Multi-scale modeling to predict sub-surface damage applied to laser-assisted machining of a particulate reinforced metal matrix composite

Journal of Materials Processing Technology 213 (2013) 153–160

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Multi-scale modeling to predict sub-surface damage applied to laser-assisted machining of a particulate reinforced metal matrix composite Chinmaya R. Dandekar, Yung C. Shin ∗ Center for Laser-based Manufacturing, School of Mechanical Engineering, Purdue University, West Lafayette, IN, United States

a r t i c l e

i n f o

Article history: Received 24 February 2012 Received in revised form 6 September 2012 Accepted 13 September 2012 Available online 23 September 2012 Keywords: Finite element analysis Damage prediction Laser-assisted machining Metal matrix composite Multiscale modeling

a b s t r a c t A multi-scale finite element model (FEM) is developed to predict the post machined sub-surface damage in a particle reinforced metal matrix composite (MMC) subjected to laser-assisted machining (LAM). The MMC studied is an A359 aluminum matrix composite reinforced with 20% by volume fraction silicon carbide particles. In this model, molecular dynamics (MD) simulations are carried out to parameterize traction–separation laws for the aluminum–silicon carbide interface. The parameterized traction–separation laws are then input into a finite element model, in the form of a cohesive zone model to subsequently simulate the sub-surface damage. In this manner, the multi-scale hierarchical model successfully bridges the atomic, micro and macro scales. Average values of the predicted quantities are compared with experimental results, and the favorable agreement confirms the validity of the multi-scale FEM. © 2012 Elsevier B.V. All rights reserved.

1. Introduction In a push towards lightweight materials in the structural, automotive and aerospace industries, metal matrix composites (MMC) have garnered a lot of focus. Aluminum is a popular choice for lightweight applications, albeit in many cases it does not have the requisite strength or wear resistance. Addition of reinforcement materials such as ceramics increases the wear resistance and improves the specific stiffness and strength of the material, but this addition result in difficulty in machining. The addition of these reinforcement materials, size of reinforcement, volume fraction of the reinforcement and matrix properties as well as the distribution of these particles in the matrix are the factors that affect the overall machinability of these composites. Silicon carbide particle reinforced aluminum matrix composites (SiCp /Al) have been the most popular amongst previous studies, where the primary focus of experiments has been on the measurement of the attendant tool wear, surface roughness and sub-surface damage. In this study, we examine the modeling of laser-assisted machining (LAM) of particulate composites with an aim to minimize the sub-surface damage and compare the simulated cutting forces and sub-surface damage predictions to the experimental results. A number of modeling studies, primarily focused on 2D modeling of orthogonal cutting, have previously been conducted for

∗ Corresponding author. Tel.: +1 765 494 9775; fax: +1 765 494 0539. E-mail address: [email protected] (Y.C. Shin). 0924-0136/$ – see front matter © 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.jmatprotec.2012.09.010

conventional machining of MMC’s. The modeling work has been focused on studying the failure at particle–matrix interface by Monaghan and Brazil (1998), and residual stresses with sub-surface damage by El-Gallab and Sklad (2004). In studying the tool–particle interaction, Zhu and Kishawy (2005) simulated the machining of alumina/aluminum 6061 MMC with a tungsten carbide tool, while Pramanik et al. (2007) modeled the machining of a silicon carbide/aluminum 6061 MMC. The studies that focused on predicting sub-surface damage so far have lacked in a good representation of the interface, since the particles were considered to be perfectly bonded to the matrix. Recently, Dandekar and Shin (2008) have successfully predicted sub-surface damage during conventional machining of an A359/SiC/20p composite by considering the particle–matrix interface. The authors developed a multistep approach to predict the deformation, fracture and debonding behavior of composites during machining. The multi-step approach combines two modeling strategies: (a) an equivalent homogeneous material (EHM) based approach and (b) a micromechanics based approach. 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 model. The local model mesh is based on distinct properties of the particle, matrix and particle–matrix interface. In this manner the model harnesses the advantages of both the continuum (computational speed and simplicity) and micromechanics (consideration of local effects) models, enabling it to accurately predict cutting forces and sub-surface damage.

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In the multi-step model the particle–matrix interface is represented using a cohesive zone model (CZM); commonly used to describe idealized traction-displacement behavior for modeling interface debonding, transgranular and intergranular fracture. The traction–separation relationship in a CZM is generally parameterized through empirical data, such as the macroscopic fracture toughness data of the material (Zavattieri et al., 2001). Stress–strain data were obtained from the tests conducted on a large number of grains with an average grain size of 15–40 nm. The problem with inputting macroscopic/empirical values of fracture toughness is that these are aggregate responses of hundreds of thousands of grains applied to local interfaces where the fracture/debonding occurs. In this study, the multi-step model developed by Dandekar and Shin (2008) is improved upon by incorporating an additional step in the simulation procedure. The additional step involves obtaining the CZM properties of the particle–matrix interface via molecular dynamics (MD) simulations and subsequently applying these properties to the CZM used in the multi-step model. This step is important for estimating the CZM law of the Al–SiC composite interface as a function of temperature as data on the CZM law as a function of temperature for the material under study is not available. In Dandekar and Shin (2008), the traction–separation law was not only based on the cohesive strength and separation distance of the interface at room temperature but was also based on empirical results. These results are unacceptable for conducting LAM simulations; hence a need arises to provide data on the traction–separation law of the composite system at higher temperatures. The temperature dependent interface behavior for Al/SiC was determined by Dandekar and Shin (2011), through MD analysis. The results of that study are incorporated into the existing multi-step model presented in Dandekar and Shin (2008) to provide a more accurate analysis at elevated temperatures. This study therefore provides evidence on the applicability of multi-scale models (atomistic to continuum) in predicting complex processes such as laser assisted machining.

Fig. 1. Block diagram showing the simulation procedure for the multi-scale machining model.

investigation of interface behavior is necessary to deepen our understanding of the material behavior during composite machining. Fig. 1 shows, a flowchart of the overall methodology used in this study. MD simulations are first carried out to characterize the interface by obtaining a traction–separation law which is then input into the micro-scale Local Microstructure Model created in ABAQUS. Another model is used in running the 3-D machining simulations to obtain the cutting forces, stress and temperature distributions and is referred to as the EHM Machining Simulation model. The deformation history and temperature distributions from the EHM Machining Model are applied to the Local Microstructure Model to predict the sub-surface damage. 2.1. EHM machining simulation

2. Simulation procedure The necessity for multi-scale analysis of damage modeling in machining composite materials arises from the need to understand the evolution and progression of damage from the molecular level to the macroscale. Damage, as a process, leads to a gradual reduction in the load carrying capacity and ultimately becomes unstable, resulting in complete failure. In composite materials, damage happens at a number of length scales: (a) bond-breaking at the quantum scale, (b) dislocation and interface separation at the nanoscale, (c) particle/fiber and matrix microcracking at the microscale, and (d) finally, evolution of the microcracks into macrocracks. A number of methods have been proposed to simulate multiscale damage modeling. This is necessitated from a drive to reduce the computational cost, as it is not always necessary to calculate the full atomistic information for the entire simulation. This is achieved through the combination of atomistic simulations with continuum mechanics simulations. There are two trains of thought in implementing multi-scale simulations: on-the-fly concurrent multi-scale methods and hierarchical multi-scale methods. In this study, the hierarchical multi-scale method has been used in predicting the machining induced damage. While numerous studies have been performed to develop material constitutive models to represent the reinforcement and matrix, little work has been done to truly understand the physical contribution of the interface at the atomic scale for composite materials. An

In the multi-scale method, the deformation history and temperature distribution in the composite is firstly calculated by running a 3D equivalent homogenous model (EHM) shown in Fig. 2. An appropriate constitutive equation to model the EHM material properties of the composite was presented in Dandekar and Shin (2008). The form of the constitutive equation and relevant parameters are presented in Eqs. (1) and (2) and Table 1 respectively, where  is the overall flow stress, ε and ε´ are the overall strain and strain rate

Fig. 2. Stress distribution obtained from machining simulation software of an EHM MMC model using the 3-D nose turning option in Third Wave Systems AdvantEdge code.

C.R. Dandekar, Y.C. Shin / Journal of Materials Processing Technology 213 (2013) 153–160 Table 2 Constants for aluminum matrix constitutive model.

Table 1 Constants for constitutive equation in EHM model.

ε´ o Tr Tm E

v y 

1.47 × 105 s−1 23 ◦ C 615 ◦ C 98.6 GPa 0.26 260 MPa 2.77 gm/cm3

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

respectively, T is the temperature, vf is the particulate volume fraction and  o (ε) is a reference stress strain response at quasi-static deformation rates.



˙ T ) = o (ε)g(vf ) (vf , ε, ε,



× 1−

1+

 ε˙ 0.45   ε˙ o

 T − T 5.8 r Tm − Tr

g(vf ) = 1 + 1.17vf + 2.28v2f + 21.0v3f

155

1+

 ε˙ 0.45  ε˙ o

vf

(1)

(2)

The workpiece material model is inputted in the FEM code AdvantEdge© in the form of a user defined material, which includes the power-law strain hardening, thermal softening, and rate sensitivity (Third Wave, 2008). The calculated deformation history and temperature distribution is then applied to the local model of the machined sub-surface to determine the sub-surface damage. 2.2. Local microstructure model In the local model implemented in AbaqusTM , 3D, 20 node displacement, trilinear temperature, reduced integration elements (C3D20T) are used for meshing the particle and matrix, while the interface layer is modeled using the zero thickness 3D cohesive elements. The details of the local model, i.e., boundary conditions, mesh size, algorithm used in randomizing the particles and convergence studies, were presented in Dandekar and Shin (2008) and are not repeated here. An example of the local model structure, indicating the typical size and distribution of particles in the matrix is given in Fig. 3. Relevant constitutive models for the matrix, particle and interface are presented in the following sections. 2.2.1. Constitutive models The aluminum matrix was modeled using the Johnson–Cook type constitutive model in the form of a user material (VUMAT) in ABAQUS. A modification done to the material models in Dandekar and Shin (2008) is the addition of a strain gradient plasticity (SGP) model to the aluminum matrix. Traditional plasticity models

ε´ o

1.47 × 105 s−1 20 ◦ C 593 ◦ C 72 GPa 0.33 255 MPa 2.7 gm/cm3

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

Tr Tm E

v y 

describing crack growth can only be used for predicting weak to moderately strong interfaces. At small length scales experimental evidence has suggested that in metal parts having a characteristic dimension less than 100 micron, plasticity exhibits the size effect. In FEM codes elements usually follow the definition of classical continuum plasticity (CP). The drawback of using CP in crack simulations is that it neglects the length scale, viz., the size effect as indicated by Fleck and Hutchinson (1997) and Gao et al. (1999). Also crack growth is prevented due to the phenomenon of crack blunting in continuum plasticity, a result of the interface strength being 4–5 times larger than the material yield strength. It has been shown that cohesive strengths determined by MD are approximately 5–10 times larger than the yield strength of the material at the macroscale. Therefore in contradiction to experimental observations, numerical simulations would result in a crack unable to grow. In this study the SGP model of Gao et al. (1999) is used, which is built on the Taylor-based nonlocal theory of plasticity. This model has proven to be successful in representing the size effect in plasticity for various applications. Details of the implementation in the form of a user material (VUMAT) can be obtained from literature. One of the key features of the Taylor-based nonlocal theory of plasticity is that it does not involve higher order terms while preserving the structure of classical continuum mechanics. Therefore, the model has the advantages of a simpler implementation as compared to other strain gradient plasticity theories found in literature. The non-local theory of plasticity has proven to be successful in representing the size effect in plasticity for a number of different problems such as bending (Gao and Huang, 2001), growth of voids and microvoids (Huang et al., 2004), particle size effect in composites (Hwang et al., 2004), microindentation (Gao and Huang, 2001) and micromachining (Liu and Melkote, 2006). For the SGP model used in this study the following material parameters are necessary: the Burgers vector b of aluminum is 0.283 nm, shear modulus G is 28 GPa and the coefficient ␥ in the Taylor dislocation model is 0.248 for aluminum. Corresponding to this the material length scale is calculated as 3.77 ␮m, at a reference stress of 255 MPa. The extended Johnson–Cook type constitutive model with strain gradient plasticity is given in Eq. (3), where the relevant constants are given in Table 2.



˙ T ) = o (ε) JC (ε, ε,

1+

 ×

 1+

 ε˙ 0.45   ε˙ o

18 2 G2 b JC LSG

1−

 T − T 5.5 r Tm − Tr

 (3)

Silicon carbide particles were modeled as an isotropic linearly elastic material; with Young’s modulus of 408 GPa, Poisson’s ratio of 0.183, 3.2 g/cm3 density and thermal expansion of 5.12 × 10−6 ◦ C−1 .

Fig. 3. Local model structure: Randomly oriented 20 vol% SiC particles joined by an interface layer to an aluminum matrix.

2.2.2. Cohesive zone model 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 in accordance with a

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C.R. Dandekar, Y.C. Shin / Journal of Materials Processing Technology 213 (2013) 153–160 Table 4 Factors considered and their corresponding levels. Factor

Level-1

Level-2

Level-3

CO2 Laser power – PCO2 (W) Workpiece diameter –Dw (mm) Cutting speed – Vc (m/min) Feed – f (mm/rev)

100 20 50 0.01

800 45 200 0.1

1500 70 450 0.2

law, the maximum cohesive strength and the maximum separation distances. Fig. 4. Traction–separation relationship for Mode I failure in an Al–SiC interface.

specified traction–separation law. In this study, an exponential traction–separation law is adopted based on the MD simulation results. Dandekar and Shin (2011) modeled the interface behavior between two dissimilar materials of Al and SiC. Details of the modeling procedure are not presented and interested readers are referred to Dandekar and Shin (2011). In this study traction–separation laws parameterized via MD simulations for a plastic (Al)–brittle (SiC) interface are used as inputs to the CZM embedded in the 3D multi-phase model of the composite. In order to determine the temperature dependence of the interface, constant temperature MD simulations were carried out at 23 ◦ C, 200 ◦ C, 400 ◦ C, and 600 ◦ C. An example of the traction–separation curve under Mode I loading is shown in Fig. 4. Regardless of the temperature of the system or the mode of failure, the traction always initially increases to a peak value and decreases to near zero when the crack opening becomes large. A 3D CZM is utilized in the FEM model. The non-dimensional parameter () in Eq. (4) relates the normal (un ) and tangential (ut and us ) separation to the maximum allowable normal (ın ) and tangential (ıt and ıs ) separation of the cohesive element and hence accounts for the damage of the cohesive element. The cohesive element then fails when the value of  reaches 1. =



un ın

2

+

 u 2 t

ıt

+

 u 2 1/2 s

3. Experimental procedure 3.1. LAM thermal modeling The temperature distribution in the workpiece undergoing LAM needs to be predicted so that the experimental process of LAM can be accurately explored and controlled. A transient, three-dimensional, finite volume thermal model for a cylindrical workpiece has been developed at Purdue University. A detailed description of the thermal model, including the governing heat transfer equations, boundary conditions, and the numerical scheme is provided by Tian and Shin (2006). The thermal model is used for determining the material removal temperature only for experimental purposes and is not used for the finite element simulations. To conduct thermal model simulations, homogenized thermal properties and the absorptivity of the surface to the CO2 laser wavelength are necessary so as to determine the amount of laser heating needed. The thermal properties were provided by the manufacturer: 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. (6) as a function of temperature (T). The coefficient of thermal expansion is 21.4 × 10−6 /K in the temperature range of 25–500 ◦ C. The density of the composite is kept constant over the temperature range and is obtained through a simple rule of mixtures as 2770 kg/m3 .

(4)

ıs

Cp (T ) = 819.4 + 0.9(T )

The traction–separation law (F()) is then implemented through Eq. (5). In Eq. (5) the maximum cohesive strength ( max = 3.77 GPa) is simulated at room temperature, with the temperature (T) in degrees Celsius. The constants parameterized from the MD results of Mode I and Mode II failure are A = 15.98 and B = 5.906. Also obtained from the MD results is the ratio of the shear to normal strength of 0.73, which is necessary in modeling the CZM. F() = Amax  exp(−B) × (1 − 0.001T )

(5)

˚ and tangential (ıt The maximum allowable normal (ın = 28 A) ˚ separation of the cohesive element corresponds to and ıs = 37 A) the separation distance at which the traction decreases to near zero value. The result for the maximum tractions as a function of the simulated temperature is summarized in Table 3. The model presented here is similar to the one in Dandekar and Shin (2008) with the differences being in the functional form of the traction–separation Table 3 Simulation results to gage the effect of temperature on the traction. Case

Simulated Temperature (◦ C)

Maximum Mode I traction (GPa)

Maximum Mode II traction (GPa)

1 2 3 4

23 200 400 600

3.77 3.30 2.42 1.90

2.76 2.41 1.76 1.40

25 < T < 500

(6)

The absorptivity of the graphite-coated and uncoated composite surfaces to the CO2 laser wavelength is generally necessary to determine the amount of heat influx due to laser-heating. The laser can interact with both uncoated and graphite-coated regions of the workpiece. The extent to which these interactions occur depends on the axial distance between the laser and the tool, or laser lead distance. As the laser lead distance increases, the laser irradiates less of the uncoated chamfer of the workpiece and more of the coated surface. Through a sensitivity analysis it was established that the optimal laser-tool lead distance needs to be larger than 2.4 mm to maintain a steady state temperature. In this scenario the laser only irradiates the coated surface. The absorptivity of the graphite coating was previously measured to be 0.80 for a wavelength of 10.6 ␮m by Anderson et al. (2006). In order to design experiments with controlled temperatures, a parametric relationship was established between the average material removal temperature (Tmr ), and CO2 laser power (PCO2 ), the workpiece diameter (DW ), the feed (f) and the cutting speed (VC ). An L27 experimental design was chosen and the thermal model was run for the conditions in Table 4. Several other parameters such as depth of cut (d), absorptivity (˛), emissivity (εIR ), laser beam diameter (Dl = 4 mm) and laser tool lead distance (Ll = 3 mm), were held constant. The resulting equation for Tmr is given in the results section.

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Fig. 5. Schematic of LAM experimental setup with the CO2 laser.

Table 5 Tooling summary. Parameter

Level

Tool material Tool geometry Tool holder Side rake angle (◦ ) Lead angle (◦ ) Back rake angle (◦ ) Nose radius (mm) Edge radius (mm)

Kennametal K68 SPG422 CSRPL-164D +5 +15 0 0.8 0.024

157

Prior to each LAM test, the surface of each workpiece was sandblasted and coated with Cotronics 931 Graphite Adhesive. This preparation increased the absorptivity of the workpieces at the laser’s wavelength of 10.6 ␮m. During machining tests, cutting forces were measured with a three-component Kistler 9121 dynamometer and Kistler 5184B1 amplifier at a sampling rate of 100 Hz. Temperature profiles during LAM were measured using a noncontact FLIR SC3000 infrared camera. The IR camera was set horizontally and located 225◦ downstream from the tool. An emissivity value of 0.85 known from previous work (Anderson et al., 2006) was used for the graphite-coated surface. The IR camera tracked the maximum temperature along the center line of the workpiece at 10 frames per second. The following parameters were used to validate the thermal model: a cutting speed of 50 m/min, a feed of 0.05 mm/rev, a depth of cut of 0.76 mm, laser power of 400 W, 600 W and 900 W, and a preheating time of 6 s. Debonding depth was measured for the damage characterization using a scanning electron microscope (SEM) with an accelerating voltage of 20 keV. The specimens for damage measurement were first sectioned using a diamond wheel, incased in Bakelite, then polished using standard metallographic techniques (320, 400, 500, 800 grit) and the final polishing stage used an OIL suspension of 6 ␮m diamond and an aqueous suspension of 0.05 ␮m silica. Debonding was identified by voids in the matrix at the interface with the particle while particle fracture was considered when voids were present in a large solitary particle, as seen in Fig. 6. The depth of damage was recorded by finding the transition location from the damaged zone to the undamaged zone.

4. Results 3.2. Experiment details 4.1. Laser heating validation The machining experiments were conducted on a laser-assisted machining setup, which is comprised of a 20 Hp Jones and Lampson CNC turret lathe and a 1.5 kW CO2 Coherent Everlase S51 laser. The 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. A coolant was not used for any of the machining experiments, and air was introduced to the cutting zone to prevent contamination of the laser optics. The laser irradiates a circular spot (laser spot size = 4 mm) on the workpiece, which is 55◦ upstream of the cutting tool in the circumferential direction and 3 mm upstream of the tool in the axial direction. A schematic of the LAM experimental setup is shown in Fig. 5, while details of the tooling setup are summarized in Table 5.

Measured thermal histories agreed well with simulations in validation experiments. A sample comparison for laser power of 600 W is shown in Fig. 7. The large fluctuations primarily during the pre-heating cycle are due to the burning of the graphite coating. It is evident from the figure that there is a good agreement between the measured and predicted data, thereby proving the validity of the material properties inputted in the model. A multivariate regression analysis was performed on the thermal model simulation results to obtain an equation for Tmr . The high R2 value of 0.953 indicates that the equation developed accurately captures the simulation data. Subsequently, the laser power corresponding to the material removal temperature and

Fig. 6. Examples of particle debonding, left, and particle fracture right when analyzing sub surface damage.

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Fig. 7. Thermal model validation for a laser power of 600 W, the solid line corresponds to the 10 point moving average. VC = 50 m/min, f = 0.05 mm/rev, d = 0.76 mm.

the cutting conditions can be calculated using Eq. (7). This was utilized to obtain the desired Tmr for experimental trials. Tmr = 210.6

PCO2 0.56 Dw 0.86 f 0.15 v0.28

25 < T < 500

Fig. 9. Cross section of the A359/SiC/20p composite showing the initial microstructure far from the surface.

(7)

4.2. Cutting force results It has been exhaustively shown for various materials that during LAM, cutting forces decrease with an increase in the Tmr . The resultant cutting forces are an average of six measurements for each condition. The error bars in all the figures stand for the standard deviation of the measurements and Table 6 summarizes the experimental data of the cutting forces. As expected the cutting forces decreased with an increase in Tmr : 13% for cutting force (Fc ) and 27% for thrust force (Ft ) for LAM at Tmr of 400 ◦ C. The multi-scale FEM simulations conducted to predict the cutting forces show a good agreement to the experiments (Table 6) and this comparison is shown in Fig. 8. Overall, the good agreement seen in Fig. 8 justifies the use of the EHM machining model for predicting deformation history and temperature generated in machining and subsequently the sub-surface damage. The trend observed in all the cases is similar with the simulation over-predicting the cutting force by 5–7% and thrust force by 12–15%. 4.3. Sub-surface damage To inspect damage after machining, SEM images were obtained by studying the interior cross-sections of the workpieces. Fig. 9 shows the initial microstructure of the composite sample that was used for the machining experiments. The initial sample is relatively damage free with only a few pores observable in the matrix. For each cutting condition, three measurements from each workpieces were done. The reported value is the average value of these 6 measurements, where a variation of 14% was observed in the

Fig. 8. Comparison between experimental and simulated results for the cutting forces for machining at VC = 50 m/min, f = 0.1 mm/rev, and d = 0.76 mm (1 cm3 of material removed).

experimental measurements. The images indicate the extent of debonding between the particles and the matrix along with particle fracture. Consistent with the observation of a small range of the Ft /Fc ratio, the sub-surface damage of the composite for Tmr of 200, 300 and 400 ◦ C remained fairly constant. The results indicate that the damage depth with LAM is relatively independent of the Tmr . Figs. 10–12 show the SEM images of the cross sections of the machined parts at the feed rate of 0.1 mm/rev, cutting speed of 150 m/min and depth of cut of 0.76 mm and Tmr of 200, 300 and 400 ◦ C respectively. On the other hand, conventional machining resulted in excessive particle fracture, which is very prominent as shown in Fig. 13, while it was nearly absent in the parts produced by LAM. For all cutting conditions the sub-surface damage has been measured after machining 20 mm (length of cut) with fresh cutting tools. At a cutting speed of 150 m/min the average subsurface damage depth was 68 ± 14 ␮m, 45 ± 6 ␮m, 39 ± 6 ␮m and 41 ± 4 ␮m for Tmr of 23, 200, 300 and 400 ◦ C respectively. A good agreement between the experimental and simulated sub-surface damage measurements was obtained as shown in Fig. 14. With the % discrepancy between experimental and simulated values varying from 7% to 12% in all the cases considered. 5. Discussion One of the advantages of the model is the significant reduction of computation time due to the treatment of the machining problem

Fig. 10. Machined cross section at Tmr of 200 ◦ C, cutting speed of 150 m/min, depth of cut of 0.76 mm and a feed rate of 0.05 mm/rev. The top surface of the image is 10–15 ␮m below the machined free surface.

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159

Table 6 Cutting conditions and results after machining 1 cm3 of material. Case

Tmr (◦ C)

f (mm/rev)

VC (m/min)

d (mm)

Fc (N) Expt.

Fc (N) Sim.

Ft (N) Expt.

Ft (N) Sim.

1 2 3 4

23 200 300 400

0.1 0.1 0.1 0.1

50 50 50 50

0.76 0.76 0.76 0.76

117 112 104 101

126 118 110 109

70 58 51 51

82 68 60 58

Fig. 11. Machined cross section at Tmr of 300 ◦ C, cutting speed of 150 m/min, depth of cut of 0.76 mm and a feed rate of 0.05 mm/rev. The top surface of the image is 10–15 ␮m below the machined free surface.

Fig. 12. Machined cross section at Tmr of 400 ◦ C, cutting speed of 150 m/min, depth of cut of 0.76 mm and a feed rate of 0.05 mm/rev. The top surface of the image is 10–15 ␮m below the machined free surface.

Fig. 13. Machined cross section for conventional machining case at cutting speed of 150 m/min, depth of cut of 0.76 mm and a feed rate of 0.05 mm/rev. The top surface of the image is 10–15 ␮m below the machined free surface. There is significant damage and hence only a few measurements are marked.

as a multi-scale simulation. Another key aspect is the applicability of the MD results for characterizing the interface at various temperatures. This is extremely important when simulating LAM as machining is carried out at high temperatures, while experimental values of CZM are usually obtained from room temperature tests and hence CZM parameters are unknown at those elevated temperatures. Another advantage of the model is in its inherent simplicity to apply and to extend the model to include numerous materials. The limitation of the proposed multiscale model is the use of the EHM model in predicting the deformation history as it neglects the interaction of the tool with the particles. A comprehensive model would incorporate an on-the-fly type concurrent multi-scale model, wherein 3-D machining simulations can be carried out with discrete particles embedded in the matrix in the form of an FEM domain with the interface between the particles and matrix discretized by a molecular dynamics domain. In absence of an on-the-fly concurrent multi-scale method, which is computationally costly, the multi-scale model presented in this study, while being computationally efficient, is a good tool in predicting subsurface damage in laser-assisted machining. Improvements to the modeling results can allow for prediction of tool wear based on a methodology outlined by Rao et al. (2011), who predicted tool wear in face milling of titanium alloy, Ti–6Al–4V. The tool wear model can be parameterized to predict the tool wear rate by using the output from the FEM simulations along the flank face of the normal stress, chip velocity and temperature and inputting it into the appropriate wear rate model such as the model developed by Usui et al. (1984). Similar approaches were used by others. Filice et al. (2007) showed the feasibility of tool wear prediction for uncoated carbide tools by adopting Takeyama and Murata’s model (1963) in FEM simulation. Attanasio et al. (2008) successfully predicted flank wear of uncoated WC tool during 3D turning of AISI 1045 steel, based on the modified Takeyama and Murata’s (1963) diffusion model. Yen et al. (2004) adopted Usui’s (1978) model to predict tool wear of uncoated carbide tool during machining of plain carbon steel and Özel (2009) recently successfully predicted the tool wear rate of polycrystalline cubic Boron nitride for turning of AISI 4340 using the adhesive wear model by Usui et al. (1978) based on the interface temperature, normal stress and sliding velocity. Other predictions such as surface roughness are difficult to predict through only FEM analysis. Lin et al. (2007) predicted the

Fig. 14. Comparison of damage measurement between simulated and experimental measurements as a function of the material removal temperature (Tmr ).

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surface roughness using AdvantEdge©, for turning of various materials and obtained favorable results. The authors have provided a detailed description of the methodology used in their study. Sartkulvanich et al. (2007) simulated hard roller burnishing and qualitatively predicted the surface finish through FEM simulations. The authors state that only qualitative results of surface roughness can be provided through FEM simulations and this can be explained by the numerical error produced during FEM calculations, due to the 2D plane strain assumption in 2D machining simulations and the absence of stiffness and dynamics of the machine tool and workpiece setup. 6. Conclusions A multi-scale 3-D machining model was developed to simulate LAM of A359 aluminum (Al) matrix composite reinforced with 20% by volume fraction silicon carbide (SiC) particles. A good agreement has been found between model predictions and experimental measurements of the cutting forces and the sub-surface damage. The results obtained from the EHM machining model compared well with the experimental data in terms of the measured cutting force. Molecular dynamics (MD) simulations were carried out to obtain traction–separation laws for Al–SiC interface, which were embedded in a cohesive zone model (CZM). CZM laws for Mode I and Mode II loading at high temperatures were successfully parameterized via MD simulations. By successfully applying the EHM results in the stress and temperature distribution to the local multi-phase model damage depth was predicted to within 7% to 12% of the experimental results. Acknowledgements The authors wish to gratefully acknowledge the financial support provided for this study by the National Science Foundation (Grant Nos: 0538786-IIP and 0917936-IIP), State of Indiana through the 21st Century R&T Fund, and Industrial Consortium members of the Center for Laser-based Manufacturing. References Anderson, M., Patwa, R., Shin, Y.C., 2006. Laser-assisted machining of Inconel 718 with an economic analysis. International Journal of Machine Tools and Manufacture 46, 1879–1891. Attanasio, A., Ceretti, E., Rizzuti, S., Umbrello, D., Micari, F., 2008. 3D finite element analysis of tool wear in machining. CIRP Annals – Manufacturing Technology 57, 61–64. Dandekar, C.R., Shin, Y.C., 2008. Multi-step 3D finite element modeling of subsurface damage in machining particulate reinforced metal matrix composites. Composites Part A Applied Science and Manufacturing 40 (8), 1231–1239. Dandekar, C.R., Shin, Y.C., 2011. Molecular dynamics based cohesive zone law for describing Al–SiC interface mechanics. Composites Part A Applied Science and Manufacturing 42 (4), 355–363.

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