to calculate the plastic multiplier

k_ ¼

f 3G þ H

ð6Þ

and the increment in the plastic strain is given by

e_ p ¼

3ðr0  xÞ k_ 2r e

ð7Þ

At the end of the time step the elastic/plastic strains along with the stress matrix are updated. The material is considered damaged once the equivalent plastic strain exceeds the plastic strain allowable by the aluminum matrix for all material integration points. 2.2. 3-D cohesive zone modeling Modeling of the interface between the particle and the matrix is achieved using cohesive zone elements. The cohesive zone model (CZM) has been successfully implemented in machining of ceramics [18] and predicting debonding at the fiber–matrix interface in machining of fiber reinforced composites [11]. A 3-D cohesive zone model has been developed for studying the damage during machining of the metal matrix composite. The cohesive model describes a relationship between the interfacial force and the crack opening displacement. In the CZM, the fracture process zone is simplified as being an initially zero-thickness zone, composed of two coinciding cohesive surfaces. Under loading, the two surfaces separate and the traction between them varies with separation distance according to a specified traction separation law. The cohesive element progressively degrades in stiffness as interfacial separation increases. When the opening displacement reaches the prescribed maximum, the cohesive element fails, suggesting separation and debonding of the interface. The crack propagation between the continuum elements progresses along the boundary. This feature of cohesive elements allows one to simulate debonding at the particle–matrix interface. The cohesive response addressed in the model here is based on Tvergaard’s assumed traction separation law [15] and applied by Foulk et al. [19] in studying the 3-D response of a SCS-6Trimetal21S[O]4 metal matrix composite to simulation fiber–matrix debonding. The cohesive equations necessary for defining the model are given below in Eqs. (8)–(14). The nondimensional parameter (n) in Eq. (8) relates the normal (un) and tangential (ut and us) separation to the maximum allowable normal (dn) and tangential (dt ds) separation of the cohesive element and hence accounts for the damage of the cohesive element. The cohesive element then fails when the value of n reaches 1.

1233

C.R. Dandekar, Y.C. Shin / Composites: Part A 40 (2009) 1231–1239

n¼

(   2  2 )1=2 2 un ut us þ þ dn dt ds

ð8Þ

The traction separation law is then implemented using Eq. (9) where rmax is the cohesive strength. In applying the traction separation law, the important parameters are the rmax and the normal separation energy (Gc), or n, while the shape of the traction separation law F(n) is considered to be of second order relevance [20,21].

FðnÞ ¼

27 rmax ð1  2n þ n2 Þ 4

ð9Þ

The normal separation energy (Gc) is the area under the traction separation curve and is shown in Eq. (10). Knowing the cohesive strength (Tn, Ts and Tt) and the Mode I (GIC) and Mode II (GIIC) fracture energies, where Mode I refers to the opening mode (tensile) while Mode II refers to the sliding mode (shear) of fracture. Eq. (10) then calculates the maximum allowable separation (d) distance of the cohesive element. In Eq. (14), a is the ratio of the shear to normal strength of the cohesive elements, which can be calculated from the given material properties.

9 Gc ¼ rmax d 16 un T n ¼ FðnÞ dn ut T t ¼ a FðnÞ dt us T s ¼ a FðnÞ ds GIIC a¼ GIC

ð10Þ ð11Þ ð12Þ ð13Þ ð14Þ

3. Material properties 3.1. Equivalent homogenous material properties

C p ðTÞ ¼ 819:4 þ 0:9ðTÞ 25 < T < 500

ð17Þ

3.2. Silicon carbide particles The silicon carbide particles are modeled as a linearly elastic material until complete failure, which depends on the failure stress. The particle average diameter modeled is 28 lm. The fracture properties for these particles are borrowed from scratch tests, which were carried out on Al–SiCp composites for measuring the wear of the composites [26–29]. Table 2 summarizes the additional material properties used for modeling the behavior of silicon carbide. The thermal conductivity (h(T)) in W/m K and the specific heat (Cp(T)) in J/g K of silicon carbide are calculated by Eqs. (18) and (19) as a function of the temperature (T), respectively [30].

hðTÞ ¼ 35:15  0:0537T þ 6  105 T 2  2  108 T 3

ð18Þ

C p ðTÞ ¼ 0:68 þ 1:3  103 T  1  106 T 2 þ 3  1010 T 3

ð19Þ

3.3. Aluminum matrix (A359)

The constitutive equation chosen to model the EHM material properties is based on the work of Li et al. [14,22], who studied high-strain rate deformation behavior of a A359/SiC/20p composite. The study was directed towards understanding the behavior of these composites under impact loading for ballistic applications where the experimental measurements were done using a Kolsky bar setup. The proposed constitutive equation is given in Eqs. (15) and (16). The temperature dependency is added to the constitutive model in the form of the last term in Eq. (15) based on the experimental tests carried out by Miguelez and Navarro [23] on a A359/ SiC/20p composite. Table 1 summarizes the values of the material constants and other material parameters necessary for modeling.

 0:45 !  0:45 ! _ e e_ 1þ rðvf ; e; e_ ; TÞ ¼ ro ðeÞgðvf Þ 1 þ _ vf eo e_ o   5:8 T  Tr 1 Tm  Tr gðvf Þ ¼ 1 þ 1:17vf þ 2:28v2f þ 21:0v3f

where r is the overall flow stress, vf the particle volume fraction, e the overall strain,e_ theOverall strain rate, T the temperature, ro(e) the stress–strain response of the matrix at quasistatic rates of deformation and g(vf) is the strengthening function dependent on the volume fraction. The workpiece material model is inputted in the FEM code AdvantEdgeÓ in the form of a user defined material, which includes the power-law strain hardening, thermal softening, and rate sensitivity [25]. Amongst the thermal properties provided by the manufacturer [24], the thermal conductivity at 22 °C is 185 W/m K and at 260 °C is 201 W/m-K. The specific heat (Cp(T)) in J/kg K is calculated by Eq. (17) as a function of the temperature (T). The coefficient of thermal expansion is 21.4  106 K1 in the temperature range of 25–500 °C.

Li et al. [14,22] conducted hardness tests on the A359/SiC/20p composite and the unreinforced A359 aluminum alloy. The measured hardness values of the matrix material and the unreinforced alloy were found to be very similar indicating that the rate dependent properties of the alloy and that of the matrix can be considered similar for the purposes of theoretical and analytical modeling. Eq. (20) is the constitutive model and the corresponding model coefficients are given in Table 3. Temperature dependent yield strength and ultimate strength properties for the A359 aluminum matrix were obtained from the ASM metals handbook [31]. The material model is written in the form of a User Material (VUMAT) in FORTRAN.

ð15Þ

 0:45 !  5:5 e_ T  Tr 1 rðe; e_ ; TÞ ¼ ro ðeÞ 1 þ _ eo Tm  Tr

ð16Þ

Thermal conductivity values were calculated from the thermal resistivity tests conducted by Brandt and Neuer [32] as these measurements were for an Al–Si alloy with % of Si as 9%, which has a similar composition to the A359 alloy. The value for the specific heat of aluminum A359 was obtained from the ASM metals hand-

ð20Þ

Table 1 Material constants for the EHM model.

e_ o Tr Tm E

m ry q

Rate sensitivity parameter Reference temperature Melting point [23] Young’s modulus [24] Poisson’s ratio Yield strength [14] Density [24]

1.47  105 s1 23 °C 615 °C 98.6 GPa 0.26 260 MPa 2.77 gm/cm3

Table 2 Properties of silicon carbide [30]. K E

m q a

Fracture toughness Young’s modulus Poisson’s ratio Density Coefficient of linear thermal expansion

3.9 MPa 408 GPa 0.183 3.2 gm/cm3 5.12  106 °C1

1234

C.R. Dandekar, Y.C. Shin / Composites: Part A 40 (2009) 1231–1239

Table 3 Material constants for the aluminum matrix model [31].

e_ o

Rate sensitivity parameter Reference temperature Melting point Young’s modulus Poisson’s ratio Yield strength Density

Tr Tm E

m ry q

1.47  105 s1 20 °C 593 °C 72 GPa 0.33 255 MPa 2.7 gm cm3

book [31]. The coefficient of thermal expansion of the A359 alloy ranges from 21  106 °C to 23.2  106 °C1 for a temperature range of 38 °C1–262 °C1 [33]. 3.4. Interface property The interfacial separation energy (U) is one of the most crucial property definitions for the cohesive zone model. This interfacial separation energy has a strong effect on the material response. Zhang et al. [34] have characterized the interfacial debonding computationally for an aluminum matrix reinforced with Boron carbide particles (Al/B4C). The parameters varied were the interfacial strength, interfacial energy, particle size and shape, volume fraction and strain rate and were checked with the stressstrain behavior of the composite in tension and compression. Since the Al–B4C composite shows similar behavior to the Al–SiC composite, it is possible to infer some important effects of the bond strength on the material behavior. Based on their results, the best description of a strong-brittle interface for the case of Al–SiC composites is given by a = 2 and U = 50 J/m2. These values correspond to the values used by Tvergaard [35] for carrying out the simulations for Silicon carbide whisker reinforced aluminum alloy composites. The interface strength is then calculated by Eq. (21). The value for the interfacial conductivity is kept constant at 3  107 W/m K [36].

a¼

rmax ry

Fig. 1. Global and local picture during machining of the MMC in a 2-D FEM representation.

ð21Þ

where rmax is the interface strength and ry is the matrix yield strength. 4. Simulation procedure In the multi-step method, the stress distribution in the composite is firstly calculated by running a 3-D (Equivalent Homogenous Model) EHM model. The calculated stress distribution is then applied to the local model of the machined surface to determine the sub-surface damage. A 2-D schematic of this method is shown in Fig. 1. Similarly other regions of 100 lm  100 lm  100 lm are selected along the cutting path at different locations in the workpiece. The 3-D EHM model is run using Third Wave Systems, AdvantEdgeTM FEM 5.1 machining simulation software. The module used for the simulations is the 3-D nose turning model. This model best approximates an actual turning process, as it accounts for the nose radius of the tool and also represents cutting by the primary and secondary cutting edges of the tool as compared to just the primary cutting edge in 2-D modeling. Fig. 2 shows the schematic of the nose turning module along with the mesh used in the analysis. The updated-Lagrangian finite element method along with continuous remeshing and adaptive meshing techniques is applied in the model. The XYZ coordinate system is defined as shown in Fig. 2 and it corresponds to the right-handed turning configuration. Four node, 12 degree-of-freedom tetrahedral finite elements are used to model the workpiece and tool. The boundary conditions specified are the fixed top and back surfaces of the tool in all directions.

Fig. 2. Initial mesh for machining of EHM MMC for 3-D nose turning model.

The workpiece is constrained in vertical (Z) and lateral (Y) directions on the bottom surface and workpiece moves at the specified cutting speed in the horizontal direction (X). In the local model, 3-D, eight node trilinear coupled temperature displacement elements (C3D8RT) with reduced integration and hourglass control [37] are used for meshing the particle and matrix, while the interface layer is modeled using the zero thickness 3-D cohesive elements. To confirm mesh size convergence in both the EHM and local models, test simulations with varying mesh sizes were conducted a cutting speed of 300 m/min and feed of 0.1 mm/rev. A comparison is made for the ratio of simulated to experimental measurements of the cutting force and damage depth, this ratio henceforth is referred to as normalized results for cutting forces and damage depth. In the EHM model the minimum element size close to the cutting edge is reduced in descending order of 0.05, 0.030, 0.022, 0.015 and 0.010 mm, corresponding to this the normalized cutting force is 0.891, 0.913, 0.927, 0.932 and 0.934, respectively. A minimum element size of 0.022 mm was finally selected for all other cutting conditions. For the local

1235

C.R. Dandekar, Y.C. Shin / Composites: Part A 40 (2009) 1231–1239

model, the number of elements along the interface was 16, 26, 39, 52 and 79 and the normalized damage depth was 0.83, 0.858, 0.874, 0.882 and 0.885. The number of elements along the interface selected is 52 elements which is a good balance in terms of computation time and the required accuracy. Prior to running the damage simulation, material properties inputted in the local model were verified by conducting a simple uniaxial tensile test on the 3-D representative volume element (RVE) used in the machining model. The RVE microstructure is periodic along the axes and hence periodic boundary conditions have been applied on the cube faces of the 3-D RVE used in the machining simulations. The mesh used in this study coincides with the meshes used in the machining analysis when considering mesh sensitivity. The simulated Young’s modulus varied less than 2% when simulated by the coarsest and finest mesh selected. The mesh with 52 elements along the interface gave a value of the Young’s modulus for the composite as 104.78 GPa which compares well with the analytical results for the elastic modulus. The lower limit of the Hashin–Shtrikman [38] bound predicts a Young’s modulus of 96.01 GPa while the upper limit predicts a Young’s modulus of 115.71 GPa. The cutting tool is a solid carbide tool with the nose radius of 80 lm, rake angle of 5° and the clearance angle equal to 11°. The depth of cut used is 1 mm and the friction coefficient at the tool–chip interface is calculated from the machining tests and is summarized in Table 4 along with the cutting conditions. The postprocessing is done in AdvantEdge to obtain the stress and temperature distribution and a sample result is shown in Fig. 3. Three regions are chosen to calculate the sub-surface damage as marked in Fig. 3. The actual locations of these regions are on the machined surface below the cutting tool near the marked areas. The resultant stress and temperature distribution is then applied to the local model.

Fig. 3. Stress distribution obtained from machining simulation software of a EHM MMC model using the 3-D nose turning option in Third Wave Systems AdvantEdge code.

4.1. Local multi-phase model The 3-D microstructure of the local model is generated using the (Random Sequential Adsorption) RSA algorithm proposed by Rintoul and Torquato [39]. Llorca and Segurado [40,41] used the RSA algorithm to calculate the coordinates of the spherical silicon carbide particles in an aluminum matrix composite. The RSA algorithm satisfies the condition of statistical isotropicity and is suitable for use in a finite element setting. Furthermore the particle volume fraction considered is 20% which is lower than the jamming limit of the RSA algorithm when considering a minimum separation distance between particles (30%) [40,41]. The constraints on the spherical particles are discussed in great detail in the aforementioned references. An additional constraint is added wherein the diameters of the particles are varied based on a normal distribution with a standard deviation of 4 lm. The standard deviation and average size of the particles for the normal distribution were calculated by using an image analysis code on an actual representative microstructure. The algorithm generates the coordinates for the spherical particles as shown in Fig. 4. Fig. 4 represents a random distribution for a 20% volume fraction of particles without the matrix surrounding it. The stress distribution obtained using the 3-D EHM model is then applied to this cubic cell sub-model. The boundary conditions

Fig. 4. Multiparticle spheres in a random arrangement for 20 vol% fraction.

for the local model are; the free surfaces below the machined surface are in contact with a region of elements defined by the EHM properties of the composite and the outer nodes of the cubic sample are constrained to move in the X and Y directions, where in the Z direction, the bottom surface is constrained. The cohesive section is defined by the *TRACTION SEPERATION [37] law. The damage initiation for the cohesive section is based on the *QUADS [37] function, which specifies the onset of damage based on the quadratic-traction interaction law for cohesive elements. The progressive damage evolution of the cohesive section is then based on the * ENERGY [37] approach, which accounts for the strain energy release rate. To ensure the stability of the model following measures were undertaken. In the simulation, numerical damping of 0.5 was used

Table 4 Cutting conditions. Cutting speed (m/min)

Feed rate (mm/rev)

Coefficient of friction

Rake angle

Nose radius (lm)

Depth of cut (mm)

Length of cut (mm)

150 150 300 300

0.05 0.1 0.05 0.1

0.45 0.43 0.45 0.48

5°

80

1

30

1236

C.R. Dandekar, Y.C. Shin / Composites: Part A 40 (2009) 1231–1239

for the quadratic bulk viscosity parameter in the ABAQUS/Explicit numerical scheme [37]. Another consideration in the stability of the model involves the contact definition between the continuum elements surrounding the cohesive zone. This is due to the inability of cohesive elements to sustain forces in the normal or tangential direction after element failure, resulting in penetration of the surrounding continuum elements. The penetration of the continuum elements is avoided by defining a soft contact pressure-overclosure relationship. The values for the pressure constant (P0) and the clearance constant (C0) used in the simulation are 500 MPa and 0.01 lm, respectively, which corresponds to the interface strength. In case of the clearance constant, previous research by Tian and Shin [18] showed that varying the clearance constant between 0.004 lm and 0.02 lm resulted in a negligible effect on the model. On the other hand reducing the value below 0.004 lm causes the simulation to be numerically unstable. 5. Experiments Machining tests were carried out on cast cylinders of A359/SiC/ 20p composites, supplied by MC-21 Inc. in the form of 68.5 mm diameter cylinders with a cut length of 152.4 mm. All machining experiments were conducted on a Jones and Lampson turning lathe. The cutting tool and conditions used for these experiments were the same as those used in simulations of MMC machining. No coolant was used in the machining of these composites. Force measurements were conducted during machining using a Kistler 9121 type dynamometer, the debonding depth and particle fracture was measured for the damage characterization using a scanning electron microscope (SEM) with an accelerating voltage of 20 keV. Several samples were first sectioned using a diamond wheel cutting machine and later the sectioned edge was polished using standard metallographic techniques (300, 400, 500, 600 grit) and the final stages used an aqueous suspension of 0.3 lm and 0.05 lm alumina.

for the condition of 300 m/min cutting speed and a feed rate of 0.05 mm/rev were 80 N and 56 N, respectively. For the case of feed rate of 0.1 mm/rev the simulated results were 128 N and 55 N, respectively. The coefficient of friction used in the simulations for all the cases was calculated from the experimental data. On the whole the cutting forces as well as the thrust force match very well with experimental data. The trend observed in all the cases is similar such that the simulation under-predicts the cutting force by 7–8% and the thrust force by 6–12%. Fig. 5 shows a representative comparison between the simulated and experimental data for a cutting speed of 300 m/min. The measurement of damage during machining of MMC samples was done by obtaining the SEM images. The images indicate the extent of debonding between the particles and the matrix along with particle fracture. The results indicate that the damage depth is primarily a function of the feed rate. Figs. 6 and 7 show the SEM images of the machined cross section at the feed rate of 0.05 mm/rev and 0.1 mm/rev at a cutting speed of 300 m/min, illustrating average sub-surface damage at 46 lm and 76 lm, respectively. As observed from the images it is clear that at the feed rates of 0.1 mm/rev there is presence of higher damage, which corresponds to the higher cutting forces observed during machining at higher feed rates. Regions of particle fracture have also been identified while machining at 300 m/min as marked in Fig. 7. Similar results were obtained from the SEM images for a cutting speed of

6. Experimental and simulation results The final reported value of the cutting force in Table 5 is the average of the steady state values for the two experiments conducted under the same cutting condition. The depth of cut was 1 mm and the length of each cut was 30 mm. For the measurement of damage, five measurements each from two different samples were done for all the cutting conditions. The reported value is the average value of these 10 measurements. A variation of 10– 15% is observed in the experimental measurements. At a cutting speed of 150 m/min and a feed rate of 0.05 mm/rev the simulated values of the cutting and thrust force were 78 N and 56 N, respectively. On the other hand at a feed rate of 0.1 mm/rev the simulated, cutting and thrust forces were found to be 126 N and 55 N, respectively. The simulated cutting force and thrust force

Fig. 5. Comparison of experimental and simulated results for cutting forces for machining at a cutting speed of 300 m/min.

Table 5 Cutting force data for machining of A359/SiC/20p specimens. Force data (N)

Main force (Fc)

Cutting speed (m/min)

Feed rate (mm/rev)

Data points 1

2

150

0.05 0.1 0.05 0.1

84 128 88 136

89 140 94 140

86 134 91 138

0.05 0.1 0.05 0.1

63 57 58 58

57 58 63 57

60 58 61 58

300 Thrust force (Ft)

150 300

Average

Fig. 6. Machined cross section at cutting speed of 300 m/min and a feed rate of 0.05 mm/rev.

C.R. Dandekar, Y.C. Shin / Composites: Part A 40 (2009) 1231–1239

Fig. 7. Machined cross section at cutting speed of 300 m/min and a feed rate of 0.1 mm/rev.

150 m/min at feed rates of 0.05 mm/rev and 0.1 mm/rev, where the average sub-surface damage depth was 36 lm and 68 lm, respectively. As with the case of machining at 300 m/min the maximum damage was observed for a feed rate of 0.1 mm/rev. It has been shown that the cutting speed has a minimal effect on the extent of damage.

1237

Representative sectioned images of the simulated 100 lm cubic local damage model are shown in Figs. 8 and 9 and for feed rates of 0.05 mm/rev and 0.1 mm/rev, respectively, at a cutting speed of 300 m/min, where the simulated von Mises stress distribution in MPa is shown. The regions of debonding and particle fracture are shown as insets of the regions where debonding and particle fracture occurred in Figs. 8 and 9. Similar simulation results were obtained for the cutting speed of 150 m/min. Overall the experimental measurements compared extremely well with the simulated results, wherein the simulated results were lower for all cases. This was consistent with the force comparisons while the thrust force was under predicted by the simulations. At a cutting speed of 150 m/min the simulated and experimental damage depths are 32 lm and 36 lm, respectively, for a feed rate of 0.05 mm/rev, while for a feed rate of 0.1 mm/rev the simulated and experimental measurements are 65 lm and 68 lm, respectively. At a cutting speed of 300 m/min and a feed rate of 0.05 and 0.1 mm/rev the simulated damage depths are 40.7 lm and 72 lm, respectively, as shown in Figs. 8 and 9, while experimentally measured damage depths are 46 lm and 76 lm for a feed rate of 0.05 and 0.1 mm/rev, respectively. Fig. 10 shows the comparison of the simulated and experimental damage depths. The% discrepancy varied from 3% to 12% in all the cases considered. During machining higher cutting forces create more damage in terms of particle fracture and increase in the debonding depth. This

Fig. 8. Damage observed to a depth of 40.7 lm for a cutting speed of 300 m/min and a feed rate of 0.05 mm/rev.

Fig. 9. Damage observed to a depth of 72 lm for a cutting speed of 300 m/min and a feed rate of 0.1 mm/rev.

1238

C.R. Dandekar, Y.C. Shin / Composites: Part A 40 (2009) 1231–1239

Acknowledgements The authors wish to gratefully acknowledge that this research was partially supported by the 21st Century Research and Technology Fund and the National Science Foundation (Grant No.: IIP0538786). References

Fig. 10. Comparison of damage measurement between simulated and experimental measurements as a function of the feed rate and the cutting speed.

phenomenon is due to the interaction between the matrix and the particles. In the MMC material it is seen that the strain in the particles is much less than that observed in the matrix due to the high difference in the modulus of elasticity of the two phases. At higher cutting forces there is a further increase in stress along the particle–matrix interface, resulting in particle fracture and deformation occurring at the bottom of the particle as seen in Fig. 9. The cutting forces and the damage prediction by the present model are comparable to the experimental results. The sub-surface damage model includes capabilities in predicting debonding, particle fracture and matrix void formation. One of the advantages of the model is the significant reduction of computation time due to the treatment of the machining problem as a multi-step simulation. The other advantage of the model is in its inherent simplicity in application and the ability to extend the model to include numerous materials. A limitation of the existing model is the use of the EHM model in predicting the cutting forces as it neglects the interaction of the tool with the particles. The interaction of the particles with the tool has been studied comprehensively by Pramanik et al. [8] and hence, for simplicity in applying the 3-D machining model, has been neglected in this study. Nevertheless the treatment of machining simulation as a 3-D nose turning results in incorporation of the effect of the tool nose radius and damage due to machining by the primary and secondary cutting edges. 7. Conclusions Multi-step 3-D machining simulations were conducted for an A359 aluminum matrix composite reinforced with 20 vol% fraction silicon carbide particles. The simultaneous use of the thermo-elastic–plastic failure model and the cohesive zone model to describe material behavior was successful in predicting the damage during machining of MMC’s. The results obtained from the EHM machining model compared well with the experimental data in terms of the measured cutting force. By successfully applying the EHM results for the stress and temperature distribution to the local multi-phase model damage depth was predicted to within 3–12% of the experimental results. The damage depth increased with an increase in the cutting force, which confirmed that the damage depth is a function of the cutting force. The model presented in this study was able to predict all the failure phenomena; particle fracture, debonding at the particulate–matrix interface and matrix void formation. The presented multi-step 3-D machining model therefore has been able to successfully predict the cutting forces and sub-surface damage for a particulate reinforced MMC.

[1] Pramanik A, Zhang LC, Arsecularatne JA. Prediction of cutting forces in machining of metal matrix composites. Int J Mach Tools Manuf 2006;46:1795–803. [2] Kishawy HA, Kannan S, Balzainski M. An energy based analytical force model for orthogonal cutting of metal matrix composites. Ann CIRP 2004;53(1):91–4. [3] El-Gallab M, Sklad M. Machining of Al/SiC particulate metal matrix composites – Part I: Tool performance. J Mater Process Technol 1998;83:277–85. [4] Lin JT, Bhattacharyya D, Ferguson WG. Chip formation in the machining of SiC particle reinforced aluminum matrix composites. Compos Sci Technol 1998;58:285–91. [5] Kannan S, Kishawy HA, Balazinski M. Flank wear progression during machining metal matrix composites. J Manuf Sci Eng 2006;128:787–91. [6] Ramesh MV, Chan KC, Lee WB, Cheung CF. Finite-element analysis of diamond turning of aluminum matrix composites. Composites Sci Technol 2001;61:1449–56. [7] Monaghnan J, Brazil D. Modeling the flow processes of a particle reinforced metal matrix composite during machining. Compos Part A 1998;29(A):87–99. [8] Pramanik A, Zhang LC, Arsecularatne JA. An FEM investigation into the behavior of metal matrix composites: tool–particle interaction during orthogonal cutting. Int J Mach Tools Manuf 2007;47:1497–506. [9] Zhu Y, Kishawy HA. Influence of alumina particles on the mechanics of machining metal matrix composite during machining. Int J Mach Tools Manuf 2005;45:389–98. [10] El-Gallab M, Sklad M. Machining of aluminum/silicon carbide particulate metal matrix composites – Part IV: Residual stresses in the machined workpiece. J Mater Process Technol 2004;152:23–34. [11] Dandekar CR, Shin YC. Multiphase finite element modeling of machining unidirectional composites: prediction of debonding and fiber damage. J Manuf Sci Eng, Trans ASME 2008;130:051016-1–051016-12. [12] Camus G. Modelling of the mechanical behavior and damage processes of fibrous ceramic matrix composites: application to a 2-D SiC/SiC. Int J Solids Struct 2000;37:919–42. [13] Grabowski A, Nowak M, Sleziona J. Optical and conductive properties of AlSialloy/SiCp composites: application in modeling CO2 laser processing of composites. Opt Lasers Eng 2005;43:233–46. [14] Li Y, Ramesh KT, Chin ESC. Comparison of the plastic deformation and failure of A359/SiC and 6061-T6/Al2O3 metal matrix composites under dynamic tension. Mater Sci Eng 2004;371(A):359–70. [15] Tvergaard V. Effect of fiber debonding in a whisker-reinforced metal. Mater Sci Eng 1990;A25:203–13. [16] Lemaitre J, Desmorat R. Engineering damage mechanics: ductile, creep, fatigue and brittle failures. Berlin, Heidelberg: Springer-Verlag; 2005. [17] Dunne F, Petrinic N. Introduction to computational plasticity. New York: Oxford University Press; 2005. [18] Tian Y, Shin YC. Multiscale finite element modeling of silicon nitride ceramics undergoing laser-assisted machining. J Manuf Sci Eng, Trans ASME 2007;129:287–95. [19] Foulk JW, Allen DH, Helms KLE. Formulation of three-dimensional cohesive zone model for application to a finite element algorithm. Comput Methods Appl Mech Eng 2000;183:51–66. [20] Tvergaard V, Hutchinson JW. The relation between crack growth resistance and fracture process parameters in elastic–plastic solids. J Mech Phys Solids 1992;40:1377–97. [21] Hutchinson JW, Evans AG. Mechanics of materials: top–down approaches to fracture. Acta Mater 2000;48:125–35. [22] Li Y, Ramesh KT, Chin ESC. Plastic deformation and failure in A359 aluminum and an A359-SiCp MMC under quasistatic and high-strain-rate tension. J Compos Mater 2007;41:27–40. [23] Miguelez MH, Navarro C. Dynamic characterization at high temperature of MMCs with discontinuous reinforcement. J Phys IV 2000;10:305–10. [24] Duralcan MMC brochure. San Diego (CA): Alcan International Inc.; 1991. [25] Third Wave Systems, Inc. AdvantEdgeTM FEM 5.1 user’s manual. Minneapolis; 2008. [26] Zhang Z, Zhang L, Mai Y-W. Modelling friction and wear of scratching ceramic particle reinforced metal composites. Wear 1994;176:231–7. [27] Karamis MB, Tasdemirci F, Nair F. Failure and tribological behavior of the AA5083 and AA6063 composites reinforced by SiC particles under ballistic impact. Composites Part A 2003;34:217–26. [28] Zhang Z, Zhang L, Mai Y-W. Subsurface damage of ceramic particulate reinforced Al–Li alloy composite induced by scratching at elevated temperature. Mater Sci Eng 1998;A242:304–7. [29] Das S, Mondal DP, Dasgupta R, Prasad BK. Mechanisms of material removal during erosion-corrosion of an Al–SiC particle composite. Wear 1999;236:295–302.

C.R. Dandekar, Y.C. Shin / Composites: Part A 40 (2009) 1231–1239 [30] Handbook of ceramic composites. Kluwer Academic Publishers; 2005. [31] Metals handbook: properties and selection-nonferrous alloys and specialpurpose materials. ASM International; 1990. [32] Brandt R, Neuer G. Electrical resistivity and thermal conductivity of pure aluminum and aluminum alloys up to and above the melting temperature. Int J Thermophys 2007;28(5):1429–46. [33] Rohatgi PK, Gupta N, Alaraj S. Thermal expansion of aluminum-fly ash cenosphere composites synthesized by pressure infiltration technique. J Compos Mater 2006;40:1163–74. [34] Zhang H, Ramesh KT, Chin ESC. Effects of interfacial debonding on rate dependent response of metal matrix composites. Acta Mater 2005;53:4687–700. [35] Tvergaard V. Debonding of short fibres among particulates in a metal matrix composites. Int J Solids Struct 2003;40:6957–67.

1239

[36] Hasselman DPH, Donaldson KY, Geiger AL. Effect of reinforced particle size on thermal conductivity of particulate-silicon carbide-reinforced aluminum matrix composites. J Am Ceram Soc 1992;75:3137–40. [37] Hibbit, Karlesson and Sorenson Inc. ABAQUS user’s manual, version 6.5. Pawtucket, RI; 2004. [38] Hashin Z, Shtrikman S. A variational approach to the elastic behaviour of multiphase materials. J Mech Phys Solids 1963;11:127–40. [39] Rintoul MD, Torquato S. Reconstructions of the structure of dispersions. J Colloids Interf Sci 1997;186:467–76. [40] LLorca J, Segurado J. Three-dimensional multiparticle cell simulations of deformation and damage in a sphere-reinforced composites. Mater Sci Eng 2004;A365:267–74. [41] LLorca J, Segurado J. A numerical approximation to the elastic properties of sphere-reinforced composites. J Mech Phys Solids 2002;50:2107–21.