Polymer Composites

Lingyun Jiang Department of Mechanical Engineering, University of Illinois at Urbana-Champaign, 1206 W. Green Street, Urbana, IL 61801 e-mail: [email protected]

Chandra Nath Post Doctorate Research Associate Department of Mechanical Engineering, University of Illinois at Urbana-Champaign, 1206 W. Green Street, Urbana, IL 61801 e-mail: [email protected]

Johnson Samuel Assistant Professor Department of Mechanical Aerospace and Nuclear Engineering, Rensselaer Polytechnic Institute, Troy, NY 12180 e-mail: [email protected]

Shiv G. Kapoor1 Professor Department of Mechanical Engineering, University of Illinois at Urbana-Champaign, 1206 W. Green Street, Urbana, IL 61801 e-mail: [email protected]

An Enhanced MicrostructureLevel Finite Element Machining Model for Carbon NanotubePolymer Composites During the machining of carbon nanotube (CNT)-polymer composites, the interface plays a critical role in the load transfer between polymer and CNT. Therefore, the interface for these composites has to be explicitly considered in the microstructure-level finite element (FE) machining model, so as to better understand their machinability and the interfacial failure mechanisms. In this study, a microstructure-level FE machining model for CNTpolymer composites has been developed by considering the interface as the third phase, in addition to the polymer and the CNT phases. For the interface, two interfacial properties, viz., interfacial strength and fracture energy have been included. To account for variable temperature and strain rate over the deformation zone during machining, temperature and strain rate-dependent mechanical properties for the interface and the polymer material have also been included in the model. It is found that the FE machining model predicts cutting force within 6% of the experimental values at different machining conditions and CNT loadings. The cutting force data reveals that the model can accurately capture the CNT pull-out/protrusion, and the subsequent surface damage. Simulated surface damage characteristics are supported by the surface topographies and roughness values obtained from the machining experiments. The study suggests that the model can be utilized to design the new generation of CNT-polymer composites with specific interfacial properties that minimize the surface/subsurface damage and improve the surface finish. [DOI: 10.1115/1.4028200] Keywords: CNT-polymer composite, interface, microstructure-level machining model, finite element, machining responses

1

Introduction

In the last two decades, CNT-polymer composites have received much attention in many micro-/mesoscale applications, including light-weight structures, microfluidic devices, textiles, actuators, and biomedical implants [1–6]. This is due to the superior mechanical, thermal and electrical properties, and biocompatibility of CNTs that drastically improve the thermophysical properties of CNT-polymer composites over that of pure polymer [1–4,7]. Among different polymer materials, polyvinyl alcohol (PVA) is highly preferred because it is soluble in water; and the resulting PVA aqueous solution can homogeneously disperse multiwalled CNTs that are functionalized mainly with-COONa group [4]. Moreover, PVA is a biocompatible polymer material. As a result, CNT-PVA composites are commonly used in bioimplants and in producing actuators and sensors [5,6]. Although extensive research has been done on fabrication and characterization of CNT-PVA composites, their machinability has yet to be studied in detail. Recently, Dikshit et al. [8–10] developed a microstructure-level FE machining model for studying the machinability of CNTpolycarbonate composites by considering two distinct phases in the microstructure, viz., the CNT phase and the polycarbonate phase, thereby assuming a perfect interfacial bonding between these two phases. However, subsequent experimental 1 Corresponding author. Contributed by the Manufacturing Engineering Division of ASME for publication in the JOURNAL OF MANUFACTURING SCIENCE AND ENGINEERING. Manuscript received May 23, 2014; final manuscript received July 30, 2014; published online December 12, 2014. Assoc. Editor: Donggang Yao.

investigations revealed that the failure mechanism during machining is primarily governed by the CNT-polymer interface [11,12]. Since the interface is critical to the load transfer between polymer and CNT [13,14], the assumption of a perfect bonding in the model leads to poor prediction of the machining responses, including cutting force, surface/subsurface damage, and failure mechanism. Therefore, it is imperative to explicitly consider the interface in the microstructure-level FE machining model to better understand the machinability of these composites. The objective of this study is to develop an enhanced microstructure-level FE machining model for CNT–PVA composites by considering all three distinct phases, viz., CNT, PVA, and the interface. This modeling strategy extends the existing microstructure-level FE machining model developed for CNTpolymer composite with two phases [8–10]. The CNT–PVA interface is represented by the cohesive zone model (CZM). Since the composite, especially the PVA phase and the interface, experiences variable temperatures and strain rates during machining, temperature-dependent and strain rate-dependent PVA material model and CZM are included in the present machining model. Machining simulations are performed for CNT–PVA composites by varying the depth of cut (DOC) and rake angle for CNT loadings of 2 wt.% and 4 wt.%, and validated through orthogonal machining experiments in terms of cutting force. The model is also used to study surface/subsurface damage, and failure mechanism for different machining conditions and interfacial properties. The remainder of this paper is organized as follows. Section 2 presents an enhanced microstructure-level FE machining model for CNT-polymer composites, which includes three distinct phases, viz., CNT, PVA, and the interface. It also describes the

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procedures applied to obtain the temperature-dependent and strain rate-dependent material behaviors of PVA. It is followed by the microstructure characterization/simulation, and the integration of material behaviors, and the failure criteria for CNT, PVA, and CNT-PVA interface in the machining model. Validation of the machining model through orthogonal cutting experiments is presented in Sec. 3. Section 4 discusses how the model can capture the surface/subsurface damage due to interfacial failure when varying machining conditions and interfacial properties. Finally, Sec. 5 draws specific conclusions from this study.

2 Enhanced Microstructure-Level FE Machining Model In the enhanced microstructure-level FE machining model, the interface between the CNT and the PVA phases has been considered as an additional distinct physical phase in the microstructure of a CNT-PVA composite. Also, constitutive material model for the PVA phase and the CZM for the interface phase are developed so that they can account for variable temperatures and strain rates that occur over the plastic deformation zone during machining. The CNT constitutive material model is not modified to account for these two effects, since material properties such as Young’s modulus and plastic stress of the CNT fiber are much larger than that of the polymer materials and the interface, and therefore assumed to be not influenced considerably by both temperature and strain rate at the nanoscale/microscale machining. The microstructure of the CNT–PVA composite is simulated based on the statistical characterization of CNTs such as shape, orientation, and distribution. The microstructure and material models are fed into the FE solver to obtain machining responses in terms of cutting force, chip formation, and surface/subsurface damage due to interfacial failure. The remainder of this section describes the following key aspects of the model: (1) temperature- and/or strain ratedependent constitutive material models both for the PVA phase and the CNT–PVA interface, (2) constitutive material model for the CNT phase, (3) CNT–PVA composite sample fabrication, CNT characterization, and microstructure development for machining simulation, and (4) machining model development and implementation by the FE solver. 2.1 Material Model for PVA. During machining of CNT–PVA composites, the PVA material experiences variable cutting temperatures and plastic strain rates over the deformation zone. This section presents the model details pertaining to the, temperature- and/or strain rate-dependent dependence of the Young’s modulus and plastic stress of the PVA phase. 2.1.1 Young’s Modulus of PVA. Young’s modulus of PVA can be estimated from the simplified relationship given by [13,14] E ¼ ð1 2 ÞEr

(1)

where E is the Young’s modulus, is the Possion’s ratio, and Er is the reduced modulus that is commonly used to account for the compliance of the indenter used in nanoindentation tests. To obtain Er, the Oliver–Pharr data analysis procedure [13] is used, where the unloading portion of load–displacement data plot from nanoindentation test is fitted to a power-law relation pffiffiffi p S pffiffiffi (2) Er ¼ 2 b A where b is a constant that depends on the geometry of the indenter (e.g., b ¼ 1.034 for the Berkovich indenter), A is the projected area of the indenter, and S is the slope of the initial portion of the unloading curve. The slope, S is defined as S ¼ dP=dh 021009-2 / Vol. 137, APRIL 2015

(3)

where P is the indentation load and h is the indentation depth of indenter. In Eq. (1), Possion’s ratio, of PVA is experimentally estimated to be about 0.46 [15]. In order to obtain reduced modulus, Er, of PVA at varying temperatures, nanoindentation tests are performed using the Berkovich indenter for 1 lm indentation depth and the temperature range of 25 C–80 C with an increment of 5 C by controlling the temperature of the stage that holds the work sample. This temperature range is chosen because the glass transition temperature of PVA is 85 C [6]. Five nanoindentation tests are performed at different locations of the PVA sample to obtain an average value of Er. Temperature-dependent Young’s moduli of PVA are then obtained using the Possion’s ratio, , and the reduced modulus, Er, found at different temperatures, as shown in Fig. 1.

Fig. 1 Young’s temperatures

modulus

of

PVA

material

at

different

2.1.2 Plastic Stress of PVA. Since plastic stress of PVA remains constant beyond the yield point (i.e., equal to its yield stress) [16,17], the Eyring rate equation, which is mainly used to characterize the yield stress of materials for a thermally activated process [18], can be used to obtain temperature-dependent and strain rate-dependent plastic stress of PVA. The Eyring rate equation is described as rp E k e_ (4) ¼ Y þ ln e_0 T V T V where rp is the plastic stress, T is the temperature, e_ is the effective strain rate, e_0 is a reference strain rate, V* is the activation volume governing the effectiveness of the stress in reducing the activation barrier, EY is the activation energy, and k is the Boltzman’s constant (1.38 10–23 kg m2/s2). The terms EY , V*, e_0 are constants for a given material, and these can be estimated by performing nanoindentation tests which give the values of plastic _ stress for varying temperatures, T and effective strain rates, e. Nanoindentation tests are performed using Berkovich indenter for the temperature range of 25 C–65 C with an increment of 10 C by controlling the temperature of the composite sample stage. Plastic stress, rp of PVA is then calculated by using the following relationship [19,20]: rp ¼ H=c1 ¼ P=c1 A ¼ P=c1 c2 h2

(5)

where H is the hardness of material, A is the projection area, and c1 is a constant that was experimentally found to be about 3.0 [21–23], and c2 is a constant equal to 24.5 for the Berkovich Transactions of the ASME


indenter [24]. The indentation depth, h, is kept constant at 1 lm, however, the load, P, varies with the change in temperature. In order to obtain strain rate-dependent plastic stress of PVA at any temperature, the following expression for the indentation strain rate, e_I can be used e_I ¼

1 dh h dt

where a is the equivalent semiapical angle of the Berkovich indenter and its value was found to be 70.3 deg [24]. In this study, the effective strain rate, e_I is varied from 10–2 to 102 s–1 at each temperature of the PVA sample by keeping indentation depth constant at 1 lm (i.e., 103 nm), but by varying indentation speed at 10, 102, 103, 104, and 105 nm/s, respectively. Obtained values of rp at different T and e_ from the nanoindentation tests are used to draw rp/T versus ln e_ plots at different temperatures as shown in Fig. 2. As seen in figure, the plots at different temperatures are always linear with a slope k/V*. This slope can be used to estimate the activation volume, V*, as Boltzman’s constant, k is known. Further, to estimate EY , Eq. (4) can be reformatted as kðln e_T2 ln e_T1 Þ 1 1 T1 T2

Constants

Values 6.01 10–19 J 0.826 nm3 3.17 1044/s

Activation energy, EY Activation volume, V* Reference strain rate, e_0

(6)

In the above equation, indentation depth, h, or indentation speed dh/dt can be varied to vary the indentation strain rate, e_I , and the effective strain rate, e_ of PVA can be obtained from e_I and the indenter geometry as [25] 1 dh =tan a (7) e_ ¼ e_I =tan a ¼ h dt

EY ¼

Table 1 Estimated constants for PVA material model

(8)

where e_T1 and e_T2 are strain rates at temperatures T1 and T2, respectively, at a constant value of rP/T. Knowing EY , V*, the reference strain rates, e_0 can finally be obtained using Eq. (4). The calculated values of EY , V*, and e_0 are listed in Table 1, and they are used in Eq. (4) for the temperature-dependent and strain rate-dependent plastic stress of PVA in the enhanced FE machining model. Other physical and thermal properties of PVA including density, thermal conductivity, specific heat capacity, and failure strain were taken for the microstructure as 1290 kg/m3, 0.39 W/(m K), 5 kJ/(kg K), and 1.6, respectively [26–29].

2.2 Material Model for CNT. Extensive work has been performed to investigate physical and mechanical properties of CNTs [1–3]. High Young’s modulus values (300–1000 GPa) and high elongation–to–break values (13%) of CNTs imply a stress state in a range of 39–130 GPa in the composite upon the failure of a CNT [1,2]. Since the PVA polymer phase is expected to fail at a significantly lower stress level than that of CNTs [7,8], the CNT phase is modeled to be perfectly elastic in this study. Poisson’s ratio of CNTs is considered to be 0.28, which is within the range of 0.2–0.35 [1–3,30]. Also, thermal properties such as heat capacity and thermal conductivity of CNT are chosen to be 600 J/(kg K) and 6600 W/(m K), respectively [31,32]. 2.3 CZM for the Interface. CZM for the CNT–PVA interface is characterized by considering a bilinear traction–separation curve [14]. The CZM with the bilinear traction-separation curve is shown to match with the experimental results and is easy to implement [12,19]. In CZM, the traction of interface linearly increases with the interfacial separation until it reaches the interfacial shear strength, sc. The interfacial separation at the interfacial strength is referred to as the critical separation distance, dc. Beyond dc, traction linearly decreases until it reaches zero at the failure separation distance, df. The area under the traction-separation curve is called the interfacial fracture energy, U. Values of these parameters for the CNT–PVA interface were obtained at room temperature (25 C) and the quasi-static state (strain rate 0.025 s1) in the recent study by the authors [14], and are listed in Table 2. Like the PVA phase, the CNT–PVA interface is also influenced with varying temperature and strain rate during the machining process. Therefore, interfacial properties shown in Table 2 need to be updated with temperature and strain rate during machining simulation. According to Detassis et al. [20], interfacial shear strength of the short carbon fibers–epoxy interface is proportional to shear strength of the epoxy matrix when temperature or strain rate changes. Therefore, in this study, it is assumed that interfacial shear strength of the CNT–PVA interface is proportional to temperature-dependent and strain rate-dependent plastic stress of PVA sc ¼ KrP

(9)

where K is a constant independent of temperature and strain rate. The value of K can be estimated as 0.23 based on the interfacial shear strength, sc in Table 2, and the plastic stress, rp of PVA at the same temperature and strain rate (Sec. 2.1). As the value of sc is known, interfacial fracture energy, U can be obtained from the bilinear traction-separation relationship [14] U¼

sc df 2

(10)

Table 2 CNT–PVA interfacial parameters at room temperature and quasi-static state [14] CNT–PVA interfacial parameters

Fig. 2 Eyring rate plots showing dependence of plastic stress on temperature and strain rate in PVA (* data points)

Journal of Manufacturing Science and Engineering

Interfacial shear strength, sc Interfacial fracture energy, U Critical separation distance, dc Failure separation distance, df

Values 42 MPa 0.018 J/m2 0.260 nm 0.857 nm

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Fig. 3 SEM images of typical CNT–PVA composite samples at: (a) 2 wt.% and (b) 4 wt.% CNT loadings

The values of the critical separation distance, dc and the failure separation distance, df for the CNT–PVA interface are assumed to be constant (see Table 2), because van der Waals force between carbon atoms of the CNT and polymer matrix reaches the maximum value after the critical separation [33]. 2.4 Characterization of Microstructure. For machining simulation, CNT–PVA composites at the CNT loadings of 2 wt.% and 4 wt.% were studied. CNTs were considered to be randomly oriented and well-distributed in the PVA matrix. To develop the microstructure, samples at the same loadings were prepared and characterized as described below. 2.4.1 Composite Sample Fabrication. The solution for the CNT–PVA composite samples was prepared following the procedure described in the authors’ recent study [14]. The resulting viscous and homogeneous solution was then poured into a petri dish and dried in oven at 60 C for 3 days. The typical thickness of the

Fig. 4 Parameterization of individual CNTs [5]

composite samples prepared using this procedure is found to be in the range of 0.3–0.6 mm. The top view of the samples was captured under the Hitachi S-4800 SEM at 1 kV and examined to characterize geometry, orientation, distribution of CNTs in PVA. Figures 3(a) and 3(b) show SEM images of top view of typical composite films containing 2 wt.% and 4 wt.% of CNTs, respectively. They are observed to be distributed in random fashion across the entire sample. 2.4.2 Statistical Characterization of CNTs. Statistical characterization including geometry, orientation, and distribution of CNTs in the composite samples observed in Fig. 3 at both the loadings of 2 wt.% and 4 wt.% have been performed for developing similar microstructures that are required for machining simulation. As shown in Fig. 4, the CNT in the composite sample can be characterized by the straight-line distance, D between their end points, the angle h between the straight line joining the ends of the CNTs and x–direction, and the end slopes, h1 and h2 [8]. Although characterization of individual CNTs has been well established [8], their distribution in the polymer matrix has not been explicitly explained. In this study, distribution of CNTs in the fabricated samples has been statistically characterized by estimating the interspace (in x- and y-coordinates) between two adjacent CNTs as shown in Fig. 5. First, straight lines are drawn between the two ends of individual CNTs. Then, the linear distance between the centers of two adjacent CNTs is considered to be the interspace. The interspace between two adjacent CNTs is found to follow the normal distribution with a mean value of 411 nm and a standard deviation of 257 nm in x-direction, and a mean of 384 nm and a standard deviation of 218 nm in y-direction for the 2 wt.% CNT–PVA composites. The interspace in the 4 wt.% CNT–PVA composites also follows normal distribution with a mean value of 242 nm and a standard deviation of 132 nm in xdirection, and a mean value of 261 nm and a standard deviation of 142 nm in y-direction.

Fig. 5 Interspace between two adjacent CNTs for two typical cases at: (a) 2 wt.% and (b) 4 wt.% CNT loadings

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Fig. 8 Machining model for composites with interface

Fig. 6 Shape, orientation and distribution of CNTs in simulated microstructure at the loading of: (a) 2 wt.% and (b) 4 wt.%

2.5 Microstructure Simulation. Geometry, orientation and distribution of CNTs obtained from the fabricated samples are now used to develop microstructures for the same CNT loadings using the MATLAB software. Geometry of individual CNTs is obtained by first fitting a cubic spline with the angles, h1 and h2, at two ends and the distance, D between these ends. The spline is then rotated at a random angle, h with respect to any end point. The spline is then placed by the interspace estimated for two adjacent CNTs in both x-direction and y-direction. The resulting simulated microstructures for both the 2 wt.% and 4 wt.% loadings are shown in Figs. 6(a) and 6(b), respectively, which represent the samples observed in Figs. 3(a) and 3(b). The interface in the microstructure between the CNT phase and the PVA phase is modeled with the third phase, i.e., the cohesive zone, as shown in Fig. 7(a). Thickness of this interface, b is considered to be 0.15 times that of the CNT diameter, dCNT as observed from the CNT pull-out experiment in Ref. [34], which is also within the range of 0.03–0.25 in previous CNT-polymer interface modeling studies [35,36]. Accordingly, in this study, for the average CNT diameter of 16 nm (ranging from 13 to 18 nm), the value of b is 2.4 nm. A slice of the resulting composite microstructure with the interface is shown in Fig. 7(b). 2.6 Machining Model Development and Implementation. After simulating the microstructure, material properties described in Sec. 2 for all three phases are incorporated in the FE machining

Fig. 7 (a) Representation of the CZM for the CNT–PVA interface, and (b) interface (i.e., cohesive zone) in the composite microstructure


model. The size of the microstructure model for machining simulation is considered to be 6 2 lm2. A part of the composite microstructure (workpiece) with the rigid cutting tool is shown in Fig. 8. The composite was constrained on the left and bottom surfaces. The tool is designed with an edge radius of 50 nm. The coefficient of friction between tool and workpiece in this study is measured as 0.95 by scribing tests, and is incorporated in the machining model. Initial temperature of the workpiece was set to room temperature. It is critical to consider the rise in temperature caused by the plastic deformation of the material during machining. It is assumed that 60% of plastic work is converted into heat [37]. Adaptive meshing was applied to avoid convergence problems due to excessively distorted elements and to improve the aspect ratio of elements.

3

Machining Model Validation

The model validation involves comparing simulated cutting force with the experimental data for varying DOC and rake angle at different loadings of CNTs. Orthogonal cutting experiments were conducted for validation. The enhanced machining model is also compared with the machining model assuming perfect bonding at the CNT–PVA interface. 3.1 Machining Experiments and Results. A numerically controlled Leica ultramicrotome machine, as shown in Fig. 9(a), was used to perform orthogonal cutting experiments. The CNT–PVA composite sample (size 1.0 mm 1.0 0.6 mm) was fixed on the face of a cylindrical rigid rod (Fig. 9(b)) and the rod was fastened with the holder in the lever arm of the machine. During experiment, the cutter starts cutting from the bottom of the sample when the lever arm moves from top in the z-direction (see Fig. 9(c)). For each cut, the work stage moves or feeds towards the y-direction according to the given DOC, and then the lever arm starts cutting according to a desired cutting speed. For orthogonal cutting experiments, a number of glass knives were prepared as the cutting tool using the LKB Knifemaker. After preparing the knives of the wedge angle of 45 deg, they were inspected under the optical microscope to ensure quality of the knife edge. The edge radii of these glass knives were measured to be in the range of 32–57 nm. The glass knives of 16 mm width are used to cut the sample of 1.0 mm width. Rake and clearance angles of the cutter (glass knife) are adjusted by placing a wedge under the cutter, as depicted in Fig. 9(c). A three-component Kistler load-cell (type 9251 A), a threecomponent Kistler charge amplifier (type 5010), and a National Instruments data acquisition system along with LABVIEW software were used in-conjunction to collect the cutting force data. Note that the force in z-direction is the cutting force for orthogonal cutting. Before collecting the cutting force data, the sample was trimmed several times in order to confirm uniform DOC for the entire composite sample. Orthogonal cutting experiments are performed for four different cutting conditions: case 1—400 nm DOC, 23 deg rake; case 2— APRIL 2015, Vol. 137 / 021009-5


Fig. 9 Experimental setup with: (a) the Leica ultramicrotome machine; (b) closeup view of the composite sample with reciprocating arm; (c) tool geometry and sample in the setup (side view)

400 nm DOC, 35 deg rake; case 3—800 nm DOC, 23 deg rake; and case 4—800 nm DOC, 35 deg rake. The selected rake angles are within the range of rake angles for polymer/polymer composite recommended by Jesior [38]. The cutting speed was selected to be 1 mm/s. For every combination of DOC and rake angle, experiments were repeated for three times, and the cutting forces obtained from these repeated cutting experiments are averaged. Figure 10 shows the captured cutting forces (in z-direction) for the cutting condition: 400 nm DOC and 35 deg (case 2). Table 3 shows the cutting force data obtained from orthogonal cutting experiments. It is observed that the error in force data for pure PVA (i.e., 0 wt.%) is less than 4%, and thus the temperaturedependent and strain rate-dependent material properties for PVA used in the FE machining model are accurate. It is also seen that the cutting force increases with the increase in CNT loading. The machining simulation was performed for all the composite microstructures developed for the 2 wt.% and the 4 wt.% CNT loadings at all four machining conditions. Average cutting forces obtained from the enhanced machining model simulation are also shown in Table 3. It can be seen that the microstructure-level machining model that considers the interface and the temperaturedependent and strain rate-dependent material properties can accurately predict the cutting force as experiments for all machining conditions at different loadings. The error between experimental and simulation force data is less than 6%, although the model often

Fig. 10 Experimental cutting force data for case 2

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under–predicts the cutting force. The under-prediction of the cutting force with the present model may be due to two main reasons: (i) the error in the thickness estimation for the interface in the CZM and (ii) the experimental error. The interface thickness of 2.4 nm was considered based on the experimental studies reported in Ref. [34]. Since the interface is the weakest zone among the three phases in the microstructure of CNT–PVA composites, the assumption of its thickness could also impact the force data. Moreover, the machining set up, and the tool sharpness and geometry may not be as accurate as the theoretical one employed in machining simulation. 3.2 Comparison of Cutting Force Predicted From the Model With and Without Considering the CNT–PVA Interface. In this section, the cutting force predicted by the enhanced model (i.e., 3-phase) is compared with that found from the model that does not consider the interface (i.e., 2-phase or perfect bonding) at different CNT loadings and machining conditions. As seen in Table 3, the machining simulation that considers perfect bonding over-predicts the cutting force by 11–15%. Dikshit et al. [8–10] also reported similar results when simulating the machining of CNTpolycarbonate composites considering perfect bonding. The reason behind the larger cutting force in this case is due to comparatively higher strength of the PVA phase than that of the interface. As described in Eq. (9), the shear strength of the interface is about 0.23 times of the plastic stress of PVA. Since the interface does not exist in the two-phase model, the PVA phase can sustain a higher stress level during the load transfer between CNT and PVA, and that eventually leads to increase in cutting force. In order to understand the failure mechanism, surface/subsurface damage, chip formation, and their effect on the cutting force, machining simulation of composites are also obtained. Figures 11(a) and 11(b), with their close-up views (see side figures), depict the simulation of cutting instants for both the machining models, i.e., with and without considering the interface, respectively, for the 4 wt.% CNT–PVA composite machined at 400 nm DOC and 35 deg rake (case 2). It is observed that, in the case of perfect bonding, the first CNT (at the right end in Fig. 11(a)) that is inclined against the cutting direction was bent excessively by the tool. The tool then pulled-out the second CNT with a more vigorous bending action that left behind a surface with a big cavity (Fig. 11(a)). While the CNTs bend, shear localization and plastic deformation occur around the CNT periphery. This causes the PVA (viscoelastic polymer material) around the CNTs to be thermally softened. As the CNT is in perfect bonding with the PVA and is in excessive bending mode, the softened PVA gets easily fractured with the tool movement causing damage on the top surface and subsurface (beneath the surface) near the CNT locations. Transactions of the ASME


Table 3 Comparison of experimental and simulated tangential cutting force (mN/mm) Case 1

Case 2

Case 3

400 nm

Case 4 800 nm

DOC Rake angle

23 deg

35 deg

23 deg

35 deg

0 wt.% (pure PVA)

Experiment Simulation Difference (%)

113.7 109.5 –3.7

94.1 96.3 2.3

187.5 190.0 1.3

170.4 166.8 –2.1

2 wt.% (CNT–PVA composites)

Experiment Simulation with CZM Difference (%) Simulation with perfect bonding Difference (%)

131.0 126.7 –3.3 148.0 12.9

115.8 111.6 –3.6 128.4 10.9

215.2 204.4 –5.0 239.2 11.2

195.2 184.7 –5.4 221.9 13.5

4 wt.% (CNT–PVA composites)

Experiment Simulation with CZM Difference (%) Simulation with perfect bonding Difference (%)

146.3 137.4 –4.1 167.5 15.2

131.7 124.1 –5.8 147.6 12.1

223.2 212.8 –4.7 252.3 13.0

211.9 209.7 –1.0 242.8 14.6

CNT loading

Fig. 11 FE machining simulation showing failure, surface/subsurface damage, material shear, and chip formation when considering: (a) perfect bonding; and (b) CZM for the conditions of 400 nm DOC and 35 deg rake at 4 wt.% CNT loading (case 2)

In contrast, for the model that considers the CZM for the interface (Fig. 11(b)), the CNTs did not suffer from the vigorous “bending” action, although the first CNT protruded and the second CNT pulled-out. Also, as the shear strength of the interface is smaller than that of the PVA, shear failure is seen to take place early along the interface before the load is transferred to the PVA. Due to these, the fracture and surface/subsurface damage did not seem to be severe. The machining simulations clearly reveal that the bending action due to the perfect bonding at the interface causes more local deformation of the PVA phase. This leads to comparatively higher stress (based on von Mises scale) development in both the PVA and the CNT phases with a larger area around of the tool tip and in the chip formation zone, and eventually results in a higher cutting force for the same conditions in machining simulation Journal of Manufacturing Science and Engineering

(Table 3). In contrast, the existence of the interface in the enhanced model causes early interfacial failure with limited deformation of the PVA phase, smaller stress development in uncut material and chip formation area, and thus lessens surface damage and cutting force.

4 Model-Based Study of Surface/Subsurface Damage Characteristics As seen in Sec. 3, the microstructure-level FE machining model can accurately predict the cutting force during the machining of CNT–PVA composites, and is able to determine the corresponding CNT pull-out and/or protrusion and the subsequent surface/ subsurface damage characteristics. For precision parts that are fabricated from CNT composites, it is important to minimize the APRIL 2015, Vol. 137 / 021009-7


damage for improving part quality, especially, surface roughness. This section focuses on how the model can be used to study the effect of machining conditions as well as interfacial properties on surface/subsurface damage characteristics. 4.1 Damage Minimization Through Machining Conditions. Simulation results for different machining conditions including DOC and rake angle for pure PVA, 2 wt.% and 4 wt.% CNT loadings are depicted in Figs. 12(a)–12(f). Machining of PVA in Fig. 12(a) is seen to result in a continuous chip and the machined surface is free of damage. However, the presence of CNTs in PVA makes the material heterogeneous and causes uneven or damaged machined surface because they protrude and/ or pull–out as seen in Figs. 12(b)–12(f). The evidence of CNT pull-out was presented in the authors’ earlier experimental results [10,39]. Surface topographies and roughness profiles/values obtained after machining experiments using atomic force microscope (AFM) over a 3 lm 3 lm surface region of machined samples support this phenomenon (see Figs. 13(a)–13(c)). Table 4 shows that average roughness value increases with the increase in CNT loading. It is because a higher CNT loading causes a number of CNT protrusion and pull-out on the machined surface and that results in surface topographies and corresponding profiles even rougher as depicted in Figs. 13(a) and 13(b) for the 2 wt.% and 4 wt.% loadings, respectively. It can also be observed by peak and valleys from these two roughness profiles that the number of CNT pull-out and protrusion at the 4 wt.% is higher as compared to that at the 2 wt.% loading. The increase in CNT reinforcement in the PVA matrix also causes larger cutting forces during machining, as shown in Table 3, as number of CNT protrusion and pull-out increases. The effect of DOC on machining responses can be observed by comparing simulated results in Figs. 12(c) and 12(e) and Figs. 12(d) and 12(f), while the CNT loading and the rake angle are kept fixed. The increase in DOC is found to influence the chip size with larger deformation zone ahead of the tool tip. This along with an increase in chip load at a higher DOC cause the cutting force to be larger as the chip load increases (Table 3). However, the experimental roughness data provided in Table 4 also shows that the machined surfaces at a lower DOC are comparatively rough. The reason behind this higher roughness may be the elastic recovery of PVA at a lower DOC. As PVA is an elastic-perfectly

plastic material, it experiences mainly elastic deformation with less stress (Figs. 12(a)–12(d)) at a lower DOC of 400 nm, whereas more plastic deformation with a higher stress at a DOC of 800 nm. Moreover, at lower DOC values, the polymer is likely to undergo more ploughing and rubbing rather than plastic shear failure, thereby increasing the surface roughness. Figures 12(c) and 12(d) and Figs. 12(e) and 12(f) compare the effect of rake angle, showing that the chip is continuous and its thickness is smaller at a larger rake angle. It is due to the fact that a larger rake angle better facilitates the material shearing and deformation [40], and produces a larger shear angle during machining. As a result, the tool produces a smaller cutting force (see Table 3). Average surface roughness values listed in Table 4 and surface topographies shown in Figs. 13(a) and 13(c) are also found to improve significantly with the increase in rake angle in these tests. In summary, the machining responses such as surface damage, chip formation, cutting force, and surface roughness improve with the increase in both DOC and rake angle. Elastic property of PVA seems to be dominant in the case of DOC. A larger rake angle better facilitates the material shearing. As the CNT loading increases, the number density of the interfacial failure increases, which in turn results in higher cutting force and worsen machined surface. Both the simulation and the experimental results reveal the similar trend of the machining responses. 4.2 Damage Minimization by Controlling Interfacial Properties. Interfacial properties, viz., strength and fracture energy play a vital role during the load transfer between the CNT and the polymer phases. These two properties determine the failure behavior or surface/subsurface damage at the interface, which can have a great impact on the functionality of the CNT–PVA composite parts. While surface damage affects the surface roughness/finish, subsurface damage can cause defects and lower the strength of the final product [41]. Though the interfacial properties are constant for a particular set of the CNT-polymer composite [14], one can design a new composite with different interfacial properties in an effort to minimize such damage by varying the following physical parameters, for example, the CNT and polymer types, CNT functionalization group (chemical), and CNT diameter, polymer solvent, etc. The machining response of such a new composite design can be studied using the present model. In this

Fig. 12 Simulation results of microstructure-level machining model with interface (CZM)

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Transactions of the ASME


Fig. 13 Typical 3D surface topographies of the machined CNT–PVA composite samples, and their corresponding roughness profiles

Table 4 Average surface roughness for the machined surfaces of PVA and CNT–PVA composites Machining condition DOC (nm)

2 wt.% 4 wt.% Pure PVA CNT–PVA CNT–PVA Rake (nm) composites (nm) composites (nm) angle (deg)

400

23 35

3.10 2.19

4.40 2.90

7.93 5.10

800

23 35

2.53 2.02

3.52 2.15

5.84 2.63


section, machining simulations are conducted by varying interfacial properties with the aim of controlling mainly subsurface damage (i.e., damage beneath the machined surface) from the manufacturing aspects of CNT–polymer composites. Machining simulation is conducted for the 4 wt.% CNT–PVA composite at a DOC of 800 nm and a rake angle of 35 deg (case 4) using the original interfacial properties (see Table 2). Figure 14(a) shows the machined surface with subsurface damage. The occurrence of subsurface damage is due to the stress development in the material domain under the tool as it passes. The presence of CNT in this stress-affected zone can lead to the CNT–PVA interfacial failure and thus subsurface damage, if the interfacial APRIL 2015, Vol. 137 / 021009-9


Fig. 14 Effect of interfacial strength on surface/subsurface damage for the 4 wt.% CNT–PVA composite at 800 nm DOC and 35 deg rake angle (case 4)

strength is weaker than the stress occurs. The interfacial strength is now assumed to vary due to the change in physical parameters such as CNT functionalization group and/or polymer solvent. Three values of interfacial properties at 50%, 150%, and 200% of their original values are considered, while keeping the critical separation distance and failure separation distance constant (see Table 2). Simulation results for these three conditions are then compared with the one shown in Fig. 14(a) for the original values of both the interfacial strength and the fracture energy. As shown in Fig. 14(b), subsurface damage enlarges when the interfacial strength and fracture energy are reduced to 50% of their original values. It is because the interface at lower strength and fracture energy is easy to fail. Figure 14(c) shows that subsurface damage disappears when the interfacial strength and fracture energy reach 150% of their original values, indicating that the interfacial failure does not happen, as the interface can sustain a higher load when their values increase. However, higher interfacial strength and fracture energy do not always reduce the subsurface damage. When interfacial strength increased to 200% of its original value (Fig. 14(d)), the subsurface damage occurs again. It is because the tool, before pulling out, bent the CNT excessively during its movement in the cutting direction from the right side, causing larger stress and strain in subsurface area.

5

Conclusions •

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An enhanced microstructure-level FE machining model for CNT–PVA composites has been developed in this study. The CNT–PVA interface is modeled as the third phase along with the CNT phase and the PVA phase, in the model. Constitutive material model for each phase has been developed and implemented. The constitutive material model for PVA polymer accounts for variable temperature and strain rate over the deformation zone during machining process. The temperature-dependent and strain rate-dependent plastic stress was captured by nanoindentation tests and then fitted with the Eyring rate equation to predict the plastic stress of PVA over a wide range of temperatures and strain rates. For the 2 wt.% and the 4 wt.% CNT–PVA composites at different machining conditions, the composite machining model

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with the interface is seen to successfully predict the cutting forces with an error less than 6%. In contrast, the model assuming perfect bonding at the CNT–PVA interface overpredicts the cutting forces by 11–15%. The cutting force data reveals that the CNT pull-out/protrusion due to interfacial failure, and the subsequent surface damage are captured accurately by the enhanced machining model. The trend of damage against the DOC and rake angle at both the CNT loadings is found similar to the trend observed for surface topographies and roughness values from the machining experiments. Increase in both the DOC and the rake angle better facilitates the material removal process resulting in lower cutting force, minimal surface damage, and improved surface finish. A study on the effect of interfacial properties, including strength and fracture energy during the machining of CNT–PVA composites shows that the subsurface damage reduces when their values increase. However, excessive interfacial strength like perfect bonding results in more surface/subsurface damage because CNTs severely bend in the cutting direction, causing more local deformation and higher stress in composites. The study suggests that the microstructure-level FE machining model developed in this study can be used to minimize the surface/subsurface damages, and improving surface finish during the machining of CNT-polymer composites. The model can help improve manufacturing of the new generation of CNT-polymer composites with better control of interfacial properties by selecting a right combination of physical constituents such as CNT and polymer types, CNT functionalization group that controls chemical bonding at the interface, and polymer solvent type.

Acknowledgment The authors are grateful to the National Science Foundation for funding this research (Grant No. NSF CMMI 10-29221). The authors would like to thank the Center for Microanalysis of Materials, University of Illinois (which is partially supported by the U.S. Department of Energy under Grant No. DEFG02-91ER45439), and the Micro-Nano Mechanical System Cleanroom (MNMS) Laboratory for sample fabrication. Transactions of the ASME


Nomenclature A¼ b¼ c1 , c2 ¼ D¼ dCNT ¼ dh/dt ¼ E¼ Er ¼ EY ¼ h¼ H¼ k¼ K¼ P¼ S¼ T¼ T¼ V* ¼ a¼ b¼ d¼ dc ¼ df ¼ _ e_I , e_0 ¼ e, h¼ h1, h2 ¼ ¼ rp ¼ sc ¼ U¼

projected area of indenter thickness of the CNT-polymer interface constants for plastic stress and hardness, respectively straight-line distance between the ends of a CNT diameter of CNTs indentation speed Young’s modulus of pure PVA sample reduced elastic modulus activation energy indentation depth hardness of the sample Boltzman’s constant (1.38 10–23 kg m2/s2) constant relating interfacial strength and plastic stress load on indenter slope of initial proportion of the unloading curve shear stress in CZM temperature of sample activation volume equivalent semi-apical angle of Berkovich indenter constant for indenter geometry separation of two phases in CZM critical separation at maximum interfacial strength separation of two phases at final failure effective, indentation and reference strain rate, respectively angle between the straight line joining the ends of the CNTs and the radial direction of the composite sample end slopes of CNTs Possion’s ratio of pure PVA sample plastic stress interfacial shear strength in CZM fracture energy in CZM

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